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\begin{verbatim}#|
     Copyright (C) 1990-1994 Computational Logic, Inc.  All Rights
     Reserved.

                        FM9001 PUBLIC SOFTWARE LICENSE
                          Computational Logic, Inc.
                          1717 West Sixth, Suite 290
                           Austin, Texas 78703-4776

Please  read this license carefully before using the FM9001 Software. By using
the FM9001 Software, you are agreeing  to  be  bound  by  the  terms  of  this
license. If you do not agree to the terms of this license, promptly return the
FM9001 Software to the place where you obtained it.

The FM9001 Software was developed by Computational Logic, Inc.(CLI).  You  own
the  disk  or  other  medium on which the FM9001 Software is recorded, but CLI
retains title to the FM9001 Software.  The purposes of  this  license  are  to
identify  the  FM9001  Software and to make the FM9001 Software, including its
source code, freely  available.    This  license  allows  you  to  use,  copy,
distribute  and  modify  the FM9001 Software, on the condition that you comply
with all the Copying Policies set out below.

COPYING POLICIES

1. You may copy and distribute verbatim copies of the FM9001 Software  as  you
receive  it,  in  any  medium,  including  embedding it verbatim in derivative
works, provided that you a) conspicuously and appropriately  publish  on  each
copy a valid copyright notice "Copyright (C) 1990-1994 by Computational Logic,
Inc. All Rights Reserved.", b) keep intact on all files the notices that refer
to  this License Agreement and to the absence of any warranty, and c) give all
recipients of the FM9001 Software a copy of this License Agreement along  with
the program.

2. You may modify your copy or copies of the FM9001 Software or any portion of
it, and copy and distribute such modifications provided  you  tell  recipients
that  what they have is a modification by your organization of the CLI version
of the FM9001 Software.

3. You may incorporate parts  of  the  FM9001  Software  into  other  programs
provided  that  you  acknowledge  Computational  Logic  Inc.  in  the  program
documentation.

CLI also requests, but does not require, that any improvements  or  extensions
to the FM9001 Software be returned to one of the addresses below, so that they
may be shared with other FM9001 users.  The  FM9001  Software,  including  its
source, can be obtained by contacting one of these addresses.

    Software-Request                 or     Software-Request@CLI.COM
    Computational Logic Inc.
    1717 West Sixth, Suite 290
    Austin, TX 78703-4776

NO WARRANTY

BECAUSE  THE FM9001 SOFTWARE IS LICENSED FREE OF CHARGE, WE PROVIDE ABSOLUTELY
NO WARRANTY.  THE SOFTWARE IS PROVIDED "AS IS" WITHOUT WARRANTY OF  ANY  KIND,
EITHER  EXPRESS  OR  IMPLIED,  INCLUDING,  BUT  NOT  LIMITED  TO,  ANY IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS  FOR  A  PARTICULAR  PURPOSE.    THE
ENTIRE  RISK  AS  TO  THE  QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU.
SHOULD THE FM9001 SOFTWARE  PROVE  DEFECTIVE,  YOU  ASSUME  THE  COST  OF  ALL
NECESSARY SERVICING, REPAIR OR CORRECTION.

IN  NO  EVENT  WILL COMPUTATIONAL LOGIC INC. BE LIABLE TO YOU FOR ANY DAMAGES,
ANY LOST PROFITS, LOST MONIES, OR OTHER SPECIAL, INCIDENTAL  OR  CONSEQUENTIAL
DAMAGES  ARISING  OUT  OF  THE  USE  OR  INABILITY  TO USE THE FM9001 SOFTWARE
(INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING  RENDERED  INACCURATE
OR  LOSSES  SUSTAINED  BY  THIRD  PARTIES), EVEN IF YOU HAVE ADVISED US OF THE
POSSIBILITY OF SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY.

|#

\end{verbatim}
\noindent{\sc Event}:   Start with the initial {\bf nqthm} theory.

\addvspace{18pt}


\noindent{\sc Event}:   Give the Nqthm control variable {\tt reduce-term-clock} the value {\tt 2000}.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{delete} \\  
\=\+{\rm{delete}}\,({\it{x\/}}, {\it{l\/}})\index{delete} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}}) \\ 
{\bf then }\=\+{\bf if }{\it{x\/}} $=$ {\rm{car}}\,({\it{l\/}})$\;\;${\bf then }{\rm{cdr}}\,({\it{l\/}}) \\ 
{\bf else }{\rm{cons}}\,({\rm{car}}\,({\it{l\/}}), {\rm{delete}}\,({\it{x\/}}, {\rm{cdr}}\,({\it{l\/}}))\index{delete})$\;${\bf  endif}\- \\ 
{\bf else }{\it{l\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{bagdiff} \\  
\=\+{\rm{bagdiff}}\,({\it{x\/}}, {\it{y\/}})\index{bagdiff} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{y\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{y\/}}) $\in$ {\it{x\/}}$\;\;${\bf then }{\rm{bagdiff}}\,({\rm{delete}}\,({\rm{car}}\,({\it{y\/}}), {\it{x\/}})\index{delete}, {\rm{cdr}}\,({\it{y\/}}))\index{bagdiff} \\ 
{\bf else }{\rm{bagdiff}}\,({\it{x\/}}, {\rm{cdr}}\,({\it{y\/}}))\index{bagdiff}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{bagint} \\  
\=\+{\rm{bagint}}\,({\it{x\/}}, {\it{y\/}})\index{bagint} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $\in$ {\it{y\/}} \\ 
{\bf then }{\rm{cons}}\,({\rm{car}}\,({\it{x\/}}), {\rm{bagint}}\,({\rm{cdr}}\,({\it{x\/}}), {\rm{delete}}\,({\rm{car}}\,({\it{x\/}}), {\it{y\/}})\index{delete})\index{bagint}) \\ 
{\bf else }{\rm{bagint}}\,({\rm{cdr}}\,({\it{x\/}}), {\it{y\/}})\index{bagint}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{occurrences} \\  
\=\+{\rm{occurrences}}\,({\it{x\/}}, {\it{l\/}})\index{occurrences} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}}) \\ 
{\bf then }\=\+{\bf if }{\it{x\/}} $=$ {\rm{car}}\,({\it{l\/}})$\;\;${\bf then }$1\;+$ {\rm{occurrences}}\,({\it{x\/}}, {\rm{cdr}}\,({\it{l\/}}))\index{occurrences} \\ 
{\bf else }{\rm{occurrences}}\,({\it{x\/}}, {\rm{cdr}}\,({\it{l\/}}))\index{occurrences}$\;${\bf  endif}\- \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{subbagp} \\  
\=\+{\rm{subbagp}}\,({\it{x\/}}, {\it{y\/}})\index{subbagp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $\in$ {\it{y\/}}$\;\;${\bf then }{\rm{subbagp}}\,({\rm{cdr}}\,({\it{x\/}}), {\rm{delete}}\,({\rm{car}}\,({\it{x\/}}), {\it{y\/}})\index{delete})\index{subbagp} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  listp-delete \\ \index{listp-delete}
\=\+{\rm{listp}}\,({\rm{delete}}\,({\it{x\/}}, {\it{l\/}})\index{delete}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}})$\;\;${\bf then }({\it{x\/}} $\not=$ {\rm{car}}\,({\it{l\/}})) $\vee$ {\rm{listp}}\,({\rm{cdr}}\,({\it{l\/}})) \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable listp-delete; name this event `listp-delete-off'.\index{listp-delete-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  delete-non-member \\ \index{delete-non-member}
({\it{x\/}} $\not\in$ {\it{y\/}}) $\rightarrow$ ({\rm{delete}}\,({\it{x\/}}, {\it{y\/}})\index{delete} $=$ {\it{y\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  delete-delete \\ \index{delete-delete}
{\rm{delete}}\,({\it{y\/}}, {\rm{delete}}\,({\it{x\/}}, {\it{z\/}})\index{delete})\index{delete} $=$ {\rm{delete}}\,({\it{x\/}}, {\rm{delete}}\,({\it{y\/}}, {\it{z\/}})\index{delete})\index{delete}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-occurrences-zero \\ \index{equal-occurrences-zero}
({\rm{occurrences}}\,({\it{x\/}}, {\it{l\/}})\index{occurrences} $=$ {\tt{0}}) $=$ ({\it{x\/}} $\not\in$ {\it{l\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  member-non-list \\ \index{member-non-list}
($\neg$ {\rm{listp}}\,({\it{l\/}})) $\rightarrow$ ({\it{x\/}} $\not\in$ {\it{l\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  member-delete \\ \index{member-delete}
\=\+({\it{x\/}} $\in$ {\rm{delete}}\,({\it{y\/}}, {\it{l\/}})\index{delete}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\in$ {\it{l\/}} \\ 
{\bf then }\=\+{\bf if }{\it{x\/}} $=$ {\it{y\/}}$\;\;${\bf then }{\tt{1}} $<$ {\rm{occurrences}}\,({\it{x\/}}, {\it{l\/}})\index{occurrences} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  member-delete-implies-membership \\ \index{member-delete-implies-membership}
({\it{x\/}} $\in$ {\rm{delete}}\,({\it{y\/}}, {\it{l\/}})\index{delete}) $\rightarrow$ ({\it{x\/}} $\in$ {\it{l\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  occurrences-delete \\ \index{occurrences-delete}
\=\+{\rm{occurrences}}\,({\it{x\/}}, {\rm{delete}}\,({\it{y\/}}, {\it{l\/}})\index{delete})\index{occurrences} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $=$ {\it{y\/}} \\ 
{\bf then }\=\+{\bf if }{\it{x\/}} $\in$ {\it{l\/}}$\;\;${\bf then }{\rm{occurrences}}\,({\it{x\/}}, {\it{l\/}})\index{occurrences} $-\;1$ \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{occurrences}}\,({\it{x\/}}, {\it{l\/}})\index{occurrences}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  member-bagdiff \\ \index{member-bagdiff}
({\it{x\/}} $\in$ {\rm{bagdiff}}\,({\it{a\/}}, {\it{b\/}})\index{bagdiff}) $=$ ({\rm{occurrences}}\,({\it{x\/}}, {\it{b\/}})\index{occurrences} $<$ {\rm{occurrences}}\,({\it{x\/}}, {\it{a\/}})\index{occurrences})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bagdiff-delete \\ \index{bagdiff-delete}
{\rm{bagdiff}}\,({\rm{delete}}\,({\it{e\/}}, {\it{x\/}})\index{delete}, {\it{y\/}})\index{bagdiff} $=$ {\rm{delete}}\,({\it{e\/}}, {\rm{bagdiff}}\,({\it{x\/}}, {\it{y\/}})\index{bagdiff})\index{delete}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  subbagp-delete \\ \index{subbagp-delete}
{\rm{subbagp}}\,({\it{x\/}}, {\rm{delete}}\,({\it{u\/}}, {\it{y\/}})\index{delete})\index{subbagp} $\rightarrow$ {\rm{subbagp}}\,({\it{x\/}}, {\it{y\/}})\index{subbagp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  subbagp-cdr1 \\ \index{subbagp-cdr1}
{\rm{subbagp}}\,({\it{x\/}}, {\it{y\/}})\index{subbagp} $\rightarrow$ {\rm{subbagp}}\,({\rm{cdr}}\,({\it{x\/}}), {\it{y\/}})\index{subbagp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  subbagp-cdr2 \\ \index{subbagp-cdr2}
{\rm{subbagp}}\,({\it{x\/}}, {\rm{cdr}}\,({\it{y\/}}))\index{subbagp} $\rightarrow$ {\rm{subbagp}}\,({\it{x\/}}, {\it{y\/}})\index{subbagp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  subbagp-bagint1 \\ \index{subbagp-bagint1}
{\rm{subbagp}}\,({\rm{bagint}}\,({\it{x\/}}, {\it{y\/}})\index{bagint}, {\it{x\/}})\index{subbagp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  subbagp-bagint2 \\ \index{subbagp-bagint2}
{\rm{subbagp}}\,({\rm{bagint}}\,({\it{x\/}}, {\it{y\/}})\index{bagint}, {\it{y\/}})\index{subbagp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  occurrences-bagint \\ \index{occurrences-bagint}
\=\+{\rm{occurrences}}\,({\it{x\/}}, {\rm{bagint}}\,({\it{a\/}}, {\it{b\/}})\index{bagint})\index{occurrences} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{occurrences}}\,({\it{x\/}}, {\it{a\/}})\index{occurrences} $<$ {\rm{occurrences}}\,({\it{x\/}}, {\it{b\/}})\index{occurrences}$\;\;${\bf then }{\rm{occurrences}}\,({\it{x\/}}, {\it{a\/}})\index{occurrences} \\ 
{\bf else }{\rm{occurrences}}\,({\it{x\/}}, {\it{b\/}})\index{occurrences}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  occurrences-bagdiff \\ \index{occurrences-bagdiff}
{\rm{occurrences}}\,({\it{x\/}}, {\rm{bagdiff}}\,({\it{a\/}}, {\it{b\/}})\index{bagdiff})\index{occurrences} $=$ ({\rm{occurrences}}\,({\it{x\/}}, {\it{a\/}})\index{occurrences} $-$ {\rm{occurrences}}\,({\it{x\/}}, {\it{b\/}})\index{occurrences})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  member-bagint \\ \index{member-bagint}
({\it{x\/}} $\in$ {\rm{bagint}}\,({\it{a\/}}, {\it{b\/}})\index{bagint}) $=$ (({\it{x\/}} $\in$ {\it{a\/}}) $\wedge$ ({\it{x\/}} $\in$ {\it{b\/}}))
\end{tabbing}


\noindent{\sc Event}:   Let us define the theory {\it{bags}} to consist of the following events: occurrences-bagint,
bagdiff-delete,
occurrences-bagdiff,
member-bagint,
member-bagdiff,
subbagp-bagint2,
subbagp-bagint1,
subbagp-cdr2,
subbagp-cdr1,
subbagp-delete.\index{bags}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  equal-plus-0 \\ \index{equal-plus-0}
(({\it{a\/}} $+$ {\it{b\/}}) $=$ {\tt{0}}) $=$ (({\it{a\/}} $\simeq {\tt{0}}$) $\wedge$ ({\it{b\/}} $\simeq {\tt{0}}$))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plus-cancellation \\ \index{plus-cancellation}
(({\it{a\/}} $+$ {\it{b\/}}) $=$ ({\it{a\/}} $+$ {\it{c\/}})) $=$ ({\rm{fix}}\,({\it{b\/}}) $=$ {\rm{fix}}\,({\it{c\/}}))
\end{tabbing}


\noindent{\sc Event}:   Enable plus-cancellation; name this event `plus-cancellation-off'.\index{plus-cancellation-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  equal-difference-0 \\ \index{equal-difference-0}
((({\it{x\/}} $-$ {\it{y\/}}) $=$ {\tt{0}}) $=$ ({\it{y\/}} $\not<$ {\it{x\/}})) $\wedge$ (({\tt{0}} $=$ ({\it{x\/}} $-$ {\it{y\/}})) $=$ ({\it{y\/}} $\not<$ {\it{x\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  difference-cancellation \\ \index{difference-cancellation}
\=\+(({\it{x\/}} $-$ {\it{y\/}}) $=$ ({\it{z\/}} $-$ {\it{y\/}})) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $<$ {\it{y\/}}$\;\;${\bf then }{\it{y\/}} $\not<$ {\it{z\/}} \\ 
{\bf elseif }{\it{z\/}} $<$ {\it{y\/}}$\;\;${\bf then }{\it{y\/}} $\not<$ {\it{x\/}} \\ 
{\bf else }{\rm{fix}}\,({\it{x\/}}) $=$ {\rm{fix}}\,({\it{z\/}})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable difference-cancellation; name this event `difference-cancellation-off'.\index{difference-cancellation-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  commutativity-of-plus \\ \index{commutativity-of-plus}
({\it{x\/}} $+$ {\it{y\/}}) $=$ ({\it{y\/}} $+$ {\it{x\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  commutativity2-of-plus \\ \index{commutativity2-of-plus}
({\it{x\/}} $+$ {\it{y\/}} $+$ {\it{z\/}}) $=$ ({\it{y\/}} $+$ {\it{x\/}} $+$ {\it{z\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plus-zero-arg2 \\ \index{plus-zero-arg2}
({\it{y\/}} $\simeq {\tt{0}}$) $\rightarrow$ (({\it{x\/}} $+$ {\it{y\/}}) $=$ {\rm{fix}}\,({\it{x\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plus-add1-arg1 \\ \index{plus-add1-arg1}
(($1\;+$ {\it{a\/}}) $+$ {\it{b\/}}) $=$ ($1\;+$ ({\it{a\/}} $+$ {\it{b\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plus-add1-arg2 \\ \index{plus-add1-arg2}
\=\+({\it{x\/}} $+$ ($1\;+$ {\it{y\/}})) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{y\/}} $\in\;${\bf{N}}${}$$\;\;${\bf then }$1\;+$ ({\it{x\/}} $+$ {\it{y\/}}) \\ 
{\bf else }$1\;+$ {\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  associativity-of-plus \\ \index{associativity-of-plus}
(({\it{x\/}} $+$ {\it{y\/}}) $+$ {\it{z\/}}) $=$ ({\it{x\/}} $+$ {\it{y\/}} $+$ {\it{z\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plus-difference-arg1 \\ \index{plus-difference-arg1}
\=\+(({\it{a\/}} $-$ {\it{b\/}}) $+$ {\it{c\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{b\/}} $<$ {\it{a\/}}$\;\;${\bf then }({\it{a\/}} $+$ {\it{c\/}}) $-$ {\it{b\/}} \\ 
{\bf else }{\tt{0}} $+$ {\it{c\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plus-difference-arg2 \\ \index{plus-difference-arg2}
\=\+({\it{a\/}} $+$ ({\it{b\/}} $-$ {\it{c\/}})) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{c\/}} $<$ {\it{b\/}}$\;\;${\bf then }({\it{a\/}} $+$ {\it{b\/}}) $-$ {\it{c\/}} \\ 
{\bf else }{\it{a\/}} $+$ {\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  difference-plus-cancellation-proof \\ \index{difference-plus-cancellation-pr!oof}
(({\it{x\/}} $+$ {\it{y\/}}) $-$ {\it{x\/}}) $=$ {\rm{fix}}\,({\it{y\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  difference-plus-cancellation \\ \index{difference-plus-cancellation}
((({\it{x\/}} $+$ {\it{y\/}}) $-$ {\it{x\/}}) $=$ {\rm{fix}}\,({\it{y\/}})) $\wedge$ ((({\it{y\/}} $+$ {\it{x\/}}) $-$ {\it{x\/}}) $=$ {\rm{fix}}\,({\it{y\/}}))
\end{tabbing}


\noindent{\sc Event}:   Enable difference-plus-cancellation; name this event `difference-plus-cancellation-off'.\index{difference-plus-cancellation-of!f}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-plus-plus-cancellation-proof \\ \index{difference-plus-plus-cancellati!on-proof}
(({\it{x\/}} $+$ {\it{y\/}}) $-$ ({\it{x\/}} $+$ {\it{z\/}})) $=$ ({\it{y\/}} $-$ {\it{z\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  difference-plus-plus-cancellation \\ \index{difference-plus-plus-cancellati!on}
\=\+((({\it{x\/}} $+$ {\it{y\/}}) $-$ ({\it{x\/}} $+$ {\it{z\/}})) $=$ ({\it{y\/}} $-$ {\it{z\/}})) \\ 
$\wedge$$\;\;\;\;$((({\it{y\/}} $+$ {\it{x\/}}) $-$ ({\it{x\/}} $+$ {\it{z\/}})) $=$ ({\it{y\/}} $-$ {\it{z\/}})) \\ 
$\wedge$$\;\;\;\;$((({\it{x\/}} $+$ {\it{y\/}}) $-$ ({\it{z\/}} $+$ {\it{x\/}})) $=$ ({\it{y\/}} $-$ {\it{z\/}})) \\ 
$\wedge$$\;\;\;\;$((({\it{y\/}} $+$ {\it{x\/}}) $-$ ({\it{z\/}} $+$ {\it{x\/}})) $=$ ({\it{y\/}} $-$ {\it{z\/}}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable difference-plus-plus-cancellation; name this event `difference-plus-plus-cancellation-off'.\index{difference-plus-plus-cancellati!on-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-plus-plus-cancellation-hack \\ \index{difference-plus-plus-cancellati!on-hack}
(({\it{w\/}} $+$ {\it{x\/}} $+$ {\it{a\/}}) $-$ ({\it{y\/}} $+$ {\it{z\/}} $+$ {\it{a\/}})) $=$ (({\it{w\/}} $+$ {\it{x\/}}) $-$ ({\it{y\/}} $+$ {\it{z\/}}))
\end{tabbing}


\noindent{\sc Event}:   Enable difference-plus-plus-cancellation-hack; name this event `difference-plus-plus-cancellation-hack-off'.\index{difference-plus-plus-cancellati!on-hack-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  diff-sub1-arg2 \\ \index{diff-sub1-arg2}
\=\+({\it{a\/}} $-$ ({\it{b\/}} $-\;1$)) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{b\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\rm{fix}}\,({\it{a\/}}) \\ 
{\bf elseif }{\it{a\/}} $<$ {\it{b\/}}$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }$1\;+$ ({\it{a\/}} $-$ {\it{b\/}})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable diff-sub1-arg2; name this event `diff-sub1-arg2-off'.\index{diff-sub1-arg2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  diff-diff-arg1 \\ \index{diff-diff-arg1}
(({\it{x\/}} $-$ {\it{y\/}}) $-$ {\it{z\/}}) $=$ ({\it{x\/}} $-$ ({\it{y\/}} $+$ {\it{z\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  diff-diff-arg2 \\ \index{diff-diff-arg2}
\=\+({\it{a\/}} $-$ ({\it{b\/}} $-$ {\it{c\/}})) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{b\/}} $<$ {\it{c\/}}$\;\;${\bf then }{\rm{fix}}\,({\it{a\/}}) \\ 
{\bf else }({\it{a\/}} $+$ {\it{c\/}}) $-$ {\it{b\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  diff-diff-diff \\ \index{diff-diff-diff}
\=\+(\=\+\=\+{\bf if }{\it{a\/}} $<$ {\it{b\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{c\/}} $<$ {\it{d\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$((({\it{a\/}} $-$ {\it{b\/}}) $-$ ({\it{c\/}} $-$ {\it{d\/}})) $=$ (({\it{a\/}} $+$ {\it{d\/}}) $-$ ({\it{b\/}} $+$ {\it{c\/}})))\-
\end{tabbing}


\noindent{\sc Event}:   Enable diff-diff-diff; name this event `diff-diff-diff-off'.\index{diff-diff-diff-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-lessp-arg1 \\ \index{difference-lessp-arg1}
({\it{a\/}} $<$ {\it{b\/}}) $\rightarrow$ (({\it{a\/}} $-$ {\it{b\/}}) $=$ {\tt{0}})
\end{tabbing}


\noindent{\sc Event}:   Enable difference-lessp-arg1; name this event `difference-lessp-arg1-off'.\index{difference-lessp-arg1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{plus-fringe} \\  
\=\+{\rm{plus-fringe}}\,({\it{x\/}})\index{plus-fringe} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) $\wedge$ ({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{plus}}) \\ 
{\bf then }{\rm{append}}\,({\rm{plus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{plus-fringe}, {\rm{plus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{plus-fringe}) \\ 
{\bf else }{\rm{list}}\,({\it{x\/}})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{plus-tree} \\  
\=\+{\rm{plus-tree}}\,({\it{l\/}})\index{plus-tree} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{l\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\tt{'}}{\tt{'}}{\tt{0}} \\ 
{\bf elseif }{\rm{cdr}}\,({\it{l\/}}) $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{list}}\,({\tt{'}}{\tt{fix}}, {\rm{car}}\,({\it{l\/}})) \\ 
{\bf elseif }{\rm{cddr}}\,({\it{l\/}}) $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{list}}\,({\tt{'}}{\tt{plus}}, {\rm{car}}\,({\it{l\/}}), {\rm{cadr}}\,({\it{l\/}})) \\ 
{\bf else }{\rm{list}}\,({\tt{'}}{\tt{plus}}, {\rm{car}}\,({\it{l\/}}), {\rm{plus-tree}}\,({\rm{cdr}}\,({\it{l\/}}))\index{plus-tree})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  numberp-eval\$-plus \\ \index{numberp-eval\$-plus}
({\rm{listp}}\,({\it{x\/}}) $\wedge$ ({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{plus}})) $\rightarrow$ ({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $\in\;${\bf{N}}${}$)
\end{tabbing}


\noindent{\sc Event}:   Enable numberp-eval\$-plus; name this event `numberp-eval\$-plus-off'.\index{numberp-eval\$-plus-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-eval\$-plus-tree \\ \index{numberp-eval\$-plus-tree}
{\rm{eval\$}}\,({\bf{t}}, {\rm{plus-tree}}\,({\it{l\/}})\index{plus-tree}, {\it{a\/}}) $\in\;${\bf{N}}${}$
\end{tabbing}


\noindent{\sc Event}:   Enable numberp-eval\$-plus-tree; name this event `numberp-eval\$-plus-tree-off'.\index{numberp-eval\$-plus-tree-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  member-implies-plus-tree-greatereqp \\ \index{member-implies-plus-tree-greate!reqp}
({\it{x\/}} $\in$ {\it{y\/}}) $\rightarrow$ ({\rm{eval\$}}\,({\bf{t}}, {\rm{plus-tree}}\,({\it{y\/}})\index{plus-tree}, {\it{a\/}}) $\not<$ {\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}))
\end{tabbing}


\noindent{\sc Event}:   Enable member-implies-plus-tree-greatereqp; name this event `member-implies-plus-tree-greatereqp-off'.\index{member-implies-plus-tree-greate!reqp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plus-tree-delete \\ \index{plus-tree-delete}
\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{plus-tree}}\,({\rm{delete}}\,({\it{x\/}}, {\it{y\/}})\index{delete})\index{plus-tree}, {\it{a\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\in$ {\it{y\/}}$\;\;${\bf then }{\rm{eval\$}}\,({\bf{t}}, {\rm{plus-tree}}\,({\it{y\/}})\index{plus-tree}, {\it{a\/}}) $-$ {\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) \\ 
{\bf else }{\rm{eval\$}}\,({\bf{t}}, {\rm{plus-tree}}\,({\it{y\/}})\index{plus-tree}, {\it{a\/}})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable plus-tree-delete; name this event `plus-tree-delete-off'.\index{plus-tree-delete-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  subbagp-implies-plus-tree-greatereqp \\ \index{subbagp-implies-plus-tree-greate!reqp}
{\rm{subbagp}}\,({\it{x\/}}, {\it{y\/}})\index{subbagp} $\rightarrow$ ({\rm{eval\$}}\,({\bf{t}}, {\rm{plus-tree}}\,({\it{y\/}})\index{plus-tree}, {\it{a\/}}) $\not<$ {\rm{eval\$}}\,({\bf{t}}, {\rm{plus-tree}}\,({\it{x\/}})\index{plus-tree}, {\it{a\/}}))
\end{tabbing}


\noindent{\sc Event}:   Enable subbagp-implies-plus-tree-greatereqp; name this event `subbagp-implies-plus-tree-greatereqp-off'.\index{subbagp-implies-plus-tree-greate!reqp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plus-tree-bagdiff \\ \index{plus-tree-bagdiff}
\=\+{\rm{subbagp}}\,({\it{x\/}}, {\it{y\/}})\index{subbagp} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{plus-tree}}\,({\rm{bagdiff}}\,({\it{y\/}}, {\it{x\/}})\index{bagdiff})\index{plus-tree}, {\it{a\/}}) \\ 
$=$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\rm{plus-tree}}\,({\it{y\/}})\index{plus-tree}, {\it{a\/}}) $-$ {\rm{eval\$}}\,({\bf{t}}, {\rm{plus-tree}}\,({\it{x\/}})\index{plus-tree}, {\it{a\/}})))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable plus-tree-bagdiff; name this event `plus-tree-bagdiff-off'.\index{plus-tree-bagdiff-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-eval\$-bridge \\ \index{numberp-eval\$-bridge}
({\rm{eval\$}}\,({\bf{t}}, {\it{z\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{plus-tree}}\,({\it{x\/}})\index{plus-tree}, {\it{a\/}})) $\rightarrow$ ({\rm{eval\$}}\,({\bf{t}}, {\it{z\/}}, {\it{a\/}}) $\in\;${\bf{N}}${}$)
\end{tabbing}


\noindent{\sc Event}:   Enable numberp-eval\$-bridge; name this event `numberp-eval\$-bridge-off'.\index{numberp-eval\$-bridge-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  bridge-to-subbagp-implies-plus-tree-greatereqp \\ \index{bridge-to-subbagp-implies-plus-t!ree-greatereqp}
\=\+(\=\+{\rm{subbagp}}\,({\it{y\/}}, {\rm{plus-fringe}}\,({\it{z\/}})\index{plus-fringe})\index{subbagp} \\ 
$\wedge$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\it{z\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{plus-tree}}\,({\rm{plus-fringe}}\,({\it{z\/}})\index{plus-fringe})\index{plus-tree}, {\it{a\/}})))\- \\ 
$\rightarrow$$\;\;\;\;$(({\rm{eval\$}}\,({\bf{t}}, {\it{z\/}}, {\it{a\/}}) $<$ {\rm{eval\$}}\,({\bf{t}}, {\rm{plus-tree}}\,({\it{y\/}})\index{plus-tree}, {\it{a\/}})) $=$ {\bf{f}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable bridge-to-subbagp-implies-plus-tree-greatereqp; name this event `bridge-to-subbagp-implies-plus-tree-greatereqp-off'.\index{bridge-to-subbagp-implies-plus-t!ree-greatereqp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  eval\$-plus-tree-append \\ \index{eval\$-plus-tree-append}
\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{plus-tree}}\,({\rm{append}}\,({\it{x\/}}, {\it{y\/}}))\index{plus-tree}, {\it{a\/}}) \\ 
$=$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\rm{plus-tree}}\,({\it{x\/}})\index{plus-tree}, {\it{a\/}}) $+$ {\rm{eval\$}}\,({\bf{t}}, {\rm{plus-tree}}\,({\it{y\/}})\index{plus-tree}, {\it{a\/}}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable eval\$-plus-tree-append; name this event `eval\$-plus-tree-append-off'.\index{eval\$-plus-tree-append-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plus-tree-plus-fringe \\ \index{plus-tree-plus-fringe}
{\rm{eval\$}}\,({\bf{t}}, {\rm{plus-tree}}\,({\rm{plus-fringe}}\,({\it{x\/}})\index{plus-fringe})\index{plus-tree}, {\it{a\/}}) $=$ {\rm{fix}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}))
\end{tabbing}


\noindent{\sc Event}:   Enable plus-tree-plus-fringe; name this event `plus-tree-plus-fringe-off'.\index{plus-tree-plus-fringe-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  member-implies-numberp \\ \index{member-implies-numberp}
(({\it{c\/}} $\in$ {\rm{plus-fringe}}\,({\it{x\/}})\index{plus-fringe}) $\wedge$ ({\rm{eval\$}}\,({\bf{t}}, {\it{c\/}}, {\it{a\/}}) $\in\;${\bf{N}}${}$)) $\rightarrow$ ({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $\in\;${\bf{N}}${}$)
\end{tabbing}


\noindent{\sc Event}:   Enable member-implies-numberp; name this event `member-implies-numberp-off'.\index{member-implies-numberp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cadr-eval\$-list \\ \index{cadr-eval\$-list}
\=\+({\rm{car}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}})) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{car}}\,({\it{x\/}}), {\it{a\/}})) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cdr}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}})) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}})$\;\;${\bf then }{\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{cdr}}\,({\it{x\/}}), {\it{a\/}}) \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cadr-eval\$-list; name this event `cadr-eval\$-list-off'.\index{cadr-eval\$-list-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  eval\$-quote \\ \index{eval\$-quote}
{\rm{eval\$}}\,({\bf{t}}, {\rm{cons}}\,({\tt{'}}{\tt{quote}}, {\it{args\/}}), {\it{a\/}}) $=$ {\rm{car}}\,({\it{args\/}})
\end{tabbing}


\noindent{\sc Event}:   Enable eval\$-quote; name this event `eval\$-quote-off'.\index{eval\$-quote-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  listp-eval\$ \\ \index{listp-eval\$}
{\rm{listp}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}})) $=$ {\rm{listp}}\,({\it{x\/}})
\end{tabbing}


\noindent{\sc Event}:   Enable listp-eval\$; name this event `listp-eval\$-off'.\index{listp-eval\$-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{cancel-equal-plus} \\  
\=\+{\rm{cancel-equal-plus}}\,({\it{x\/}})\index{cancel-equal-plus} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) $\wedge$ ({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{equal}}) \\ 
{\bf then }\=\+{\bf if }\=\+{\rm{listp}}\,({\rm{cadr}}\,({\it{x\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{caadr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{plus}}) \\ 
$\wedge$$\;\;\;\;${\rm{listp}}\,({\rm{caddr}}\,({\it{x\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{caaddr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{plus}})\- \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{plus-tree}}\,({\rm{bagdiff}}\,(\=\+{\rm{plus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{plus-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{plus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{plus-fringe}, \\ 
{\rm{plus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{plus-fringe})\-\index{bagint})\-\index{bagdiff})\index{plus-tree}, \\ 
{\rm{plus-tree}}\,({\rm{bagdiff}}\,(\=\+{\rm{plus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{plus-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{plus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{plus-fringe}, \\ 
{\rm{plus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{plus-fringe})\-\index{bagint})\-\index{bagdiff})\index{plus-tree})\- \\ 
{\bf elseif }\=\+{\rm{listp}}\,({\rm{cadr}}\,({\it{x\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{caadr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{plus}}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\it{x\/}}) $\in$ {\rm{plus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{plus-fringe})\- \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{numberp}}, {\rm{caddr}}\,({\it{x\/}})), \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{cons}}\,(\=\+{\rm{plus-tree}}\,({\rm{delete}}\,(\=\+{\rm{caddr}}\,({\it{x\/}}), \\ 
{\rm{plus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{plus-fringe})\-\index{delete})\index{plus-tree}, \\ 
{\tt{'}}{\tt{(}}{\tt{'}}{\tt{0}}{\tt{)}})\-)\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\- \\ 
{\bf elseif }\=\+{\rm{listp}}\,({\rm{caddr}}\,({\it{x\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{caaddr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{plus}}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadr}}\,({\it{x\/}}) $\in$ {\rm{plus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{plus-fringe})\- \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{numberp}}, {\rm{cadr}}\,({\it{x\/}})), \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\tt{'}}{\tt{'}}{\tt{0}}, \\ 
{\rm{plus-tree}}\,({\rm{delete}}\,({\rm{cadr}}\,({\it{x\/}}), {\rm{plus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{plus-fringe})\index{delete})\index{plus-tree})\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-equal-plus \\ \index{correctness-of-cancel-equal-plu!s}
{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{cancel-equal-plus}}\,({\it{x\/}})\index{cancel-equal-plus}, {\it{a\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cancel-difference-plus} \\  
\=\+{\rm{cancel-difference-plus}}\,({\it{x\/}})\index{cancel-difference-plus} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) $\wedge$ ({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{difference}}) \\ 
{\bf then }\=\+{\bf if }\=\+{\rm{listp}}\,({\rm{cadr}}\,({\it{x\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{caadr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{plus}}) \\ 
$\wedge$$\;\;\;\;${\rm{listp}}\,({\rm{caddr}}\,({\it{x\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{caaddr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{plus}})\- \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{difference}}, \\ 
{\rm{plus-tree}}\,({\rm{bagdiff}}\,(\=\+{\rm{plus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{plus-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{plus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{plus-fringe}, \\ 
{\rm{plus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{plus-fringe})\-\index{bagint})\-\index{bagdiff})\index{plus-tree}, \\ 
{\rm{plus-tree}}\,({\rm{bagdiff}}\,(\=\+{\rm{plus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{plus-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{plus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{plus-fringe}, \\ 
{\rm{plus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{plus-fringe})\-\index{bagint})\-\index{bagdiff})\index{plus-tree})\- \\ 
{\bf elseif }\=\+{\rm{listp}}\,({\rm{cadr}}\,({\it{x\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{caadr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{plus}}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\it{x\/}}) $\in$ {\rm{plus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{plus-fringe})\- \\ 
{\bf then }{\rm{plus-tree}}\,({\rm{delete}}\,({\rm{caddr}}\,({\it{x\/}}), {\rm{plus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{plus-fringe})\index{delete})\index{plus-tree} \\ 
{\bf elseif }\=\+{\rm{listp}}\,({\rm{caddr}}\,({\it{x\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{caaddr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{plus}}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadr}}\,({\it{x\/}}) $\in$ {\rm{plus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{plus-fringe})\-$\;\;${\bf then }{\tt{'}}{\tt{'}}{\tt{0}} \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-difference-plus \\ \index{correctness-of-cancel-difference!-plus}
{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{cancel-difference-plus}}\,({\it{x\/}})\index{cancel-difference-plus}, {\it{a\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  difference-elim \\ \index{difference-elim}
(({\it{y\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{y\/}} $\not<$ {\it{x\/}})) $\rightarrow$ (({\it{x\/}} $+$ ({\it{y\/}} $-$ {\it{x\/}})) $=$ {\it{y\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  difference-leq-arg1 \\ \index{difference-leq-arg1}
\=\+\=\+{\bf if }{\it{b\/}} $<$ {\it{a\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$(({\it{a\/}} $-$ {\it{b\/}}) $=$ {\tt{0}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  difference-add1-arg2 \\ \index{difference-add1-arg2}
\=\+({\it{a\/}} $-$ ($1\;+$ {\it{b\/}})) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{b\/}} $<$ {\it{a\/}}$\;\;${\bf then }({\it{a\/}} $-$ {\it{b\/}}) $-\;1$ \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  difference-sub1-arg2 \\ \index{difference-sub1-arg2}
\=\+({\it{a\/}} $-$ ({\it{b\/}} $-\;1$)) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{b\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\rm{fix}}\,({\it{a\/}}) \\ 
{\bf elseif }{\it{a\/}} $<$ {\it{b\/}}$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }$1\;+$ ({\it{a\/}} $-$ {\it{b\/}})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  difference-difference-arg1 \\ \index{difference-difference-arg1}
(({\it{x\/}} $-$ {\it{y\/}}) $-$ {\it{z\/}}) $=$ ({\it{x\/}} $-$ ({\it{y\/}} $+$ {\it{z\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  difference-difference-arg2 \\ \index{difference-difference-arg2}
\=\+({\it{a\/}} $-$ ({\it{b\/}} $-$ {\it{c\/}})) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{b\/}} $<$ {\it{c\/}}$\;\;${\bf then }{\rm{fix}}\,({\it{a\/}}) \\ 
{\bf else }({\it{a\/}} $+$ {\it{c\/}}) $-$ {\it{b\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  difference-x-x \\ \index{difference-x-x}
({\it{x\/}} $-$ {\it{x\/}}) $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-difference-cancellation \\ \index{lessp-difference-cancellation}
\=\+(({\it{a\/}} $-$ {\it{c\/}}) $<$ ({\it{b\/}} $-$ {\it{c\/}})) \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\bf if }{\it{a\/}} $<$ {\it{c\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-$\;\;${\bf then }{\it{a\/}} $<$ {\it{b\/}} \\ 
{\bf else }{\it{c\/}} $<$ {\it{b\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable lessp-difference-cancellation; name this event `lessp-difference-cancellation-off'.\index{lessp-difference-cancellation-o!ff}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{cancel-lessp-plus} \\  
\=\+{\rm{cancel-lessp-plus}}\,({\it{x\/}})\index{cancel-lessp-plus} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) $\wedge$ ({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{lessp}}) \\ 
{\bf then }\=\+{\bf if }\=\+{\rm{listp}}\,({\rm{cadr}}\,({\it{x\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{caadr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{plus}}) \\ 
$\wedge$$\;\;\;\;${\rm{listp}}\,({\rm{caddr}}\,({\it{x\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{caaddr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{plus}})\- \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{lessp}}, \\ 
{\rm{plus-tree}}\,({\rm{bagdiff}}\,(\=\+{\rm{plus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{plus-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{plus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{plus-fringe}, \\ 
{\rm{plus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{plus-fringe})\-\index{bagint})\-\index{bagdiff})\index{plus-tree}, \\ 
{\rm{plus-tree}}\,({\rm{bagdiff}}\,(\=\+{\rm{plus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{plus-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{plus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{plus-fringe}, \\ 
{\rm{plus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{plus-fringe})\-\index{bagint})\-\index{bagdiff})\index{plus-tree})\- \\ 
{\bf elseif }\=\+{\rm{listp}}\,({\rm{cadr}}\,({\it{x\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{caadr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{plus}}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\it{x\/}}) $\in$ {\rm{plus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{plus-fringe})\- \\ 
{\bf then }{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}) \\ 
{\bf elseif }\=\+{\rm{listp}}\,({\rm{caddr}}\,({\it{x\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{caaddr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{plus}}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadr}}\,({\it{x\/}}) $\in$ {\rm{plus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{plus-fringe})\- \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{not}}, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{zerop}}, \\ 
{\rm{plus-tree}}\,({\rm{delete}}\,({\rm{cadr}}\,({\it{x\/}}), {\rm{plus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{plus-fringe})\index{delete})\index{plus-tree})\-)\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-lessp-plus \\ \index{correctness-of-cancel-lessp-plu!s}
{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{cancel-lessp-plus}}\,({\it{x\/}})\index{cancel-lessp-plus}, {\it{a\/}})
\end{tabbing}


\noindent{\sc Event}:   Let us define the theory {\it{addition}} to consist of the following events: equal-plus-0,
equal-difference-0,
commutativity-of-plus,
commutativity2-of-plus,
plus-zero-arg2,
plus-add1-arg2,
plus-add1-arg1,
associativity-of-plus,
plus-difference-arg1,
plus-difference-arg2,
diff-diff-arg1,
diff-diff-arg2,
correctness-of-cancel-equal-plus,
correctness-of-cancel-difference-plus,
difference-elim,
difference-leq-arg1,
difference-add1-arg2,
difference-sub1-arg2,
difference-difference-arg1,
difference-difference-arg2,
difference-x-x,
correctness-of-cancel-lessp-plus.\index{addition}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  equal-times-0 \\ \index{equal-times-0}
(({\it{x\/}} $*$ {\it{y\/}}) $=$ {\tt{0}}) $=$ (({\it{x\/}} $\simeq {\tt{0}}$) $\vee$ ({\it{y\/}} $\simeq {\tt{0}}$))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-times-1 \\ \index{equal-times-1}
(({\it{a\/}} $*$ {\it{b\/}}) $=$ {\tt{1}}) $=$ (({\it{a\/}} $=$ {\tt{1}}) $\wedge$ ({\it{b\/}} $=$ {\tt{1}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-sub1-0 \\ \index{equal-sub1-0}
(({\it{x\/}} $-\;1$) $=$ {\tt{0}}) $=$ (({\it{x\/}} $\simeq {\tt{0}}$) $\vee$ ({\it{x\/}} $=$ {\tt{1}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  times-zero \\ \index{times-zero}
({\it{y\/}} $\simeq {\tt{0}}$) $\rightarrow$ (({\it{x\/}} $*$ {\it{y\/}}) $=$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  times-add1 \\ \index{times-add1}
\=\+({\it{x\/}} $*$ ($1\;+$ {\it{y\/}})) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{y\/}} $\in\;${\bf{N}}${}$$\;\;${\bf then }{\it{x\/}} $+$ ({\it{x\/}} $*$ {\it{y\/}}) \\ 
{\bf else }{\rm{fix}}\,({\it{x\/}})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  commutativity-of-times \\ \index{commutativity-of-times}
({\it{y\/}} $*$ {\it{x\/}}) $=$ ({\it{x\/}} $*$ {\it{y\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  times-distributes-over-plus-proof \\ \index{times-distributes-over-plus-pro!of}
({\it{x\/}} $*$ ({\it{y\/}} $+$ {\it{z\/}})) $=$ (({\it{x\/}} $*$ {\it{y\/}}) $+$ ({\it{x\/}} $*$ {\it{z\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  times-distributes-over-plus \\ \index{times-distributes-over-plus}
\=\+(({\it{x\/}} $*$ ({\it{y\/}} $+$ {\it{z\/}})) $=$ (({\it{x\/}} $*$ {\it{y\/}}) $+$ ({\it{x\/}} $*$ {\it{z\/}}))) \\ 
$\wedge$$\;\;\;\;$((({\it{x\/}} $+$ {\it{y\/}}) $*$ {\it{z\/}}) $=$ (({\it{x\/}} $*$ {\it{z\/}}) $+$ ({\it{y\/}} $*$ {\it{z\/}})))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  commutativity2-of-times \\ \index{commutativity2-of-times}
({\it{x\/}} $*$ {\it{y\/}} $*$ {\it{z\/}}) $=$ ({\it{y\/}} $*$ {\it{x\/}} $*$ {\it{z\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  associativity-of-times \\ \index{associativity-of-times}
(({\it{x\/}} $*$ {\it{y\/}}) $*$ {\it{z\/}}) $=$ ({\it{x\/}} $*$ {\it{y\/}} $*$ {\it{z\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  times-distributes-over-difference-proof \\ \index{times-distributes-over-differen!ce-proof}
(({\it{a\/}} $-$ {\it{b\/}}) $*$ {\it{c\/}}) $=$ (({\it{a\/}} $*$ {\it{c\/}}) $-$ ({\it{b\/}} $*$ {\it{c\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  times-distributes-over-difference \\ \index{times-distributes-over-differen!ce}
\=\+((({\it{a\/}} $-$ {\it{b\/}}) $*$ {\it{c\/}}) $=$ (({\it{a\/}} $*$ {\it{c\/}}) $-$ ({\it{b\/}} $*$ {\it{c\/}}))) \\ 
$\wedge$$\;\;\;\;$(({\it{a\/}} $*$ ({\it{b\/}} $-$ {\it{c\/}})) $=$ (({\it{a\/}} $*$ {\it{b\/}}) $-$ ({\it{a\/}} $*$ {\it{c\/}})))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  times-quotient-proof \\ \index{times-quotient-proof}
(({\it{x\/}} $\not\simeq {\tt{0}}$) $\wedge$ (({\it{y\/}} ${}${\bf{mod}}${}$ {\it{x\/}}) $=$ {\tt{0}})) $\rightarrow$ ((({\it{y\/}} $\div$ {\it{x\/}}) $*$ {\it{x\/}}) $=$ {\rm{fix}}\,({\it{y\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  times-quotient \\ \index{times-quotient}
\=\+(({\it{y\/}} $\not\simeq {\tt{0}}$) $\wedge$ (({\it{x\/}} ${}${\bf{mod}}${}$ {\it{y\/}}) $=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$(((({\it{x\/}} $\div$ {\it{y\/}}) $*$ {\it{y\/}}) $=$ {\rm{fix}}\,({\it{x\/}})) $\wedge$ (({\it{y\/}} $*$ ({\it{x\/}} $\div$ {\it{y\/}})) $=$ {\rm{fix}}\,({\it{x\/}})))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  times-1-arg1 \\ \index{times-1-arg1}
({\tt{1}} $*$ {\it{x\/}}) $=$ {\rm{fix}}\,({\it{x\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-times1-proof \\ \index{lessp-times1-proof}
(({\it{a\/}} $<$ {\it{b\/}}) $\wedge$ ({\it{c\/}} $\not\simeq {\tt{0}}$)) $\rightarrow$ (({\it{a\/}} $<$ ({\it{b\/}} $*$ {\it{c\/}})) $=$ {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-times1 \\ \index{lessp-times1}
\=\+(({\it{a\/}} $<$ {\it{b\/}}) $\wedge$ ({\it{c\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$((({\it{a\/}} $<$ ({\it{b\/}} $*$ {\it{c\/}})) $=$ {\bf{t}}) $\wedge$ (({\it{a\/}} $<$ ({\it{c\/}} $*$ {\it{b\/}})) $=$ {\bf{t}}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-times2-proof \\ \index{lessp-times2-proof}
\=\+(\=\+\=\+{\bf if }{\it{b\/}} $<$ {\it{a\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$({\it{c\/}} $\not\simeq {\tt{0}}$))\- \\ 
$\rightarrow$$\;\;\;\;$((({\it{b\/}} $*$ {\it{c\/}}) $<$ {\it{a\/}}) $=$ {\bf{f}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-times2 \\ \index{lessp-times2}
\=\+(\=\+\=\+{\bf if }{\it{b\/}} $<$ {\it{a\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$({\it{c\/}} $\not\simeq {\tt{0}}$))\- \\ 
$\rightarrow$$\;\;\;\;$(((({\it{b\/}} $*$ {\it{c\/}}) $<$ {\it{a\/}}) $=$ {\bf{f}}) $\wedge$ ((({\it{c\/}} $*$ {\it{b\/}}) $<$ {\it{a\/}}) $=$ {\bf{f}}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-times3-proof1 \\ \index{lessp-times3-proof1}
(({\it{a\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\tt{1}} $<$ {\it{b\/}})) $\rightarrow$ ({\it{a\/}} $<$ ({\it{a\/}} $*$ {\it{b\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-times3-proof2 \\ \index{lessp-times3-proof2}
({\it{a\/}} $<$ ({\it{a\/}} $*$ {\it{b\/}})) $\rightarrow$ (({\it{a\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\tt{1}} $<$ {\it{b\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-times3 \\ \index{lessp-times3}
\=\+(({\it{a\/}} $<$ ({\it{a\/}} $*$ {\it{b\/}})) $=$ (({\it{a\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\tt{1}} $<$ {\it{b\/}}))) \\ 
$\wedge$$\;\;\;\;$(({\it{a\/}} $<$ ({\it{b\/}} $*$ {\it{a\/}})) $=$ (({\it{a\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\tt{1}} $<$ {\it{b\/}})))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-times-cancellation-proof \\ \index{lessp-times-cancellation-proof}
(({\it{x\/}} $*$ {\it{z\/}}) $<$ ({\it{y\/}} $*$ {\it{z\/}})) $=$ (({\it{z\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\it{x\/}} $<$ {\it{y\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-times-cancellation1 \\ \index{lessp-times-cancellation1}
\=\+((({\it{x\/}} $*$ {\it{z\/}}) $<$ ({\it{y\/}} $*$ {\it{z\/}})) $=$ (({\it{z\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\it{x\/}} $<$ {\it{y\/}}))) \\ 
$\wedge$$\;\;\;\;$((({\it{z\/}} $*$ {\it{x\/}}) $<$ ({\it{y\/}} $*$ {\it{z\/}})) $=$ (({\it{z\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\it{x\/}} $<$ {\it{y\/}}))) \\ 
$\wedge$$\;\;\;\;$((({\it{x\/}} $*$ {\it{z\/}}) $<$ ({\it{z\/}} $*$ {\it{y\/}})) $=$ (({\it{z\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\it{x\/}} $<$ {\it{y\/}}))) \\ 
$\wedge$$\;\;\;\;$((({\it{z\/}} $*$ {\it{x\/}}) $<$ ({\it{z\/}} $*$ {\it{y\/}})) $=$ (({\it{z\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\it{x\/}} $<$ {\it{y\/}})))\-
\end{tabbing}


\noindent{\sc Event}:   Enable lessp-times-cancellation1; name this event `lessp-times-cancellation1-off'.\index{lessp-times-cancellation1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-plus-times-proof \\ \index{lessp-plus-times-proof}
({\it{x\/}} $<$ {\it{a\/}}) $\rightarrow$ ((({\it{x\/}} $+$ ({\it{a\/}} $*$ {\it{b\/}})) $<$ ({\it{a\/}} $*$ {\it{c\/}})) $=$ ({\it{b\/}} $<$ {\it{c\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-plus-times1 \\ \index{lessp-plus-times1}
\=\+((({\it{a\/}} $+$ ({\it{b\/}} $*$ {\it{c\/}})) $<$ {\it{b\/}}) $=$ (({\it{a\/}} $<$ {\it{b\/}}) $\wedge$ ({\it{c\/}} $\simeq {\tt{0}}$))) \\ 
$\wedge$$\;\;\;\;$((({\it{a\/}} $+$ ({\it{c\/}} $*$ {\it{b\/}})) $<$ {\it{b\/}}) $=$ (({\it{a\/}} $<$ {\it{b\/}}) $\wedge$ ({\it{c\/}} $\simeq {\tt{0}}$))) \\ 
$\wedge$$\;\;\;\;$(((({\it{c\/}} $*$ {\it{b\/}}) $+$ {\it{a\/}}) $<$ {\it{b\/}}) $=$ (({\it{a\/}} $<$ {\it{b\/}}) $\wedge$ ({\it{c\/}} $\simeq {\tt{0}}$))) \\ 
$\wedge$$\;\;\;\;$(((({\it{b\/}} $*$ {\it{c\/}}) $+$ {\it{a\/}}) $<$ {\it{b\/}}) $=$ (({\it{a\/}} $<$ {\it{b\/}}) $\wedge$ ({\it{c\/}} $\simeq {\tt{0}}$)))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-plus-times2 \\ \index{lessp-plus-times2}
\=\+(({\it{a\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\it{x\/}} $<$ {\it{a\/}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+((({\it{x\/}} $+$ ({\it{a\/}} $*$ {\it{b\/}})) $<$ ({\it{a\/}} $*$ {\it{c\/}})) $=$ ({\it{b\/}} $<$ {\it{c\/}})) \\ 
$\wedge$$\;\;\;\;$((({\it{x\/}} $+$ ({\it{b\/}} $*$ {\it{a\/}})) $<$ ({\it{a\/}} $*$ {\it{c\/}})) $=$ ({\it{b\/}} $<$ {\it{c\/}})) \\ 
$\wedge$$\;\;\;\;$((({\it{x\/}} $+$ ({\it{a\/}} $*$ {\it{b\/}})) $<$ ({\it{c\/}} $*$ {\it{a\/}})) $=$ ({\it{b\/}} $<$ {\it{c\/}})) \\ 
$\wedge$$\;\;\;\;$((({\it{x\/}} $+$ ({\it{b\/}} $*$ {\it{a\/}})) $<$ ({\it{c\/}} $*$ {\it{a\/}})) $=$ ({\it{b\/}} $<$ {\it{c\/}})) \\ 
$\wedge$$\;\;\;\;$(((({\it{a\/}} $*$ {\it{b\/}}) $+$ {\it{x\/}}) $<$ ({\it{a\/}} $*$ {\it{c\/}})) $=$ ({\it{b\/}} $<$ {\it{c\/}})) \\ 
$\wedge$$\;\;\;\;$(((({\it{b\/}} $*$ {\it{a\/}}) $+$ {\it{x\/}}) $<$ ({\it{a\/}} $*$ {\it{c\/}})) $=$ ({\it{b\/}} $<$ {\it{c\/}})) \\ 
$\wedge$$\;\;\;\;$(((({\it{a\/}} $*$ {\it{b\/}}) $+$ {\it{x\/}}) $<$ ({\it{c\/}} $*$ {\it{a\/}})) $=$ ({\it{b\/}} $<$ {\it{c\/}})) \\ 
$\wedge$$\;\;\;\;$(((({\it{b\/}} $*$ {\it{a\/}}) $+$ {\it{x\/}}) $<$ ({\it{c\/}} $*$ {\it{a\/}})) $=$ ({\it{b\/}} $<$ {\it{c\/}})))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-1-times \\ \index{lessp-1-times}
\=\+({\tt{1}} $<$ ({\it{a\/}} $*$ {\it{b\/}})) \\ 
$=$$\;\;\;\;$($\neg$ (({\it{a\/}} $\simeq {\tt{0}}$) $\vee$ ({\it{b\/}} $\simeq {\tt{0}}$) $\vee$ (({\it{a\/}} $=$ {\tt{1}}) $\wedge$ ({\it{b\/}} $=$ {\tt{1}}))))\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{times-tree} \\  
\=\+{\rm{times-tree}}\,({\it{x\/}})\index{times-tree} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\tt{'}}{\tt{'}}{\tt{1}} \\ 
{\bf elseif }{\rm{cdr}}\,({\it{x\/}}) $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{list}}\,({\tt{'}}{\tt{fix}}, {\rm{car}}\,({\it{x\/}})) \\ 
{\bf elseif }{\rm{cddr}}\,({\it{x\/}}) $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{list}}\,({\tt{'}}{\tt{times}}, {\rm{car}}\,({\it{x\/}}), {\rm{cadr}}\,({\it{x\/}})) \\ 
{\bf else }{\rm{list}}\,({\tt{'}}{\tt{times}}, {\rm{car}}\,({\it{x\/}}), {\rm{times-tree}}\,({\rm{cdr}}\,({\it{x\/}}))\index{times-tree})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{times-fringe} \\  
\=\+{\rm{times-fringe}}\,({\it{x\/}})\index{times-fringe} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) $\wedge$ ({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{times}}) \\ 
{\bf then }{\rm{append}}\,({\rm{times-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{times-fringe}, {\rm{times-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{times-fringe}) \\ 
{\bf else }{\rm{list}}\,({\it{x\/}})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{or-zerop-tree} \\  
\=\+{\rm{or-zerop-tree}}\,({\it{x\/}})\index{or-zerop-tree} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\tt{'}}{\tt{(}}{\tt{false}}{\tt{)}} \\ 
{\bf elseif }{\rm{cdr}}\,({\it{x\/}}) $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{list}}\,({\tt{'}}{\tt{zerop}}, {\rm{car}}\,({\it{x\/}})) \\ 
{\bf elseif }{\rm{cddr}}\,({\it{x\/}}) $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }{\rm{list}}\,({\tt{'}}{\tt{or}}, {\rm{list}}\,({\tt{'}}{\tt{zerop}}, {\rm{car}}\,({\it{x\/}})), {\rm{list}}\,({\tt{'}}{\tt{zerop}}, {\rm{cadr}}\,({\it{x\/}}))) \\ 
{\bf else }{\rm{list}}\,({\tt{'}}{\tt{or}}, {\rm{list}}\,({\tt{'}}{\tt{zerop}}, {\rm{car}}\,({\it{x\/}})), {\rm{or-zerop-tree}}\,({\rm{cdr}}\,({\it{x\/}}))\index{or-zerop-tree})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{and-not-zerop-tree} \\  
\=\+{\rm{and-not-zerop-tree}}\,({\it{x\/}})\index{and-not-zerop-tree} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\tt{'}}{\tt{(}}{\tt{true}}{\tt{)}} \\ 
{\bf elseif }{\rm{cdr}}\,({\it{x\/}}) $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{list}}\,({\tt{'}}{\tt{not}}, {\rm{list}}\,({\tt{'}}{\tt{zerop}}, {\rm{car}}\,({\it{x\/}}))) \\ 
{\bf else }{\rm{list}}\,(\=\+{\tt{'}}{\tt{and}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{not}}, {\rm{list}}\,({\tt{'}}{\tt{zerop}}, {\rm{car}}\,({\it{x\/}}))), \\ 
{\rm{and-not-zerop-tree}}\,({\rm{cdr}}\,({\it{x\/}}))\index{and-not-zerop-tree})\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  numberp-eval\$-times \\ \index{numberp-eval\$-times}
({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{times}}) $\rightarrow$ ({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $\in\;${\bf{N}}${}$)
\end{tabbing}


\noindent{\sc Event}:   Enable numberp-eval\$-times; name this event `numberp-eval\$-times-off'.\index{numberp-eval\$-times-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  eval\$-times \\ \index{eval\$-times}
\=\+({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{times}}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ ({\rm{eval\$}}\,({\bf{t}}, {\rm{cadr}}\,({\it{x\/}}), {\it{a\/}}) $*$ {\rm{eval\$}}\,({\bf{t}}, {\rm{caddr}}\,({\it{x\/}}), {\it{a\/}})))\-
\end{tabbing}


\noindent{\sc Event}:   Enable eval\$-times; name this event `eval\$-times-off'.\index{eval\$-times-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  eval\$-or \\ \index{eval\$-or}
\=\+({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{or}}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ ({\rm{eval\$}}\,({\bf{t}}, {\rm{cadr}}\,({\it{x\/}}), {\it{a\/}}) $\vee$ {\rm{eval\$}}\,({\bf{t}}, {\rm{caddr}}\,({\it{x\/}}), {\it{a\/}})))\-
\end{tabbing}


\noindent{\sc Event}:   Enable eval\$-or; name this event `eval\$-or-off'.\index{eval\$-or-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  eval\$-equal \\ \index{eval\$-equal}
\=\+({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{equal}}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ ({\rm{eval\$}}\,({\bf{t}}, {\rm{cadr}}\,({\it{x\/}}), {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{caddr}}\,({\it{x\/}}), {\it{a\/}})))\-
\end{tabbing}


\noindent{\sc Event}:   Enable eval\$-equal; name this event `eval\$-equal-off'.\index{eval\$-equal-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  eval\$-lessp \\ \index{eval\$-lessp}
\=\+({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{lessp}}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ ({\rm{eval\$}}\,({\bf{t}}, {\rm{cadr}}\,({\it{x\/}}), {\it{a\/}}) $<$ {\rm{eval\$}}\,({\bf{t}}, {\rm{caddr}}\,({\it{x\/}}), {\it{a\/}})))\-
\end{tabbing}


\noindent{\sc Event}:   Enable eval\$-lessp; name this event `eval\$-lessp-off'.\index{eval\$-lessp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  eval\$-quotient \\ \index{eval\$-quotient}
\=\+({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{quotient}}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ ({\rm{eval\$}}\,({\bf{t}}, {\rm{cadr}}\,({\it{x\/}}), {\it{a\/}}) $\div$ {\rm{eval\$}}\,({\bf{t}}, {\rm{caddr}}\,({\it{x\/}}), {\it{a\/}})))\-
\end{tabbing}


\noindent{\sc Event}:   Enable eval\$-quotient; name this event `eval\$-quotient-off'.\index{eval\$-quotient-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  eval\$-if \\ \index{eval\$-if}
\=\+({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{if}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{eval\$}}\,({\bf{t}}, {\rm{cadr}}\,({\it{x\/}}), {\it{a\/}})$\;\;${\bf then }{\rm{eval\$}}\,({\bf{t}}, {\rm{caddr}}\,({\it{x\/}}), {\it{a\/}}) \\ 
{\bf else }{\rm{eval\$}}\,({\bf{t}}, {\rm{cadddr}}\,({\it{x\/}}), {\it{a\/}})$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable eval\$-if; name this event `eval\$-if-off'.\index{eval\$-if-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-eval\$-times-tree \\ \index{numberp-eval\$-times-tree}
{\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\it{x\/}})\index{times-tree}, {\it{a\/}}) $\in\;${\bf{N}}${}$
\end{tabbing}


\noindent{\sc Event}:   Enable numberp-eval\$-times-tree; name this event `numberp-eval\$-times-tree-off'.\index{numberp-eval\$-times-tree-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-times-arg1 \\ \index{lessp-times-arg1}
({\it{a\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ ((({\it{a\/}} $*$ {\it{x\/}}) $\not<$ ({\it{a\/}} $*$ {\it{y\/}})) $=$ ({\it{x\/}} $\not<$ {\it{y\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  infer-equality-from-not-lessp \\ \index{infer-equality-from-not-lessp}
(({\it{a\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{b\/}} $\in\;${\bf{N}}${}$)) $\rightarrow$ ((({\it{a\/}} $\not<$ {\it{b\/}}) $\wedge$ ({\it{b\/}} $\not<$ {\it{a\/}})) $=$ ({\it{a\/}} $=$ {\it{b\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-times-arg1 \\ \index{equal-times-arg1}
({\it{a\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ ((({\it{a\/}} $*$ {\it{x\/}}) $=$ ({\it{a\/}} $*$ {\it{y\/}})) $=$ ({\rm{fix}}\,({\it{x\/}}) $=$ {\rm{fix}}\,({\it{y\/}})))
\end{tabbing}


\noindent{\sc Event}:   Enable equal-times-arg1; name this event `equal-times-arg1-off'.\index{equal-times-arg1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  equal-times-bridge \\ \index{equal-times-bridge}
(({\it{a\/}} $*$ {\it{b\/}}) $=$ ({\it{c\/}} $*$ {\it{a\/}} $*$ {\it{d\/}})) $=$ (({\it{a\/}} $\simeq {\tt{0}}$) $\vee$ ({\rm{fix}}\,({\it{b\/}}) $=$ ({\it{c\/}} $*$ {\it{d\/}})))
\end{tabbing}


\noindent{\sc Event}:   Enable equal-times-bridge; name this event `equal-times-bridge-off'.\index{equal-times-bridge-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  eval\$-times-member \\ \index{eval\$-times-member}
\=\+({\it{e\/}} $\in$ {\it{x\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\it{x\/}})\index{times-tree}, {\it{a\/}}) \\ 
$=$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\it{e\/}}, {\it{a\/}}) $*$ {\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\rm{delete}}\,({\it{e\/}}, {\it{x\/}})\index{delete})\index{times-tree}, {\it{a\/}})))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable eval\$-times-member; name this event `eval\$-times-member-off'.\index{eval\$-times-member-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  zerop-makes-times-tree-zero \\ \index{zerop-makes-times-tree-zero}
\=\+(($\neg$ {\rm{eval\$}}\,({\bf{t}}, {\rm{and-not-zerop-tree}}\,({\it{x\/}})\index{and-not-zerop-tree}, {\it{a\/}})) $\wedge$ {\rm{subbagp}}\,({\it{x\/}}, {\it{y\/}})\index{subbagp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\it{y\/}})\index{times-tree}, {\it{a\/}}) $=$ {\tt{0}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable zerop-makes-times-tree-zero; name this event `zerop-makes-times-tree-zero-off'.\index{zerop-makes-times-tree-zero-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  or-zerop-tree-is-not-zerop-tree \\ \index{or-zerop-tree-is-not-zerop-tree}
{\rm{eval\$}}\,({\bf{t}}, {\rm{or-zerop-tree}}\,({\it{x\/}})\index{or-zerop-tree}, {\it{a\/}}) $=$ ($\neg$ {\rm{eval\$}}\,({\bf{t}}, {\rm{and-not-zerop-tree}}\,({\it{x\/}})\index{and-not-zerop-tree}, {\it{a\/}}))
\end{tabbing}


\noindent{\sc Event}:   Enable or-zerop-tree-is-not-zerop-tree; name this event `or-zerop-tree-is-not-zerop-tree-off'.\index{or-zerop-tree-is-not-zerop-tree!-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  zerop-makes-times-tree-zero2 \\ \index{zerop-makes-times-tree-zero2}
\=\+({\rm{eval\$}}\,({\bf{t}}, {\rm{or-zerop-tree}}\,({\it{x\/}})\index{or-zerop-tree}, {\it{a\/}}) $\wedge$ {\rm{subbagp}}\,({\it{x\/}}, {\it{y\/}})\index{subbagp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\it{y\/}})\index{times-tree}, {\it{a\/}}) $=$ {\tt{0}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable zerop-makes-times-tree-zero2; name this event `zerop-makes-times-tree-zero2-off'.\index{zerop-makes-times-tree-zero2-of!f}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  times-tree-append \\ \index{times-tree-append}
\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\rm{append}}\,({\it{x\/}}, {\it{y\/}}))\index{times-tree}, {\it{a\/}}) \\ 
$=$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\it{x\/}})\index{times-tree}, {\it{a\/}}) $*$ {\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\it{y\/}})\index{times-tree}, {\it{a\/}}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable times-tree-append; name this event `times-tree-append-off'.\index{times-tree-append-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  times-tree-of-times-fringe \\ \index{times-tree-of-times-fringe}
{\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\rm{times-fringe}}\,({\it{x\/}})\index{times-fringe})\index{times-tree}, {\it{a\/}}) $=$ {\rm{fix}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}))
\end{tabbing}


\noindent{\sc Event}:   Enable times-tree-of-times-fringe; name this event `times-tree-of-times-fringe-off'.\index{times-tree-of-times-fringe-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{cancel-lessp-times} \\  
\=\+{\rm{cancel-lessp-times}}\,({\it{x\/}})\index{cancel-lessp-times} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{lessp}}) \\ 
$\wedge$$\;\;\;\;$({\rm{caadr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{times}}) \\ 
$\wedge$$\;\;\;\;$({\rm{caaddr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{times}})\- \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{bagint}}\,({\rm{times-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{times-fringe}, {\rm{times-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{times-fringe})\index{bagint}) \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{and}}, \\ 
{\rm{and-not-zerop-tree}}\,({\rm{bagint}}\,(\=\+{\rm{times-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{times-fringe}, \\ 
{\rm{times-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{times-fringe})\-\index{bagint})\index{and-not-zerop-tree}, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{lessp}}, \\ 
{\rm{times-tree}}\,({\rm{bagdiff}}\,(\=\+{\rm{times-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{times-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{times-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{times-fringe}, \\ 
{\rm{times-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{times-fringe})\-\index{bagint})\-\index{bagdiff})\index{times-tree}, \\ 
{\rm{times-tree}}\,({\rm{bagdiff}}\,(\=\+{\rm{times-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{times-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{times-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{times-fringe}, \\ 
{\rm{times-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{times-fringe})\-\index{bagint})\-\index{bagdiff})\index{times-tree})\-)\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-lessp-times-tree-bagdiff \\ \index{eval\$-lessp-times-tree-bagdiff}
\=\+({\rm{subbagp}}\,({\it{x\/}}, {\it{y\/}})\index{subbagp} $\wedge$ {\rm{subbagp}}\,({\it{x\/}}, {\it{z\/}})\index{subbagp} $\wedge$ {\rm{eval\$}}\,({\bf{t}}, {\rm{and-not-zerop-tree}}\,({\it{x\/}})\index{and-not-zerop-tree}, {\it{a\/}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\rm{bagdiff}}\,({\it{y\/}}, {\it{x\/}})\index{bagdiff})\index{times-tree}, {\it{a\/}}) \\ 
$<$$\;\;\;\;${\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\rm{bagdiff}}\,({\it{z\/}}, {\it{x\/}})\index{bagdiff})\index{times-tree}, {\it{a\/}}))\- \\ 
$=$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\it{y\/}})\index{times-tree}, {\it{a\/}}) $<$ {\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\it{z\/}})\index{times-tree}, {\it{a\/}})))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable eval\$-lessp-times-tree-bagdiff; name this event `eval\$-lessp-times-tree-bagdiff-off'.\index{eval\$-lessp-times-tree-bagdiff!-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  zerop-makes-lessp-false-bridge \\ \index{zerop-makes-lessp-false-bridge}
\=\+(\=\+({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{times}}) \\ 
$\wedge$$\;\;\;\;$({\rm{car}}\,({\it{y\/}}) $=$ {\tt{'}}{\tt{times}}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\rm{and-not-zerop-tree}}\,({\rm{bagint}}\,({\rm{times-fringe}}\,({\it{x\/}})\index{times-fringe}, {\rm{times-fringe}}\,({\it{y\/}})\index{times-fringe})\index{bagint})\index{and-not-zerop-tree}, \\ 
{\it{a\/}})\-))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+({\rm{eval\$}}\,({\bf{t}}, {\rm{cadr}}\,({\it{x\/}}), {\it{a\/}}) $*$ {\rm{eval\$}}\,({\bf{t}}, {\rm{caddr}}\,({\it{x\/}}), {\it{a\/}})) \\ 
$<$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\rm{cadr}}\,({\it{y\/}}), {\it{a\/}}) $*$ {\rm{eval\$}}\,({\bf{t}}, {\rm{caddr}}\,({\it{y\/}}), {\it{a\/}})))\- \\ 
$=$$\;\;\;\;${\bf{f}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable zerop-makes-lessp-false-bridge; name this event `zerop-makes-lessp-false-bridge-off'.\index{zerop-makes-lessp-false-bridge-!off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-lessp-times \\ \index{correctness-of-cancel-lessp-time!s}
{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{cancel-lessp-times}}\,({\it{x\/}})\index{cancel-lessp-times}, {\it{a\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cancel-equal-times} \\  
\=\+{\rm{cancel-equal-times}}\,({\it{x\/}})\index{cancel-equal-times} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{equal}}) \\ 
$\wedge$$\;\;\;\;$({\rm{caadr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{times}}) \\ 
$\wedge$$\;\;\;\;$({\rm{caaddr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{times}})\- \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{bagint}}\,({\rm{times-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{times-fringe}, {\rm{times-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{times-fringe})\index{bagint}) \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{or}}, \\ 
{\rm{or-zerop-tree}}\,({\rm{bagint}}\,(\=\+{\rm{times-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{times-fringe}, \\ 
{\rm{times-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{times-fringe})\-\index{bagint})\index{or-zerop-tree}, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{times-tree}}\,({\rm{bagdiff}}\,(\=\+{\rm{times-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{times-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{times-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{times-fringe}, \\ 
{\rm{times-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{times-fringe})\-\index{bagint})\-\index{bagdiff})\index{times-tree}, \\ 
{\rm{times-tree}}\,({\rm{bagdiff}}\,(\=\+{\rm{times-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{times-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{times-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{times-fringe}, \\ 
{\rm{times-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{times-fringe})\-\index{bagint})\-\index{bagdiff})\index{times-tree})\-)\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  zerop-makes-equal-true-bridge \\ \index{zerop-makes-equal-true-bridge}
\=\+(\=\+({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{times}}) \\ 
$\wedge$$\;\;\;\;$({\rm{car}}\,({\it{y\/}}) $=$ {\tt{'}}{\tt{times}}) \\ 
$\wedge$$\;\;\;\;${\rm{eval\$}}\,({\bf{t}}, {\rm{or-zerop-tree}}\,({\rm{bagint}}\,({\rm{times-fringe}}\,({\it{x\/}})\index{times-fringe}, {\rm{times-fringe}}\,({\it{y\/}})\index{times-fringe})\index{bagint})\index{or-zerop-tree}, {\it{a\/}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+({\rm{eval\$}}\,({\bf{t}}, {\rm{cadr}}\,({\it{x\/}}), {\it{a\/}}) $*$ {\rm{eval\$}}\,({\bf{t}}, {\rm{caddr}}\,({\it{x\/}}), {\it{a\/}})) \\ 
$=$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\rm{cadr}}\,({\it{y\/}}), {\it{a\/}}) $*$ {\rm{eval\$}}\,({\bf{t}}, {\rm{caddr}}\,({\it{y\/}}), {\it{a\/}})))\- \\ 
$=$$\;\;\;\;${\bf{t}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable zerop-makes-equal-true-bridge; name this event `zerop-makes-equal-true-bridge-off'.\index{zerop-makes-equal-true-bridge-o!ff}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  eval\$-equal-times-tree-bagdiff \\ \index{eval\$-equal-times-tree-bagdiff}
\=\+({\rm{subbagp}}\,({\it{x\/}}, {\it{y\/}})\index{subbagp} $\wedge$ {\rm{subbagp}}\,({\it{x\/}}, {\it{z\/}})\index{subbagp} $\wedge$ ($\neg$ {\rm{eval\$}}\,({\bf{t}}, {\rm{or-zerop-tree}}\,({\it{x\/}})\index{or-zerop-tree}, {\it{a\/}}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\rm{bagdiff}}\,({\it{y\/}}, {\it{x\/}})\index{bagdiff})\index{times-tree}, {\it{a\/}}) \\ 
$=$$\;\;\;\;${\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\rm{bagdiff}}\,({\it{z\/}}, {\it{x\/}})\index{bagdiff})\index{times-tree}, {\it{a\/}}))\- \\ 
$=$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\it{y\/}})\index{times-tree}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\it{z\/}})\index{times-tree}, {\it{a\/}})))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable eval\$-equal-times-tree-bagdiff; name this event `eval\$-equal-times-tree-bagdiff-off'.\index{eval\$-equal-times-tree-bagdiff!-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cancel-equal-times-preserves-inequality \\ \index{cancel-equal-times-preserves-ineq!uality}
\=\+(\=\+{\rm{subbagp}}\,({\it{z\/}}, {\it{x\/}})\index{subbagp} \\ 
$\wedge$$\;\;\;\;${\rm{subbagp}}\,({\it{z\/}}, {\it{y\/}})\index{subbagp} \\ 
$\wedge$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\it{x\/}})\index{times-tree}, {\it{a\/}}) $\not=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\it{y\/}})\index{times-tree}, {\it{a\/}})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\rm{bagdiff}}\,({\it{x\/}}, {\it{z\/}})\index{bagdiff})\index{times-tree}, {\it{a\/}}) \\ 
$\not=$$\;\;\;\;${\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\rm{bagdiff}}\,({\it{y\/}}, {\it{z\/}})\index{bagdiff})\index{times-tree}, {\it{a\/}}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cancel-equal-times-preserves-inequality; name this event `cancel-equal-times-preserves-inequality-off'.\index{cancel-equal-times-preserves-ineq!uality-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cancel-equal-times-preserves-inequality-bridge \\ \index{cancel-equal-times-preserves-ineq!uality-bridge}
\=\+(\=\+({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{times}}) \\ 
$\wedge$$\;\;\;\;$({\rm{car}}\,({\it{y\/}}) $=$ {\tt{'}}{\tt{times}}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{eval\$}}\,({\bf{t}}, {\rm{cadr}}\,({\it{x\/}}), {\it{a\/}}) $*$ {\rm{eval\$}}\,({\bf{t}}, {\rm{caddr}}\,({\it{x\/}}), {\it{a\/}})) \\ 
$\not=$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\rm{cadr}}\,({\it{y\/}}), {\it{a\/}}) $*$ {\rm{eval\$}}\,({\bf{t}}, {\rm{caddr}}\,({\it{y\/}}), {\it{a\/}})))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\rm{times-tree}}\,({\rm{bagdiff}}\,(\=\+{\rm{times-fringe}}\,({\it{x\/}})\index{times-fringe}, \\ 
{\rm{bagint}}\,({\rm{times-fringe}}\,({\it{x\/}})\index{times-fringe}, {\rm{times-fringe}}\,({\it{y\/}})\index{times-fringe})\index{bagint})\-\index{bagdiff})\index{times-tree}, \\ 
{\it{a\/}})\- \\ 
$\not=$$\;\;\;\;${\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\rm{times-tree}}\,({\rm{bagdiff}}\,(\=\+{\rm{times-fringe}}\,({\it{y\/}})\index{times-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{times-fringe}}\,({\it{x\/}})\index{times-fringe}, \\ 
{\rm{times-fringe}}\,({\it{y\/}})\index{times-fringe})\-\index{bagint})\-\index{bagdiff})\index{times-tree}, \\ 
{\it{a\/}})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cancel-equal-times-preserves-inequality-bridge; name this event `cancel-equal-times-preserves-inequality-bridge-off'.\index{cancel-equal-times-preserves-ineq!uality-bridge-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-equal-times \\ \index{correctness-of-cancel-equal-time!s}
{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{cancel-equal-times}}\,({\it{x\/}})\index{cancel-equal-times}, {\it{a\/}})
\end{tabbing}


\noindent{\sc Event}:   Let us define the theory {\it{multiplication}} to consist of the following events: equal-times-0,
equal-times-1,
equal-sub1-0,
times-zero,
times-add1,
commutativity-of-times,
times-distributes-over-plus,
commutativity2-of-times,
associativity-of-times,
times-distributes-over-difference,
times-quotient,
times-1-arg1,
lessp-times1,
lessp-times2,
lessp-times3,
lessp-plus-times1,
lessp-plus-times2,
lessp-1-times,
correctness-of-cancel-lessp-times,
correctness-of-cancel-equal-times.\index{multiplication}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-remainder \\ \index{lessp-remainder}
(({\it{x\/}} ${}${\bf{mod}}${}$ {\it{y\/}}) $<$ {\it{y\/}}) $=$ ({\it{y\/}} $\not\simeq {\tt{0}}$)
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-noop \\ \index{remainder-noop}
({\it{a\/}} $<$ {\it{b\/}}) $\rightarrow$ (({\it{a\/}} ${}${\bf{mod}}${}$ {\it{b\/}}) $=$ {\rm{fix}}\,({\it{a\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-of-non-number \\ \index{remainder-of-non-number}
({\it{a\/}} $\not\in\;${\bf{N}}${}$) $\rightarrow$ (({\it{a\/}} ${}${\bf{mod}}${}$ {\it{n\/}}) $=$ ({\tt{0}} ${}${\bf{mod}}${}$ {\it{n\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-zero \\ \index{remainder-zero}
({\it{x\/}} $\simeq {\tt{0}}$) $\rightarrow$ (({\it{y\/}} ${}${\bf{mod}}${}$ {\it{x\/}}) $=$ {\rm{fix}}\,({\it{y\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plus-remainder-times-quotient \\ \index{plus-remainder-times-quotient}
(({\it{x\/}} ${}${\bf{mod}}${}$ {\it{y\/}}) $+$ ({\it{y\/}} $*$ ({\it{x\/}} $\div$ {\it{y\/}}))) $=$ {\rm{fix}}\,({\it{x\/}})
\end{tabbing}


\noindent{\sc Event}:   Enable plus-remainder-times-quotient; name this event `plus-remainder-times-quotient-off'.\index{plus-remainder-times-quotient-o!ff}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  remainder-quotient-elim \\ \index{remainder-quotient-elim}
(({\it{y\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\it{x\/}} $\in\;${\bf{N}}${}$)) $\rightarrow$ ((({\it{x\/}} ${}${\bf{mod}}${}$ {\it{y\/}}) $+$ ({\it{y\/}} $*$ ({\it{x\/}} $\div$ {\it{y\/}}))) $=$ {\it{x\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-add1 \\ \index{remainder-add1}
(({\it{a\/}} ${}${\bf{mod}}${}$ {\it{b\/}}) $=$ {\tt{0}}) $\rightarrow$ ((($1\;+$ {\it{a\/}}) ${}${\bf{mod}}${}$ {\it{b\/}}) $=$ ({\tt{1}} ${}${\bf{mod}}${}$ {\it{b\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-plus-proof \\ \index{remainder-plus-proof}
(({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}) $\rightarrow$ ((({\it{a\/}} $+$ {\it{b\/}}) ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ ({\it{a\/}} ${}${\bf{mod}}${}$ {\it{c\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-plus \\ \index{remainder-plus}
\=\+(({\it{a\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+((({\it{a\/}} $+$ {\it{b\/}}) ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ ({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}})) \\ 
$\wedge$$\;\;\;\;$((({\it{b\/}} $+$ {\it{a\/}}) ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ ({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}})) \\ 
$\wedge$$\;\;\;\;$((({\it{x\/}} $+$ {\it{y\/}} $+$ {\it{a\/}}) ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ (({\it{x\/}} $+$ {\it{y\/}}) ${}${\bf{mod}}${}$ {\it{c\/}})))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-remainder-plus-0-proof \\ \index{equal-remainder-plus-0-proof}
(({\it{a\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}) $\rightarrow$ (((({\it{a\/}} $+$ {\it{b\/}}) ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}) $=$ (({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-remainder-plus-0 \\ \index{equal-remainder-plus-0}
\=\+(({\it{a\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(((({\it{a\/}} $+$ {\it{b\/}}) ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}) $=$ (({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}})) \\ 
$\wedge$$\;\;\;\;$(((({\it{b\/}} $+$ {\it{a\/}}) ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}) $=$ (({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}})) \\ 
$\wedge$$\;\;\;\;$(\=\+((({\it{x\/}} $+$ {\it{y\/}} $+$ {\it{a\/}}) ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}) \\ 
$=$$\;\;\;\;$((({\it{x\/}} $+$ {\it{y\/}}) ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-remainder-plus-remainder-proof \\ \index{equal-remainder-plus-remainder-p!roof}
({\it{a\/}} $<$ {\it{c\/}}) $\rightarrow$ (((({\it{a\/}} $+$ {\it{b\/}}) ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ ({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}})) $=$ ({\it{a\/}} $\simeq {\tt{0}}$))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-remainder-plus-remainder \\ \index{equal-remainder-plus-remainder}
\=\+({\it{a\/}} $<$ {\it{c\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(((({\it{a\/}} $+$ {\it{b\/}}) ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ ({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}})) $=$ ({\it{a\/}} $\simeq {\tt{0}}$)) \\ 
$\wedge$$\;\;\;\;$(((({\it{b\/}} $+$ {\it{a\/}}) ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ ({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}})) $=$ ({\it{a\/}} $\simeq {\tt{0}}$)))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable equal-remainder-plus-remainder; name this event `equal-remainder-plus-remainder-off'.\index{equal-remainder-plus-remainder-!off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  remainder-times1-proof \\ \index{remainder-times1-proof}
(({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}) $\rightarrow$ ((({\it{a\/}} $*$ {\it{b\/}}) ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-times1 \\ \index{remainder-times1}
\=\+(({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}) \\ 
$\rightarrow$$\;\;\;\;$(((({\it{a\/}} $*$ {\it{b\/}}) ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}) $\wedge$ ((({\it{b\/}} $*$ {\it{a\/}}) ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-times1-instance-proof \\ \index{remainder-times1-instance-proof}
(({\it{x\/}} $*$ {\it{y\/}}) ${}${\bf{mod}}${}$ {\it{y\/}}) $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-times1-instance \\ \index{remainder-times1-instance}
((({\it{x\/}} $*$ {\it{y\/}}) ${}${\bf{mod}}${}$ {\it{y\/}}) $=$ {\tt{0}}) $\wedge$ ((({\it{x\/}} $*$ {\it{y\/}}) ${}${\bf{mod}}${}$ {\it{x\/}}) $=$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-times-times-proof \\ \index{remainder-times-times-proof}
(({\it{x\/}} $*$ {\it{y\/}}) ${}${\bf{mod}}${}$ ({\it{x\/}} $*$ {\it{z\/}})) $=$ ({\it{x\/}} $*$ ({\it{y\/}} ${}${\bf{mod}}${}$ {\it{z\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-times-times \\ \index{remainder-times-times}
\=\+((({\it{x\/}} $*$ {\it{y\/}}) ${}${\bf{mod}}${}$ ({\it{x\/}} $*$ {\it{z\/}})) $=$ ({\it{x\/}} $*$ ({\it{y\/}} ${}${\bf{mod}}${}$ {\it{z\/}}))) \\ 
$\wedge$$\;\;\;\;$((({\it{x\/}} $*$ {\it{z\/}}) ${}${\bf{mod}}${}$ ({\it{y\/}} $*$ {\it{z\/}})) $=$ (({\it{x\/}} ${}${\bf{mod}}${}$ {\it{y\/}}) $*$ {\it{z\/}}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable remainder-times-times; name this event `remainder-times-times-off'.\index{remainder-times-times-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  remainder-times2-proof \\ \index{remainder-times2-proof}
(({\it{a\/}} ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{0}}) $\rightarrow$ (({\it{a\/}} ${}${\bf{mod}}${}$ ({\it{z\/}} $*$ {\it{y\/}})) $=$ ({\it{z\/}} $*$ (({\it{a\/}} $\div$ {\it{z\/}}) ${}${\bf{mod}}${}$ {\it{y\/}})))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-times2 \\ \index{remainder-times2}
\=\+(({\it{a\/}} ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{0}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(({\it{a\/}} ${}${\bf{mod}}${}$ ({\it{y\/}} $*$ {\it{z\/}})) $=$ ({\it{z\/}} $*$ (({\it{a\/}} $\div$ {\it{z\/}}) ${}${\bf{mod}}${}$ {\it{y\/}}))) \\ 
$\wedge$$\;\;\;\;$(({\it{a\/}} ${}${\bf{mod}}${}$ ({\it{z\/}} $*$ {\it{y\/}})) $=$ ({\it{z\/}} $*$ (({\it{a\/}} $\div$ {\it{z\/}}) ${}${\bf{mod}}${}$ {\it{y\/}}))))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-times2-instance \\ \index{remainder-times2-instance}
\=\+((({\it{x\/}} $*$ {\it{y\/}}) ${}${\bf{mod}}${}$ ({\it{x\/}} $*$ {\it{z\/}})) $=$ ({\it{x\/}} $*$ ({\it{y\/}} ${}${\bf{mod}}${}$ {\it{z\/}}))) \\ 
$\wedge$$\;\;\;\;$((({\it{x\/}} $*$ {\it{z\/}}) ${}${\bf{mod}}${}$ ({\it{y\/}} $*$ {\it{z\/}})) $=$ (({\it{x\/}} ${}${\bf{mod}}${}$ {\it{y\/}}) $*$ {\it{z\/}}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-difference1 \\ \index{remainder-difference1}
\=\+(({\it{a\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ ({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}})) \\ 
$\rightarrow$$\;\;\;\;$((({\it{a\/}} $-$ {\it{b\/}}) ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ (({\it{a\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $-$ ({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}})))\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{double-remainder-induction} \\  
\=\+{\rm{double-remainder-induction}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{double-remainder-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{c\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf elseif }{\it{a\/}} $<$ {\it{c\/}}$\;\;${\bf then }{\tt{0}} \\ 
{\bf elseif }{\it{b\/}} $<$ {\it{c\/}}$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }{\rm{double-remainder-induction}}\,({\it{a\/}} $-$ {\it{c\/}}, {\it{b\/}} $-$ {\it{c\/}}, {\it{c\/}})\index{double-remainder-induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-difference2 \\ \index{remainder-difference2}
\=\+((({\it{a\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}) $\wedge$ (({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(({\it{a\/}} $-$ {\it{b\/}}) ${}${\bf{mod}}${}$ {\it{c\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{b\/}} $<$ {\it{a\/}}$\;\;${\bf then }{\it{c\/}} $-$ ({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-difference3 \\ \index{remainder-difference3}
\=\+((({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}) $\wedge$ (({\it{a\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(({\it{a\/}} $-$ {\it{b\/}}) ${}${\bf{mod}}${}$ {\it{c\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{b\/}} $<$ {\it{a\/}}$\;\;${\bf then }{\it{a\/}} ${}${\bf{mod}}${}$ {\it{c\/}} \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable remainder-difference3; name this event `remainder-difference3-off'.\index{remainder-difference3-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  equal-remainder-difference-0 \\ \index{equal-remainder-difference-0}
\=\+((({\it{a\/}} $-$ {\it{b\/}}) ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\bf if }{\it{a\/}} $<$ {\it{b\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-$\;\;${\bf then }({\it{a\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ ({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable equal-remainder-difference-0; name this event `equal-remainder-difference-0-off'.\index{equal-remainder-difference-0-of!f}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-plus-fact \\ \index{lessp-plus-fact}
\=\+((({\it{b\/}} ${}${\bf{mod}}${}$ {\it{x\/}}) $=$ {\tt{0}}) $\wedge$ (({\it{c\/}} ${}${\bf{mod}}${}$ {\it{x\/}}) $=$ {\tt{0}}) $\wedge$ ({\it{b\/}} $<$ {\it{c\/}}) $\wedge$ ({\it{a\/}} $<$ {\it{x\/}})) \\ 
$\rightarrow$$\;\;\;\;$((({\it{a\/}} $+$ {\it{b\/}}) $<$ {\it{c\/}}) $=$ {\bf{t}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable lessp-plus-fact; name this event `lessp-plus-fact-off'.\index{lessp-plus-fact-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  remainder-plus-fact \\ \index{remainder-plus-fact}
\=\+((({\it{b\/}} ${}${\bf{mod}}${}$ {\it{x\/}}) $=$ {\tt{0}}) $\wedge$ (({\it{c\/}} ${}${\bf{mod}}${}$ {\it{x\/}}) $=$ {\tt{0}}) $\wedge$ ({\it{a\/}} $<$ {\it{x\/}})) \\ 
$\rightarrow$$\;\;\;\;$((({\it{a\/}} $+$ {\it{b\/}}) ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ ({\it{a\/}} $+$ ({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}})))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-plus-times-times-proof \\ \index{remainder-plus-times-times-proo!f}
\=\+({\it{a\/}} $<$ {\it{b\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(({\it{a\/}} $+$ ({\it{b\/}} $*$ {\it{c\/}})) ${}${\bf{mod}}${}$ ({\it{b\/}} $*$ {\it{d\/}})) \\ 
$=$$\;\;\;\;$({\it{a\/}} $+$ (({\it{b\/}} $*$ {\it{c\/}}) ${}${\bf{mod}}${}$ ({\it{b\/}} $*$ {\it{d\/}}))))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-plus-times-times \\ \index{remainder-plus-times-times}
\=\+({\it{a\/}} $<$ {\it{b\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+(({\it{a\/}} $+$ ({\it{b\/}} $*$ {\it{c\/}})) ${}${\bf{mod}}${}$ ({\it{b\/}} $*$ {\it{d\/}})) \\ 
$=$$\;\;\;\;$({\it{a\/}} $+$ (({\it{b\/}} $*$ {\it{c\/}}) ${}${\bf{mod}}${}$ ({\it{b\/}} $*$ {\it{d\/}}))))\- \\ 
$\wedge$$\;\;\;\;$(\=\+(({\it{a\/}} $+$ ({\it{c\/}} $*$ {\it{b\/}})) ${}${\bf{mod}}${}$ ({\it{d\/}} $*$ {\it{b\/}})) \\ 
$=$$\;\;\;\;$({\it{a\/}} $+$ (({\it{c\/}} $*$ {\it{b\/}}) ${}${\bf{mod}}${}$ ({\it{d\/}} $*$ {\it{b\/}}))))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-plus-times-times-instance \\ \index{remainder-plus-times-times-inst!ance}
\=\+({\it{a\/}} $<$ {\it{b\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+(({\it{a\/}} $+$ ({\it{b\/}} $*$ {\it{c\/}}) $+$ ({\it{b\/}} $*$ {\it{d\/}})) ${}${\bf{mod}}${}$ ({\it{b\/}} $*$ {\it{e\/}})) \\ 
$=$$\;\;\;\;$({\it{a\/}} $+$ ({\it{b\/}} $*$ (({\it{c\/}} $+$ {\it{d\/}}) ${}${\bf{mod}}${}$ {\it{e\/}}))))\- \\ 
$\wedge$$\;\;\;\;$(\=\+(({\it{a\/}} $+$ ({\it{c\/}} $*$ {\it{b\/}}) $+$ ({\it{d\/}} $*$ {\it{b\/}})) ${}${\bf{mod}}${}$ ({\it{e\/}} $*$ {\it{b\/}})) \\ 
$=$$\;\;\;\;$({\it{a\/}} $+$ ({\it{b\/}} $*$ (({\it{c\/}} $+$ {\it{d\/}}) ${}${\bf{mod}}${}$ {\it{e\/}}))))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-remainder \\ \index{remainder-remainder}
(({\it{b\/}} ${}${\bf{mod}}${}$ {\it{a\/}}) $=$ {\tt{0}}) $\rightarrow$ ((({\it{n\/}} ${}${\bf{mod}}${}$ {\it{b\/}}) ${}${\bf{mod}}${}$ {\it{a\/}}) $=$ ({\it{n\/}} ${}${\bf{mod}}${}$ {\it{a\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-1-arg1 \\ \index{remainder-1-arg1}
\=\+({\tt{1}} ${}${\bf{mod}}${}$ {\it{x\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $=$ {\tt{1}}$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }{\tt{1}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-1-arg2 \\ \index{remainder-1-arg2}
({\it{y\/}} ${}${\bf{mod}}${}$ {\tt{1}}) $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-x-x \\ \index{remainder-x-x}
({\it{x\/}} ${}${\bf{mod}}${}$ {\it{x\/}}) $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  transitivity-of-divides \\ \index{transitivity-of-divides}
((({\it{a\/}} ${}${\bf{mod}}${}$ {\it{b\/}}) $=$ {\tt{0}}) $\wedge$ (({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}})) $\rightarrow$ (({\it{a\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}})
\end{tabbing}


\noindent{\sc Event}:   Let us define the theory {\it{remainders}} to consist of the following events: lessp-remainder,
remainder-noop,
remainder-of-non-number,
remainder-zero,
remainder-quotient-elim,
remainder-add1,
remainder-plus,
equal-remainder-plus-0,
remainder-times1,
remainder-times1-instance,
remainder-times2,
remainder-times2-instance,
remainder-difference1,
remainder-difference2,
remainder-plus-times-times,
remainder-plus-times-times-instance,
remainder-remainder,
remainder-1-arg1,
remainder-1-arg2,
remainder-x-x.\index{remainders}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  quotient-noop \\ \index{quotient-noop}
({\it{b\/}} $=$ {\tt{1}}) $\rightarrow$ (({\it{a\/}} $\div$ {\it{b\/}}) $=$ {\rm{fix}}\,({\it{a\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-of-non-number \\ \index{quotient-of-non-number}
({\it{a\/}} $\not\in\;${\bf{N}}${}$) $\rightarrow$ (({\it{a\/}} $\div$ {\it{n\/}}) $=$ ({\tt{0}} $\div$ {\it{n\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-zero \\ \index{quotient-zero}
({\it{x\/}} $\simeq {\tt{0}}$) $\rightarrow$ (({\it{y\/}} $\div$ {\it{x\/}}) $=$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-add1 \\ \index{quotient-add1}
\=\+(({\it{a\/}} ${}${\bf{mod}}${}$ {\it{b\/}}) $=$ {\tt{0}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(($1\;+$ {\it{a\/}}) $\div$ {\it{b\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{b\/}} $=$ {\tt{1}}$\;\;${\bf then }$1\;+$ ({\it{a\/}} $\div$ {\it{b\/}}) \\ 
{\bf else }{\it{a\/}} $\div$ {\it{b\/}}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-quotient-0 \\ \index{equal-quotient-0}
(({\it{a\/}} $\div$ {\it{b\/}}) $=$ {\tt{0}}) $=$ (({\it{b\/}} $\simeq {\tt{0}}$) $\vee$ ({\it{a\/}} $<$ {\it{b\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-sub1 \\ \index{quotient-sub1}
\=\+(({\it{a\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\it{b\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(({\it{a\/}} $-\;1$) $\div$ {\it{b\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{a\/}} ${}${\bf{mod}}${}$ {\it{b\/}}) $=$ {\tt{0}}$\;\;${\bf then }({\it{a\/}} $\div$ {\it{b\/}}) $-\;1$ \\ 
{\bf else }{\it{a\/}} $\div$ {\it{b\/}}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-plus-proof \\ \index{quotient-plus-proof}
(({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}) $\rightarrow$ ((({\it{a\/}} $+$ {\it{b\/}}) $\div$ {\it{c\/}}) $=$ (({\it{a\/}} $\div$ {\it{c\/}}) $+$ ({\it{b\/}} $\div$ {\it{c\/}})))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-plus \\ \index{quotient-plus}
\=\+(({\it{a\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+((({\it{a\/}} $+$ {\it{b\/}}) $\div$ {\it{c\/}}) $=$ (({\it{a\/}} $\div$ {\it{c\/}}) $+$ ({\it{b\/}} $\div$ {\it{c\/}}))) \\ 
$\wedge$$\;\;\;\;$((({\it{b\/}} $+$ {\it{a\/}}) $\div$ {\it{c\/}}) $=$ (({\it{a\/}} $\div$ {\it{c\/}}) $+$ ({\it{b\/}} $\div$ {\it{c\/}}))) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\it{x\/}} $+$ {\it{y\/}} $+$ {\it{a\/}}) $\div$ {\it{c\/}}) \\ 
$=$$\;\;\;\;$((({\it{x\/}} $+$ {\it{y\/}}) $\div$ {\it{c\/}}) $+$ ({\it{a\/}} $\div$ {\it{c\/}})))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-times-instance-temp-proof \\ \index{quotient-times-instance-temp-pr!oof}
\=\+(({\it{y\/}} $*$ {\it{x\/}}) $\div$ {\it{y\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{y\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }{\rm{fix}}\,({\it{x\/}})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-times-instance-temp \\ \index{quotient-times-instance-temp}
\=\+(\=\+(({\it{y\/}} $*$ {\it{x\/}}) $\div$ {\it{y\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{y\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }{\rm{fix}}\,({\it{x\/}})$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+(({\it{x\/}} $*$ {\it{y\/}}) $\div$ {\it{y\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{y\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }{\rm{fix}}\,({\it{x\/}})$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable quotient-times-instance-temp; name this event `quotient-times-instance-temp-off'.\index{quotient-times-instance-temp-of!f}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  quotient-times-proof \\ \index{quotient-times-proof}
(({\it{a\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}) $\rightarrow$ ((({\it{a\/}} $*$ {\it{b\/}}) $\div$ {\it{c\/}}) $=$ ({\it{b\/}} $*$ ({\it{a\/}} $\div$ {\it{c\/}})))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-times \\ \index{quotient-times}
\=\+(({\it{a\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+((({\it{a\/}} $*$ {\it{b\/}}) $\div$ {\it{c\/}}) $=$ ({\it{b\/}} $*$ ({\it{a\/}} $\div$ {\it{c\/}}))) \\ 
$\wedge$$\;\;\;\;$((({\it{b\/}} $*$ {\it{a\/}}) $\div$ {\it{c\/}}) $=$ ({\it{b\/}} $*$ ({\it{a\/}} $\div$ {\it{c\/}}))))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-times-instance \\ \index{quotient-times-instance}
\=\+(\=\+(({\it{y\/}} $*$ {\it{x\/}}) $\div$ {\it{y\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{y\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }{\rm{fix}}\,({\it{x\/}})$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+(({\it{x\/}} $*$ {\it{y\/}}) $\div$ {\it{y\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{y\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }{\rm{fix}}\,({\it{x\/}})$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-times-times-proof \\ \index{quotient-times-times-proof}
\=\+(({\it{x\/}} $*$ {\it{y\/}}) $\div$ ({\it{x\/}} $*$ {\it{z\/}})) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }{\it{y\/}} $\div$ {\it{z\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-times-times \\ \index{quotient-times-times}
\=\+(\=\+(({\it{x\/}} $*$ {\it{y\/}}) $\div$ ({\it{x\/}} $*$ {\it{z\/}})) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }{\it{y\/}} $\div$ {\it{z\/}}$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+(({\it{x\/}} $*$ {\it{z\/}}) $\div$ ({\it{y\/}} $*$ {\it{z\/}})) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{z\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }{\it{x\/}} $\div$ {\it{y\/}}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable quotient-times-times; name this event `quotient-times-times-off'.\index{quotient-times-times-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  quotient-difference1 \\ \index{quotient-difference1}
\=\+(({\it{a\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ ({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}})) \\ 
$\rightarrow$$\;\;\;\;$((({\it{a\/}} $-$ {\it{b\/}}) $\div$ {\it{c\/}}) $=$ (({\it{a\/}} $\div$ {\it{c\/}}) $-$ ({\it{b\/}} $\div$ {\it{c\/}})))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-lessp-arg1 \\ \index{quotient-lessp-arg1}
({\it{a\/}} $<$ {\it{b\/}}) $\rightarrow$ (({\it{a\/}} $\div$ {\it{b\/}}) $=$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-difference2 \\ \index{quotient-difference2}
\=\+((({\it{a\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}) $\wedge$ (({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(({\it{a\/}} $-$ {\it{b\/}}) $\div$ {\it{c\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{b\/}} $<$ {\it{a\/}}$\;\;${\bf then }({\it{a\/}} $\div$ {\it{c\/}}) $-$ ($1\;+$ ({\it{b\/}} $\div$ {\it{c\/}})) \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-difference3 \\ \index{quotient-difference3}
\=\+((({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}) $\wedge$ (({\it{a\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(({\it{a\/}} $-$ {\it{b\/}}) $\div$ {\it{c\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{b\/}} $<$ {\it{a\/}}$\;\;${\bf then }({\it{a\/}} $\div$ {\it{c\/}}) $-$ ({\it{b\/}} $\div$ {\it{c\/}}) \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-equals-its-first-argument \\ \index{remainder-equals-its-first-argu!ment}
({\it{a\/}} $=$ ({\it{a\/}} ${}${\bf{mod}}${}$ {\it{b\/}})) $=$ (({\it{a\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{b\/}} $\simeq {\tt{0}}$) $\vee$ ({\it{a\/}} $<$ {\it{b\/}})))
\end{tabbing}


\noindent{\sc Event}:   Enable remainder-equals-its-first-argument; name this event `remainder-equals-its-first-argument-off'.\index{remainder-equals-its-first-argu!ment-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  quotient-remainder-times \\ \index{quotient-remainder-times}
(({\it{x\/}} ${}${\bf{mod}}${}$ ({\it{a\/}} $*$ {\it{b\/}})) $\div$ {\it{a\/}}) $=$ (({\it{x\/}} $\div$ {\it{a\/}}) ${}${\bf{mod}}${}$ {\it{b\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-remainder \\ \index{quotient-remainder}
(({\it{c\/}} ${}${\bf{mod}}${}$ {\it{a\/}}) $=$ {\tt{0}}) $\rightarrow$ ((({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $\div$ {\it{a\/}}) $=$ (({\it{b\/}} $\div$ {\it{a\/}}) ${}${\bf{mod}}${}$ ({\it{c\/}} $\div$ {\it{a\/}})))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-remainder-instance \\ \index{quotient-remainder-instance}
(({\it{x\/}} ${}${\bf{mod}}${}$ ({\it{a\/}} $*$ {\it{b\/}})) $\div$ {\it{a\/}}) $=$ (({\it{x\/}} $\div$ {\it{a\/}}) ${}${\bf{mod}}${}$ {\it{b\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-plus-fact \\ \index{quotient-plus-fact}
\=\+((({\it{b\/}} ${}${\bf{mod}}${}$ {\it{x\/}}) $=$ {\tt{0}}) $\wedge$ (({\it{c\/}} ${}${\bf{mod}}${}$ {\it{x\/}}) $=$ {\tt{0}}) $\wedge$ ({\it{a\/}} $<$ {\it{x\/}})) \\ 
$\rightarrow$$\;\;\;\;$((({\it{a\/}} $+$ {\it{b\/}}) $\div$ {\it{c\/}}) $=$ ({\it{b\/}} $\div$ {\it{c\/}}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-plus-times-times-proof \\ \index{quotient-plus-times-times-proof}
\=\+({\it{a\/}} $<$ {\it{b\/}}) \\ 
$\rightarrow$$\;\;\;\;$((({\it{a\/}} $+$ ({\it{b\/}} $*$ {\it{c\/}})) $\div$ ({\it{b\/}} $*$ {\it{d\/}})) $=$ (({\it{b\/}} $*$ {\it{c\/}}) $\div$ ({\it{b\/}} $*$ {\it{d\/}})))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-plus-times-times \\ \index{quotient-plus-times-times}
\=\+({\it{a\/}} $<$ {\it{b\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+((({\it{a\/}} $+$ ({\it{b\/}} $*$ {\it{c\/}})) $\div$ ({\it{b\/}} $*$ {\it{d\/}})) $=$ (({\it{b\/}} $*$ {\it{c\/}}) $\div$ ({\it{b\/}} $*$ {\it{d\/}}))) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\it{a\/}} $+$ ({\it{b\/}} $*$ {\it{c\/}})) $\div$ ({\it{b\/}} $*$ {\it{d\/}})) \\ 
$=$$\;\;\;\;$(({\it{b\/}} $*$ {\it{c\/}}) $\div$ ({\it{b\/}} $*$ {\it{d\/}})))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-plus-times-times-instance \\ \index{quotient-plus-times-times-insta!nce}
\=\+({\it{a\/}} $<$ {\it{b\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+(({\it{a\/}} $+$ ({\it{b\/}} $*$ {\it{c\/}}) $+$ ({\it{b\/}} $*$ {\it{d\/}})) $\div$ ({\it{b\/}} $*$ {\it{e\/}})) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{b\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }({\it{c\/}} $+$ {\it{d\/}}) $\div$ {\it{e\/}}$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+(({\it{a\/}} $+$ ({\it{c\/}} $*$ {\it{b\/}}) $+$ ({\it{d\/}} $*$ {\it{b\/}})) $\div$ ({\it{e\/}} $*$ {\it{b\/}})) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{b\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }({\it{d\/}} $+$ {\it{c\/}}) $\div$ {\it{e\/}}$\;${\bf  endif}\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-quotient \\ \index{quotient-quotient}
(({\it{b\/}} $\div$ {\it{a\/}}) $\div$ {\it{c\/}}) $=$ ({\it{b\/}} $\div$ ({\it{a\/}} $*$ {\it{c\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  leq-quotient \\ \index{leq-quotient}
\=\+({\it{a\/}} $<$ {\it{b\/}}) \\ 
$\rightarrow$$\;\;\;\;$\=\+{\bf if }({\it{b\/}} $\div$ {\it{c\/}}) $<$ ({\it{a\/}} $\div$ {\it{c\/}})$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-1-arg2 \\ \index{quotient-1-arg2}
({\it{n\/}} $\div$ {\tt{1}}) $=$ {\rm{fix}}\,({\it{n\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-1-arg1-casesplit \\ \index{quotient-1-arg1-casesplit}
({\it{n\/}} $\simeq {\tt{0}}$) $\vee$ ({\it{n\/}} $=$ {\tt{1}}) $\vee$ ({\tt{1}} $<$ {\it{n\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-1-arg1 \\ \index{quotient-1-arg1}
\=\+({\tt{1}} $\div$ {\it{n\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $=$ {\tt{1}}$\;\;${\bf then }{\tt{1}} \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-x-x \\ \index{quotient-x-x}
({\it{x\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ (({\it{x\/}} $\div$ {\it{x\/}}) $=$ {\tt{1}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-quotient \\ \index{lessp-quotient}
(({\it{i\/}} $\div$ {\it{j\/}}) $<$ {\it{i\/}}) $=$ (({\it{i\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\it{j\/}} $\not=$ {\tt{1}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cancel-quotient-times} \\  
\=\+{\rm{cancel-quotient-times}}\,({\it{x\/}})\index{cancel-quotient-times} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{quotient}}) \\ 
$\wedge$$\;\;\;\;$({\rm{caadr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{times}}) \\ 
$\wedge$$\;\;\;\;$({\rm{caaddr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{times}})\- \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{bagint}}\,({\rm{times-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{times-fringe}, {\rm{times-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{times-fringe})\index{bagint}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{cons}}\,(\=\+{\rm{and-not-zerop-tree}}\,({\rm{bagint}}\,(\=\+{\rm{times-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{times-fringe}, \\ 
{\rm{times-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{times-fringe})\-\index{bagint})\index{and-not-zerop-tree}, \\ 
{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{quotient}}, \\ 
{\rm{times-tree}}\,({\rm{bagdiff}}\,(\=\+{\rm{times-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{times-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{times-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{times-fringe}, \\ 
{\rm{times-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{times-fringe})\-\index{bagint})\-\index{bagdiff})\index{times-tree}, \\ 
{\rm{times-tree}}\,({\rm{bagdiff}}\,(\=\+{\rm{times-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{times-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{times-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{times-fringe}, \\ 
{\rm{times-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{times-fringe})\-\index{bagint})\-\index{bagdiff})\index{times-tree})\-, \\ 
{\tt{'}}{\tt{(}}{\tt{(}}{\tt{zero}}{\tt{)}}{\tt{)}})\-)\-)\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  zerop-makes-quotient-zero-bridge \\ \index{zerop-makes-quotient-zero-bridge}
\=\+(\=\+({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{times}}) \\ 
$\wedge$$\;\;\;\;$({\rm{car}}\,({\it{y\/}}) $=$ {\tt{'}}{\tt{times}}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\rm{and-not-zerop-tree}}\,({\rm{bagint}}\,({\rm{times-fringe}}\,({\it{x\/}})\index{times-fringe}, {\rm{times-fringe}}\,({\it{y\/}})\index{times-fringe})\index{bagint})\index{and-not-zerop-tree}, \\ 
{\it{a\/}})\-))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+({\rm{eval\$}}\,({\bf{t}}, {\rm{cadr}}\,({\it{x\/}}), {\it{a\/}}) $*$ {\rm{eval\$}}\,({\bf{t}}, {\rm{caddr}}\,({\it{x\/}}), {\it{a\/}})) \\ 
$\div$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\rm{cadr}}\,({\it{y\/}}), {\it{a\/}}) $*$ {\rm{eval\$}}\,({\bf{t}}, {\rm{caddr}}\,({\it{y\/}}), {\it{a\/}})))\- \\ 
$=$$\;\;\;\;${\tt{0}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable zerop-makes-quotient-zero-bridge; name this event `zerop-makes-quotient-zero-bridge-off'.\index{zerop-makes-quotient-zero-bridge!-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  eval\$-quotient-times-tree-bagdiff \\ \index{eval\$-quotient-times-tree-bagdi!ff}
\=\+({\rm{subbagp}}\,({\it{x\/}}, {\it{y\/}})\index{subbagp} $\wedge$ {\rm{subbagp}}\,({\it{x\/}}, {\it{z\/}})\index{subbagp} $\wedge$ {\rm{eval\$}}\,({\bf{t}}, {\rm{and-not-zerop-tree}}\,({\it{x\/}})\index{and-not-zerop-tree}, {\it{a\/}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\rm{bagdiff}}\,({\it{y\/}}, {\it{x\/}})\index{bagdiff})\index{times-tree}, {\it{a\/}}) \\ 
$\div$$\;\;\;\;${\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\rm{bagdiff}}\,({\it{z\/}}, {\it{x\/}})\index{bagdiff})\index{times-tree}, {\it{a\/}}))\- \\ 
$=$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\it{y\/}})\index{times-tree}, {\it{a\/}}) $\div$ {\rm{eval\$}}\,({\bf{t}}, {\rm{times-tree}}\,({\it{z\/}})\index{times-tree}, {\it{a\/}})))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable eval\$-quotient-times-tree-bagdiff; name this event `eval\$-quotient-times-tree-bagdiff-off'.\index{eval\$-quotient-times-tree-bagdi!ff-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-quotient-times \\ \index{correctness-of-cancel-quotient-ti!mes}
{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{cancel-quotient-times}}\,({\it{x\/}})\index{cancel-quotient-times}, {\it{a\/}})
\end{tabbing}


\noindent{\sc Event}:   Let us define the theory {\it{quotients}} to consist of the following events: quotient-noop,
quotient-of-non-number,
quotient-zero,
quotient-add1,
equal-quotient-0,
quotient-sub1,
quotient-plus,
quotient-times,
quotient-times-instance,
quotient-difference1,
quotient-lessp-arg1,
quotient-difference2,
quotient-difference3,
quotient-remainder-times,
quotient-remainder,
quotient-remainder-instance,
quotient-plus-times-times,
quotient-plus-times-times-instance,
quotient-quotient,
quotient-1-arg2,
quotient-1-arg1,
quotient-x-x,
lessp-quotient,
correctness-of-cancel-quotient-times.\index{quotients}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{exp} \\  
\=\+{\rm{exp}}\,({\it{i\/}}, {\it{j\/}})\index{exp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{j\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{1}} \\ 
{\bf else }{\it{i\/}} $*$ {\rm{exp}}\,({\it{i\/}}, {\it{j\/}} $-\;1$)\index{exp}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{log} \\  
\=\+{\rm{log}}\,({\it{base\/}}, {\it{n\/}})\index{log} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{base\/}} $<$ {\tt{2}}$\;\;${\bf then }{\tt{0}} \\ 
{\bf elseif }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }$1\;+$ {\rm{log}}\,({\it{base\/}}, {\it{n\/}} $\div$ {\it{base\/}})\index{log}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{gcd} \\  
\=\+{\rm{gcd}}\,({\it{x\/}}, {\it{y\/}})\index{gcd} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\rm{fix}}\,({\it{y\/}}) \\ 
{\bf elseif }{\it{y\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\it{x\/}} \\ 
{\bf elseif }{\it{x\/}} $<$ {\it{y\/}}$\;\;${\bf then }{\rm{gcd}}\,({\it{x\/}}, {\it{y\/}} $-$ {\it{x\/}})\index{gcd} \\ 
{\bf else }{\rm{gcd}}\,({\it{x\/}} $-$ {\it{y\/}}, {\it{y\/}})\index{gcd}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-exp \\ \index{remainder-exp}
({\it{k\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ (({\rm{exp}}\,({\it{n\/}}, {\it{k\/}})\index{exp} ${}${\bf{mod}}${}$ {\it{n\/}}) $=$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{double-number-induction} \\  
\=\+{\rm{double-number-induction}}\,({\it{i\/}}, {\it{j\/}})\index{double-number-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{i\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf elseif }{\it{j\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }{\rm{double-number-induction}}\,({\it{i\/}} $-\;1$, {\it{j\/}} $-\;1$)\index{double-number-induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-exp-exp \\ \index{remainder-exp-exp}
\=\+\=\+{\bf if }{\it{j\/}} $<$ {\it{i\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$(({\rm{exp}}\,({\it{a\/}}, {\it{j\/}})\index{exp} ${}${\bf{mod}}${}$ {\rm{exp}}\,({\it{a\/}}, {\it{i\/}})\index{exp}) $=$ {\tt{0}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-exp \\ \index{quotient-exp}
\=\+({\it{k\/}} $\not\simeq {\tt{0}}$) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{exp}}\,({\it{n\/}}, {\it{k\/}})\index{exp} $\div$ {\it{n\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }{\rm{exp}}\,({\it{n\/}}, {\it{k\/}} $-\;1$)\index{exp}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  exp-zero \\ \index{exp-zero}
({\it{k\/}} $\simeq {\tt{0}}$) $\rightarrow$ ({\rm{exp}}\,({\it{n\/}}, {\it{k\/}})\index{exp} $=$ {\tt{1}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  exp-add1 \\ \index{exp-add1}
{\rm{exp}}\,({\it{n\/}}, $1\;+$ {\it{k\/}})\index{exp} $=$ ({\it{n\/}} $*$ {\rm{exp}}\,({\it{n\/}}, {\it{k\/}})\index{exp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  exp-plus \\ \index{exp-plus}
{\rm{exp}}\,({\it{i\/}}, {\it{j\/}} $+$ {\it{k\/}})\index{exp} $=$ ({\rm{exp}}\,({\it{i\/}}, {\it{j\/}})\index{exp} $*$ {\rm{exp}}\,({\it{i\/}}, {\it{k\/}})\index{exp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  exp-0-arg1 \\ \index{exp-0-arg1}
\=\+{\rm{exp}}\,({\tt{0}}, {\it{k\/}})\index{exp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{k\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{1}} \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  exp-1-arg1 \\ \index{exp-1-arg1}
{\rm{exp}}\,({\tt{1}}, {\it{k\/}})\index{exp} $=$ {\tt{1}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  exp-0-arg2 \\ \index{exp-0-arg2}
{\rm{exp}}\,({\it{n\/}}, {\tt{0}})\index{exp} $=$ {\tt{1}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  exp-times \\ \index{exp-times}
{\rm{exp}}\,({\it{i\/}} $*$ {\it{j\/}}, {\it{k\/}})\index{exp} $=$ ({\rm{exp}}\,({\it{i\/}}, {\it{k\/}})\index{exp} $*$ {\rm{exp}}\,({\it{j\/}}, {\it{k\/}})\index{exp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  exp-exp \\ \index{exp-exp}
{\rm{exp}}\,({\rm{exp}}\,({\it{i\/}}, {\it{j\/}})\index{exp}, {\it{k\/}})\index{exp} $=$ {\rm{exp}}\,({\it{i\/}}, {\it{j\/}} $*$ {\it{k\/}})\index{exp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-exp-0 \\ \index{equal-exp-0}
({\rm{exp}}\,({\it{n\/}}, {\it{k\/}})\index{exp} $=$ {\tt{0}}) $=$ (({\it{n\/}} $\simeq {\tt{0}}$) $\wedge$ ({\it{k\/}} $\not\simeq {\tt{0}}$))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-exp-1 \\ \index{equal-exp-1}
\=\+({\rm{exp}}\,({\it{n\/}}, {\it{k\/}})\index{exp} $=$ {\tt{1}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{k\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\it{n\/}} $=$ {\tt{1}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  exp-difference \\ \index{exp-difference}
\=\+(\=\+\=\+{\bf if }{\it{b\/}} $<$ {\it{c\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$({\it{a\/}} $\not\simeq {\tt{0}}$))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{exp}}\,({\it{a\/}}, {\it{b\/}} $-$ {\it{c\/}})\index{exp} $=$ ({\rm{exp}}\,({\it{a\/}}, {\it{b\/}})\index{exp} $\div$ {\rm{exp}}\,({\it{a\/}}, {\it{c\/}})\index{exp}))\-
\end{tabbing}


\noindent{\sc Event}:   Let us define the theory {\it{exponentiation}} to consist of the following events: equal-exp-0,
equal-exp-1,
exp-exp,
exp-add1,
exp-times,
exp-1-arg1,
exp-zero,
exp-0-arg2,
exp-0-arg1,
exp-difference,
exp-plus,
quotient-exp,
remainder-exp-exp,
remainder-exp.\index{exponentiation}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  equal-log-0 \\ \index{equal-log-0}
({\rm{log}}\,({\it{base\/}}, {\it{n\/}})\index{log} $=$ {\tt{0}}) $=$ (({\it{base\/}} $<$ {\tt{2}}) $\vee$ ({\it{n\/}} $\simeq {\tt{0}}$))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  log-0 \\ \index{log-0}
({\it{n\/}} $\simeq {\tt{0}}$) $\rightarrow$ ({\rm{log}}\,({\it{base\/}}, {\it{n\/}})\index{log} $=$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  log-1 \\ \index{log-1}
({\tt{1}} $<$ {\it{base\/}}) $\rightarrow$ ({\rm{log}}\,({\it{base\/}}, {\tt{1}})\index{log} $=$ {\tt{1}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{double-log-induction} \\  
\=\+{\rm{double-log-induction}}\,({\it{base\/}}, {\it{a\/}}, {\it{b\/}})\index{double-log-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{base\/}} $<$ {\tt{2}}$\;\;${\bf then }{\tt{0}} \\ 
{\bf elseif }{\it{a\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf elseif }{\it{b\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }{\rm{double-log-induction}}\,({\it{base\/}}, {\it{a\/}} $\div$ {\it{base\/}}, {\it{b\/}} $\div$ {\it{base\/}})\index{double-log-induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  leq-log-log \\ \index{leq-log-log}
\=\+\=\+{\bf if }{\it{m\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$\=\+{\bf if }{\rm{log}}\,({\it{c\/}}, {\it{m\/}})\index{log} $<$ {\rm{log}}\,({\it{c\/}}, {\it{n\/}})\index{log}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  log-quotient \\ \index{log-quotient}
({\tt{1}} $<$ {\it{c\/}}) $\rightarrow$ ({\rm{log}}\,({\it{c\/}}, {\it{n\/}} $\div$ {\it{c\/}})\index{log} $=$ ({\rm{log}}\,({\it{c\/}}, {\it{n\/}})\index{log} $-\;1$))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  log-quotient-times-proof \\ \index{log-quotient-times-proof}
({\tt{1}} $<$ {\it{c\/}}) $\rightarrow$ ({\rm{log}}\,({\it{c\/}}, {\it{n\/}} $\div$ ({\it{c\/}} $*$ {\it{m\/}}))\index{log} $=$ ({\rm{log}}\,({\it{c\/}}, {\it{n\/}} $\div$ {\it{m\/}})\index{log} $-\;1$))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  log-quotient-times \\ \index{log-quotient-times}
\=\+({\tt{1}} $<$ {\it{c\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{log}}\,({\it{c\/}}, {\it{n\/}} $\div$ ({\it{c\/}} $*$ {\it{m\/}}))\index{log} $=$ ({\rm{log}}\,({\it{c\/}}, {\it{n\/}} $\div$ {\it{m\/}})\index{log} $-\;1$)) \\ 
$\wedge$$\;\;\;\;$({\rm{log}}\,({\it{c\/}}, {\it{n\/}} $\div$ ({\it{m\/}} $*$ {\it{c\/}}))\index{log} $=$ ({\rm{log}}\,({\it{c\/}}, {\it{n\/}} $\div$ {\it{m\/}})\index{log} $-\;1$)))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  log-quotient-exp \\ \index{log-quotient-exp}
({\tt{1}} $<$ {\it{c\/}}) $\rightarrow$ ({\rm{log}}\,({\it{c\/}}, {\it{n\/}} $\div$ {\rm{exp}}\,({\it{c\/}}, {\it{m\/}})\index{exp})\index{log} $=$ ({\rm{log}}\,({\it{c\/}}, {\it{n\/}})\index{log} $-$ {\it{m\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  log-times-proof \\ \index{log-times-proof}
(({\tt{1}} $<$ {\it{c\/}}) $\wedge$ ({\it{n\/}} $\not\simeq {\tt{0}}$)) $\rightarrow$ ({\rm{log}}\,({\it{c\/}}, {\it{c\/}} $*$ {\it{n\/}})\index{log} $=$ ($1\;+$ {\rm{log}}\,({\it{c\/}}, {\it{n\/}})\index{log}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  log-times \\ \index{log-times}
\=\+(({\tt{1}} $<$ {\it{c\/}}) $\wedge$ ({\it{n\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{log}}\,({\it{c\/}}, {\it{c\/}} $*$ {\it{n\/}})\index{log} $=$ ($1\;+$ {\rm{log}}\,({\it{c\/}}, {\it{n\/}})\index{log})) \\ 
$\wedge$$\;\;\;\;$({\rm{log}}\,({\it{c\/}}, {\it{n\/}} $*$ {\it{c\/}})\index{log} $=$ ($1\;+$ {\rm{log}}\,({\it{c\/}}, {\it{n\/}})\index{log})))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  log-times-exp-proof \\ \index{log-times-exp-proof}
(({\tt{1}} $<$ {\it{c\/}}) $\wedge$ ({\it{n\/}} $\not\simeq {\tt{0}}$)) $\rightarrow$ ({\rm{log}}\,({\it{c\/}}, {\it{n\/}} $*$ {\rm{exp}}\,({\it{c\/}}, {\it{m\/}})\index{exp})\index{log} $=$ ({\rm{log}}\,({\it{c\/}}, {\it{n\/}})\index{log} $+$ {\it{m\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  log-times-exp \\ \index{log-times-exp}
\=\+(({\tt{1}} $<$ {\it{c\/}}) $\wedge$ ({\it{n\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{log}}\,({\it{c\/}}, {\it{n\/}} $*$ {\rm{exp}}\,({\it{c\/}}, {\it{m\/}})\index{exp})\index{log} $=$ ({\rm{log}}\,({\it{c\/}}, {\it{n\/}})\index{log} $+$ {\it{m\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{log}}\,({\it{c\/}}, {\rm{exp}}\,({\it{c\/}}, {\it{m\/}})\index{exp} $*$ {\it{n\/}})\index{log} $=$ ({\rm{log}}\,({\it{c\/}}, {\it{n\/}})\index{log} $+$ {\it{m\/}})))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  log-exp \\ \index{log-exp}
({\tt{1}} $<$ {\it{c\/}}) $\rightarrow$ ({\rm{log}}\,({\it{c\/}}, {\rm{exp}}\,({\it{c\/}}, {\it{n\/}})\index{exp})\index{log} $=$ ($1\;+$ {\it{n\/}}))
\end{tabbing}


\noindent{\sc Event}:   Let us define the theory {\it{logs}} to consist of the following events: log-exp,
log-times-exp,
log-times,
log-quotient-exp,
log-quotient-times,
log-quotient,
log-1,
log-0,
equal-log-0,
exp-exp.\index{logs}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  commutativity-of-gcd \\ \index{commutativity-of-gcd}
{\rm{gcd}}\,({\it{b\/}}, {\it{a\/}})\index{gcd} $=$ {\rm{gcd}}\,({\it{a\/}}, {\it{b\/}})\index{gcd}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{single-number-induction} \\  
\=\+{\rm{single-number-induction}}\,({\it{n\/}})\index{single-number-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }{\rm{single-number-induction}}\,({\it{n\/}} $-\;1$)\index{single-number-induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  gcd-0 \\ \index{gcd-0}
({\rm{gcd}}\,({\tt{0}}, {\it{x\/}})\index{gcd} $=$ {\rm{fix}}\,({\it{x\/}})) $\wedge$ ({\rm{gcd}}\,({\it{x\/}}, {\tt{0}})\index{gcd} $=$ {\rm{fix}}\,({\it{x\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  gcd-1 \\ \index{gcd-1}
({\rm{gcd}}\,({\tt{1}}, {\it{x\/}})\index{gcd} $=$ {\tt{1}}) $\wedge$ ({\rm{gcd}}\,({\it{x\/}}, {\tt{1}})\index{gcd} $=$ {\tt{1}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-gcd-0 \\ \index{equal-gcd-0}
({\rm{gcd}}\,({\it{a\/}}, {\it{b\/}})\index{gcd} $=$ {\tt{0}}) $=$ (({\it{a\/}} $\simeq {\tt{0}}$) $\wedge$ ({\it{b\/}} $\simeq {\tt{0}}$))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-gcd \\ \index{lessp-gcd}
({\it{b\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ ((({\it{b\/}} $<$ {\rm{gcd}}\,({\it{a\/}}, {\it{b\/}})\index{gcd}) $=$ {\bf{f}}) $\wedge$ (({\it{b\/}} $<$ {\rm{gcd}}\,({\it{b\/}}, {\it{a\/}})\index{gcd}) $=$ {\bf{f}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  gcd-plus-instance-temp-proof \\ \index{gcd-plus-instance-temp-proof}
{\rm{gcd}}\,({\it{a\/}}, {\it{a\/}} $+$ {\it{b\/}})\index{gcd} $=$ {\rm{gcd}}\,({\it{a\/}}, {\it{b\/}})\index{gcd}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  gcd-plus-instance-temp \\ \index{gcd-plus-instance-temp}
({\rm{gcd}}\,({\it{a\/}}, {\it{a\/}} $+$ {\it{b\/}})\index{gcd} $=$ {\rm{gcd}}\,({\it{a\/}}, {\it{b\/}})\index{gcd}) $\wedge$ ({\rm{gcd}}\,({\it{a\/}}, {\it{b\/}} $+$ {\it{a\/}})\index{gcd} $=$ {\rm{gcd}}\,({\it{a\/}}, {\it{b\/}})\index{gcd})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  gcd-plus-proof \\ \index{gcd-plus-proof}
(({\it{b\/}} ${}${\bf{mod}}${}$ {\it{a\/}}) $=$ {\tt{0}}) $\rightarrow$ ({\rm{gcd}}\,({\it{a\/}}, {\it{b\/}} $+$ {\it{c\/}})\index{gcd} $=$ {\rm{gcd}}\,({\it{a\/}}, {\it{c\/}})\index{gcd})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  gcd-plus \\ \index{gcd-plus}
\=\+(({\it{b\/}} ${}${\bf{mod}}${}$ {\it{a\/}}) $=$ {\tt{0}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{gcd}}\,({\it{a\/}}, {\it{b\/}} $+$ {\it{c\/}})\index{gcd} $=$ {\rm{gcd}}\,({\it{a\/}}, {\it{c\/}})\index{gcd}) \\ 
$\wedge$$\;\;\;\;$({\rm{gcd}}\,({\it{a\/}}, {\it{c\/}} $+$ {\it{b\/}})\index{gcd} $=$ {\rm{gcd}}\,({\it{a\/}}, {\it{c\/}})\index{gcd}) \\ 
$\wedge$$\;\;\;\;$({\rm{gcd}}\,({\it{b\/}} $+$ {\it{c\/}}, {\it{a\/}})\index{gcd} $=$ {\rm{gcd}}\,({\it{a\/}}, {\it{c\/}})\index{gcd}) \\ 
$\wedge$$\;\;\;\;$({\rm{gcd}}\,({\it{c\/}} $+$ {\it{b\/}}, {\it{a\/}})\index{gcd} $=$ {\rm{gcd}}\,({\it{a\/}}, {\it{c\/}})\index{gcd}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  gcd-plus-instance \\ \index{gcd-plus-instance}
({\rm{gcd}}\,({\it{a\/}}, {\it{a\/}} $+$ {\it{b\/}})\index{gcd} $=$ {\rm{gcd}}\,({\it{a\/}}, {\it{b\/}})\index{gcd}) $\wedge$ ({\rm{gcd}}\,({\it{a\/}}, {\it{b\/}} $+$ {\it{a\/}})\index{gcd} $=$ {\rm{gcd}}\,({\it{a\/}}, {\it{b\/}})\index{gcd})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-gcd \\ \index{remainder-gcd}
(({\it{a\/}} ${}${\bf{mod}}${}$ {\rm{gcd}}\,({\it{a\/}}, {\it{b\/}})\index{gcd}) $=$ {\tt{0}}) $\wedge$ (({\it{b\/}} ${}${\bf{mod}}${}$ {\rm{gcd}}\,({\it{a\/}}, {\it{b\/}})\index{gcd}) $=$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  distributivity-of-times-over-gcd-proof \\ \index{distributivity-of-times-over-gc!d-proof}
{\rm{gcd}}\,({\it{x\/}} $*$ {\it{z\/}}, {\it{y\/}} $*$ {\it{z\/}})\index{gcd} $=$ ({\it{z\/}} $*$ {\rm{gcd}}\,({\it{x\/}}, {\it{y\/}})\index{gcd})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  distributivity-of-times-over-gcd \\ \index{distributivity-of-times-over-gc!d}
\=\+({\rm{gcd}}\,({\it{x\/}} $*$ {\it{z\/}}, {\it{y\/}} $*$ {\it{z\/}})\index{gcd} $=$ ({\it{z\/}} $*$ {\rm{gcd}}\,({\it{x\/}}, {\it{y\/}})\index{gcd})) \\ 
$\wedge$$\;\;\;\;$({\rm{gcd}}\,({\it{z\/}} $*$ {\it{x\/}}, {\it{y\/}} $*$ {\it{z\/}})\index{gcd} $=$ ({\it{z\/}} $*$ {\rm{gcd}}\,({\it{x\/}}, {\it{y\/}})\index{gcd})) \\ 
$\wedge$$\;\;\;\;$({\rm{gcd}}\,({\it{x\/}} $*$ {\it{z\/}}, {\it{z\/}} $*$ {\it{y\/}})\index{gcd} $=$ ({\it{z\/}} $*$ {\rm{gcd}}\,({\it{x\/}}, {\it{y\/}})\index{gcd})) \\ 
$\wedge$$\;\;\;\;$({\rm{gcd}}\,({\it{z\/}} $*$ {\it{x\/}}, {\it{z\/}} $*$ {\it{y\/}})\index{gcd} $=$ ({\it{z\/}} $*$ {\rm{gcd}}\,({\it{x\/}}, {\it{y\/}})\index{gcd}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  gcd-is-the-greatest \\ \index{gcd-is-the-greatest}
\=\+(({\it{x\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\it{y\/}} $\not\simeq {\tt{0}}$) $\wedge$ (({\it{x\/}} ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{0}}) $\wedge$ (({\it{y\/}} ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$\=\+{\bf if }{\rm{gcd}}\,({\it{x\/}}, {\it{y\/}})\index{gcd} $<$ {\it{z\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  common-divisor-divides-gcd \\ \index{common-divisor-divides-gcd}
((({\it{x\/}} ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{0}}) $\wedge$ (({\it{y\/}} ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{0}})) $\rightarrow$ (({\rm{gcd}}\,({\it{x\/}}, {\it{y\/}})\index{gcd} ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  associativity-of-gcd-zero-case \\ \index{associativity-of-gcd-zero-case}
(({\it{a\/}} $\simeq {\tt{0}}$) $\vee$ ({\it{b\/}} $\simeq {\tt{0}}$) $\vee$ ({\it{c\/}} $\simeq {\tt{0}}$)) $\rightarrow$ ({\rm{gcd}}\,({\rm{gcd}}\,({\it{a\/}}, {\it{b\/}})\index{gcd}, {\it{c\/}})\index{gcd} $=$ {\rm{gcd}}\,({\it{a\/}}, {\rm{gcd}}\,({\it{b\/}}, {\it{c\/}})\index{gcd})\index{gcd})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  associativity-of-gcd \\ \index{associativity-of-gcd}
{\rm{gcd}}\,({\rm{gcd}}\,({\it{a\/}}, {\it{b\/}})\index{gcd}, {\it{c\/}})\index{gcd} $=$ {\rm{gcd}}\,({\it{a\/}}, {\rm{gcd}}\,({\it{b\/}}, {\it{c\/}})\index{gcd})\index{gcd}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  commutativity2-of-gcd-zero-case \\ \index{commutativity2-of-gcd-zero-case}
(({\it{a\/}} $\simeq {\tt{0}}$) $\vee$ ({\it{b\/}} $\simeq {\tt{0}}$) $\vee$ ({\it{c\/}} $\simeq {\tt{0}}$)) $\rightarrow$ ({\rm{gcd}}\,({\it{b\/}}, {\rm{gcd}}\,({\it{a\/}}, {\it{c\/}})\index{gcd})\index{gcd} $=$ {\rm{gcd}}\,({\it{a\/}}, {\rm{gcd}}\,({\it{b\/}}, {\it{c\/}})\index{gcd})\index{gcd})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  commutativity2-of-gcd \\ \index{commutativity2-of-gcd}
{\rm{gcd}}\,({\it{b\/}}, {\rm{gcd}}\,({\it{a\/}}, {\it{c\/}})\index{gcd})\index{gcd} $=$ {\rm{gcd}}\,({\it{a\/}}, {\rm{gcd}}\,({\it{b\/}}, {\it{c\/}})\index{gcd})\index{gcd}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  gcd-x-x \\ \index{gcd-x-x}
{\rm{gcd}}\,({\it{x\/}}, {\it{x\/}})\index{gcd} $=$ {\rm{fix}}\,({\it{x\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  gcd-idempotence \\ \index{gcd-idempotence}
({\rm{gcd}}\,({\it{x\/}}, {\rm{gcd}}\,({\it{x\/}}, {\it{y\/}})\index{gcd})\index{gcd} $=$ {\rm{gcd}}\,({\it{x\/}}, {\it{y\/}})\index{gcd}) $\wedge$ ({\rm{gcd}}\,({\it{y\/}}, {\rm{gcd}}\,({\it{x\/}}, {\it{y\/}})\index{gcd})\index{gcd} $=$ {\rm{gcd}}\,({\it{x\/}}, {\it{y\/}})\index{gcd})
\end{tabbing}


\noindent{\sc Event}:   Let us define the theory {\it{gcds}} to consist of the following events: commutativity2-of-gcd,
associativity-of-gcd,
common-divisor-divides-gcd,
distributivity-of-times-over-gcd,
lessp-gcd,
equal-gcd-0,
gcd-0,
gcd-idempotence,
gcd-x-x,
remainder-gcd,
gcd-plus,
gcd-plus-instance,
gcd-1,
commutativity-of-gcd.\index{gcds}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{naturals}} to consist of the following events: addition,
multiplication,
remainders,
quotients,
exponentiation,
logs,
gcds.\index{naturals}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{integerp} \\  
\=\+{\rm{integerp}}\,({\it{x\/}})\index{integerp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\in\;${\bf{N}}${}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\rm{negativep}}\,({\it{x\/}})$\;\;${\bf then }{\rm{negative-guts}}\,({\it{x\/}}) $\not\simeq {\tt{0}}$ \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fix-int} \\  
\=\+{\rm{fix-int}}\,({\it{x\/}})\index{fix-int} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{integerp}}\,({\it{x\/}})\index{integerp}$\;\;${\bf then }{\it{x\/}} \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{izerop}$\;\;$
{\rm{izerop}}\,({\it{i\/}})\index{izerop} $=$ ({\rm{fix-int}}\,({\it{i\/}})\index{fix-int} $=$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ilessp} \\  
\=\+{\rm{ilessp}}\,({\it{i\/}}, {\it{j\/}})\index{ilessp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{negativep}}\,({\it{i\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{negativep}}\,({\it{j\/}})$\;\;${\bf then }{\rm{negative-guts}}\,({\it{j\/}}) $<$ {\rm{negative-guts}}\,({\it{i\/}}) \\ 
{\bf elseif }{\it{i\/}} $=$ ($-$ {\tt{0}})$\;\;${\bf then }{\tt{0}} $<$ {\it{j\/}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{negativep}}\,({\it{j\/}})$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\it{i\/}} $<$ {\it{j\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ileq}$\;\;$
{\rm{ileq}}\,({\it{i\/}}, {\it{j\/}})\index{ileq} $=$ ($\neg$ {\rm{ilessp}}\,({\it{j\/}}, {\it{i\/}})\index{ilessp})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{iplus} \\  
\=\+{\rm{iplus}}\,({\it{x\/}}, {\it{y\/}})\index{iplus} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{negativep}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{negativep}}\,({\it{y\/}}) \\ 
{\bf then }\=\+{\bf if }({\rm{negative-guts}}\,({\it{x\/}}) $\simeq {\tt{0}}$) $\wedge$ ({\rm{negative-guts}}\,({\it{y\/}}) $\simeq {\tt{0}}$)$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }$-$ ({\rm{negative-guts}}\,({\it{x\/}}) $+$ {\rm{negative-guts}}\,({\it{y\/}}))$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{y\/}} $<$ {\rm{negative-guts}}\,({\it{x\/}})$\;\;${\bf then }$-$ ({\rm{negative-guts}}\,({\it{x\/}}) $-$ {\it{y\/}}) \\ 
{\bf else }{\it{y\/}} $-$ {\rm{negative-guts}}\,({\it{x\/}})$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{negativep}}\,({\it{y\/}}) \\ 
{\bf then }\=\+{\bf if }{\it{x\/}} $<$ {\rm{negative-guts}}\,({\it{y\/}})$\;\;${\bf then }$-$ ({\rm{negative-guts}}\,({\it{y\/}}) $-$ {\it{x\/}}) \\ 
{\bf else }{\it{x\/}} $-$ {\rm{negative-guts}}\,({\it{y\/}})$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}} $+$ {\it{y\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ineg} \\  
\=\+{\rm{ineg}}\,({\it{x\/}})\index{ineg} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{negativep}}\,({\it{x\/}})$\;\;${\bf then }{\rm{negative-guts}}\,({\it{x\/}}) \\ 
{\bf elseif }{\it{x\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }$-$ {\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{idifference}$\;\;$
{\rm{idifference}}\,({\it{x\/}}, {\it{y\/}})\index{idifference} $=$ {\rm{iplus}}\,({\it{x\/}}, {\rm{ineg}}\,({\it{y\/}})\index{ineg})\index{iplus}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{iabs} \\  
\=\+{\rm{iabs}}\,({\it{i\/}})\index{iabs} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{negativep}}\,({\it{i\/}})$\;\;${\bf then }{\rm{negative-guts}}\,({\it{i\/}}) \\ 
{\bf else }{\rm{fix}}\,({\it{i\/}})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{itimes} \\  
\=\+{\rm{itimes}}\,({\it{i\/}}, {\it{j\/}})\index{itimes} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{negativep}}\,({\it{i\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{negativep}}\,({\it{j\/}})$\;\;${\bf then }{\rm{negative-guts}}\,({\it{i\/}}) $*$ {\rm{negative-guts}}\,({\it{j\/}}) \\ 
{\bf else }{\rm{fix-int}}\,($-$ ({\rm{negative-guts}}\,({\it{i\/}}) $*$ {\it{j\/}}))\index{fix-int}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{negativep}}\,({\it{j\/}})$\;\;${\bf then }{\rm{fix-int}}\,($-$ ({\it{i\/}} $*$ {\rm{negative-guts}}\,({\it{j\/}})))\index{fix-int} \\ 
{\bf else }{\it{i\/}} $*$ {\it{j\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{iquotient} \\  
\=\+{\rm{iquotient}}\,({\it{i\/}}, {\it{j\/}})\index{iquotient} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{fix-int}}\,({\it{j\/}})\index{fix-int} $=$ {\tt{0}}$\;\;${\bf then }{\tt{0}} \\ 
{\bf elseif }{\rm{negativep}}\,({\it{i\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{negativep}}\,({\it{j\/}}) \\ 
{\bf then }\=\+{\bf if }({\rm{negative-guts}}\,({\it{i\/}}) ${}${\bf{mod}}${}$ {\rm{negative-guts}}\,({\it{j\/}})) $=$ {\tt{0}} \\ 
{\bf then }{\rm{negative-guts}}\,({\it{i\/}}) $\div$ {\rm{negative-guts}}\,({\it{j\/}}) \\ 
{\bf else }$1\;+$ ({\rm{negative-guts}}\,({\it{i\/}}) $\div$ {\rm{negative-guts}}\,({\it{j\/}}))$\;${\bf  endif}\- \\ 
{\bf elseif }({\rm{negative-guts}}\,({\it{i\/}}) ${}${\bf{mod}}${}$ {\it{j\/}}) $=$ {\tt{0}} \\ 
{\bf then }{\rm{fix-int}}\,($-$ ({\rm{negative-guts}}\,({\it{i\/}}) $\div$ {\it{j\/}}))\index{fix-int} \\ 
{\bf else }{\rm{fix-int}}\,($-$ ($1\;+$ ({\rm{negative-guts}}\,({\it{i\/}}) $\div$ {\it{j\/}})))\index{fix-int}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{negativep}}\,({\it{j\/}})$\;\;${\bf then }{\rm{fix-int}}\,($-$ ({\it{i\/}} $\div$ {\rm{negative-guts}}\,({\it{j\/}})))\index{fix-int} \\ 
{\bf else }{\it{i\/}} $\div$ {\it{j\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{iremainder} \\  
{\rm{iremainder}}\,({\it{i\/}}, {\it{j\/}})\index{iremainder} $=$ {\rm{idifference}}\,({\it{i\/}}, {\rm{itimes}}\,({\it{j\/}}, {\rm{iquotient}}\,({\it{i\/}}, {\it{j\/}})\index{iquotient})\index{itimes})\index{idifference}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{idiv} \\  
\=\+{\rm{idiv}}\,({\it{i\/}}, {\it{j\/}})\index{idiv} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{fix-int}}\,({\it{j\/}})\index{fix-int} $=$ {\tt{0}}$\;\;${\bf then }{\tt{0}} \\ 
{\bf elseif }{\rm{negativep}}\,({\it{i\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{negativep}}\,({\it{j\/}})$\;\;${\bf then }{\rm{negative-guts}}\,({\it{i\/}}) $\div$ {\rm{negative-guts}}\,({\it{j\/}}) \\ 
{\bf elseif }({\rm{negative-guts}}\,({\it{i\/}}) ${}${\bf{mod}}${}$ {\it{j\/}}) $=$ {\tt{0}} \\ 
{\bf then }{\rm{fix-int}}\,($-$ ({\rm{negative-guts}}\,({\it{i\/}}) $\div$ {\it{j\/}}))\index{fix-int} \\ 
{\bf else }{\rm{fix-int}}\,($-$ ($1\;+$ ({\rm{negative-guts}}\,({\it{i\/}}) $\div$ {\it{j\/}})))\index{fix-int}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{negativep}}\,({\it{j\/}}) \\ 
{\bf then }\=\+{\bf if }({\it{i\/}} ${}${\bf{mod}}${}$ {\rm{negative-guts}}\,({\it{j\/}})) $=$ {\tt{0}} \\ 
{\bf then }{\rm{fix-int}}\,($-$ ({\it{i\/}} $\div$ {\rm{negative-guts}}\,({\it{j\/}})))\index{fix-int} \\ 
{\bf else }{\rm{fix-int}}\,($-$ ($1\;+$ ({\it{i\/}} $\div$ {\rm{negative-guts}}\,({\it{j\/}}))))\index{fix-int}$\;${\bf  endif}\- \\ 
{\bf else }{\it{i\/}} $\div$ {\it{j\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{imod} \\  
{\rm{imod}}\,({\it{i\/}}, {\it{j\/}})\index{imod} $=$ {\rm{idifference}}\,({\rm{fix-int}}\,({\it{i\/}})\index{fix-int}, {\rm{itimes}}\,({\it{j\/}}, {\rm{idiv}}\,({\it{i\/}}, {\it{j\/}})\index{idiv})\index{itimes})\index{idifference}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{iquo} \\  
\=\+{\rm{iquo}}\,({\it{i\/}}, {\it{j\/}})\index{iquo} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{fix-int}}\,({\it{j\/}})\index{fix-int} $=$ {\tt{0}}$\;\;${\bf then }{\tt{0}} \\ 
{\bf elseif }{\rm{negativep}}\,({\it{i\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{negativep}}\,({\it{j\/}})$\;\;${\bf then }{\rm{negative-guts}}\,({\it{i\/}}) $\div$ {\rm{negative-guts}}\,({\it{j\/}}) \\ 
{\bf else }{\rm{fix-int}}\,($-$ ({\rm{negative-guts}}\,({\it{i\/}}) $\div$ {\it{j\/}}))\index{fix-int}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{negativep}}\,({\it{j\/}})$\;\;${\bf then }{\rm{fix-int}}\,($-$ ({\it{i\/}} $\div$ {\rm{negative-guts}}\,({\it{j\/}})))\index{fix-int} \\ 
{\bf else }{\it{i\/}} $\div$ {\it{j\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{irem} \\  
{\rm{irem}}\,({\it{i\/}}, {\it{j\/}})\index{irem} $=$ {\rm{idifference}}\,({\rm{fix-int}}\,({\it{i\/}})\index{fix-int}, {\rm{itimes}}\,({\it{j\/}}, {\rm{iquo}}\,({\it{i\/}}, {\it{j\/}})\index{iquo})\index{itimes})\index{idifference}
\end{tabbing}


\noindent{\sc Event}:   Let us define the theory {\it{integer-defns}} to consist of the following events: integerp,
fix-int,
ilessp,
iplus,
ineg,
iabs,
itimes,
iquotient,
iremainder,
idiv,
imod,
iquo,
irem.\index{integer-defns}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{all-integer-defns}} to consist of the following events: integerp,
fix-int,
izerop,
ilessp,
ileq,
iplus,
ineg,
idifference,
iabs,
itimes,
iquotient,
iremainder,
idiv,
imod,
iquo,
irem.\index{all-integer-defns}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp; name this event `integerp-off'.\index{integerp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int; name this event `fix-int-off'.\index{fix-int-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp; name this event `ilessp-off'.\index{ilessp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus; name this event `iplus-off'.\index{iplus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ineg; name this event `ineg-off'.\index{ineg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iabs; name this event `iabs-off'.\index{iabs-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes; name this event `itimes-off'.\index{itimes-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  integerp-fix-int \\ \index{integerp-fix-int}
{\rm{integerp}}\,({\rm{fix-int}}\,({\it{x\/}})\index{fix-int})\index{integerp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integerp-iplus \\ \index{integerp-iplus}
{\rm{integerp}}\,({\rm{iplus}}\,({\it{x\/}}, {\it{y\/}})\index{iplus})\index{integerp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integerp-idifference \\ \index{integerp-idifference}
{\rm{integerp}}\,({\rm{idifference}}\,({\it{x\/}}, {\it{y\/}})\index{idifference})\index{integerp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integerp-ineg \\ \index{integerp-ineg}
{\rm{integerp}}\,({\rm{ineg}}\,({\it{x\/}})\index{ineg})\index{integerp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integerp-iabs \\ \index{integerp-iabs}
{\rm{integerp}}\,({\rm{iabs}}\,({\it{x\/}})\index{iabs})\index{integerp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integerp-itimes \\ \index{integerp-itimes}
{\rm{integerp}}\,({\rm{itimes}}\,({\it{x\/}}, {\it{y\/}})\index{itimes})\index{integerp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fix-int-remover \\ \index{fix-int-remover}
{\rm{integerp}}\,({\it{x\/}})\index{integerp} $\rightarrow$ ({\rm{fix-int}}\,({\it{x\/}})\index{fix-int} $=$ {\it{x\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fix-int-fix-int \\ \index{fix-int-fix-int}
{\rm{fix-int}}\,({\rm{fix-int}}\,({\it{x\/}})\index{fix-int})\index{fix-int} $=$ {\rm{fix-int}}\,({\it{x\/}})\index{fix-int}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fix-int-iplus \\ \index{fix-int-iplus}
{\rm{fix-int}}\,({\rm{iplus}}\,({\it{a\/}}, {\it{b\/}})\index{iplus})\index{fix-int} $=$ {\rm{iplus}}\,({\it{a\/}}, {\it{b\/}})\index{iplus}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fix-int-idifference \\ \index{fix-int-idifference}
{\rm{fix-int}}\,({\rm{idifference}}\,({\it{a\/}}, {\it{b\/}})\index{idifference})\index{fix-int} $=$ {\rm{idifference}}\,({\it{a\/}}, {\it{b\/}})\index{idifference}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fix-int-ineg \\ \index{fix-int-ineg}
{\rm{fix-int}}\,({\rm{ineg}}\,({\it{x\/}})\index{ineg})\index{fix-int} $=$ {\rm{ineg}}\,({\it{x\/}})\index{ineg}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fix-int-iabs \\ \index{fix-int-iabs}
{\rm{fix-int}}\,({\rm{iabs}}\,({\it{x\/}})\index{iabs})\index{fix-int} $=$ {\rm{iabs}}\,({\it{x\/}})\index{iabs}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fix-int-itimes \\ \index{fix-int-itimes}
{\rm{fix-int}}\,({\rm{itimes}}\,({\it{x\/}}, {\it{y\/}})\index{itimes})\index{fix-int} $=$ {\rm{itimes}}\,({\it{x\/}}, {\it{y\/}})\index{itimes}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ineg-iplus \\ \index{ineg-iplus}
{\rm{ineg}}\,({\rm{iplus}}\,({\it{a\/}}, {\it{b\/}})\index{iplus})\index{ineg} $=$ {\rm{iplus}}\,({\rm{ineg}}\,({\it{a\/}})\index{ineg}, {\rm{ineg}}\,({\it{b\/}})\index{ineg})\index{iplus}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ineg-ineg \\ \index{ineg-ineg}
{\rm{ineg}}\,({\rm{ineg}}\,({\it{x\/}})\index{ineg})\index{ineg} $=$ {\rm{fix-int}}\,({\it{x\/}})\index{fix-int}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ineg-fix-int \\ \index{ineg-fix-int}
{\rm{ineg}}\,({\rm{fix-int}}\,({\it{x\/}})\index{fix-int})\index{ineg} $=$ {\rm{ineg}}\,({\it{x\/}})\index{ineg}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ineg-of-non-integerp \\ \index{ineg-of-non-integerp}
($\neg$ {\rm{integerp}}\,({\it{x\/}})\index{integerp}) $\rightarrow$ ({\rm{ineg}}\,({\it{x\/}})\index{ineg} $=$ {\tt{0}})
\end{tabbing}


\noindent{\sc Event}:   Enable ineg-of-non-integerp; name this event `ineg-of-non-integerp-off'.\index{ineg-of-non-integerp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ineg-0 \\ \index{ineg-0}
{\rm{ineg}}\,({\tt{0}})\index{ineg} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-left-id \\ \index{iplus-left-id}
($\neg$ {\rm{integerp}}\,({\it{x\/}})\index{integerp}) $\rightarrow$ ({\rm{iplus}}\,({\it{x\/}}, {\it{y\/}})\index{iplus} $=$ {\rm{fix-int}}\,({\it{y\/}})\index{fix-int})
\end{tabbing}


\noindent{\sc Event}:   Enable iplus-left-id; name this event `iplus-left-id-off'.\index{iplus-left-id-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  iplus-right-id \\ \index{iplus-right-id}
($\neg$ {\rm{integerp}}\,({\it{y\/}})\index{integerp}) $\rightarrow$ ({\rm{iplus}}\,({\it{x\/}}, {\it{y\/}})\index{iplus} $=$ {\rm{fix-int}}\,({\it{x\/}})\index{fix-int})
\end{tabbing}


\noindent{\sc Event}:   Enable iplus-right-id; name this event `iplus-right-id-off'.\index{iplus-right-id-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  iplus-0-left \\ \index{iplus-0-left}
{\rm{iplus}}\,({\tt{0}}, {\it{x\/}})\index{iplus} $=$ {\rm{fix-int}}\,({\it{x\/}})\index{fix-int}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-0-right \\ \index{iplus-0-right}
{\rm{iplus}}\,({\it{x\/}}, {\tt{0}})\index{iplus} $=$ {\rm{fix-int}}\,({\it{x\/}})\index{fix-int}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  commutativity2-of-iplus \\ \index{commutativity2-of-iplus}
{\rm{iplus}}\,({\it{x\/}}, {\rm{iplus}}\,({\it{y\/}}, {\it{z\/}})\index{iplus})\index{iplus} $=$ {\rm{iplus}}\,({\it{y\/}}, {\rm{iplus}}\,({\it{x\/}}, {\it{z\/}})\index{iplus})\index{iplus}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  commutativity-of-iplus \\ \index{commutativity-of-iplus}
{\rm{iplus}}\,({\it{x\/}}, {\it{y\/}})\index{iplus} $=$ {\rm{iplus}}\,({\it{y\/}}, {\it{x\/}})\index{iplus}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  associativity-of-iplus \\ \index{associativity-of-iplus}
{\rm{iplus}}\,({\rm{iplus}}\,({\it{x\/}}, {\it{y\/}})\index{iplus}, {\it{z\/}})\index{iplus} $=$ {\rm{iplus}}\,({\it{x\/}}, {\rm{iplus}}\,({\it{y\/}}, {\it{z\/}})\index{iplus})\index{iplus}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-cancellation-1 \\ \index{iplus-cancellation-1}
({\rm{iplus}}\,({\it{a\/}}, {\it{b\/}})\index{iplus} $=$ {\rm{iplus}}\,({\it{a\/}}, {\it{c\/}})\index{iplus}) $=$ ({\rm{fix-int}}\,({\it{b\/}})\index{fix-int} $=$ {\rm{fix-int}}\,({\it{c\/}})\index{fix-int})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-cancellation-2 \\ \index{iplus-cancellation-2}
({\rm{iplus}}\,({\it{b\/}}, {\it{a\/}})\index{iplus} $=$ {\rm{iplus}}\,({\it{c\/}}, {\it{a\/}})\index{iplus}) $=$ ({\rm{fix-int}}\,({\it{b\/}})\index{fix-int} $=$ {\rm{fix-int}}\,({\it{c\/}})\index{fix-int})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-ineg1 \\ \index{iplus-ineg1}
{\rm{iplus}}\,({\rm{ineg}}\,({\it{a\/}})\index{ineg}, {\it{a\/}})\index{iplus} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-ineg2 \\ \index{iplus-ineg2}
{\rm{iplus}}\,({\it{a\/}}, {\rm{ineg}}\,({\it{a\/}})\index{ineg})\index{iplus} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-fix-int1 \\ \index{iplus-fix-int1}
{\rm{iplus}}\,({\rm{fix-int}}\,({\it{a\/}})\index{fix-int}, {\it{b\/}})\index{iplus} $=$ {\rm{iplus}}\,({\it{a\/}}, {\it{b\/}})\index{iplus}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-fix-int2 \\ \index{iplus-fix-int2}
{\rm{iplus}}\,({\it{a\/}}, {\rm{fix-int}}\,({\it{b\/}})\index{fix-int})\index{iplus} $=$ {\rm{iplus}}\,({\it{a\/}}, {\it{b\/}})\index{iplus}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  idifference-fix-int1 \\ \index{idifference-fix-int1}
{\rm{idifference}}\,({\rm{fix-int}}\,({\it{a\/}})\index{fix-int}, {\it{b\/}})\index{idifference} $=$ {\rm{idifference}}\,({\it{a\/}}, {\it{b\/}})\index{idifference}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  idifference-fix-int2 \\ \index{idifference-fix-int2}
{\rm{idifference}}\,({\it{a\/}}, {\rm{fix-int}}\,({\it{b\/}})\index{fix-int})\index{idifference} $=$ {\rm{idifference}}\,({\it{a\/}}, {\it{b\/}})\index{idifference}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cancel-ineg-aux} \\  
\=\+{\rm{cancel-ineg-aux}}\,({\it{x\/}}, {\it{y\/}})\index{cancel-ineg-aux} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{ineg}} \\ 
{\bf then }\=\+{\bf if }{\it{y\/}} $=$ {\rm{cadr}}\,({\it{x\/}})$\;\;${\bf then }{\tt{'}}{\tt{'}}{\tt{0}} \\ 
{\bf elseif }{\rm{listp}}\,({\it{y\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{y\/}}) $=$ {\tt{'}}{\tt{iplus}} \\ 
{\bf then }\=\+{\bf if }{\rm{cadr}}\,({\it{y\/}}) $=$ {\rm{cadr}}\,({\it{x\/}}) \\ 
{\bf then }{\rm{list}}\,({\tt{'}}{\tt{fix-int}}, {\rm{caddr}}\,({\it{y\/}})) \\ 
{\bf elseif }{\rm{cancel-ineg-aux}}\,({\it{x\/}}, {\rm{caddr}}\,({\it{y\/}}))\index{cancel-ineg-aux} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{iplus}}, \\ 
{\rm{cadr}}\,({\it{y\/}}), \\ 
{\rm{cancel-ineg-aux}}\,({\it{x\/}}, {\rm{caddr}}\,({\it{y\/}}))\index{cancel-ineg-aux})\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{y\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{f}} \\ 
{\bf elseif }{\rm{car}}\,({\it{y\/}}) $=$ {\tt{'}}{\tt{ineg}} \\ 
{\bf then }\=\+{\bf if }{\it{x\/}} $=$ {\rm{cadr}}\,({\it{y\/}})$\;\;${\bf then }{\tt{'}}{\tt{'}}{\tt{0}} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{car}}\,({\it{y\/}}) $=$ {\tt{'}}{\tt{iplus}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{cadr}}\,({\it{y\/}})) \\ 
{\bf then }\=\+{\bf if }{\rm{caadr}}\,({\it{y\/}}) $=$ {\tt{'}}{\tt{ineg}} \\ 
{\bf then }\=\+{\bf if }{\it{x\/}} $=$ {\rm{cadadr}}\,({\it{y\/}}) \\ 
{\bf then }{\rm{list}}\,({\tt{'}}{\tt{fix-int}}, {\rm{caddr}}\,({\it{y\/}})) \\ 
{\bf elseif }{\rm{cancel-ineg-aux}}\,({\it{x\/}}, {\rm{caddr}}\,({\it{y\/}}))\index{cancel-ineg-aux} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{iplus}}, \\ 
{\rm{cadr}}\,({\it{y\/}}), \\ 
{\rm{cancel-ineg-aux}}\,({\it{x\/}}, {\rm{caddr}}\,({\it{y\/}}))\index{cancel-ineg-aux})\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{cancel-ineg-aux}}\,({\it{x\/}}, {\rm{caddr}}\,({\it{y\/}}))\index{cancel-ineg-aux} \\ 
{\bf then }{\rm{list}}\,({\tt{'}}{\tt{iplus}}, {\rm{cadr}}\,({\it{y\/}}), {\rm{cancel-ineg-aux}}\,({\it{x\/}}, {\rm{caddr}}\,({\it{y\/}}))\index{cancel-ineg-aux}) \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{cancel-ineg-aux}}\,({\it{x\/}}, {\rm{caddr}}\,({\it{y\/}}))\index{cancel-ineg-aux} \\ 
{\bf then }{\rm{list}}\,({\tt{'}}{\tt{iplus}}, {\rm{cadr}}\,({\it{y\/}}), {\rm{cancel-ineg-aux}}\,({\it{x\/}}, {\rm{caddr}}\,({\it{y\/}}))\index{cancel-ineg-aux}) \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{y\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{f}} \\ 
{\bf elseif }{\rm{car}}\,({\it{y\/}}) $=$ {\tt{'}}{\tt{ineg}} \\ 
{\bf then }\=\+{\bf if }{\it{x\/}} $=$ {\rm{cadr}}\,({\it{y\/}})$\;\;${\bf then }{\tt{'}}{\tt{'}}{\tt{0}} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{car}}\,({\it{y\/}}) $=$ {\tt{'}}{\tt{iplus}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{cadr}}\,({\it{y\/}})) \\ 
{\bf then }\=\+{\bf if }{\rm{caadr}}\,({\it{y\/}}) $=$ {\tt{'}}{\tt{ineg}} \\ 
{\bf then }\=\+{\bf if }{\it{x\/}} $=$ {\rm{cadadr}}\,({\it{y\/}})$\;\;${\bf then }{\rm{list}}\,({\tt{'}}{\tt{fix-int}}, {\rm{caddr}}\,({\it{y\/}})) \\ 
{\bf elseif }{\rm{cancel-ineg-aux}}\,({\it{x\/}}, {\rm{caddr}}\,({\it{y\/}}))\index{cancel-ineg-aux} \\ 
{\bf then }{\rm{list}}\,({\tt{'}}{\tt{iplus}}, {\rm{cadr}}\,({\it{y\/}}), {\rm{cancel-ineg-aux}}\,({\it{x\/}}, {\rm{caddr}}\,({\it{y\/}}))\index{cancel-ineg-aux}) \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{cancel-ineg-aux}}\,({\it{x\/}}, {\rm{caddr}}\,({\it{y\/}}))\index{cancel-ineg-aux} \\ 
{\bf then }{\rm{list}}\,({\tt{'}}{\tt{iplus}}, {\rm{cadr}}\,({\it{y\/}}), {\rm{cancel-ineg-aux}}\,({\it{x\/}}, {\rm{caddr}}\,({\it{y\/}}))\index{cancel-ineg-aux}) \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{cancel-ineg-aux}}\,({\it{x\/}}, {\rm{caddr}}\,({\it{y\/}}))\index{cancel-ineg-aux} \\ 
{\bf then }{\rm{list}}\,({\tt{'}}{\tt{iplus}}, {\rm{cadr}}\,({\it{y\/}}), {\rm{cancel-ineg-aux}}\,({\it{x\/}}, {\rm{caddr}}\,({\it{y\/}}))\index{cancel-ineg-aux}) \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cancel-ineg} \\  
\=\+{\rm{cancel-ineg}}\,({\it{x\/}})\index{cancel-ineg} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{iplus}} \\ 
{\bf then }\=\+{\bf if }{\rm{cancel-ineg-aux}}\,({\rm{cadr}}\,({\it{x\/}}), {\rm{caddr}}\,({\it{x\/}}))\index{cancel-ineg-aux} \\ 
{\bf then }{\rm{cancel-ineg-aux}}\,({\rm{cadr}}\,({\it{x\/}}), {\rm{caddr}}\,({\it{x\/}}))\index{cancel-ineg-aux} \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-list-cons \\ \index{eval\$-list-cons}
{\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{cons}}\,({\it{x\/}}, {\it{y\/}}), {\it{a\/}}) $=$ {\rm{cons}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}), {\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{y\/}}, {\it{a\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-list-nlistp \\ \index{eval\$-list-nlistp}
({\it{x\/}} $\simeq\;${{\bf{nil}}}${}$) $\rightarrow$ ({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}) $=$ {\bf{nil}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-litatom \\ \index{eval\$-litatom}
{\rm{litatom}}\,({\it{x\/}}) $\rightarrow$ ({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\rm{cdr}}\,({\rm{assoc}}\,({\it{x\/}}, {\it{a\/}})))
\end{tabbing}


\noindent{\sc Event}:   Disable eval\$-quote; name this event `eval\$-quote-on'.\index{eval\$-quote-on}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  eval\$-other \\ \index{eval\$-other}
(($\neg$ {\rm{litatom}}\,({\it{x\/}})) $\wedge$ ({\it{x\/}} $\simeq\;${{\bf{nil}}}${}$)) $\rightarrow$ ({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\it{x\/}})
\end{tabbing}


\noindent{\sc Event}:   Enable eval\$; name this event `eval\$-off'.\index{eval\$-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{eval\$-cancel-ineg-aux-fn} \\  
\=\+{\rm{eval\$-cancel-ineg-aux-fn}}\,({\it{x\/}}, {\it{y\/}}, {\it{a\/}})\index{eval\$-cancel-ineg-aux-fn} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) $\wedge$ ({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{ineg}}) \\ 
{\bf then }\=\+{\bf if }{\it{y\/}} $=$ {\rm{cadr}}\,({\it{x\/}})$\;\;${\bf then }{\tt{0}} \\ 
{\bf elseif }{\rm{cadr}}\,({\it{y\/}}) $=$ {\rm{cadr}}\,({\it{x\/}})$\;\;${\bf then }{\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\rm{caddr}}\,({\it{y\/}}), {\it{a\/}}))\index{fix-int} \\ 
{\bf elseif }{\rm{listp}}\,({\it{y\/}}) \\ 
{\bf then }{\rm{iplus}}\,(\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{cadr}}\,({\it{y\/}}), {\it{a\/}}), \\ 
{\rm{eval\$-cancel-ineg-aux-fn}}\,({\it{x\/}}, {\rm{caddr}}\,({\it{y\/}}), {\it{a\/}})\index{eval\$-cancel-ineg-aux-fn})\-\index{iplus} \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{car}}\,({\it{y\/}}) $=$ {\tt{'}}{\tt{ineg}}$\;\;${\bf then }{\tt{0}} \\ 
{\bf elseif }\=\+{\rm{listp}}\,({\rm{cadr}}\,({\it{y\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{caadr}}\,({\it{y\/}}) $=$ {\tt{'}}{\tt{ineg}}) \\ 
$\wedge$$\;\;\;\;$({\it{x\/}} $=$ {\rm{cadadr}}\,({\it{y\/}}))\-$\;\;${\bf then }{\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\rm{caddr}}\,({\it{y\/}}), {\it{a\/}}))\index{fix-int} \\ 
{\bf elseif }{\rm{listp}}\,({\it{y\/}}) \\ 
{\bf then }{\rm{iplus}}\,({\rm{eval\$}}\,({\bf{t}}, {\rm{cadr}}\,({\it{y\/}}), {\it{a\/}}), {\rm{eval\$-cancel-ineg-aux-fn}}\,({\it{x\/}}, {\rm{caddr}}\,({\it{y\/}}), {\it{a\/}})\index{eval\$-cancel-ineg-aux-fn})\index{iplus} \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-cancel-ineg-aux-is-its-fn \\ \index{eval\$-cancel-ineg-aux-is-its-f!n}
\=\+({\rm{cancel-ineg-aux}}\,({\it{x\/}}, {\it{y\/}})\index{cancel-ineg-aux} $\not=$ {\bf{f}}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\rm{cancel-ineg-aux}}\,({\it{x\/}}, {\it{y\/}})\index{cancel-ineg-aux}, {\it{a\/}}) $=$ {\rm{eval\$-cancel-ineg-aux-fn}}\,({\it{x\/}}, {\it{y\/}}, {\it{a\/}})\index{eval\$-cancel-ineg-aux-fn})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-ineg3 \\ \index{iplus-ineg3}
{\rm{iplus}}\,({\rm{ineg}}\,({\it{x\/}})\index{ineg}, {\rm{iplus}}\,({\it{x\/}}, {\it{y\/}})\index{iplus})\index{iplus} $=$ {\rm{fix-int}}\,({\it{y\/}})\index{fix-int}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-ineg4 \\ \index{iplus-ineg4}
{\rm{iplus}}\,({\it{x\/}}, {\rm{iplus}}\,({\rm{ineg}}\,({\it{x\/}})\index{ineg}, {\it{y\/}})\index{iplus})\index{iplus} $=$ {\rm{fix-int}}\,({\it{y\/}})\index{fix-int}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-ineg-promote \\ \index{iplus-ineg-promote}
{\rm{iplus}}\,({\it{y\/}}, {\rm{ineg}}\,({\it{x\/}})\index{ineg})\index{iplus} $=$ {\rm{iplus}}\,({\rm{ineg}}\,({\it{x\/}})\index{ineg}, {\it{y\/}})\index{iplus}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-x-y-ineg-x \\ \index{iplus-x-y-ineg-x}
{\rm{iplus}}\,({\it{x\/}}, {\rm{iplus}}\,({\it{y\/}}, {\rm{ineg}}\,({\it{x\/}})\index{ineg})\index{iplus})\index{iplus} $=$ {\rm{fix-int}}\,({\it{y\/}})\index{fix-int}
\end{tabbing}


\noindent{\sc Event}:   Enable iplus-ineg-promote; name this event `iplus-ineg-promote-off'.\index{iplus-ineg-promote-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-ineg-aux \\ \index{correctness-of-cancel-ineg-aux}
\=\+({\rm{cancel-ineg-aux}}\,({\it{x\/}}, {\it{y\/}})\index{cancel-ineg-aux} $\not=$ {\bf{f}}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{eval\$-cancel-ineg-aux-fn}}\,({\it{x\/}}, {\it{y\/}}, {\it{a\/}})\index{eval\$-cancel-ineg-aux-fn} $=$ {\rm{iplus}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}), {\rm{eval\$}}\,({\bf{t}}, {\it{y\/}}, {\it{a\/}}))\index{iplus})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-ineg \\ \index{correctness-of-cancel-ineg}
{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{cancel-ineg}}\,({\it{x\/}})\index{cancel-ineg}, {\it{a\/}})
\end{tabbing}


\noindent{\sc Event}:   Enable correctness-of-cancel-ineg-aux; name this event `correctness-of-cancel-ineg-aux-off'.\index{correctness-of-cancel-ineg-aux-!off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{iplus-fringe} \\  
\=\+{\rm{iplus-fringe}}\,({\it{x\/}})\index{iplus-fringe} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{iplus}} \\ 
{\bf then }{\rm{append}}\,({\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, {\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe}) \\ 
{\bf else }{\rm{list}}\,({\it{x\/}})$\;${\bf  endif}\- \\ 
{\bf else }{\rm{list}}\,({\it{x\/}})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-count-listp-cdr \\ \index{lessp-count-listp-cdr}
{\rm{listp}}\,({\rm{cdr}}\,({\it{x\/}})) $\rightarrow$ ({\rm{count}}\,({\rm{cdr}}\,({\it{x\/}})) $<$ {\rm{count}}\,({\it{x\/}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{iplus-tree-rec} \\  
\=\+{\rm{iplus-tree-rec}}\,({\it{l\/}})\index{iplus-tree-rec} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{cdr}}\,({\it{l\/}}) $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{car}}\,({\it{l\/}}) \\ 
{\bf else }{\rm{list}}\,({\tt{'}}{\tt{iplus}}, {\rm{car}}\,({\it{l\/}}), {\rm{iplus-tree-rec}}\,({\rm{cdr}}\,({\it{l\/}}))\index{iplus-tree-rec})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{iplus-tree} \\  
\=\+{\rm{iplus-tree}}\,({\it{l\/}})\index{iplus-tree} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{cdr}}\,({\it{l\/}}))$\;\;${\bf then }{\rm{iplus-tree-rec}}\,({\it{l\/}})\index{iplus-tree-rec} \\ 
{\bf else }{\rm{list}}\,({\tt{'}}{\tt{fix-int}}, {\rm{car}}\,({\it{l\/}}))$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{'}}{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{iplus-list} \\  
\=\+{\rm{iplus-list}}\,({\it{x\/}})\index{iplus-list} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}})$\;\;${\bf then }{\rm{iplus}}\,({\rm{car}}\,({\it{x\/}}), {\rm{iplus-list}}\,({\rm{cdr}}\,({\it{x\/}}))\index{iplus-list})\index{iplus} \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integerp-iplus-list \\ \index{integerp-iplus-list}
{\rm{integerp}}\,({\rm{iplus-list}}\,({\it{x\/}})\index{iplus-list})\index{integerp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-iplus-tree-rec \\ \index{eval\$-iplus-tree-rec}
\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{iplus-tree-rec}}\,({\it{x\/}})\index{iplus-tree-rec}, {\it{a\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{cdr}}\,({\it{x\/}}))$\;\;${\bf then }{\rm{iplus-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{iplus-list} \\ 
{\bf else }{\rm{eval\$}}\,({\bf{t}}, {\rm{car}}\,({\it{x\/}}), {\it{a\/}})$\;${\bf  endif}\- \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-iplus-tree \\ \index{eval\$-iplus-tree}
{\rm{eval\$}}\,({\bf{t}}, {\rm{iplus-tree}}\,({\it{x\/}})\index{iplus-tree}, {\it{a\/}}) $=$ {\rm{iplus-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{iplus-list}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-list-append \\ \index{eval\$-list-append}
\=\+{\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{append}}\,({\it{x\/}}, {\it{y\/}}), {\it{a\/}}) \\ 
$=$$\;\;\;\;${\rm{append}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}), {\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{y\/}}, {\it{a\/}}))\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cancel-iplus} \\  
\=\+{\rm{cancel-iplus}}\,({\it{x\/}})\index{cancel-iplus} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{equal}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{cadr}}\,({\it{x\/}})) \\ 
{\bf then }\=\+{\bf if }{\rm{caadr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{iplus}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{caddr}}\,({\it{x\/}})) \\ 
{\bf then }\=\+{\bf if }{\rm{caaddr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{iplus}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{bagint}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{bagint}) \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{iplus-tree}}\,({\rm{bagdiff}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{bagint})\-\index{bagdiff})\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{bagdiff}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{bagint})\-\index{bagdiff})\index{iplus-tree})\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{caddr}}\,({\it{x\/}}) $\in$ {\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{integerp}}, {\rm{caddr}}\,({\it{x\/}})), \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{cons}}\,(\=\+{\rm{iplus-tree}}\,({\rm{delete}}\,(\=\+{\rm{caddr}}\,({\it{x\/}}), \\ 
{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{delete})\index{iplus-tree}, \\ 
{\tt{'}}{\tt{(}}{\tt{'}}{\tt{0}}{\tt{)}})\-)\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{caddr}}\,({\it{x\/}}) $\in$ {\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{integerp}}, {\rm{caddr}}\,({\it{x\/}})), \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{cons}}\,(\=\+{\rm{iplus-tree}}\,({\rm{delete}}\,(\=\+{\rm{caddr}}\,({\it{x\/}}), \\ 
{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{delete})\index{iplus-tree}, \\ 
{\tt{'}}{\tt{(}}{\tt{'}}{\tt{0}}{\tt{)}})\-)\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{listp}}\,({\rm{caddr}}\,({\it{x\/}})) \\ 
{\bf then }\=\+{\bf if }{\rm{caaddr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{iplus}} \\ 
{\bf then }\=\+{\bf if }{\rm{cadr}}\,({\it{x\/}}) $\in$ {\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{integerp}}, {\rm{cadr}}\,({\it{x\/}})), \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\tt{'}}{\tt{'}}{\tt{0}}, \\ 
{\rm{iplus-tree}}\,({\rm{delete}}\,(\=\+{\rm{cadr}}\,({\it{x\/}}), \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{delete})\index{iplus-tree})\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{listp}}\,({\rm{caddr}}\,({\it{x\/}})) \\ 
{\bf then }\=\+{\bf if }{\rm{caaddr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{iplus}} \\ 
{\bf then }\=\+{\bf if }{\rm{cadr}}\,({\it{x\/}}) $\in$ {\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{integerp}}, {\rm{cadr}}\,({\it{x\/}})), \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\tt{'}}{\tt{'}}{\tt{0}}, \\ 
{\rm{iplus-tree}}\,({\rm{delete}}\,(\=\+{\rm{cadr}}\,({\it{x\/}}), \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{delete})\index{iplus-tree})\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-cancel-iplus \\ \index{eval\$-cancel-iplus}
\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{cancel-iplus}}\,({\it{x\/}})\index{cancel-iplus}, {\it{a\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) $\wedge$ ({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{equal}}) \\ 
{\bf then }\=\+{\bf if }\=\+{\rm{listp}}\,({\rm{cadr}}\,({\it{x\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{caadr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{iplus}}) \\ 
$\wedge$$\;\;\;\;${\rm{listp}}\,({\rm{caddr}}\,({\it{x\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{caaddr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{iplus}})\- \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{bagint}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{bagint}) \\ 
{\bf then }\=\+{\rm{iplus-list}}\,({\rm{eval\$}}\,(\=\+{\tt{'}}{\tt{list}}, \\ 
{\rm{bagdiff}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{bagint})\-\index{bagdiff}, \\ 
{\it{a\/}})\-)\index{iplus-list} \\ 
$=$$\;\;\;\;${\rm{iplus-list}}\,({\rm{eval\$}}\,(\=\+{\tt{'}}{\tt{list}}, \\ 
{\rm{bagdiff}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{bagint})\-\index{bagdiff}, \\ 
{\it{a\/}})\-)\index{iplus-list}\- \\ 
{\bf else }{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}})$\;${\bf  endif}\- \\ 
{\bf elseif }\=\+{\rm{listp}}\,({\rm{cadr}}\,({\it{x\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{caadr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{iplus}}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\it{x\/}}) $\in$ {\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe})\- \\ 
{\bf then }\=\+{\bf if }{\rm{integerp}}\,({\rm{eval\$}}\,({\bf{t}}, {\rm{caddr}}\,({\it{x\/}}), {\it{a\/}}))\index{integerp} \\ 
{\bf then }\=\+{\rm{iplus-list}}\,({\rm{eval\$}}\,(\=\+{\tt{'}}{\tt{list}}, \\ 
{\rm{delete}}\,({\rm{caddr}}\,({\it{x\/}}), {\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe})\index{delete}, \\ 
{\it{a\/}})\-)\index{iplus-list} \\ 
$=$$\;\;\;\;${\tt{0}}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }\=\+{\rm{listp}}\,({\rm{caddr}}\,({\it{x\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{caaddr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{iplus}}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadr}}\,({\it{x\/}}) $\in$ {\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\- \\ 
{\bf then }\=\+{\bf if }{\rm{integerp}}\,({\rm{eval\$}}\,({\bf{t}}, {\rm{cadr}}\,({\it{x\/}}), {\it{a\/}}))\index{integerp} \\ 
{\bf then }{\tt{0}} $=$ {\rm{iplus-list}}\,({\rm{eval\$}}\,(\=\+{\tt{'}}{\tt{list}}, \\ 
{\rm{delete}}\,(\=\+{\rm{cadr}}\,({\it{x\/}}), \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{delete}, \\ 
{\it{a\/}})\-)\index{iplus-list} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}})$\;${\bf  endif}\- \\ 
{\bf else }{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cancel-iplus; name this event `cancel-iplus-off'.\index{cancel-iplus-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  eval\$-iplus-list-delete \\ \index{eval\$-iplus-list-delete}
\=\+({\it{z\/}} $\in$ {\it{y\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{iplus-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{delete}}\,({\it{z\/}}, {\it{y\/}})\index{delete}, {\it{a\/}}))\index{iplus-list} \\ 
$=$$\;\;\;\;${\rm{idifference}}\,({\rm{iplus-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{y\/}}, {\it{a\/}}))\index{iplus-list}, {\rm{eval\$}}\,({\bf{t}}, {\it{z\/}}, {\it{a\/}}))\index{idifference})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-iplus-list-bagdiff \\ \index{eval\$-iplus-list-bagdiff}
\=\+{\rm{subbagp}}\,({\it{x\/}}, {\it{y\/}})\index{subbagp} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{iplus-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagdiff}}\,({\it{y\/}}, {\it{x\/}})\index{bagdiff}, {\it{a\/}}))\index{iplus-list} \\ 
$=$$\;\;\;\;${\rm{idifference}}\,(\=\+{\rm{iplus-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{y\/}}, {\it{a\/}}))\index{iplus-list}, \\ 
{\rm{iplus-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{iplus-list})\-\index{idifference})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-list-append \\ \index{iplus-list-append}
{\rm{iplus-list}}\,({\rm{append}}\,({\it{x\/}}, {\it{y\/}}))\index{iplus-list} $=$ {\rm{iplus}}\,({\rm{iplus-list}}\,({\it{x\/}})\index{iplus-list}, {\rm{iplus-list}}\,({\it{y\/}})\index{iplus-list})\index{iplus}
\end{tabbing}


\noindent{\sc Event}:   Enable iplus-tree; name this event `iplus-tree-off'.\index{iplus-tree-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-integerp-implies-not-equal-iplus \\ \index{not-integerp-implies-not-equal-ip!lus}
($\neg$ {\rm{integerp}}\,({\it{a\/}})\index{integerp}) $\rightarrow$ (({\it{a\/}} $=$ {\rm{iplus}}\,({\it{b\/}}, {\it{c\/}})\index{iplus}) $=$ {\bf{f}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-list-eval\$-fringe \\ \index{iplus-list-eval\$-fringe}
{\rm{iplus-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{iplus-fringe}}\,({\it{x\/}})\index{iplus-fringe}, {\it{a\/}}))\index{iplus-list} $=$ {\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}))\index{fix-int}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-ineg5-lemma-1 \\ \index{iplus-ineg5-lemma-1}
\=\+{\rm{integerp}}\,({\it{x\/}})\index{integerp} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\it{x\/}} $=$ {\rm{iplus}}\,({\it{y\/}}, {\rm{iplus}}\,({\rm{ineg}}\,({\it{z\/}})\index{ineg}, {\it{w\/}})\index{iplus})\index{iplus}) \\ 
$=$$\;\;\;\;$({\it{x\/}} $=$ {\rm{iplus}}\,({\rm{ineg}}\,({\it{z\/}})\index{ineg}, {\rm{iplus}}\,({\it{y\/}}, {\it{w\/}})\index{iplus})\index{iplus}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-ineg5-lemma-2 \\ \index{iplus-ineg5-lemma-2}
\=\+({\rm{integerp}}\,({\it{x\/}})\index{integerp} $\wedge$ {\rm{integerp}}\,({\it{v\/}})\index{integerp}) \\ 
$\rightarrow$$\;\;\;\;$(({\it{x\/}} $=$ {\rm{iplus}}\,({\rm{ineg}}\,({\it{z\/}})\index{ineg}, {\it{v\/}})\index{iplus}) $=$ ({\rm{iplus}}\,({\it{x\/}}, {\it{z\/}})\index{iplus} $=$ {\it{v\/}}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-ineg5 \\ \index{iplus-ineg5}
\=\+{\rm{integerp}}\,({\it{x\/}})\index{integerp} \\ 
$\rightarrow$$\;\;\;\;$(({\it{x\/}} $=$ {\rm{iplus}}\,({\it{y\/}}, {\rm{iplus}}\,({\rm{ineg}}\,({\it{z\/}})\index{ineg}, {\it{w\/}})\index{iplus})\index{iplus}) $=$ ({\rm{iplus}}\,({\it{x\/}}, {\it{z\/}})\index{iplus} $=$ {\rm{iplus}}\,({\it{y\/}}, {\it{w\/}})\index{iplus}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable iplus-ineg5-lemma-1; name this event `iplus-ineg5-lemma-1-off'.\index{iplus-ineg5-lemma-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-ineg5-lemma-2; name this event `iplus-ineg5-lemma-2-off'.\index{iplus-ineg5-lemma-2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  iplus-ineg6 \\ \index{iplus-ineg6}
\=\+{\rm{integerp}}\,({\it{x\/}})\index{integerp} \\ 
$\rightarrow$$\;\;\;\;$(({\it{x\/}} $=$ {\rm{iplus}}\,({\it{y\/}}, {\rm{iplus}}\,({\it{w\/}}, {\rm{ineg}}\,({\it{z\/}})\index{ineg})\index{iplus})\index{iplus}) $=$ ({\rm{iplus}}\,({\it{x\/}}, {\it{z\/}})\index{iplus} $=$ {\rm{iplus}}\,({\it{y\/}}, {\it{w\/}})\index{iplus}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-iplus \\ \index{eval\$-iplus}
\=\+({\rm{listp}}\,({\it{x\/}}) $\wedge$ ({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{iplus}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\rm{iplus}}\,({\rm{eval\$}}\,({\bf{t}}, {\rm{cadr}}\,({\it{x\/}}), {\it{a\/}}), {\rm{eval\$}}\,({\bf{t}}, {\rm{caddr}}\,({\it{x\/}}), {\it{a\/}}))\index{iplus})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-ineg7 \\ \index{iplus-ineg7}
({\tt{0}} $=$ {\rm{iplus}}\,({\it{x\/}}, {\rm{ineg}}\,({\it{y\/}})\index{ineg})\index{iplus}) $=$ ({\rm{fix-int}}\,({\it{y\/}})\index{fix-int} $=$ {\rm{fix-int}}\,({\it{x\/}})\index{fix-int})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-iplus \\ \index{correctness-of-cancel-iplus}
{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{cancel-iplus}}\,({\it{x\/}})\index{cancel-iplus}, {\it{a\/}})
\end{tabbing}


\noindent{\sc Event}:   Enable iplus-ineg5; name this event `iplus-ineg5-off'.\index{iplus-ineg5-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-ineg6; name this event `iplus-ineg6-off'.\index{iplus-ineg6-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ilessp-fix-int-1 \\ \index{ilessp-fix-int-1}
{\rm{ilessp}}\,({\rm{fix-int}}\,({\it{x\/}})\index{fix-int}, {\it{y\/}})\index{ilessp} $=$ {\rm{ilessp}}\,({\it{x\/}}, {\it{y\/}})\index{ilessp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ilessp-fix-int-2 \\ \index{ilessp-fix-int-2}
{\rm{ilessp}}\,({\it{x\/}}, {\rm{fix-int}}\,({\it{y\/}})\index{fix-int})\index{ilessp} $=$ {\rm{ilessp}}\,({\it{x\/}}, {\it{y\/}})\index{ilessp}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{make-cancel-iplus-inequality-1} \\  
\=\+{\rm{make-cancel-iplus-inequality-1}}\,({\it{x\/}}, {\it{y\/}})\index{make-cancel-iplus-inequality-1} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\tt{'}}{\tt{ilessp}}, \\ 
{\rm{iplus-tree}}\,({\rm{bagdiff}}\,({\it{x\/}}, {\rm{bagint}}\,({\it{x\/}}, {\it{y\/}})\index{bagint})\index{bagdiff})\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{bagdiff}}\,({\it{y\/}}, {\rm{bagint}}\,({\it{x\/}}, {\it{y\/}})\index{bagint})\index{bagdiff})\index{iplus-tree})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cancel-iplus-ilessp-1} \\  
\=\+{\rm{cancel-iplus-ilessp-1}}\,({\it{x\/}})\index{cancel-iplus-ilessp-1} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{ilessp}} \\ 
{\bf then }{\rm{make-cancel-iplus-inequality-1}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{make-cancel-iplus-inequality-1} \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-difference-plus-arg1 \\ \index{lessp-difference-plus-arg1}
({\it{w\/}} $<$ (({\it{w\/}} $+$ {\it{y\/}}) $-$ {\it{x\/}})) $=$ ({\it{x\/}} $<$ {\it{y\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-difference-plus-arg1-commuted \\ \index{lessp-difference-plus-arg1-comm!uted}
({\it{w\/}} $<$ (({\it{y\/}} $+$ {\it{w\/}}) $-$ {\it{x\/}})) $=$ ({\it{x\/}} $<$ {\it{y\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-cancellation-1-for-ilessp \\ \index{iplus-cancellation-1-for-ilessp}
{\rm{ilessp}}\,({\rm{iplus}}\,({\it{a\/}}, {\it{b\/}})\index{iplus}, {\rm{iplus}}\,({\it{a\/}}, {\it{c\/}})\index{iplus})\index{ilessp} $=$ {\rm{ilessp}}\,({\it{b\/}}, {\it{c\/}})\index{ilessp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-cancellation-2-for-ilessp \\ \index{iplus-cancellation-2-for-ilessp}
{\rm{ilessp}}\,({\rm{iplus}}\,({\it{b\/}}, {\it{a\/}})\index{iplus}, {\rm{iplus}}\,({\it{c\/}}, {\it{a\/}})\index{iplus})\index{ilessp} $=$ {\rm{ilessp}}\,({\it{b\/}}, {\it{c\/}})\index{ilessp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-iplus-ilessp-lemma \\ \index{correctness-of-cancel-iplus-ile!ssp-lemma}
{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{cancel-iplus-ilessp-1}}\,({\it{x\/}})\index{cancel-iplus-ilessp-1}, {\it{a\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{iplus-tree-no-fix-int} \\  
\=\+{\rm{iplus-tree-no-fix-int}}\,({\it{l\/}})\index{iplus-tree-no-fix-int} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}})$\;\;${\bf then }{\rm{iplus-tree-rec}}\,({\it{l\/}})\index{iplus-tree-rec} \\ 
{\bf else }{\tt{'}}{\tt{'}}{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-ilessp-iplus-tree-no-fix-int \\ \index{eval\$-ilessp-iplus-tree-no-fix!-int}
\=\+{\rm{ilessp}}\,(\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{iplus-tree-no-fix-int}}\,({\it{x\/}})\index{iplus-tree-no-fix-int}, {\it{a\/}}), \\ 
{\rm{eval\$}}\,({\bf{t}}, {\rm{iplus-tree-no-fix-int}}\,({\it{y\/}})\index{iplus-tree-no-fix-int}, {\it{a\/}}))\-\index{ilessp} \\ 
$=$$\;\;\;\;${\rm{ilessp}}\,({\rm{eval\$}}\,({\bf{t}}, {\rm{iplus-tree}}\,({\it{x\/}})\index{iplus-tree}, {\it{a\/}}), {\rm{eval\$}}\,({\bf{t}}, {\rm{iplus-tree}}\,({\it{y\/}})\index{iplus-tree}, {\it{a\/}}))\index{ilessp}\-
\end{tabbing}


\noindent{\sc Event}:   Enable iplus-tree-no-fix-int; name this event `iplus-tree-no-fix-int-off'.\index{iplus-tree-no-fix-int-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  make-cancel-iplus-inequality-simplifier \\ \index{make-cancel-iplus-inequality-si!mplifier}
\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{make-cancel-iplus-inequality-1}}\,({\it{x\/}}, {\it{y\/}})\index{make-cancel-iplus-inequality-1}, {\it{a\/}}) \\ 
$=$$\;\;\;\;${\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{ilessp}}, \\ 
{\rm{iplus-tree-no-fix-int}}\,({\rm{bagdiff}}\,({\it{x\/}}, {\rm{bagint}}\,({\it{x\/}}, {\it{y\/}})\index{bagint})\index{bagdiff})\index{iplus-tree-no-fix-int}, \\ 
{\rm{iplus-tree-no-fix-int}}\,({\rm{bagdiff}}\,({\it{y\/}}, {\rm{bagint}}\,({\it{x\/}}, {\it{y\/}})\index{bagint})\index{bagdiff})\index{iplus-tree-no-fix-int})\-, \\ 
{\it{a\/}})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cancel-iplus-ilessp} \\  
\=\+{\rm{cancel-iplus-ilessp}}\,({\it{x\/}})\index{cancel-iplus-ilessp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{ilessp}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{bagint}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{bagint}) \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{ilessp}}, \\ 
{\rm{iplus-tree-no-fix-int}}\,({\rm{bagdiff}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{bagint})\-\index{bagdiff})\index{iplus-tree-no-fix-int}, \\ 
{\rm{iplus-tree-no-fix-int}}\,({\rm{bagdiff}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{bagint})\-\index{bagdiff})\index{iplus-tree-no-fix-int})\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable make-cancel-iplus-inequality-1; name this event `make-cancel-iplus-inequality-1-off'.\index{make-cancel-iplus-inequality-1-!off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-iplus-ilessp \\ \index{correctness-of-cancel-iplus-ile!ssp}
{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{cancel-iplus-ilessp}}\,({\it{x\/}})\index{cancel-iplus-ilessp}, {\it{a\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-zero1 \\ \index{itimes-zero1}
({\rm{fix-int}}\,({\it{x\/}})\index{fix-int} $=$ {\tt{0}}) $\rightarrow$ ({\rm{itimes}}\,({\it{x\/}}, {\it{y\/}})\index{itimes} $=$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-0-left \\ \index{itimes-0-left}
{\rm{itimes}}\,({\tt{0}}, {\it{y\/}})\index{itimes} $=$ {\tt{0}}
\end{tabbing}


\noindent{\sc Event}:   Enable itimes-zero1; name this event `itimes-zero1-off'.\index{itimes-zero1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  itimes-zero2 \\ \index{itimes-zero2}
({\rm{fix-int}}\,({\it{y\/}})\index{fix-int} $=$ {\tt{0}}) $\rightarrow$ ({\rm{itimes}}\,({\it{x\/}}, {\it{y\/}})\index{itimes} $=$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-0-right \\ \index{itimes-0-right}
{\rm{itimes}}\,({\it{x\/}}, {\tt{0}})\index{itimes} $=$ {\tt{0}}
\end{tabbing}


\noindent{\sc Event}:   Enable itimes-zero2; name this event `itimes-zero2-off'.\index{itimes-zero2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  itimes-fix-int1 \\ \index{itimes-fix-int1}
{\rm{itimes}}\,({\rm{fix-int}}\,({\it{a\/}})\index{fix-int}, {\it{b\/}})\index{itimes} $=$ {\rm{itimes}}\,({\it{a\/}}, {\it{b\/}})\index{itimes}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-fix-int2 \\ \index{itimes-fix-int2}
{\rm{itimes}}\,({\it{a\/}}, {\rm{fix-int}}\,({\it{b\/}})\index{fix-int})\index{itimes} $=$ {\rm{itimes}}\,({\it{a\/}}, {\it{b\/}})\index{itimes}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  commutativity-of-itimes \\ \index{commutativity-of-itimes}
{\rm{itimes}}\,({\it{x\/}}, {\it{y\/}})\index{itimes} $=$ {\rm{itimes}}\,({\it{y\/}}, {\it{x\/}})\index{itimes}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-distributes-over-iplus-proof \\ \index{itimes-distributes-over-iplus-p!roof}
{\rm{itimes}}\,({\it{x\/}}, {\rm{iplus}}\,({\it{y\/}}, {\it{z\/}})\index{iplus})\index{itimes} $=$ {\rm{iplus}}\,({\rm{itimes}}\,({\it{x\/}}, {\it{y\/}})\index{itimes}, {\rm{itimes}}\,({\it{x\/}}, {\it{z\/}})\index{itimes})\index{iplus}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-distributes-over-iplus \\ \index{itimes-distributes-over-iplus}
\=\+({\rm{itimes}}\,({\it{x\/}}, {\rm{iplus}}\,({\it{y\/}}, {\it{z\/}})\index{iplus})\index{itimes} $=$ {\rm{iplus}}\,({\rm{itimes}}\,({\it{x\/}}, {\it{y\/}})\index{itimes}, {\rm{itimes}}\,({\it{x\/}}, {\it{z\/}})\index{itimes})\index{iplus}) \\ 
$\wedge$$\;\;\;\;$({\rm{itimes}}\,({\rm{iplus}}\,({\it{x\/}}, {\it{y\/}})\index{iplus}, {\it{z\/}})\index{itimes} $=$ {\rm{iplus}}\,({\rm{itimes}}\,({\it{x\/}}, {\it{z\/}})\index{itimes}, {\rm{itimes}}\,({\it{y\/}}, {\it{z\/}})\index{itimes})\index{iplus})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  commutativity2-of-itimes \\ \index{commutativity2-of-itimes}
{\rm{itimes}}\,({\it{x\/}}, {\rm{itimes}}\,({\it{y\/}}, {\it{z\/}})\index{itimes})\index{itimes} $=$ {\rm{itimes}}\,({\it{y\/}}, {\rm{itimes}}\,({\it{x\/}}, {\it{z\/}})\index{itimes})\index{itimes}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  associativity-of-itimes \\ \index{associativity-of-itimes}
{\rm{itimes}}\,({\rm{itimes}}\,({\it{x\/}}, {\it{y\/}})\index{itimes}, {\it{z\/}})\index{itimes} $=$ {\rm{itimes}}\,({\it{x\/}}, {\rm{itimes}}\,({\it{y\/}}, {\it{z\/}})\index{itimes})\index{itimes}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-itimes-0 \\ \index{equal-itimes-0}
({\rm{itimes}}\,({\it{x\/}}, {\it{y\/}})\index{itimes} $=$ {\tt{0}}) $=$ (({\rm{fix-int}}\,({\it{x\/}})\index{fix-int} $=$ {\tt{0}}) $\vee$ ({\rm{fix-int}}\,({\it{y\/}})\index{fix-int} $=$ {\tt{0}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-itimes-1 \\ \index{equal-itimes-1}
\=\+({\rm{itimes}}\,({\it{a\/}}, {\it{b\/}})\index{itimes} $=$ {\tt{1}}) \\ 
$=$$\;\;\;\;$((({\it{a\/}} $=$ {\tt{1}}) $\wedge$ ({\it{b\/}} $=$ {\tt{1}})) $\vee$ (({\it{a\/}} $=$ {\tt{-1}}) $\wedge$ ({\it{b\/}} $=$ {\tt{-1}})))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-itimes-minus-1 \\ \index{equal-itimes-minus-1}
\=\+({\rm{itimes}}\,({\it{a\/}}, {\it{b\/}})\index{itimes} $=$ {\tt{-1}}) \\ 
$=$$\;\;\;\;$((({\it{a\/}} $=$ {\tt{-1}}) $\wedge$ ({\it{b\/}} $=$ {\tt{1}})) $\vee$ (({\it{a\/}} $=$ {\tt{1}}) $\wedge$ ({\it{b\/}} $=$ {\tt{-1}})))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-1-arg1 \\ \index{itimes-1-arg1}
{\rm{itimes}}\,({\tt{1}}, {\it{x\/}})\index{itimes} $=$ {\rm{fix-int}}\,({\it{x\/}})\index{fix-int}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-remainder-uniqueness \\ \index{quotient-remainder-uniqueness}
\=\+(({\it{a\/}} $=$ ({\it{r\/}} $+$ ({\it{b\/}} $*$ {\it{q\/}}))) $\wedge$ ({\it{r\/}} $<$ {\it{b\/}})) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{fix}}\,({\it{r\/}}) $=$ ({\it{a\/}} ${}${\bf{mod}}${}$ {\it{b\/}})) $\wedge$ ({\rm{fix}}\,({\it{q\/}}) $=$ ({\it{a\/}} $\div$ {\it{b\/}})))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  division-theorem-part1 \\ \index{division-theorem-part1}
{\rm{integerp}}\,({\it{i\/}})\index{integerp} $\rightarrow$ ({\rm{iplus}}\,({\rm{iremainder}}\,({\it{i\/}}, {\it{j\/}})\index{iremainder}, {\rm{itimes}}\,({\it{j\/}}, {\rm{iquotient}}\,({\it{i\/}}, {\it{j\/}})\index{iquotient})\index{itimes})\index{iplus} $=$ {\it{i\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  division-theorem-part2 \\ \index{division-theorem-part2}
({\rm{integerp}}\,({\it{j\/}})\index{integerp} $\wedge$ ({\it{j\/}} $\not=$ {\tt{0}})) $\rightarrow$ ($\neg$ {\rm{ilessp}}\,({\rm{iremainder}}\,({\it{i\/}}, {\it{j\/}})\index{iremainder}, {\tt{0}})\index{ilessp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  division-theorem-part3 \\ \index{division-theorem-part3}
({\rm{integerp}}\,({\it{j\/}})\index{integerp} $\wedge$ ({\it{j\/}} $\not=$ {\tt{0}})) $\rightarrow$ {\rm{ilessp}}\,({\rm{iremainder}}\,({\it{i\/}}, {\it{j\/}})\index{iremainder}, {\rm{iabs}}\,({\it{j\/}})\index{iabs})\index{ilessp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  division-theorem \\ \index{division-theorem}
\=\+({\rm{integerp}}\,({\it{i\/}})\index{integerp} $\wedge$ {\rm{integerp}}\,({\it{j\/}})\index{integerp} $\wedge$ ({\it{j\/}} $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{iplus}}\,({\rm{iremainder}}\,({\it{i\/}}, {\it{j\/}})\index{iremainder}, {\rm{itimes}}\,({\it{j\/}}, {\rm{iquotient}}\,({\it{i\/}}, {\it{j\/}})\index{iquotient})\index{itimes})\index{iplus} $=$ {\it{i\/}}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{ilessp}}\,({\rm{iremainder}}\,({\it{i\/}}, {\it{j\/}})\index{iremainder}, {\tt{0}})\index{ilessp}) \\ 
$\wedge$$\;\;\;\;${\rm{ilessp}}\,({\rm{iremainder}}\,({\it{i\/}}, {\it{j\/}})\index{iremainder}, {\rm{iabs}}\,({\it{j\/}})\index{iabs})\index{ilessp})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-difference-lessp-arg2 \\ \index{quotient-difference-lessp-arg2}
\=\+((({\it{a\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ {\tt{0}}) $\wedge$ ({\it{b\/}} $<$ {\it{c\/}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(({\it{a\/}} $-$ {\it{b\/}}) $\div$ {\it{c\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{b\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\it{a\/}} $\div$ {\it{c\/}} \\ 
{\bf elseif }{\it{b\/}} $<$ {\it{a\/}}$\;\;${\bf then }({\it{a\/}} $\div$ {\it{c\/}}) $-$ ($1\;+$ ({\it{b\/}} $\div$ {\it{c\/}})) \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iquotient-iremainder-uniqueness \\ \index{iquotient-iremainder-uniqueness}
\=\+(\=\+{\rm{integerp}}\,({\it{i\/}})\index{integerp} \\ 
$\wedge$$\;\;\;\;${\rm{integerp}}\,({\it{j\/}})\index{integerp} \\ 
$\wedge$$\;\;\;\;${\rm{integerp}}\,({\it{r\/}})\index{integerp} \\ 
$\wedge$$\;\;\;\;${\rm{integerp}}\,({\it{q\/}})\index{integerp} \\ 
$\wedge$$\;\;\;\;$({\it{j\/}} $\not=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\it{i\/}} $=$ {\rm{iplus}}\,({\it{r\/}}, {\rm{itimes}}\,({\it{j\/}}, {\it{q\/}})\index{itimes})\index{iplus}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{ilessp}}\,({\it{r\/}}, {\tt{0}})\index{ilessp}) \\ 
$\wedge$$\;\;\;\;${\rm{ilessp}}\,({\it{r\/}}, {\rm{iabs}}\,({\it{j\/}})\index{iabs})\index{ilessp})\- \\ 
$\rightarrow$$\;\;\;\;$(({\it{r\/}} $=$ {\rm{iremainder}}\,({\it{i\/}}, {\it{j\/}})\index{iremainder}) $\wedge$ ({\it{q\/}} $=$ {\rm{iquotient}}\,({\it{i\/}}, {\it{j\/}})\index{iquotient}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  division-theorem-for-truncate-to-neginf-part1 \\ \index{division-theorem-for-truncate-t!o-neginf-part1}
{\rm{integerp}}\,({\it{i\/}})\index{integerp} $\rightarrow$ ({\rm{iplus}}\,({\rm{imod}}\,({\it{i\/}}, {\it{j\/}})\index{imod}, {\rm{itimes}}\,({\it{j\/}}, {\rm{idiv}}\,({\it{i\/}}, {\it{j\/}})\index{idiv})\index{itimes})\index{iplus} $=$ {\it{i\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  division-theorem-for-truncate-to-neginf-part2 \\ \index{division-theorem-for-truncate-t!o-neginf-part2}
{\rm{ilessp}}\,({\tt{0}}, {\it{j\/}})\index{ilessp} $\rightarrow$ (($\neg$ {\rm{ilessp}}\,({\rm{imod}}\,({\it{i\/}}, {\it{j\/}})\index{imod}, {\tt{0}})\index{ilessp}) $\wedge$ {\rm{ilessp}}\,({\rm{imod}}\,({\it{i\/}}, {\it{j\/}})\index{imod}, {\it{j\/}})\index{ilessp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  division-theorem-for-truncate-to-neginf-part3 \\ \index{division-theorem-for-truncate-t!o-neginf-part3}
\=\+({\rm{integerp}}\,({\it{j\/}})\index{integerp} $\wedge$ {\rm{ilessp}}\,({\it{j\/}}, {\tt{0}})\index{ilessp}) \\ 
$\rightarrow$$\;\;\;\;$(($\neg$ {\rm{ilessp}}\,({\tt{0}}, {\rm{imod}}\,({\it{i\/}}, {\it{j\/}})\index{imod})\index{ilessp}) $\wedge$ {\rm{ilessp}}\,({\it{j\/}}, {\rm{imod}}\,({\it{i\/}}, {\it{j\/}})\index{imod})\index{ilessp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  division-theorem-for-truncate-to-neginf \\ \index{division-theorem-for-truncate-t!o-neginf}
\=\+({\rm{integerp}}\,({\it{i\/}})\index{integerp} $\wedge$ {\rm{integerp}}\,({\it{j\/}})\index{integerp} $\wedge$ ({\it{j\/}} $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{iplus}}\,({\rm{imod}}\,({\it{i\/}}, {\it{j\/}})\index{imod}, {\rm{itimes}}\,({\it{j\/}}, {\rm{idiv}}\,({\it{i\/}}, {\it{j\/}})\index{idiv})\index{itimes})\index{iplus} $=$ {\it{i\/}}) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{ilessp}}\,({\tt{0}}, {\it{j\/}})\index{ilessp} \\ 
{\bf then }($\neg$ {\rm{ilessp}}\,({\rm{imod}}\,({\it{i\/}}, {\it{j\/}})\index{imod}, {\tt{0}})\index{ilessp}) $\wedge$ {\rm{ilessp}}\,({\rm{imod}}\,({\it{i\/}}, {\it{j\/}})\index{imod}, {\it{j\/}})\index{ilessp} \\ 
{\bf else }\=\+($\neg$ {\rm{ilessp}}\,({\tt{0}}, {\rm{imod}}\,({\it{i\/}}, {\it{j\/}})\index{imod})\index{ilessp}) \\ 
$\wedge$$\;\;\;\;${\rm{ilessp}}\,({\it{j\/}}, {\rm{imod}}\,({\it{i\/}}, {\it{j\/}})\index{imod})\index{ilessp}\-$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  idiv-imod-uniqueness \\ \index{idiv-imod-uniqueness}
\=\+(\=\+{\rm{integerp}}\,({\it{i\/}})\index{integerp} \\ 
$\wedge$$\;\;\;\;${\rm{integerp}}\,({\it{j\/}})\index{integerp} \\ 
$\wedge$$\;\;\;\;${\rm{integerp}}\,({\it{r\/}})\index{integerp} \\ 
$\wedge$$\;\;\;\;${\rm{integerp}}\,({\it{q\/}})\index{integerp} \\ 
$\wedge$$\;\;\;\;$({\it{j\/}} $\not=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\it{i\/}} $=$ {\rm{iplus}}\,({\it{r\/}}, {\rm{itimes}}\,({\it{j\/}}, {\it{q\/}})\index{itimes})\index{iplus}) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{ilessp}}\,({\tt{0}}, {\it{j\/}})\index{ilessp}$\;\;${\bf then }($\neg$ {\rm{ilessp}}\,({\it{r\/}}, {\tt{0}})\index{ilessp}) $\wedge$ {\rm{ilessp}}\,({\it{r\/}}, {\it{j\/}})\index{ilessp} \\ 
{\bf else }($\neg$ {\rm{ilessp}}\,({\tt{0}}, {\it{r\/}})\index{ilessp}) $\wedge$ {\rm{ilessp}}\,({\it{j\/}}, {\it{r\/}})\index{ilessp}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$(({\it{r\/}} $=$ {\rm{imod}}\,({\it{i\/}}, {\it{j\/}})\index{imod}) $\wedge$ ({\it{q\/}} $=$ {\rm{idiv}}\,({\it{i\/}}, {\it{j\/}})\index{idiv}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  division-theorem-for-truncate-to-zero-part1 \\ \index{division-theorem-for-truncate-t!o-zero-part1}
{\rm{integerp}}\,({\it{i\/}})\index{integerp} $\rightarrow$ ({\rm{iplus}}\,({\rm{irem}}\,({\it{i\/}}, {\it{j\/}})\index{irem}, {\rm{itimes}}\,({\it{j\/}}, {\rm{iquo}}\,({\it{i\/}}, {\it{j\/}})\index{iquo})\index{itimes})\index{iplus} $=$ {\it{i\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  division-theorem-for-truncate-to-zero-part2 \\ \index{division-theorem-for-truncate-t!o-zero-part2}
\=\+({\rm{integerp}}\,({\it{i\/}})\index{integerp} $\wedge$ {\rm{integerp}}\,({\it{j\/}})\index{integerp} $\wedge$ ({\it{j\/}} $\not=$ {\tt{0}}) $\wedge$ ($\neg$ {\rm{ilessp}}\,({\it{i\/}}, {\tt{0}})\index{ilessp})) \\ 
$\rightarrow$$\;\;\;\;$(($\neg$ {\rm{ilessp}}\,({\rm{irem}}\,({\it{i\/}}, {\it{j\/}})\index{irem}, {\tt{0}})\index{ilessp}) $\wedge$ {\rm{ilessp}}\,({\rm{irem}}\,({\it{i\/}}, {\it{j\/}})\index{irem}, {\rm{iabs}}\,({\it{j\/}})\index{iabs})\index{ilessp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  division-theorem-for-truncate-to-zero-part3 \\ \index{division-theorem-for-truncate-t!o-zero-part3}
\=\+({\rm{integerp}}\,({\it{i\/}})\index{integerp} $\wedge$ {\rm{integerp}}\,({\it{j\/}})\index{integerp} $\wedge$ ({\it{j\/}} $\not=$ {\tt{0}}) $\wedge$ {\rm{ilessp}}\,({\it{i\/}}, {\tt{0}})\index{ilessp}) \\ 
$\rightarrow$$\;\;\;\;$(($\neg$ {\rm{ilessp}}\,({\tt{0}}, {\rm{irem}}\,({\it{i\/}}, {\it{j\/}})\index{irem})\index{ilessp}) $\wedge$ {\rm{ilessp}}\,({\rm{ineg}}\,({\rm{iabs}}\,({\it{j\/}})\index{iabs})\index{ineg}, {\rm{irem}}\,({\it{i\/}}, {\it{j\/}})\index{irem})\index{ilessp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  division-theorem-for-truncate-to-zero \\ \index{division-theorem-for-truncate-t!o-zero}
\=\+({\rm{integerp}}\,({\it{i\/}})\index{integerp} $\wedge$ {\rm{integerp}}\,({\it{j\/}})\index{integerp} $\wedge$ ({\it{j\/}} $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{iplus}}\,({\rm{irem}}\,({\it{i\/}}, {\it{j\/}})\index{irem}, {\rm{itimes}}\,({\it{j\/}}, {\rm{iquo}}\,({\it{i\/}}, {\it{j\/}})\index{iquo})\index{itimes})\index{iplus} $=$ {\it{i\/}}) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }$\neg$ {\rm{ilessp}}\,({\it{i\/}}, {\tt{0}})\index{ilessp} \\ 
{\bf then }\=\+($\neg$ {\rm{ilessp}}\,({\rm{irem}}\,({\it{i\/}}, {\it{j\/}})\index{irem}, {\tt{0}})\index{ilessp}) \\ 
$\wedge$$\;\;\;\;${\rm{ilessp}}\,({\rm{irem}}\,({\it{i\/}}, {\it{j\/}})\index{irem}, {\rm{iabs}}\,({\it{j\/}})\index{iabs})\index{ilessp}\- \\ 
{\bf else }\=\+($\neg$ {\rm{ilessp}}\,({\tt{0}}, {\rm{irem}}\,({\it{i\/}}, {\it{j\/}})\index{irem})\index{ilessp}) \\ 
$\wedge$$\;\;\;\;${\rm{ilessp}}\,({\rm{ineg}}\,({\rm{iabs}}\,({\it{j\/}})\index{iabs})\index{ineg}, {\rm{irem}}\,({\it{i\/}}, {\it{j\/}})\index{irem})\index{ilessp}\-$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iquo-irem-uniqueness \\ \index{iquo-irem-uniqueness}
\=\+(\=\+{\rm{integerp}}\,({\it{i\/}})\index{integerp} \\ 
$\wedge$$\;\;\;\;${\rm{integerp}}\,({\it{j\/}})\index{integerp} \\ 
$\wedge$$\;\;\;\;${\rm{integerp}}\,({\it{r\/}})\index{integerp} \\ 
$\wedge$$\;\;\;\;${\rm{integerp}}\,({\it{q\/}})\index{integerp} \\ 
$\wedge$$\;\;\;\;$({\it{j\/}} $\not=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\it{i\/}} $=$ {\rm{iplus}}\,({\it{r\/}}, {\rm{itimes}}\,({\it{j\/}}, {\it{q\/}})\index{itimes})\index{iplus}) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }$\neg$ {\rm{ilessp}}\,({\it{i\/}}, {\tt{0}})\index{ilessp}$\;\;${\bf then }($\neg$ {\rm{ilessp}}\,({\it{r\/}}, {\tt{0}})\index{ilessp}) $\wedge$ {\rm{ilessp}}\,({\it{r\/}}, {\rm{iabs}}\,({\it{j\/}})\index{iabs})\index{ilessp} \\ 
{\bf else }($\neg$ {\rm{ilessp}}\,({\tt{0}}, {\it{r\/}})\index{ilessp}) $\wedge$ {\rm{ilessp}}\,({\rm{ineg}}\,({\rm{iabs}}\,({\it{j\/}})\index{iabs})\index{ineg}, {\it{r\/}})\index{ilessp}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$(({\it{r\/}} $=$ {\rm{irem}}\,({\it{i\/}}, {\it{j\/}})\index{irem}) $\wedge$ ({\it{q\/}} $=$ {\rm{iquo}}\,({\it{i\/}}, {\it{j\/}})\index{iquo}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-ineg-1 \\ \index{itimes-ineg-1}
{\rm{itimes}}\,({\rm{ineg}}\,({\it{x\/}})\index{ineg}, {\it{y\/}})\index{itimes} $=$ {\rm{ineg}}\,({\rm{itimes}}\,({\it{x\/}}, {\it{y\/}})\index{itimes})\index{ineg}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-ineg-2 \\ \index{itimes-ineg-2}
{\rm{itimes}}\,({\it{x\/}}, {\rm{ineg}}\,({\it{y\/}})\index{ineg})\index{itimes} $=$ {\rm{ineg}}\,({\rm{itimes}}\,({\it{x\/}}, {\it{y\/}})\index{itimes})\index{ineg}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-cancellation-1 \\ \index{itimes-cancellation-1}
\=\+({\rm{itimes}}\,({\it{a\/}}, {\it{b\/}})\index{itimes} $=$ {\rm{itimes}}\,({\it{a\/}}, {\it{c\/}})\index{itimes}) \\ 
$=$$\;\;\;\;$(({\rm{fix-int}}\,({\it{a\/}})\index{fix-int} $=$ {\tt{0}}) $\vee$ ({\rm{fix-int}}\,({\it{b\/}})\index{fix-int} $=$ {\rm{fix-int}}\,({\it{c\/}})\index{fix-int}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-cancellation-2 \\ \index{itimes-cancellation-2}
\=\+({\rm{itimes}}\,({\it{b\/}}, {\it{a\/}})\index{itimes} $=$ {\rm{itimes}}\,({\it{c\/}}, {\it{a\/}})\index{itimes}) \\ 
$=$$\;\;\;\;$(({\rm{fix-int}}\,({\it{a\/}})\index{fix-int} $=$ {\tt{0}}) $\vee$ ({\rm{fix-int}}\,({\it{b\/}})\index{fix-int} $=$ {\rm{fix-int}}\,({\it{c\/}})\index{fix-int}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-cancellation-3 \\ \index{itimes-cancellation-3}
\=\+({\rm{itimes}}\,({\it{a\/}}, {\it{b\/}})\index{itimes} $=$ {\rm{itimes}}\,({\it{c\/}}, {\it{a\/}})\index{itimes}) \\ 
$=$$\;\;\;\;$(({\rm{fix-int}}\,({\it{a\/}})\index{fix-int} $=$ {\tt{0}}) $\vee$ ({\rm{fix-int}}\,({\it{b\/}})\index{fix-int} $=$ {\rm{fix-int}}\,({\it{c\/}})\index{fix-int}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integerp-iquotient \\ \index{integerp-iquotient}
{\rm{integerp}}\,({\rm{iquotient}}\,({\it{i\/}}, {\it{j\/}})\index{iquotient})\index{integerp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integerp-iremainder \\ \index{integerp-iremainder}
{\rm{integerp}}\,({\rm{iremainder}}\,({\it{i\/}}, {\it{j\/}})\index{iremainder})\index{integerp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integerp-idiv \\ \index{integerp-idiv}
{\rm{integerp}}\,({\rm{idiv}}\,({\it{i\/}}, {\it{j\/}})\index{idiv})\index{integerp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integerp-imod \\ \index{integerp-imod}
{\rm{integerp}}\,({\rm{imod}}\,({\it{i\/}}, {\it{j\/}})\index{imod})\index{integerp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integerp-iquo \\ \index{integerp-iquo}
{\rm{integerp}}\,({\rm{iquo}}\,({\it{i\/}}, {\it{j\/}})\index{iquo})\index{integerp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integerp-irem \\ \index{integerp-irem}
{\rm{integerp}}\,({\rm{irem}}\,({\it{i\/}}, {\it{j\/}})\index{irem})\index{integerp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iquotient-fix-int1 \\ \index{iquotient-fix-int1}
{\rm{iquotient}}\,({\rm{fix-int}}\,({\it{i\/}})\index{fix-int}, {\it{j\/}})\index{iquotient} $=$ {\rm{iquotient}}\,({\it{i\/}}, {\it{j\/}})\index{iquotient}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iquotient-fix-int2 \\ \index{iquotient-fix-int2}
{\rm{iquotient}}\,({\it{i\/}}, {\rm{fix-int}}\,({\it{j\/}})\index{fix-int})\index{iquotient} $=$ {\rm{iquotient}}\,({\it{i\/}}, {\it{j\/}})\index{iquotient}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iremainder-fix-int1 \\ \index{iremainder-fix-int1}
{\rm{iremainder}}\,({\rm{fix-int}}\,({\it{i\/}})\index{fix-int}, {\it{j\/}})\index{iremainder} $=$ {\rm{iremainder}}\,({\it{i\/}}, {\it{j\/}})\index{iremainder}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iremainder-fix-int2 \\ \index{iremainder-fix-int2}
{\rm{iremainder}}\,({\it{i\/}}, {\rm{fix-int}}\,({\it{j\/}})\index{fix-int})\index{iremainder} $=$ {\rm{iremainder}}\,({\it{i\/}}, {\it{j\/}})\index{iremainder}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  idiv-fix-int1 \\ \index{idiv-fix-int1}
{\rm{idiv}}\,({\rm{fix-int}}\,({\it{i\/}})\index{fix-int}, {\it{j\/}})\index{idiv} $=$ {\rm{idiv}}\,({\it{i\/}}, {\it{j\/}})\index{idiv}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  idiv-fix-int2 \\ \index{idiv-fix-int2}
{\rm{idiv}}\,({\it{i\/}}, {\rm{fix-int}}\,({\it{j\/}})\index{fix-int})\index{idiv} $=$ {\rm{idiv}}\,({\it{i\/}}, {\it{j\/}})\index{idiv}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  imod-fix-int1 \\ \index{imod-fix-int1}
{\rm{imod}}\,({\rm{fix-int}}\,({\it{i\/}})\index{fix-int}, {\it{j\/}})\index{imod} $=$ {\rm{imod}}\,({\it{i\/}}, {\it{j\/}})\index{imod}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  imod-fix-int2 \\ \index{imod-fix-int2}
{\rm{imod}}\,({\it{i\/}}, {\rm{fix-int}}\,({\it{j\/}})\index{fix-int})\index{imod} $=$ {\rm{imod}}\,({\it{i\/}}, {\it{j\/}})\index{imod}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iquo-fix-int1 \\ \index{iquo-fix-int1}
{\rm{iquo}}\,({\rm{fix-int}}\,({\it{i\/}})\index{fix-int}, {\it{j\/}})\index{iquo} $=$ {\rm{iquo}}\,({\it{i\/}}, {\it{j\/}})\index{iquo}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iquo-fix-int2 \\ \index{iquo-fix-int2}
{\rm{iquo}}\,({\it{i\/}}, {\rm{fix-int}}\,({\it{j\/}})\index{fix-int})\index{iquo} $=$ {\rm{iquo}}\,({\it{i\/}}, {\it{j\/}})\index{iquo}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  irem-fix-int1 \\ \index{irem-fix-int1}
{\rm{irem}}\,({\rm{fix-int}}\,({\it{i\/}})\index{fix-int}, {\it{j\/}})\index{irem} $=$ {\rm{irem}}\,({\it{i\/}}, {\it{j\/}})\index{irem}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  irem-fix-int2 \\ \index{irem-fix-int2}
{\rm{irem}}\,({\it{i\/}}, {\rm{fix-int}}\,({\it{j\/}})\index{fix-int})\index{irem} $=$ {\rm{irem}}\,({\it{i\/}}, {\it{j\/}})\index{irem}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fix-int-iquotient \\ \index{fix-int-iquotient}
{\rm{fix-int}}\,({\rm{iquotient}}\,({\it{i\/}}, {\it{j\/}})\index{iquotient})\index{fix-int} $=$ {\rm{iquotient}}\,({\it{i\/}}, {\it{j\/}})\index{iquotient}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fix-int-iremainder \\ \index{fix-int-iremainder}
{\rm{fix-int}}\,({\rm{iremainder}}\,({\it{i\/}}, {\it{j\/}})\index{iremainder})\index{fix-int} $=$ {\rm{iremainder}}\,({\it{i\/}}, {\it{j\/}})\index{iremainder}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fix-int-idiv \\ \index{fix-int-idiv}
{\rm{fix-int}}\,({\rm{idiv}}\,({\it{i\/}}, {\it{j\/}})\index{idiv})\index{fix-int} $=$ {\rm{idiv}}\,({\it{i\/}}, {\it{j\/}})\index{idiv}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fix-int-imod \\ \index{fix-int-imod}
{\rm{fix-int}}\,({\rm{imod}}\,({\it{i\/}}, {\it{j\/}})\index{imod})\index{fix-int} $=$ {\rm{imod}}\,({\it{i\/}}, {\it{j\/}})\index{imod}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fix-int-iquo \\ \index{fix-int-iquo}
{\rm{fix-int}}\,({\rm{iquo}}\,({\it{i\/}}, {\it{j\/}})\index{iquo})\index{fix-int} $=$ {\rm{iquo}}\,({\it{i\/}}, {\it{j\/}})\index{iquo}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fix-int-irem \\ \index{fix-int-irem}
{\rm{fix-int}}\,({\rm{irem}}\,({\it{i\/}}, {\it{j\/}})\index{irem})\index{fix-int} $=$ {\rm{irem}}\,({\it{i\/}}, {\it{j\/}})\index{irem}
\end{tabbing}


\noindent{\sc Event}:   Enable iquotient; name this event `iquotient-off'.\index{iquotient-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iremainder; name this event `iremainder-off'.\index{iremainder-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable idiv; name this event `idiv-off'.\index{idiv-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable imod; name this event `imod-off'.\index{imod-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iquo; name this event `iquo-off'.\index{iquo-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable irem; name this event `irem-off'.\index{irem-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{itimes-fringe} \\  
\=\+{\rm{itimes-fringe}}\,({\it{x\/}})\index{itimes-fringe} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{itimes}} \\ 
{\bf then }{\rm{append}}\,({\rm{itimes-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-fringe}, {\rm{itimes-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-fringe}) \\ 
{\bf else }{\rm{list}}\,({\it{x\/}})$\;${\bf  endif}\- \\ 
{\bf else }{\rm{list}}\,({\it{x\/}})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{itimes-tree-rec} \\  
\=\+{\rm{itimes-tree-rec}}\,({\it{l\/}})\index{itimes-tree-rec} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{cdr}}\,({\it{l\/}}) $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{car}}\,({\it{l\/}}) \\ 
{\bf else }{\rm{list}}\,({\tt{'}}{\tt{itimes}}, {\rm{car}}\,({\it{l\/}}), {\rm{itimes-tree-rec}}\,({\rm{cdr}}\,({\it{l\/}}))\index{itimes-tree-rec})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{itimes-tree} \\  
\=\+{\rm{itimes-tree}}\,({\it{l\/}})\index{itimes-tree} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{cdr}}\,({\it{l\/}}))$\;\;${\bf then }{\rm{itimes-tree-rec}}\,({\it{l\/}})\index{itimes-tree-rec} \\ 
{\bf else }{\rm{list}}\,({\tt{'}}{\tt{fix-int}}, {\rm{car}}\,({\it{l\/}}))$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{'}}{\tt{1}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{itimes-list} \\  
\=\+{\rm{itimes-list}}\,({\it{x\/}})\index{itimes-list} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}})$\;\;${\bf then }{\rm{itimes}}\,({\rm{car}}\,({\it{x\/}}), {\rm{itimes-list}}\,({\rm{cdr}}\,({\it{x\/}}))\index{itimes-list})\index{itimes} \\ 
{\bf else }{\tt{1}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integerp-itimes-list \\ \index{integerp-itimes-list}
{\rm{integerp}}\,({\rm{itimes-list}}\,({\it{x\/}})\index{itimes-list})\index{integerp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-itimes-tree-rec \\ \index{eval\$-itimes-tree-rec}
\=\+{\rm{listp}}\,({\it{x\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{itimes-tree-rec}}\,({\it{x\/}})\index{itimes-tree-rec}, {\it{a\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\rm{cdr}}\,({\it{x\/}}))$\;\;${\bf then }{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{itimes-list} \\ 
{\bf else }{\rm{eval\$}}\,({\bf{t}}, {\rm{car}}\,({\it{x\/}}), {\it{a\/}})$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-itimes-tree \\ \index{eval\$-itimes-tree}
{\rm{eval\$}}\,({\bf{t}}, {\rm{itimes-tree}}\,({\it{x\/}})\index{itimes-tree}, {\it{a\/}}) $=$ {\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{itimes-list}
\end{tabbing}


\noindent{\sc Event}:   Enable itimes-tree; name this event `itimes-tree-off'.\index{itimes-tree-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{make-cancel-itimes-equality} \\  
\=\+{\rm{make-cancel-itimes-equality}}\,({\it{x\/}}, {\it{y\/}}, {\it{in-both\/}})\index{make-cancel-itimes-equality} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{cons}}\,({\tt{'}}{\tt{equal}}, {\rm{cons}}\,({\rm{itimes-tree}}\,({\it{in-both\/}})\index{itimes-tree}, {\tt{'}}{\tt{(}}{\tt{'}}{\tt{0}}{\tt{)}})), \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{t}}), \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{itimes-tree}}\,({\rm{bagdiff}}\,({\it{x\/}}, {\it{in-both\/}})\index{bagdiff})\index{itimes-tree}, \\ 
{\rm{itimes-tree}}\,({\rm{bagdiff}}\,({\it{y\/}}, {\it{in-both\/}})\index{bagdiff})\index{itimes-tree})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cancel-itimes} \\  
\=\+{\rm{cancel-itimes}}\,({\it{x\/}})\index{cancel-itimes} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{equal}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{cadr}}\,({\it{x\/}})) \\ 
{\bf then }\=\+{\bf if }{\rm{caadr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{itimes}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{caddr}}\,({\it{x\/}})) \\ 
{\bf then }\=\+{\bf if }{\rm{caaddr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{itimes}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{bagint}}\,(\=\+{\rm{itimes-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-fringe}, \\ 
{\rm{itimes-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-fringe})\-\index{bagint}) \\ 
{\bf then }{\rm{make-cancel-itimes-equality}}\,(\=\+{\rm{itimes-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-fringe}, \\ 
{\rm{itimes-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{itimes-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-fringe}, \\ 
{\rm{itimes-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-fringe})\-\index{bagint})\-\index{make-cancel-itimes-equality} \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{caddr}}\,({\it{x\/}}) $\in$ {\rm{itimes-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-fringe} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{integerp}}, {\rm{caddr}}\,({\it{x\/}})), \\ 
{\rm{make-cancel-itimes-equality}}\,(\=\+{\rm{itimes-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-fringe}, \\ 
{\rm{list}}\,({\rm{caddr}}\,({\it{x\/}})), \\ 
{\rm{list}}\,({\rm{caddr}}\,({\it{x\/}})))\-\index{make-cancel-itimes-equality}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{caddr}}\,({\it{x\/}}) $\in$ {\rm{itimes-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-fringe} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{integerp}}, {\rm{caddr}}\,({\it{x\/}})), \\ 
{\rm{make-cancel-itimes-equality}}\,(\=\+{\rm{itimes-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-fringe}, \\ 
{\rm{list}}\,({\rm{caddr}}\,({\it{x\/}})), \\ 
{\rm{list}}\,({\rm{caddr}}\,({\it{x\/}})))\-\index{make-cancel-itimes-equality}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{listp}}\,({\rm{caddr}}\,({\it{x\/}})) \\ 
{\bf then }\=\+{\bf if }{\rm{caaddr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{itimes}} \\ 
{\bf then }\=\+{\bf if }{\rm{cadr}}\,({\it{x\/}}) $\in$ {\rm{itimes-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-fringe} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{integerp}}, {\rm{cadr}}\,({\it{x\/}})), \\ 
{\rm{make-cancel-itimes-equality}}\,(\=\+{\rm{list}}\,({\rm{cadr}}\,({\it{x\/}})), \\ 
{\rm{itimes-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-fringe}, \\ 
{\rm{list}}\,({\rm{cadr}}\,({\it{x\/}})))\-\index{make-cancel-itimes-equality}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{listp}}\,({\rm{caddr}}\,({\it{x\/}})) \\ 
{\bf then }\=\+{\bf if }{\rm{caaddr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{itimes}} \\ 
{\bf then }\=\+{\bf if }{\rm{cadr}}\,({\it{x\/}}) $\in$ {\rm{itimes-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-fringe} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{integerp}}, {\rm{cadr}}\,({\it{x\/}})), \\ 
{\rm{make-cancel-itimes-equality}}\,(\=\+{\rm{list}}\,({\rm{cadr}}\,({\it{x\/}})), \\ 
{\rm{itimes-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-fringe}, \\ 
{\rm{list}}\,({\rm{cadr}}\,({\it{x\/}})))\-\index{make-cancel-itimes-equality}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-list-append \\ \index{itimes-list-append}
{\rm{itimes-list}}\,({\rm{append}}\,({\it{x\/}}, {\it{y\/}}))\index{itimes-list} $=$ {\rm{itimes}}\,({\rm{itimes-list}}\,({\it{x\/}})\index{itimes-list}, {\rm{itimes-list}}\,({\it{y\/}})\index{itimes-list})\index{itimes}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-list-eval\$-fringe \\ \index{itimes-list-eval\$-fringe}
{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{itimes-fringe}}\,({\it{x\/}})\index{itimes-fringe}, {\it{a\/}}))\index{itimes-list} $=$ {\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}))\index{fix-int}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integerp-eval\$-itimes \\ \index{integerp-eval\$-itimes}
({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{itimes}}) $\rightarrow$ {\rm{integerp}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}))\index{integerp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  not-integerp-implies-not-equal-itimes \\ \index{not-integerp-implies-not-equal-iti!mes}
($\neg$ {\rm{integerp}}\,({\it{a\/}})\index{integerp}) $\rightarrow$ (({\it{a\/}} $=$ {\rm{itimes}}\,({\it{b\/}}, {\it{c\/}})\index{itimes}) $=$ {\bf{f}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-list-eval\$-delete \\ \index{itimes-list-eval\$-delete}
\=\+({\it{z\/}} $\in$ {\it{y\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{y\/}}, {\it{a\/}}))\index{itimes-list} \\ 
$=$$\;\;\;\;${\rm{itimes}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{z\/}}, {\it{a\/}}), {\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{delete}}\,({\it{z\/}}, {\it{y\/}})\index{delete}, {\it{a\/}}))\index{itimes-list})\index{itimes})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-list-bagdiff \\ \index{itimes-list-bagdiff}
\=\+{\rm{subbagp}}\,({\it{x\/}}, {\it{y\/}})\index{subbagp} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{y\/}}, {\it{a\/}}))\index{itimes-list} \\ 
$=$$\;\;\;\;${\rm{itimes}}\,(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagdiff}}\,({\it{y\/}}, {\it{x\/}})\index{bagdiff}, {\it{a\/}}))\index{itimes-list}, \\ 
{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{itimes-list})\-\index{itimes})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-itimes-list-eval\$-list-delete \\ \index{equal-itimes-list-eval\$-list-de!lete}
\=\+(({\it{c\/}} $\in$ {\it{y\/}}) $\wedge$ ({\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{c\/}}, {\it{a\/}}))\index{fix-int} $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\it{x\/}} $=$ {\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{delete}}\,({\it{c\/}}, {\it{y\/}})\index{delete}, {\it{a\/}}))\index{itimes-list}) \\ 
$=$$\;\;\;\;$(\=\+{\rm{integerp}}\,({\it{x\/}})\index{integerp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{itimes}}\,({\it{x\/}}, {\rm{eval\$}}\,({\bf{t}}, {\it{c\/}}, {\it{a\/}}))\index{itimes} \\ 
$=$$\;\;\;\;${\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{y\/}}, {\it{a\/}}))\index{itimes-list})\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable itimes-list-eval\$-delete; name this event `itimes-list-eval\$-delete-off'.\index{itimes-list-eval\$-delete-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  member-append \\ \index{member-append}
({\it{a\/}} $\in$ {\rm{append}}\,({\it{x\/}}, {\it{y\/}})) $=$ (({\it{a\/}} $\in$ {\it{x\/}}) $\vee$ ({\it{a\/}} $\in$ {\it{y\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  member-izerop-itimes-fringe \\ \index{member-izerop-itimes-fringe}
\=\+(({\it{z\/}} $\in$ {\rm{itimes-fringe}}\,({\it{x\/}})\index{itimes-fringe}) $\wedge$ ({\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{z\/}}, {\it{a\/}}))\index{fix-int} $=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}))\index{fix-int} $=$ {\tt{0}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-itimes-hack-1 \\ \index{correctness-of-cancel-itimes-ha!ck-1}
\=\+(\=\+({\it{w\/}} $\in$ {\rm{itimes-fringe}}\,({\rm{cons}}\,({\tt{'}}{\tt{itimes}}, {\it{x1\/}}))\index{itimes-fringe}) \\ 
$\wedge$$\;\;\;\;$({\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{w\/}}, {\it{a\/}}))\index{fix-int} $=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\rm{car}}\,({\it{x1\/}}), {\it{a\/}}))\index{fix-int} $\not=$ {\tt{0}}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\rm{cadr}}\,({\it{x1\/}}), {\it{a\/}}))\index{fix-int} $=$ {\tt{0}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable eval\$-equal; name this event `eval\$-equal-on'.\index{eval\$-equal-on}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  eval\$-make-cancel-itimes-equality \\ \index{eval\$-make-cancel-itimes-equalit!y}
\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{make-cancel-itimes-equality}}\,({\it{x\/}}, {\it{y\/}}, {\it{in-both\/}})\index{make-cancel-itimes-equality}, {\it{a\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{eval\$}}\,({\bf{t}}, {\rm{cons}}\,({\tt{'}}{\tt{equal}}, {\rm{cons}}\,({\rm{itimes-tree}}\,({\it{in-both\/}})\index{itimes-tree}, {\tt{'}}{\tt{(}}{\tt{'}}{\tt{0}}{\tt{)}})), {\it{a\/}}) \\ 
{\bf then }{\bf{t}} \\ 
{\bf else }\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagdiff}}\,({\it{x\/}}, {\it{in-both\/}})\index{bagdiff}, {\it{a\/}}))\index{itimes-list} \\ 
$=$$\;\;\;\;${\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagdiff}}\,({\it{y\/}}, {\it{in-both\/}})\index{bagdiff}, {\it{a\/}}))\index{itimes-list}\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable make-cancel-itimes-equality; name this event `make-cancel-itimes-equality-off'.\index{make-cancel-itimes-equality-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  eval\$-make-cancel-itimes-equality-1 \\ \index{eval\$-make-cancel-itimes-equalit!y-1}
\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{make-cancel-itimes-equality}}\,({\rm{list}}\,({\it{x\/}}), {\it{y\/}}, {\rm{list}}\,({\it{x\/}}))\index{make-cancel-itimes-equality}, {\it{a\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}))\index{fix-int} $=$ {\tt{0}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\tt{1}} $=$ {\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{delete}}\,({\it{x\/}}, {\it{y\/}})\index{delete}, {\it{a\/}}))\index{itimes-list}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-fix-int \\ \index{equal-fix-int}
({\rm{fix-int}}\,({\it{x\/}})\index{fix-int} $=$ {\it{x\/}}) $=$ {\rm{integerp}}\,({\it{x\/}})\index{integerp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-make-cancel-itimes-equality-2 \\ \index{eval\$-make-cancel-itimes-equalit!y-2}
\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{make-cancel-itimes-equality}}\,({\it{x\/}}, {\rm{list}}\,({\it{y\/}}), {\rm{list}}\,({\it{y\/}}))\index{make-cancel-itimes-equality}, {\it{a\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{y\/}}, {\it{a\/}}))\index{fix-int} $=$ {\tt{0}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\tt{1}} $=$ {\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{delete}}\,({\it{y\/}}, {\it{x\/}})\index{delete}, {\it{a\/}}))\index{itimes-list}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-equal-itimes-tree-itimes-fringe-0 \\ \index{eval\$-equal-itimes-tree-itimes!-fringe-0}
\=\+(\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{cons}}\,({\tt{'}}{\tt{equal}}, {\rm{cons}}\,({\rm{itimes-tree}}\,({\rm{itimes-fringe}}\,({\it{x\/}})\index{itimes-fringe})\index{itimes-tree}, {\tt{'}}{\tt{(}}{\tt{'}}{\tt{0}}{\tt{)}})), {\it{a\/}}) \\ 
$\wedge$$\;\;\;\;$({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{itimes}}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\tt{0}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  izerop-eval-of-member-implies-itimes-list-0 \\ \index{izerop-eval-of-member-implies-iti!mes-list-0}
\=\+(({\it{z\/}} $\in$ {\it{y\/}}) $\wedge$ ({\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{z\/}}, {\it{a\/}}))\index{fix-int} $=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{y\/}}, {\it{a\/}}))\index{itimes-list} $=$ {\tt{0}})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{subsetp} \\  
\=\+{\rm{subsetp}}\,({\it{x\/}}, {\it{y\/}})\index{subsetp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\rm{car}}\,({\it{x\/}}) $\in$ {\it{y\/}}$\;\;${\bf then }{\rm{subsetp}}\,({\rm{cdr}}\,({\it{x\/}}), {\it{y\/}})\index{subsetp} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  subsetp-implies-itimes-list-eval\$-equals-0 \\ \index{subsetp-implies-itimes-list-eva!l\$-equals-0}
\=\+({\rm{subsetp}}\,({\it{x\/}}, {\it{y\/}})\index{subsetp} $\wedge$ ({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{itimes-list} $=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{y\/}}, {\it{a\/}}))\index{itimes-list} $=$ {\tt{0}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  subbagp-subsetp \\ \index{subbagp-subsetp}
{\rm{subbagp}}\,({\it{x\/}}, {\it{y\/}})\index{subbagp} $\rightarrow$ {\rm{subsetp}}\,({\it{x\/}}, {\it{y\/}})\index{subsetp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-0-itimes-list-eval\$-bagint-1 \\ \index{equal-0-itimes-list-eval\$-bagi!nt-1}
\=\+({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagint}}\,({\it{x\/}}, {\it{y\/}})\index{bagint}, {\it{a\/}}))\index{itimes-list} $=$ {\tt{0}}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{itimes-list} $=$ {\tt{0}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-0-itimes-list-eval\$-bagint-2 \\ \index{equal-0-itimes-list-eval\$-bagi!nt-2}
\=\+({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagint}}\,({\it{x\/}}, {\it{y\/}})\index{bagint}, {\it{a\/}}))\index{itimes-list} $=$ {\tt{0}}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{y\/}}, {\it{a\/}}))\index{itimes-list} $=$ {\tt{0}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-itimes-hack-2 \\ \index{correctness-of-cancel-itimes-ha!ck-2}
\=\+(\=\+{\rm{listp}}\,({\it{u\/}}) \\ 
$\wedge$$\;\;\;\;$({\rm{car}}\,({\it{u\/}}) $=$ {\tt{'}}{\tt{itimes}}) \\ 
$\wedge$$\;\;\;\;${\rm{listp}}\,({\it{v\/}}) \\ 
$\wedge$$\;\;\;\;$({\rm{car}}\,({\it{v\/}}) $=$ {\tt{'}}{\tt{itimes}}) \\ 
$\wedge$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\it{u\/}}, {\it{a\/}}) $\not=$ {\rm{eval\$}}\,({\bf{t}}, {\it{v\/}}, {\it{a\/}})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,(\=\+{\tt{'}}{\tt{list}}, \\ 
{\rm{bagdiff}}\,(\=\+{\rm{itimes-fringe}}\,({\it{u\/}})\index{itimes-fringe}, \\ 
{\rm{bagint}}\,({\rm{itimes-fringe}}\,({\it{u\/}})\index{itimes-fringe}, {\rm{itimes-fringe}}\,({\it{v\/}})\index{itimes-fringe})\index{bagint})\-\index{bagdiff}, \\ 
{\it{a\/}})\-)\index{itimes-list} \\ 
$\not=$$\;\;\;\;${\rm{itimes-list}}\,({\rm{eval\$}}\,(\=\+{\tt{'}}{\tt{list}}, \\ 
{\rm{bagdiff}}\,(\=\+{\rm{itimes-fringe}}\,({\it{v\/}})\index{itimes-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{itimes-fringe}}\,({\it{u\/}})\index{itimes-fringe}, \\ 
{\rm{itimes-fringe}}\,({\it{v\/}})\index{itimes-fringe})\-\index{bagint})\-\index{bagdiff}, \\ 
{\it{a\/}})\-)\index{itimes-list})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-itimes-hack-3-lemma \\ \index{correctness-of-cancel-itimes-ha!ck-3-lemma}
\=\+(({\it{u\/}} $=$ {\rm{itimes}}\,({\it{a\/}}, {\it{b\/}})\index{itimes}) $\wedge$ ({\rm{fix-int}}\,({\it{a\/}})\index{fix-int} $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$(({\it{u\/}} $=$ {\rm{itimes}}\,({\it{a\/}}, {\it{c\/}})\index{itimes}) $=$ ({\rm{fix-int}}\,({\it{b\/}})\index{fix-int} $=$ {\rm{fix-int}}\,({\it{c\/}})\index{fix-int}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-itimes-hack-3 \\ \index{correctness-of-cancel-itimes-ha!ck-3}
\=\+(\=\+{\rm{listp}}\,({\it{u\/}}) \\ 
$\wedge$$\;\;\;\;$({\rm{car}}\,({\it{u\/}}) $=$ {\tt{'}}{\tt{itimes}}) \\ 
$\wedge$$\;\;\;\;${\rm{listp}}\,({\it{v\/}}) \\ 
$\wedge$$\;\;\;\;$({\rm{car}}\,({\it{v\/}}) $=$ {\tt{'}}{\tt{itimes}}) \\ 
$\wedge$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\it{u\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\it{v\/}}, {\it{a\/}})) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{cons}}\,(\=\+{\rm{itimes-tree}}\,({\rm{bagint}}\,(\=\+{\rm{itimes-fringe}}\,({\it{u\/}})\index{itimes-fringe}, \\ 
{\rm{itimes-fringe}}\,({\it{v\/}})\index{itimes-fringe})\-\index{bagint})\index{itimes-tree}, \\ 
{\tt{'}}{\tt{(}}{\tt{'}}{\tt{0}}{\tt{)}})\-)\-, \\ 
{\it{a\/}})\-))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,(\=\+{\tt{'}}{\tt{list}}, \\ 
{\rm{bagdiff}}\,(\=\+{\rm{itimes-fringe}}\,({\it{u\/}})\index{itimes-fringe}, \\ 
{\rm{bagint}}\,({\rm{itimes-fringe}}\,({\it{u\/}})\index{itimes-fringe}, {\rm{itimes-fringe}}\,({\it{v\/}})\index{itimes-fringe})\index{bagint})\-\index{bagdiff}, \\ 
{\it{a\/}})\-)\index{itimes-list} \\ 
$=$$\;\;\;\;${\rm{itimes-list}}\,({\rm{eval\$}}\,(\=\+{\tt{'}}{\tt{list}}, \\ 
{\rm{bagdiff}}\,(\=\+{\rm{itimes-fringe}}\,({\it{v\/}})\index{itimes-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{itimes-fringe}}\,({\it{u\/}})\index{itimes-fringe}, \\ 
{\rm{itimes-fringe}}\,({\it{v\/}})\index{itimes-fringe})\-\index{bagint})\-\index{bagdiff}, \\ 
{\it{a\/}})\-)\index{itimes-list})\- \\ 
$=$$\;\;\;\;${\bf{t}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable correctness-of-cancel-itimes-hack-3-lemma; name this event `correctness-of-cancel-itimes-hack-3-lemma-off'.\index{correctness-of-cancel-itimes-ha!ck-3-lemma-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-itimes \\ \index{correctness-of-cancel-itimes}
{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{cancel-itimes}}\,({\it{x\/}})\index{cancel-itimes}, {\it{a\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{itimes-tree-no-fix-int} \\  
\=\+{\rm{itimes-tree-no-fix-int}}\,({\it{l\/}})\index{itimes-tree-no-fix-int} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}})$\;\;${\bf then }{\rm{itimes-tree-rec}}\,({\it{l\/}})\index{itimes-tree-rec} \\ 
{\bf else }{\tt{'}}{\tt{'}}{\tt{1}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-itimes-tree-no-fix-int-1 \\ \index{eval\$-itimes-tree-no-fix-int-1}
\=\+{\rm{ilessp}}\,({\rm{eval\$}}\,({\bf{t}}, {\rm{itimes-tree-no-fix-int}}\,({\it{x\/}})\index{itimes-tree-no-fix-int}, {\it{a\/}}), {\it{y\/}})\index{ilessp} \\ 
$=$$\;\;\;\;${\rm{ilessp}}\,({\rm{eval\$}}\,({\bf{t}}, {\rm{itimes-tree}}\,({\it{x\/}})\index{itimes-tree}, {\it{a\/}}), {\it{y\/}})\index{ilessp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-itimes-tree-no-fix-int-2 \\ \index{eval\$-itimes-tree-no-fix-int-2}
\=\+{\rm{ilessp}}\,({\it{y\/}}, {\rm{eval\$}}\,({\bf{t}}, {\rm{itimes-tree-no-fix-int}}\,({\it{x\/}})\index{itimes-tree-no-fix-int}, {\it{a\/}}))\index{ilessp} \\ 
$=$$\;\;\;\;${\rm{ilessp}}\,({\it{y\/}}, {\rm{eval\$}}\,({\bf{t}}, {\rm{itimes-tree}}\,({\it{x\/}})\index{itimes-tree}, {\it{a\/}}))\index{ilessp}\-
\end{tabbing}


\noindent{\sc Event}:   Enable itimes-tree-no-fix-int; name this event `itimes-tree-no-fix-int-off'.\index{itimes-tree-no-fix-int-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{make-cancel-itimes-inequality} \\  
\=\+{\rm{make-cancel-itimes-inequality}}\,({\it{x\/}}, {\it{y\/}}, {\it{in-both\/}})\index{make-cancel-itimes-inequality} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{cons}}\,({\tt{'}}{\tt{ilessp}}, {\rm{cons}}\,({\rm{itimes-tree-no-fix-int}}\,({\it{in-both\/}})\index{itimes-tree-no-fix-int}, {\tt{'}}{\tt{(}}{\tt{'}}{\tt{0}}{\tt{)}})), \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{ilessp}}, \\ 
{\rm{itimes-tree-no-fix-int}}\,({\rm{bagdiff}}\,({\it{y\/}}, {\it{in-both\/}})\index{bagdiff})\index{itimes-tree-no-fix-int}, \\ 
{\rm{itimes-tree-no-fix-int}}\,({\rm{bagdiff}}\,({\it{x\/}}, {\it{in-both\/}})\index{bagdiff})\index{itimes-tree-no-fix-int})\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{cons}}\,(\=\+{\rm{list}}\,({\tt{'}}{\tt{ilessp}}, {\tt{'}}{\tt{'}}{\tt{0}}, {\rm{itimes-tree-no-fix-int}}\,({\it{in-both\/}})\index{itimes-tree-no-fix-int}), \\ 
{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{ilessp}}, \\ 
{\rm{itimes-tree-no-fix-int}}\,({\rm{bagdiff}}\,({\it{x\/}}, {\it{in-both\/}})\index{bagdiff})\index{itimes-tree-no-fix-int}, \\ 
{\rm{itimes-tree-no-fix-int}}\,({\rm{bagdiff}}\,({\it{y\/}}, {\it{in-both\/}})\index{bagdiff})\index{itimes-tree-no-fix-int})\-, \\ 
{\tt{'}}{\tt{(}}{\tt{(}}{\tt{false}}{\tt{)}}{\tt{)}})\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cancel-itimes-ilessp} \\  
\=\+{\rm{cancel-itimes-ilessp}}\,({\it{x\/}})\index{cancel-itimes-ilessp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{ilessp}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{bagint}}\,(\=\+{\rm{itimes-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-fringe}, \\ 
{\rm{itimes-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-fringe})\-\index{bagint}) \\ 
{\bf then }{\rm{make-cancel-itimes-inequality}}\,(\=\+{\rm{itimes-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-fringe}, \\ 
{\rm{itimes-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-fringe}, \\ 
{\rm{bagint}}\,(\=\+{\rm{itimes-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-fringe}, \\ 
{\rm{itimes-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-fringe})\-\index{bagint})\-\index{make-cancel-itimes-inequality} \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-make-cancel-itimes-inequality \\ \index{eval\$-make-cancel-itimes-inequ!ality}
\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{make-cancel-itimes-inequality}}\,({\it{x\/}}, {\it{y\/}}, {\it{in-both\/}})\index{make-cancel-itimes-inequality}, {\it{a\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\rm{cons}}\,({\tt{'}}{\tt{ilessp}}, {\rm{cons}}\,({\rm{itimes-tree-no-fix-int}}\,({\it{in-both\/}})\index{itimes-tree-no-fix-int}, {\tt{'}}{\tt{(}}{\tt{'}}{\tt{0}}{\tt{)}})), \\ 
{\it{a\/}})\- \\ 
{\bf then }{\rm{ilessp}}\,(\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{itimes-tree-no-fix-int}}\,({\rm{bagdiff}}\,({\it{y\/}}, {\it{in-both\/}})\index{bagdiff})\index{itimes-tree-no-fix-int}, {\it{a\/}}), \\ 
{\rm{eval\$}}\,({\bf{t}}, {\rm{itimes-tree-no-fix-int}}\,({\rm{bagdiff}}\,({\it{x\/}}, {\it{in-both\/}})\index{bagdiff})\index{itimes-tree-no-fix-int}, {\it{a\/}}))\-\index{ilessp} \\ 
{\bf elseif }{\rm{eval\$}}\,({\bf{t}}, {\rm{list}}\,({\tt{'}}{\tt{ilessp}}, {\tt{'}}{\tt{'}}{\tt{0}}, {\rm{itimes-tree-no-fix-int}}\,({\it{in-both\/}})\index{itimes-tree-no-fix-int}), {\it{a\/}}) \\ 
{\bf then }{\rm{ilessp}}\,(\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{itimes-tree-no-fix-int}}\,({\rm{bagdiff}}\,({\it{x\/}}, {\it{in-both\/}})\index{bagdiff})\index{itimes-tree-no-fix-int}, {\it{a\/}}), \\ 
{\rm{eval\$}}\,({\bf{t}}, {\rm{itimes-tree-no-fix-int}}\,({\rm{bagdiff}}\,({\it{y\/}}, {\it{in-both\/}})\index{bagdiff})\index{itimes-tree-no-fix-int}, {\it{a\/}}))\-\index{ilessp} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable make-cancel-itimes-inequality; name this event `make-cancel-itimes-inequality-off'.\index{make-cancel-itimes-inequality-o!ff}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  listp-bagint-with-singleton-implies-member \\ \index{listp-bagint-with-singleton-imp!lies-member}
{\rm{listp}}\,({\rm{bagint}}\,({\it{y\/}}, {\rm{list}}\,({\it{z\/}}))\index{bagint}) $\rightarrow$ ({\it{z\/}} $\in$ {\it{y\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-list-eval\$-list-0 \\ \index{itimes-list-eval\$-list-0}
({\tt{0}} $\in$ {\it{x\/}}) $\rightarrow$ ({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{itimes-list} $=$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ilessp-itimes-right-positive \\ \index{ilessp-itimes-right-positive}
{\rm{ilessp}}\,({\tt{0}}, {\it{x\/}})\index{ilessp} $\rightarrow$ ({\rm{ilessp}}\,({\it{y\/}}, {\it{z\/}})\index{ilessp} $=$ {\rm{ilessp}}\,({\rm{itimes}}\,({\it{y\/}}, {\it{x\/}})\index{itimes}, {\rm{itimes}}\,({\it{z\/}}, {\it{x\/}})\index{itimes})\index{ilessp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-itimes-ilessp-hack-1 \\ \index{correctness-of-cancel-itimes-ile!ssp-hack-1}
\=\+(\=\+{\rm{subbagp}}\,({\it{bag\/}}, {\it{x\/}})\index{subbagp} \\ 
$\wedge$$\;\;\;\;${\rm{subbagp}}\,({\it{bag\/}}, {\it{y\/}})\index{subbagp} \\ 
$\wedge$$\;\;\;\;${\rm{ilessp}}\,({\tt{0}}, {\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag\/}}, {\it{a\/}}))\index{itimes-list})\index{ilessp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{ilessp}}\,(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagdiff}}\,({\it{x\/}}, {\it{bag\/}})\index{bagdiff}, {\it{a\/}}))\index{itimes-list}, \\ 
{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagdiff}}\,({\it{y\/}}, {\it{bag\/}})\index{bagdiff}, {\it{a\/}}))\index{itimes-list})\-\index{ilessp} \\ 
$=$$\;\;\;\;${\rm{ilessp}}\,(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{itimes-list}, \\ 
{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{y\/}}, {\it{a\/}}))\index{itimes-list})\-\index{ilessp})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  listp-bagint-with-singleton-member \\ \index{listp-bagint-with-singleton-mem!ber}
{\rm{listp}}\,({\rm{bagint}}\,({\it{y\/}}, {\rm{list}}\,({\it{z\/}}))\index{bagint}) $=$ ({\it{z\/}} $\in$ {\it{y\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-itimes-ilessp-hack-2-lemma \\ \index{correctness-of-cancel-itimes-ile!ssp-hack-2-lemma}
({\tt{0}} $\in$ {\rm{itimes-fringe}}\,({\it{w\/}})\index{itimes-fringe}) $\rightarrow$ ({\rm{eval\$}}\,({\bf{t}}, {\it{w\/}}, {\it{a\/}}) $=$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-itimes-ilessp-hack-2 \\ \index{correctness-of-cancel-itimes-ile!ssp-hack-2}
({\tt{0}} $\in$ {\rm{itimes-fringe}}\,({\it{w\/}})\index{itimes-fringe}) $\rightarrow$ ($\neg$ {\rm{ilessp}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{w\/}}, {\it{a\/}}), {\tt{0}})\index{ilessp})
\end{tabbing}


\noindent{\sc Event}:   Enable correctness-of-cancel-itimes-ilessp-hack-2-lemma; name this event `correctness-of-cancel-itimes-ilessp-hack-2-lemma-off'.\index{correctness-of-cancel-itimes-ile!ssp-hack-2-lemma-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ilessp-trichotomy \\ \index{ilessp-trichotomy}
($\neg$ {\rm{ilessp}}\,({\it{x\/}}, {\it{y\/}})\index{ilessp}) $\rightarrow$ ({\rm{ilessp}}\,({\it{y\/}}, {\it{x\/}})\index{ilessp} $=$ ({\rm{fix-int}}\,({\it{x\/}})\index{fix-int} $\not=$ {\rm{fix-int}}\,({\it{y\/}})\index{fix-int}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-itimes-ilessp-hack-3-lemma-1 \\ \index{correctness-of-cancel-itimes-ile!ssp-hack-3-lemma-1}
\=\+(({\tt{0}} $=$ {\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag\/}}, {\it{a\/}}))\index{itimes-list}) $\wedge$ {\rm{subsetp}}\,({\it{bag\/}}, {\it{z\/}})\index{subsetp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{z\/}}, {\it{a\/}}))\index{itimes-list} $=$ {\tt{0}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-itimes-ilessp-hack-3-lemma-2 \\ \index{correctness-of-cancel-itimes-ile!ssp-hack-3-lemma-2}
\=\+(({\tt{0}} $=$ {\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag\/}}, {\it{a\/}}))\index{itimes-list}) $\wedge$ {\rm{subsetp}}\,({\it{bag\/}}, {\rm{itimes-fringe}}\,({\it{x\/}})\index{itimes-fringe})\index{subsetp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}))\index{fix-int} $=$ {\tt{0}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  same-fix-int-implies-not-ilessp \\ \index{same-fix-int-implies-not-ilessp}
({\rm{fix-int}}\,({\it{x\/}})\index{fix-int} $=$ {\rm{fix-int}}\,({\it{y\/}})\index{fix-int}) $\rightarrow$ ($\neg$ {\rm{ilessp}}\,({\it{x\/}}, {\it{y\/}})\index{ilessp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-itimes-ilessp-hack-3 \\ \index{correctness-of-cancel-itimes-ile!ssp-hack-3}
\=\+(\=\+($\neg$ {\rm{ilessp}}\,({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag\/}}, {\it{a\/}}))\index{itimes-list}, {\tt{0}})\index{ilessp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{ilessp}}\,({\tt{0}}, {\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag\/}}, {\it{a\/}}))\index{itimes-list})\index{ilessp}) \\ 
$\wedge$$\;\;\;\;${\rm{subbagp}}\,({\it{bag\/}}, {\rm{itimes-fringe}}\,({\it{w\/}})\index{itimes-fringe})\index{subbagp} \\ 
$\wedge$$\;\;\;\;${\rm{subbagp}}\,({\it{bag\/}}, {\rm{itimes-fringe}}\,({\it{v\/}})\index{itimes-fringe})\index{subbagp})\- \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{ilessp}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{w\/}}, {\it{a\/}}), {\rm{eval\$}}\,({\bf{t}}, {\it{v\/}}, {\it{a\/}}))\index{ilessp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ilessp-itimes-right-negative \\ \index{ilessp-itimes-right-negative}
{\rm{ilessp}}\,({\it{x\/}}, {\tt{0}})\index{ilessp} $\rightarrow$ ({\rm{ilessp}}\,({\it{y\/}}, {\it{z\/}})\index{ilessp} $=$ {\rm{ilessp}}\,({\rm{itimes}}\,({\it{z\/}}, {\it{x\/}})\index{itimes}, {\rm{itimes}}\,({\it{y\/}}, {\it{x\/}})\index{itimes})\index{ilessp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-itimes-ilessp-hack-4 \\ \index{correctness-of-cancel-itimes-ile!ssp-hack-4}
\=\+(\=\+{\rm{subbagp}}\,({\it{bag\/}}, {\it{x\/}})\index{subbagp} \\ 
$\wedge$$\;\;\;\;${\rm{subbagp}}\,({\it{bag\/}}, {\it{y\/}})\index{subbagp} \\ 
$\wedge$$\;\;\;\;${\rm{ilessp}}\,({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag\/}}, {\it{a\/}}))\index{itimes-list}, {\tt{0}})\index{ilessp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{ilessp}}\,(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagdiff}}\,({\it{x\/}}, {\it{bag\/}})\index{bagdiff}, {\it{a\/}}))\index{itimes-list}, \\ 
{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagdiff}}\,({\it{y\/}}, {\it{bag\/}})\index{bagdiff}, {\it{a\/}}))\index{itimes-list})\-\index{ilessp} \\ 
$=$$\;\;\;\;${\rm{ilessp}}\,(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{y\/}}, {\it{a\/}}))\index{itimes-list}, \\ 
{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{itimes-list})\-\index{ilessp})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ilessp-trichotomy; name this event `ilessp-trichotomy-off'.\index{ilessp-trichotomy-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable same-fix-int-implies-not-ilessp; name this event `same-fix-int-implies-not-ilessp-off'.\index{same-fix-int-implies-not-ilessp!-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-itimes-ilessp \\ \index{correctness-of-cancel-itimes-ile!ssp}
{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{cancel-itimes-ilessp}}\,({\it{x\/}})\index{cancel-itimes-ilessp}, {\it{a\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ilessp-strict \\ \index{ilessp-strict}
{\rm{ilessp}}\,({\it{x\/}}, {\it{y\/}})\index{ilessp} $\rightarrow$ ($\neg$ {\rm{ilessp}}\,({\it{y\/}}, {\it{x\/}})\index{ilessp})
\end{tabbing}


\noindent{\sc Event}:   Enable eval\$-cancel-iplus; name this event `eval\$-cancel-iplus-off'.\index{eval\$-cancel-iplus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-iplus; name this event `eval\$-iplus-off'.\index{eval\$-iplus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-count-listp-cdr; name this event `lessp-count-listp-cdr-off'.\index{lessp-count-listp-cdr-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-iplus-tree-rec; name this event `eval\$-iplus-tree-rec-off'.\index{eval\$-iplus-tree-rec-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-iplus-tree; name this event `eval\$-iplus-tree-off'.\index{eval\$-iplus-tree-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-list-eval\$-fringe; name this event `iplus-list-eval\$-fringe-off'.\index{iplus-list-eval\$-fringe-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-iplus-list-bagdiff; name this event `eval\$-iplus-list-bagdiff-off'.\index{eval\$-iplus-list-bagdiff-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-difference-plus-arg1; name this event `lessp-difference-plus-arg1-off'.\index{lessp-difference-plus-arg1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-difference-plus-arg1-commuted; name this event `lessp-difference-plus-arg1-commuted-off'.\index{lessp-difference-plus-arg1-comm!uted-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-iplus-ilessp-lemma; name this event `correctness-of-cancel-iplus-ilessp-lemma-off'.\index{correctness-of-cancel-iplus-ile!ssp-lemma-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-ilessp-iplus-tree-no-fix-int; name this event `eval\$-ilessp-iplus-tree-no-fix-int-off'.\index{eval\$-ilessp-iplus-tree-no-fix!-int-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable make-cancel-iplus-inequality-simplifier; name this event `make-cancel-iplus-inequality-simplifier-off'.\index{make-cancel-iplus-inequality-si!mplifier-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-difference-lessp-arg2; name this event `quotient-difference-lessp-arg2-off'.\index{quotient-difference-lessp-arg2-!off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-itimes-tree-rec; name this event `eval\$-itimes-tree-rec-off'.\index{eval\$-itimes-tree-rec-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-itimes-tree; name this event `eval\$-itimes-tree-off'.\index{eval\$-itimes-tree-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-list-eval\$-fringe; name this event `itimes-list-eval\$-fringe-off'.\index{itimes-list-eval\$-fringe-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-eval\$-itimes; name this event `integerp-eval\$-itimes-off'.\index{integerp-eval\$-itimes-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-list-bagdiff; name this event `itimes-list-bagdiff-off'.\index{itimes-list-bagdiff-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-itimes-list-eval\$-list-delete; name this event `equal-itimes-list-eval\$-list-delete-off'.\index{equal-itimes-list-eval\$-list-de!lete-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable member-izerop-itimes-fringe; name this event `member-izerop-itimes-fringe-off'.\index{member-izerop-itimes-fringe-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-itimes-hack-1; name this event `correctness-of-cancel-itimes-hack-1-off'.\index{correctness-of-cancel-itimes-ha!ck-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-make-cancel-itimes-equality; name this event `eval\$-make-cancel-itimes-equality-off'.\index{eval\$-make-cancel-itimes-equalit!y-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-make-cancel-itimes-equality-1; name this event `eval\$-make-cancel-itimes-equality-1-off'.\index{eval\$-make-cancel-itimes-equalit!y-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-make-cancel-itimes-equality-2; name this event `eval\$-make-cancel-itimes-equality-2-off'.\index{eval\$-make-cancel-itimes-equalit!y-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-equal-itimes-tree-itimes-fringe-0; name this event `eval\$-equal-itimes-tree-itimes-fringe-0-off'.\index{eval\$-equal-itimes-tree-itimes!-fringe-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable izerop-eval-of-member-implies-itimes-list-0; name this event `izerop-eval-of-member-implies-itimes-list-0-off'.\index{izerop-eval-of-member-implies-iti!mes-list-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable subsetp-implies-itimes-list-eval\$-equals-0; name this event `subsetp-implies-itimes-list-eval\$-equals-0-off'.\index{subsetp-implies-itimes-list-eva!l\$-equals-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-0-itimes-list-eval\$-bagint-1; name this event `equal-0-itimes-list-eval\$-bagint-1-off'.\index{equal-0-itimes-list-eval\$-bagi!nt-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-0-itimes-list-eval\$-bagint-2; name this event `equal-0-itimes-list-eval\$-bagint-2-off'.\index{equal-0-itimes-list-eval\$-bagi!nt-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-itimes-hack-2; name this event `correctness-of-cancel-itimes-hack-2-off'.\index{correctness-of-cancel-itimes-ha!ck-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-itimes-hack-3-lemma; name this event `correctness-of-cancel-itimes-hack-3-lemma-off1'.\index{correctness-of-cancel-itimes-ha!ck-3-lemma-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-itimes-hack-3; name this event `correctness-of-cancel-itimes-hack-3-off'.\index{correctness-of-cancel-itimes-ha!ck-3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-itimes-tree-no-fix-int-1; name this event `eval\$-itimes-tree-no-fix-int-1-off'.\index{eval\$-itimes-tree-no-fix-int-1!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-itimes-tree-no-fix-int-2; name this event `eval\$-itimes-tree-no-fix-int-2-off'.\index{eval\$-itimes-tree-no-fix-int-2!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-make-cancel-itimes-inequality; name this event `eval\$-make-cancel-itimes-inequality-off'.\index{eval\$-make-cancel-itimes-inequ!ality-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable listp-bagint-with-singleton-implies-member; name this event `listp-bagint-with-singleton-implies-member-off'.\index{listp-bagint-with-singleton-imp!lies-member-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-list-eval\$-list-0; name this event `itimes-list-eval\$-list-0-off'.\index{itimes-list-eval\$-list-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-itimes-ilessp-hack-1; name this event `correctness-of-cancel-itimes-ilessp-hack-1-off'.\index{correctness-of-cancel-itimes-ile!ssp-hack-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable listp-bagint-with-singleton-member; name this event `listp-bagint-with-singleton-member-off'.\index{listp-bagint-with-singleton-mem!ber-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-itimes-ilessp-hack-2; name this event `correctness-of-cancel-itimes-ilessp-hack-2-off'.\index{correctness-of-cancel-itimes-ile!ssp-hack-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-itimes-ilessp-hack-3-lemma-1; name this event `correctness-of-cancel-itimes-ilessp-hack-3-lemma-1-off'.\index{correctness-of-cancel-itimes-ile!ssp-hack-3-lemma-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-itimes-ilessp-hack-3-lemma-2; name this event `correctness-of-cancel-itimes-ilessp-hack-3-lemma-2-off'.\index{correctness-of-cancel-itimes-ile!ssp-hack-3-lemma-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-itimes-ilessp-hack-3; name this event `correctness-of-cancel-itimes-ilessp-hack-3-off'.\index{correctness-of-cancel-itimes-ile!ssp-hack-3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-itimes-ilessp-hack-4; name this event `correctness-of-cancel-itimes-ilessp-hack-4-off'.\index{correctness-of-cancel-itimes-ile!ssp-hack-4-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{itimes-tree-ineg} \\  
\=\+{\rm{itimes-tree-ineg}}\,({\it{l\/}})\index{itimes-tree-ineg} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{l\/}}) $=$ {\tt{'}}{\tt{'}}{\tt{-1}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{cdr}}\,({\it{l\/}}))$\;\;${\bf then }{\rm{list}}\,({\tt{'}}{\tt{ineg}}, {\rm{itimes-tree-rec}}\,({\rm{cdr}}\,({\it{l\/}}))\index{itimes-tree-rec}) \\ 
{\bf else }{\rm{car}}\,({\it{l\/}})$\;${\bf  endif}\- \\ 
{\bf else }{\rm{itimes-tree-rec}}\,({\it{l\/}})\index{itimes-tree-rec}$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{'}}{\tt{1}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{itimes-factors} \\  
\=\+{\rm{itimes-factors}}\,({\it{x\/}})\index{itimes-factors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf case on }{\rm{car}}\,({\it{x\/}}): \\ 
{\bf case = }{\it{itimes\/}} \\ 
{\bf then }{\rm{append}}\,({\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors}, {\rm{itimes-factors}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-factors}) \\ 
{\bf case = }{\it{iplus\/}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\rm{listp}}\,({\rm{bagint}}\,(\=\+{\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\rm{itimes-factors}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-factors})\-\index{bagint}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{iplus}}, \\ 
{\rm{itimes-tree-ineg}}\,({\rm{bagdiff}}\,(\=\+{\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\rm{bagint}}\,(\=\+{\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\rm{itimes-factors}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-factors})\-\index{bagint})\-\index{bagdiff})\index{itimes-tree-ineg}, \\ 
{\rm{itimes-tree-ineg}}\,({\rm{bagdiff}}\,(\=\+{\rm{itimes-factors}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\rm{bagint}}\,(\=\+{\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\rm{itimes-factors}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-factors})\-\index{bagint})\-\index{bagdiff})\index{itimes-tree-ineg})\-, \\ 
{\rm{bagint}}\,(\=\+{\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\rm{itimes-factors}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-factors})\-\index{bagint})\- \\ 
{\bf else }{\rm{list}}\,({\it{x\/}})$\;${\bf  endif}\- \\ 
{\bf case = }{\it{ineg\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,({\tt{'}}{\tt{'}}{\tt{-1}}, {\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors}) \\ 
{\bf otherwise }{\rm{list}}\,({\it{x\/}})$\;${\bf  endcase}\- \\ 
{\bf else }{\rm{list}}\,({\it{x\/}})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes--1 \\ \index{itimes--1}
{\rm{itimes}}\,({\tt{-1}}, {\it{x\/}})\index{itimes} $=$ {\rm{ineg}}\,({\it{x\/}})\index{ineg}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-ineg-ineg \\ \index{equal-ineg-ineg}
({\rm{ineg}}\,({\it{x\/}})\index{ineg} $=$ {\rm{ineg}}\,({\it{y\/}})\index{ineg}) $=$ ({\rm{fix-int}}\,({\it{x\/}})\index{fix-int} $=$ {\rm{fix-int}}\,({\it{y\/}})\index{fix-int})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ilessp-ineg-ineg \\ \index{ilessp-ineg-ineg}
{\rm{ilessp}}\,({\rm{ineg}}\,({\it{x\/}})\index{ineg}, {\rm{ineg}}\,({\it{y\/}})\index{ineg})\index{ilessp} $=$ {\rm{ilessp}}\,({\it{y\/}}, {\it{x\/}})\index{ilessp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fix-int-eval\$-itimes-tree-rec \\ \index{fix-int-eval\$-itimes-tree-rec}
\=\+{\rm{listp}}\,({\it{x\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\rm{itimes-tree-rec}}\,({\it{x\/}})\index{itimes-tree-rec}, {\it{a\/}}))\index{fix-int} \\ 
$=$$\;\;\;\;${\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{itimes-list})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-itimes-tree-ineg \\ \index{eval\$-itimes-tree-ineg}
{\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\rm{itimes-tree-ineg}}\,({\it{x\/}})\index{itimes-tree-ineg}, {\it{a\/}}))\index{fix-int} $=$ {\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{itimes-list}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ineg-eval\$-itimes-tree-ineg \\ \index{ineg-eval\$-itimes-tree-ineg}
\=\+{\rm{ineg}}\,({\rm{eval\$}}\,({\bf{t}}, {\rm{itimes-tree-ineg}}\,({\it{x\/}})\index{itimes-tree-ineg}, {\it{a\/}}))\index{ineg} \\ 
$=$$\;\;\;\;${\rm{ineg}}\,({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{itimes-list})\index{ineg}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-eval\$-itimes-tree-ineg \\ \index{iplus-eval\$-itimes-tree-ineg}
\=\+(\=\+{\rm{iplus}}\,({\rm{eval\$}}\,({\bf{t}}, {\rm{itimes-tree-ineg}}\,({\it{x\/}})\index{itimes-tree-ineg}, {\it{a\/}}), {\it{y\/}})\index{iplus} \\ 
$=$$\;\;\;\;${\rm{iplus}}\,({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{itimes-list}, {\it{y\/}})\index{iplus})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{iplus}}\,({\it{y\/}}, {\rm{eval\$}}\,({\bf{t}}, {\rm{itimes-tree-ineg}}\,({\it{x\/}})\index{itimes-tree-ineg}, {\it{a\/}}))\index{iplus} \\ 
$=$$\;\;\;\;${\rm{iplus}}\,({\it{y\/}}, {\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{itimes-list})\index{iplus})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-eval\$-itimes-tree-ineg \\ \index{itimes-eval\$-itimes-tree-ineg}
\=\+(\=\+{\rm{itimes}}\,({\rm{eval\$}}\,({\bf{t}}, {\rm{itimes-tree-ineg}}\,({\it{x\/}})\index{itimes-tree-ineg}, {\it{a\/}}), {\it{y\/}})\index{itimes} \\ 
$=$$\;\;\;\;${\rm{itimes}}\,({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{itimes-list}, {\it{y\/}})\index{itimes})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{itimes}}\,({\it{y\/}}, {\rm{eval\$}}\,({\bf{t}}, {\rm{itimes-tree-ineg}}\,({\it{x\/}})\index{itimes-tree-ineg}, {\it{a\/}}))\index{itimes} \\ 
$=$$\;\;\;\;${\rm{itimes}}\,({\it{y\/}}, {\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{itimes-list})\index{itimes})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable itimes-tree-ineg; name this event `itimes-tree-ineg-off'.\index{itimes-tree-ineg-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{iplus-or-itimes-term} \\  
\=\+{\rm{iplus-or-itimes-term}}\,({\it{x\/}})\index{iplus-or-itimes-term} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf case on }{\rm{car}}\,({\it{x\/}}): \\ 
{\bf case = }{\it{iplus\/}} \\ 
{\bf then }{\bf{t}} \\ 
{\bf case = }{\it{itimes\/}} \\ 
{\bf $\;\;$then }{\bf{t}} \\ 
{\bf case = }{\it{ineg\/}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\rm{listp}}\,({\rm{cadr}}\,({\it{x\/}}))$\;\;${\bf then }{\rm{caadr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{itimes}} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf otherwise }{\bf{f}}$\;${\bf  endcase}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cancel-itimes-factors} \\  
\=\+{\rm{cancel-itimes-factors}}\,({\it{x\/}})\index{cancel-itimes-factors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) $\wedge$ ({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{equal}}) \\ 
{\bf then }\=\+{\bf if }{\rm{iplus-or-itimes-term}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-or-itimes-term} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{bagint}}\,(\=\+{\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\rm{itimes-factors}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-factors})\-\index{bagint}) \\ 
{\bf then }\=\+{\bf if }{\rm{iplus-or-itimes-term}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-or-itimes-term} \\ 
{\bf then }{\rm{make-cancel-itimes-equality}}\,(\=\+{\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\rm{itimes-factors}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\rm{bagint}}\,(\=\+{\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\rm{itimes-factors}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-factors})\-\index{bagint})\-\index{make-cancel-itimes-equality} \\ 
{\bf else }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{integerp}}, {\rm{caddr}}\,({\it{x\/}})), \\ 
{\rm{make-cancel-itimes-equality}}\,(\=\+{\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\rm{itimes-factors}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\rm{bagint}}\,(\=\+{\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\rm{itimes-factors}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-factors})\-\index{bagint})\-\index{make-cancel-itimes-equality}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\-$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{iplus-or-itimes-term}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-or-itimes-term} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{bagint}}\,(\=\+{\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\rm{itimes-factors}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-factors})\-\index{bagint}) \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{integerp}}, {\rm{cadr}}\,({\it{x\/}})), \\ 
{\rm{make-cancel-itimes-equality}}\,(\=\+{\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\rm{itimes-factors}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\rm{bagint}}\,(\=\+{\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\rm{itimes-factors}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-factors})\-\index{bagint})\-\index{make-cancel-itimes-equality}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN CANCEL-ITIMES-FACTORS-EXPANDED
 (X)
 (IF
  (LISTP X)
  (IF
   (EQUAL (CAR X) 'EQUAL)
   (COND
    ((LISTP (CADR X))
     (CASE
      (CAADR X)
      (IPLUS
       (IF
        (LISTP (BAGINT (ITIMES-FACTORS (CADR X))
                       (ITIMES-FACTORS (CADDR X))))
        (IF
         (LISTP (CADDR X))
         (CASE
          (CAADDR X)
          (IPLUS
             (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                          (ITIMES-FACTORS (CADDR X))
                                          (BAGINT (ITIMES-FACTORS (CADR X))
                                                  (ITIMES-FACTORS (CADDR X)))))
          (ITIMES
             (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                          (ITIMES-FACTORS (CADDR X))
                                          (BAGINT (ITIMES-FACTORS (CADR X))
                                                  (ITIMES-FACTORS (CADDR X)))))
          (INEG
           (IF
            (LISTP (CADADDR X))
            (IF
             (EQUAL (CAADADDR X) 'ITIMES)
             (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                          (ITIMES-FACTORS (CADDR X))
                                          (BAGINT (ITIMES-FACTORS (CADR X))
                                                  (ITIMES-FACTORS (CADDR X))))
             (LIST 'IF
              (LIST 'INTEGERP (CADDR X))
              (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
              (LIST 'QUOTE F)))
            (LIST 'IF
              (LIST 'INTEGERP (CADDR X))
              (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
              (LIST 'QUOTE F))))
          (OTHERWISE
           (LIST 'IF
              (LIST 'INTEGERP (CADDR X))
              (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
              (LIST 'QUOTE F))))
         (LIST 'IF
              (LIST 'INTEGERP (CADDR X))
              (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
              (LIST 'QUOTE F)))
        X))
      (ITIMES
       (IF
        (LISTP (BAGINT (ITIMES-FACTORS (CADR X))
                       (ITIMES-FACTORS (CADDR X))))
        (IF
         (LISTP (CADDR X))
         (CASE
          (CAADDR X)
          (IPLUS
             (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                          (ITIMES-FACTORS (CADDR X))
                                          (BAGINT (ITIMES-FACTORS (CADR X))
                                                  (ITIMES-FACTORS (CADDR X)))))
          (ITIMES
             (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                          (ITIMES-FACTORS (CADDR X))
                                          (BAGINT (ITIMES-FACTORS (CADR X))
                                                  (ITIMES-FACTORS (CADDR X)))))
          (INEG
           (IF
            (LISTP (CADADDR X))
            (IF
             (EQUAL (CAADADDR X) 'ITIMES)
             (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                          (ITIMES-FACTORS (CADDR X))
                                          (BAGINT (ITIMES-FACTORS (CADR X))
                                                  (ITIMES-FACTORS (CADDR X))))
             (LIST 'IF
              (LIST 'INTEGERP (CADDR X))
              (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
              (LIST 'QUOTE F)))
            (LIST 'IF
              (LIST 'INTEGERP (CADDR X))
              (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
              (LIST 'QUOTE F))))
          (OTHERWISE
           (LIST 'IF
              (LIST 'INTEGERP (CADDR X))
              (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
              (LIST 'QUOTE F))))
         (LIST 'IF
              (LIST 'INTEGERP (CADDR X))
              (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
              (LIST 'QUOTE F)))
        X))
      (INEG
       (COND
        ((LISTP (CADADR X))
         (COND
          ((EQUAL (CAADADR X) 'ITIMES)
           (IF
            (LISTP (BAGINT (ITIMES-FACTORS (CADR X))
                           (ITIMES-FACTORS (CADDR X))))
            (IF
             (LISTP (CADDR X))
             (CASE
              (CAADDR X)
              (IPLUS
               (MAKE-CANCEL-ITIMES-EQUALITY
                                          (ITIMES-FACTORS (CADR X))
                                          (ITIMES-FACTORS (CADDR X))
                                          (BAGINT (ITIMES-FACTORS (CADR X))
                                                  (ITIMES-FACTORS (CADDR X)))))
              (ITIMES
               (MAKE-CANCEL-ITIMES-EQUALITY
                                          (ITIMES-FACTORS (CADR X))
                                          (ITIMES-FACTORS (CADDR X))
                                          (BAGINT (ITIMES-FACTORS (CADR X))
                                                  (ITIMES-FACTORS (CADDR X)))))
              (INEG
               (IF
                (LISTP (CADADDR X))
                (IF
                 (EQUAL (CAADADDR X) 'ITIMES)
                 (MAKE-CANCEL-ITIMES-EQUALITY
                                           (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
                 (LIST 'IF
                  (LIST 'INTEGERP (CADDR X))
                  (MAKE-CANCEL-ITIMES-EQUALITY
                                           (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
                  (LIST 'QUOTE F)))
                (LIST 'IF
                 (LIST 'INTEGERP (CADDR X))
                 (MAKE-CANCEL-ITIMES-EQUALITY
                                           (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
                 (LIST 'QUOTE F))))
              (OTHERWISE
               (LIST 'IF
                (LIST 'INTEGERP (CADDR X))
                (MAKE-CANCEL-ITIMES-EQUALITY
                                           (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
                (LIST 'QUOTE F))))
             (LIST 'IF
              (LIST 'INTEGERP (CADDR X))
              (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
              (LIST 'QUOTE F)))
            X))
          ((LISTP (CADDR X))
           (CASE
            (CAADDR X)
            (IPLUS
             (IF
              (LISTP (BAGINT (ITIMES-FACTORS (CADR X))
                             (ITIMES-FACTORS (CADDR X))))
              (LIST 'IF
               (LIST 'INTEGERP (CADR X))
               (MAKE-CANCEL-ITIMES-EQUALITY
                                           (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
               (LIST 'QUOTE F))
              X))
            (ITIMES
             (IF
              (LISTP (BAGINT (ITIMES-FACTORS (CADR X))
                             (ITIMES-FACTORS (CADDR X))))
              (LIST 'IF
               (LIST 'INTEGERP (CADR X))
               (MAKE-CANCEL-ITIMES-EQUALITY
                                           (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
               (LIST 'QUOTE F))
              X))
            (INEG
             (IF
              (LISTP (CADADDR X))
              (IF
               (EQUAL (CAADADDR X) 'ITIMES)
               (IF
                (LISTP (BAGINT (ITIMES-FACTORS (CADR X))
                               (ITIMES-FACTORS (CADDR X))))
                (LIST 'IF
                 (LIST 'INTEGERP (CADR X))
                 (MAKE-CANCEL-ITIMES-EQUALITY
                                           (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
                 (LIST 'QUOTE F))
                X)
               X)
              X))
            (OTHERWISE X)))
          (T X)))
        ((LISTP (CADDR X))
         (CASE
          (CAADDR X)
          (IPLUS
           (IF
            (LISTP (BAGINT (ITIMES-FACTORS (CADR X))
                           (ITIMES-FACTORS (CADDR X))))
            (LIST 'IF
              (LIST 'INTEGERP (CADR X))
              (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
              (LIST 'QUOTE F))
            X))
          (ITIMES
           (IF
            (LISTP (BAGINT (ITIMES-FACTORS (CADR X))
                           (ITIMES-FACTORS (CADDR X))))
            (LIST 'IF
              (LIST 'INTEGERP (CADR X))
              (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
              (LIST 'QUOTE F))
            X))
          (INEG
           (IF
            (LISTP (CADADDR X))
            (IF
             (EQUAL (CAADADDR X) 'ITIMES)
             (IF
              (LISTP (BAGINT (ITIMES-FACTORS (CADR X))
                             (ITIMES-FACTORS (CADDR X))))
              (LIST 'IF
               (LIST 'INTEGERP (CADR X))
               (MAKE-CANCEL-ITIMES-EQUALITY
                                           (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
               (LIST 'QUOTE F))
              X)
             X)
            X))
          (OTHERWISE X)))
        (T X)))
      (OTHERWISE
       (IF
        (LISTP (CADDR X))
        (CASE
         (CAADDR X)
         (IPLUS
          (IF
           (LISTP (BAGINT (ITIMES-FACTORS (CADR X))
                          (ITIMES-FACTORS (CADDR X))))
           (LIST 'IF
              (LIST 'INTEGERP (CADR X))
              (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
              (LIST 'QUOTE F))
           X))
         (ITIMES
          (IF
           (LISTP (BAGINT (ITIMES-FACTORS (CADR X))
                          (ITIMES-FACTORS (CADDR X))))
           (LIST 'IF
              (LIST 'INTEGERP (CADR X))
              (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
              (LIST 'QUOTE F))
           X))
         (INEG
          (IF
           (LISTP (CADADDR X))
           (IF
            (EQUAL (CAADADDR X) 'ITIMES)
            (IF
             (LISTP (BAGINT (ITIMES-FACTORS (CADR X))
                            (ITIMES-FACTORS (CADDR X))))
             (LIST 'IF
              (LIST 'INTEGERP (CADR X))
              (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
              (LIST 'QUOTE F))
             X)
            X)
           X))
         (OTHERWISE X))
        X))))
    ((LISTP (CADDR X))
     (CASE
      (CAADDR X)
      (IPLUS
       (IF
        (LISTP (BAGINT (ITIMES-FACTORS (CADR X))
                       (ITIMES-FACTORS (CADDR X))))
        (LIST 'IF
              (LIST 'INTEGERP (CADR X))
              (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
              (LIST 'QUOTE F))
        X))
      (ITIMES
       (IF
        (LISTP (BAGINT (ITIMES-FACTORS (CADR X))
                       (ITIMES-FACTORS (CADDR X))))
        (LIST 'IF
              (LIST 'INTEGERP (CADR X))
              (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
              (LIST 'QUOTE F))
        X))
      (INEG
       (IF
        (LISTP (CADADDR X))
        (IF
         (EQUAL (CAADADDR X) 'ITIMES)
         (IF
          (LISTP (BAGINT (ITIMES-FACTORS (CADR X))
                         (ITIMES-FACTORS (CADDR X))))
          (LIST 'IF
              (LIST 'INTEGERP (CADR X))
              (MAKE-CANCEL-ITIMES-EQUALITY (ITIMES-FACTORS (CADR X))
                                           (ITIMES-FACTORS (CADDR X))
                                           (BAGINT (ITIMES-FACTORS (CADR X))
                                                   (ITIMES-FACTORS (CADDR X))))
              (LIST 'QUOTE F))
          X)
         X)
        X))
      (OTHERWISE X)))
    (T X))
   X)
  X))
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  cancel-itimes-factors-expanded-cancel-itimes-factors \\ \index{cancel-itimes-factors-expanded-!cancel-itimes-factors}
{\rm{cancel-itimes-factors-expanded}}\,({\it{x\/}})\index{cancel-itimes-factors-expanded} $=$ {\rm{cancel-itimes-factors}}\,({\it{x\/}})\index{cancel-itimes-factors}
\end{tabbing}


\noindent{\sc Event}:   Enable cancel-itimes-factors-expanded; name this event `cancel-itimes-factors-expanded-off'.\index{cancel-itimes-factors-expanded-!off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-or-itimes-term; name this event `iplus-or-itimes-term-off'.\index{iplus-or-itimes-term-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  equal-itimes-list-eval\$-list-delete-new-1 \\ \index{equal-itimes-list-eval\$-list-de!lete-new-1}
\=\+({\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{elt\/}}, {\it{a\/}}))\index{fix-int} $\not=$ {\tt{0}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\it{x\/}} $=$ {\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{delete}}\,({\it{elt\/}}, {\it{bag\/}})\index{delete}, {\it{a\/}}))\index{itimes-list}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{elt\/}} $\in$ {\it{bag\/}} \\ 
{\bf then }\=\+{\rm{integerp}}\,({\it{x\/}})\index{integerp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{itimes}}\,({\it{x\/}}, {\rm{eval\$}}\,({\bf{t}}, {\it{elt\/}}, {\it{a\/}}))\index{itimes} \\ 
$=$$\;\;\;\;${\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag\/}}, {\it{a\/}}))\index{itimes-list})\-\- \\ 
{\bf else }{\it{x\/}} $=$ {\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag\/}}, {\it{a\/}}))\index{itimes-list}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-itimes-list-eval\$-list-delete-new-2 \\ \index{equal-itimes-list-eval\$-list-de!lete-new-2}
\=\+({\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{elt\/}}, {\it{a\/}}))\index{fix-int} $\not=$ {\tt{0}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{delete}}\,({\it{elt\/}}, {\it{bag\/}})\index{delete}, {\it{a\/}}))\index{itimes-list} $=$ {\it{x\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{elt\/}} $\in$ {\it{bag\/}} \\ 
{\bf then }\=\+{\rm{integerp}}\,({\it{x\/}})\index{integerp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{itimes}}\,({\it{x\/}}, {\rm{eval\$}}\,({\bf{t}}, {\it{elt\/}}, {\it{a\/}}))\index{itimes} \\ 
$=$$\;\;\;\;${\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag\/}}, {\it{a\/}}))\index{itimes-list})\-\- \\ 
{\bf else }{\it{x\/}} $=$ {\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag\/}}, {\it{a\/}}))\index{itimes-list}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-itimes-list-eval\$-list-delete \\ \index{itimes-itimes-list-eval\$-list-!delete}
\=\+({\it{x\/}} $\in$ {\it{bag\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{itimes}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}), {\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{delete}}\,({\it{x\/}}, {\it{bag\/}})\index{delete}, {\it{a\/}}))\index{itimes-list})\index{itimes} \\ 
$=$$\;\;\;\;${\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag\/}}, {\it{a\/}}))\index{itimes-list})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-itimes-list-eval\$-list-bagdiff \\ \index{equal-itimes-list-eval\$-list-b!agdiff}
\=\+(\=\+{\rm{subbagp}}\,({\it{in-both\/}}, {\it{bag1\/}})\index{subbagp} \\ 
$\wedge$$\;\;\;\;${\rm{subbagp}}\,({\it{in-both\/}}, {\it{bag2\/}})\index{subbagp} \\ 
$\wedge$$\;\;\;\;$({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{in-both\/}}, {\it{a\/}}))\index{itimes-list} $\not=$ {\tt{0}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagdiff}}\,({\it{bag1\/}}, {\it{in-both\/}})\index{bagdiff}, {\it{a\/}}))\index{itimes-list} \\ 
$=$$\;\;\;\;${\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagdiff}}\,({\it{bag2\/}}, {\it{in-both\/}})\index{bagdiff}, {\it{a\/}}))\index{itimes-list})\- \\ 
$=$$\;\;\;\;$(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag1\/}}, {\it{a\/}}))\index{itimes-list} \\ 
$=$$\;\;\;\;${\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag2\/}}, {\it{a\/}}))\index{itimes-list})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  membership-of-0-implies-itimes-list-is-0 \\ \index{membership-of-0-implies-itimes-!list-is-0}
({\tt{0}} $\in$ {\it{x\/}}) $\rightarrow$ ({\rm{itimes-list}}\,({\it{x\/}})\index{itimes-list} $=$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  member-0-eval\$-list \\ \index{member-0-eval\$-list}
({\tt{0}} $\in$ {\it{x\/}}) $\rightarrow$ ({\tt{0}} $\in$ {\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-list-eval\$-factors-lemma \\ \index{itimes-list-eval\$-factors-lemm!a}
\=\+{\rm{itimes}}\,(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagint}}\,({\it{bag1\/}}, {\it{bag2\/}})\index{bagint}, {\it{a\/}}))\index{itimes-list}, \\ 
{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagdiff}}\,({\it{bag2\/}}, {\rm{bagint}}\,({\it{bag1\/}}, {\it{bag2\/}})\index{bagint})\index{bagdiff}, {\it{a\/}}))\index{itimes-list})\-\index{itimes} \\ 
$=$$\;\;\;\;${\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag2\/}}, {\it{a\/}}))\index{itimes-list}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-list-eval\$-factors-lemma-prime \\ \index{itimes-list-eval\$-factors-lemm!a-prime}
\=\+{\rm{itimes}}\,(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagint}}\,({\it{bag1\/}}, {\it{bag2\/}})\index{bagint}, {\it{a\/}}))\index{itimes-list}, \\ 
{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagdiff}}\,({\it{bag1\/}}, {\rm{bagint}}\,({\it{bag1\/}}, {\it{bag2\/}})\index{bagint})\index{bagdiff}, {\it{a\/}}))\index{itimes-list})\-\index{itimes} \\ 
$=$$\;\;\;\;${\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag1\/}}, {\it{a\/}}))\index{itimes-list}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  itimes-list-eval\$-factors \\ \index{itimes-list-eval\$-factors}
{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{itimes-factors}}\,({\it{x\/}})\index{itimes-factors}, {\it{a\/}}))\index{itimes-list} $=$ {\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}))\index{fix-int}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-or-itimes-term-integerp-eval\$ \\ \index{iplus-or-itimes-term-integerp-ev!al\$}
{\rm{iplus-or-itimes-term}}\,({\it{x\/}})\index{iplus-or-itimes-term} $\rightarrow$ {\rm{integerp}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}))\index{integerp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-list-bagint-0 \\ \index{eval\$-list-bagint-0}
\=\+({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagint}}\,({\it{x\/}}, {\it{y\/}})\index{bagint}, {\it{a\/}}))\index{itimes-list} $=$ {\tt{0}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{itimes-list} $=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{y\/}}, {\it{a\/}}))\index{itimes-list} $=$ {\tt{0}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-list-bagint-0-implies-equal \\ \index{eval\$-list-bagint-0-implies-eq!ual}
\=\+(\=\+(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagint}}\,({\rm{itimes-factors}}\,({\it{v\/}})\index{itimes-factors}, {\rm{itimes-factors}}\,({\it{w\/}})\index{itimes-factors})\index{bagint}, {\it{a\/}}))\index{itimes-list} \\ 
$=$$\;\;\;\;${\tt{0}})\- \\ 
$\wedge$$\;\;\;\;${\rm{integerp}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{v\/}}, {\it{a\/}}))\index{integerp} \\ 
$\wedge$$\;\;\;\;${\rm{integerp}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{w\/}}, {\it{a\/}}))\index{integerp})\- \\ 
$\rightarrow$$\;\;\;\;$(({\rm{eval\$}}\,({\bf{t}}, {\it{v\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\it{w\/}}, {\it{a\/}})) $=$ {\bf{t}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-itimes-factors \\ \index{correctness-of-cancel-itimes-fa!ctors}
{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{cancel-itimes-factors-expanded}}\,({\it{x\/}})\index{cancel-itimes-factors-expanded}, {\it{a\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cancel-itimes-ilessp-factors} \\  
\=\+{\rm{cancel-itimes-ilessp-factors}}\,({\it{x\/}})\index{cancel-itimes-ilessp-factors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{ilessp}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{bagint}}\,(\=\+{\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\rm{itimes-factors}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-factors})\-\index{bagint}) \\ 
{\bf then }{\rm{make-cancel-itimes-inequality}}\,(\=\+{\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\rm{itimes-factors}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\rm{bagint}}\,(\=\+{\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\rm{itimes-factors}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-factors})\-\index{bagint})\-\index{make-cancel-itimes-inequality} \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bagint-singleton \\ \index{bagint-singleton}
\=\+{\rm{bagint}}\,({\it{x\/}}, {\rm{list}}\,({\it{y\/}}))\index{bagint} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{y\/}} $\in$ {\it{x\/}}$\;\;${\bf then }{\rm{list}}\,({\it{y\/}}) \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  izerop-ilessp-0-relationship \\ \index{izerop-ilessp-0-relationship}
({\rm{fix-int}}\,({\it{x\/}})\index{fix-int} $=$ {\tt{0}}) $=$ (($\neg$ {\rm{ilessp}}\,({\it{x\/}}, {\tt{0}})\index{ilessp}) $\wedge$ ($\neg$ {\rm{ilessp}}\,({\tt{0}}, {\it{x\/}})\index{ilessp}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ilessp-itimes-list-eval\$-list-delete-helper-1 \\ \index{ilessp-itimes-list-eval\$-list-!delete-helper-1}
{\rm{ilessp}}\,({\tt{0}}, {\it{w\/}})\index{ilessp} $\rightarrow$ ({\rm{ilessp}}\,({\rm{itimes}}\,({\it{x\/}}, {\it{w\/}})\index{itimes}, {\rm{itimes}}\,({\it{w\/}}, {\it{u\/}})\index{itimes})\index{ilessp} $=$ {\rm{ilessp}}\,({\it{x\/}}, {\it{u\/}})\index{ilessp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ilessp-itimes-list-eval\$-list-delete-helper-2 \\ \index{ilessp-itimes-list-eval\$-list-!delete-helper-2}
{\rm{ilessp}}\,({\it{w\/}}, {\tt{0}})\index{ilessp} $\rightarrow$ ({\rm{ilessp}}\,({\rm{itimes}}\,({\it{w\/}}, {\it{u\/}})\index{itimes}, {\rm{itimes}}\,({\it{x\/}}, {\it{w\/}})\index{itimes})\index{ilessp} $=$ {\rm{ilessp}}\,({\it{x\/}}, {\it{u\/}})\index{ilessp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ilessp-itimes-list-eval\$-list-delete \\ \index{ilessp-itimes-list-eval\$-list-!delete}
\=\+(({\it{z\/}} $\in$ {\it{y\/}}) $\wedge$ ({\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{z\/}}, {\it{a\/}}))\index{fix-int} $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{ilessp}}\,({\it{x\/}}, {\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{delete}}\,({\it{z\/}}, {\it{y\/}})\index{delete}, {\it{a\/}}))\index{itimes-list})\index{ilessp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{ilessp}}\,({\tt{0}}, {\rm{eval\$}}\,({\bf{t}}, {\it{z\/}}, {\it{a\/}}))\index{ilessp} \\ 
{\bf then }{\rm{ilessp}}\,(\=\+{\rm{itimes}}\,({\it{x\/}}, {\rm{eval\$}}\,({\bf{t}}, {\it{z\/}}, {\it{a\/}}))\index{itimes}, \\ 
{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{y\/}}, {\it{a\/}}))\index{itimes-list})\-\index{ilessp} \\ 
{\bf elseif }{\rm{ilessp}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{z\/}}, {\it{a\/}}), {\tt{0}})\index{ilessp} \\ 
{\bf then }{\rm{ilessp}}\,(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{y\/}}, {\it{a\/}}))\index{itimes-list}, \\ 
{\rm{itimes}}\,({\it{x\/}}, {\rm{eval\$}}\,({\bf{t}}, {\it{z\/}}, {\it{a\/}}))\index{itimes})\-\index{ilessp} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ilessp-itimes-list-eval\$-list-delete-prime-helper-1 \\ \index{ilessp-itimes-list-eval\$-list-!delete-prime-helper-1}
{\rm{ilessp}}\,({\tt{0}}, {\it{w\/}})\index{ilessp} $\rightarrow$ ({\rm{ilessp}}\,({\rm{itimes}}\,({\it{w\/}}, {\it{u\/}})\index{itimes}, {\rm{itimes}}\,({\it{x\/}}, {\it{w\/}})\index{itimes})\index{ilessp} $=$ {\rm{ilessp}}\,({\it{u\/}}, {\it{x\/}})\index{ilessp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ilessp-itimes-list-eval\$-list-delete-prime-helper-2 \\ \index{ilessp-itimes-list-eval\$-list-!delete-prime-helper-2}
{\rm{ilessp}}\,({\it{w\/}}, {\tt{0}})\index{ilessp} $\rightarrow$ ({\rm{ilessp}}\,({\rm{itimes}}\,({\it{x\/}}, {\it{w\/}})\index{itimes}, {\rm{itimes}}\,({\it{w\/}}, {\it{u\/}})\index{itimes})\index{ilessp} $=$ {\rm{ilessp}}\,({\it{u\/}}, {\it{x\/}})\index{ilessp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ilessp-itimes-list-eval\$-list-delete-prime \\ \index{ilessp-itimes-list-eval\$-list-!delete-prime}
\=\+(({\it{z\/}} $\in$ {\it{y\/}}) $\wedge$ ({\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{z\/}}, {\it{a\/}}))\index{fix-int} $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{ilessp}}\,({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{delete}}\,({\it{z\/}}, {\it{y\/}})\index{delete}, {\it{a\/}}))\index{itimes-list}, {\it{x\/}})\index{ilessp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{ilessp}}\,({\tt{0}}, {\rm{eval\$}}\,({\bf{t}}, {\it{z\/}}, {\it{a\/}}))\index{ilessp} \\ 
{\bf then }{\rm{ilessp}}\,(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{y\/}}, {\it{a\/}}))\index{itimes-list}, \\ 
{\rm{itimes}}\,({\it{x\/}}, {\rm{eval\$}}\,({\bf{t}}, {\it{z\/}}, {\it{a\/}}))\index{itimes})\-\index{ilessp} \\ 
{\bf elseif }{\rm{ilessp}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{z\/}}, {\it{a\/}}), {\tt{0}})\index{ilessp} \\ 
{\bf then }{\rm{ilessp}}\,(\=\+{\rm{itimes}}\,({\it{x\/}}, {\rm{eval\$}}\,({\bf{t}}, {\it{z\/}}, {\it{a\/}}))\index{itimes}, \\ 
{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{y\/}}, {\it{a\/}}))\index{itimes-list})\-\index{ilessp} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ilessp-0-itimes \\ \index{ilessp-0-itimes}
\=\+{\rm{ilessp}}\,({\tt{0}}, {\rm{itimes}}\,({\it{x\/}}, {\it{y\/}})\index{itimes})\index{ilessp} \\ 
$=$$\;\;\;\;$(({\rm{ilessp}}\,({\tt{0}}, {\it{x\/}})\index{ilessp} $\wedge$ {\rm{ilessp}}\,({\tt{0}}, {\it{y\/}})\index{ilessp}) $\vee$ ({\rm{ilessp}}\,({\it{x\/}}, {\tt{0}})\index{ilessp} $\wedge$ {\rm{ilessp}}\,({\it{y\/}}, {\tt{0}})\index{ilessp}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ilessp-itimes-0 \\ \index{ilessp-itimes-0}
\=\+{\rm{ilessp}}\,({\rm{itimes}}\,({\it{x\/}}, {\it{y\/}})\index{itimes}, {\tt{0}})\index{ilessp} \\ 
$=$$\;\;\;\;$(({\rm{ilessp}}\,({\tt{0}}, {\it{x\/}})\index{ilessp} $\wedge$ {\rm{ilessp}}\,({\it{y\/}}, {\tt{0}})\index{ilessp}) $\vee$ ({\rm{ilessp}}\,({\it{x\/}}, {\tt{0}})\index{ilessp} $\wedge$ {\rm{ilessp}}\,({\tt{0}}, {\it{y\/}})\index{ilessp}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ilessp-itimes-list-eval\$-list-bagdiff \\ \index{ilessp-itimes-list-eval\$-list-!bagdiff}
\=\+(\=\+{\rm{subbagp}}\,({\it{in-both\/}}, {\it{bag1\/}})\index{subbagp} \\ 
$\wedge$$\;\;\;\;${\rm{subbagp}}\,({\it{in-both\/}}, {\it{bag2\/}})\index{subbagp} \\ 
$\wedge$$\;\;\;\;$({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{in-both\/}}, {\it{a\/}}))\index{itimes-list} $\not=$ {\tt{0}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{ilessp}}\,(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagdiff}}\,({\it{bag1\/}}, {\it{in-both\/}})\index{bagdiff}, {\it{a\/}}))\index{itimes-list}, \\ 
{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagdiff}}\,({\it{bag2\/}}, {\it{in-both\/}})\index{bagdiff}, {\it{a\/}}))\index{itimes-list})\-\index{ilessp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{ilessp}}\,({\tt{0}}, {\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{in-both\/}}, {\it{a\/}}))\index{itimes-list})\index{ilessp} \\ 
{\bf then }{\rm{ilessp}}\,(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag1\/}}, {\it{a\/}}))\index{itimes-list}, \\ 
{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag2\/}}, {\it{a\/}}))\index{itimes-list})\-\index{ilessp} \\ 
{\bf else }{\rm{ilessp}}\,(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag2\/}}, {\it{a\/}}))\index{itimes-list}, \\ 
{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag1\/}}, {\it{a\/}}))\index{itimes-list})\-\index{ilessp}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  zero-ilessp-implies-not-equal \\ \index{zero-ilessp-implies-not-equal}
{\rm{ilessp}}\,({\tt{0}}, {\it{x\/}})\index{ilessp} $\rightarrow$ ({\tt{0}} $\not=$ {\it{x\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ilessp-itimes-list-eval\$-list-bagdiff-corollary-1 \\ \index{ilessp-itimes-list-eval\$-list-!bagdiff-corollary-1}
\=\+(\=\+{\rm{subbagp}}\,({\it{in-both\/}}, {\it{bag1\/}})\index{subbagp} \\ 
$\wedge$$\;\;\;\;${\rm{subbagp}}\,({\it{in-both\/}}, {\it{bag2\/}})\index{subbagp} \\ 
$\wedge$$\;\;\;\;${\rm{ilessp}}\,({\tt{0}}, {\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{in-both\/}}, {\it{a\/}}))\index{itimes-list})\index{ilessp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{ilessp}}\,(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagdiff}}\,({\it{bag1\/}}, {\it{in-both\/}})\index{bagdiff}, {\it{a\/}}))\index{itimes-list}, \\ 
{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagdiff}}\,({\it{bag2\/}}, {\it{in-both\/}})\index{bagdiff}, {\it{a\/}}))\index{itimes-list})\-\index{ilessp} \\ 
$=$$\;\;\;\;${\rm{ilessp}}\,(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag1\/}}, {\it{a\/}}))\index{itimes-list}, \\ 
{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag2\/}}, {\it{a\/}}))\index{itimes-list})\-\index{ilessp})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ilessp-zero-implies-not-equal \\ \index{ilessp-zero-implies-not-equal}
{\rm{ilessp}}\,({\it{x\/}}, {\tt{0}})\index{ilessp} $\rightarrow$ ({\tt{0}} $\not=$ {\it{x\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ilessp-itimes-list-eval\$-list-bagdiff-corollary-2 \\ \index{ilessp-itimes-list-eval\$-list-!bagdiff-corollary-2}
\=\+(\=\+{\rm{subbagp}}\,({\it{in-both\/}}, {\it{bag1\/}})\index{subbagp} \\ 
$\wedge$$\;\;\;\;${\rm{subbagp}}\,({\it{in-both\/}}, {\it{bag2\/}})\index{subbagp} \\ 
$\wedge$$\;\;\;\;${\rm{ilessp}}\,({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{in-both\/}}, {\it{a\/}}))\index{itimes-list}, {\tt{0}})\index{ilessp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{ilessp}}\,(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagdiff}}\,({\it{bag1\/}}, {\it{in-both\/}})\index{bagdiff}, {\it{a\/}}))\index{itimes-list}, \\ 
{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagdiff}}\,({\it{bag2\/}}, {\it{in-both\/}})\index{bagdiff}, {\it{a\/}}))\index{itimes-list})\-\index{ilessp} \\ 
$=$$\;\;\;\;${\rm{ilessp}}\,(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag2\/}}, {\it{a\/}}))\index{itimes-list}, \\ 
{\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{bag1\/}}, {\it{a\/}}))\index{itimes-list})\-\index{ilessp})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  member-0-itimes-factors-yields-0 \\ \index{member-0-itimes-factors-yields-!0}
({\rm{eval\$}}\,({\bf{t}}, {\it{w\/}}, {\it{a\/}}) $\not=$ {\tt{0}}) $\rightarrow$ ({\tt{0}} $\not\in$ {\rm{itimes-factors}}\,({\it{w\/}})\index{itimes-factors})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  member-0-itimes-factors-yields-0-ilessp-consequence-1 \\ \index{member-0-itimes-factors-yields-!0-ilessp-consequence-1}
{\rm{ilessp}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{w\/}}, {\it{a\/}}), {\tt{0}})\index{ilessp} $\rightarrow$ ({\tt{0}} $\not\in$ {\rm{itimes-factors}}\,({\it{w\/}})\index{itimes-factors})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  member-0-itimes-factors-yields-0-ilessp-consequence-2 \\ \index{member-0-itimes-factors-yields-!0-ilessp-consequence-2}
{\rm{ilessp}}\,({\tt{0}}, {\rm{eval\$}}\,({\bf{t}}, {\it{w\/}}, {\it{a\/}}))\index{ilessp} $\rightarrow$ ({\tt{0}} $\not\in$ {\rm{itimes-factors}}\,({\it{w\/}})\index{itimes-factors})
\end{tabbing}


\noindent{\sc Event}:   Disable ilessp-trichotomy; name this event `ilessp-trichotomy-on'.\index{ilessp-trichotomy-on}

\addvspace{18pt}


\noindent{\sc Event}:   Enable izerop-ilessp-0-relationship; name this event `izerop-ilessp-0-relationship-off'.\index{izerop-ilessp-0-relationship-of!f}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  eval\$-list-bagint-0-for-ilessp \\ \index{eval\$-list-bagint-0-for-ilessp}
\=\+(\=\+($\neg$ {\rm{ilessp}}\,({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagint}}\,({\it{x\/}}, {\it{y\/}})\index{bagint}, {\it{a\/}}))\index{itimes-list}, {\tt{0}})\index{ilessp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{ilessp}}\,({\tt{0}}, {\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{bagint}}\,({\it{x\/}}, {\it{y\/}})\index{bagint}, {\it{a\/}}))\index{itimes-list})\index{ilessp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{fix-int}}\,({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{itimes-list})\index{fix-int} $=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\rm{fix-int}}\,({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{y\/}}, {\it{a\/}}))\index{itimes-list})\index{fix-int} $=$ {\tt{0}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-list-bagint-0-implies-equal-for-ilessp-lemma \\ \index{eval\$-list-bagint-0-implies-eq!ual-for-ilessp-lemma}
\=\+(\=\+($\neg$ {\rm{ilessp}}\,(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,(\=\+{\tt{'}}{\tt{list}}, \\ 
{\rm{bagint}}\,({\rm{itimes-factors}}\,({\it{v\/}})\index{itimes-factors}, {\rm{itimes-factors}}\,({\it{w\/}})\index{itimes-factors})\index{bagint}, \\ 
{\it{a\/}})\-)\index{itimes-list}, \\ 
{\tt{0}})\-\index{ilessp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{ilessp}}\,(\=\+{\tt{0}}, \\ 
{\rm{itimes-list}}\,({\rm{eval\$}}\,(\=\+{\tt{'}}{\tt{list}}, \\ 
{\rm{bagint}}\,(\=\+{\rm{itimes-factors}}\,({\it{v\/}})\index{itimes-factors}, \\ 
{\rm{itimes-factors}}\,({\it{w\/}})\index{itimes-factors})\-\index{bagint}, \\ 
{\it{a\/}})\-)\index{itimes-list})\-\index{ilessp}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{v\/}}, {\it{a\/}}))\index{fix-int} $=$ {\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{w\/}}, {\it{a\/}}))\index{fix-int})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-fix-int-to-ilessp \\ \index{equal-fix-int-to-ilessp}
({\rm{fix-int}}\,({\it{x\/}})\index{fix-int} $=$ {\rm{fix-int}}\,({\it{y\/}})\index{fix-int}) $\rightarrow$ ($\neg$ {\rm{ilessp}}\,({\it{x\/}}, {\it{y\/}})\index{ilessp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-list-bagint-0-implies-equal-for-ilessp \\ \index{eval\$-list-bagint-0-implies-eq!ual-for-ilessp}
\=\+(\=\+($\neg$ {\rm{ilessp}}\,(\=\+{\rm{itimes-list}}\,({\rm{eval\$}}\,(\=\+{\tt{'}}{\tt{list}}, \\ 
{\rm{bagint}}\,({\rm{itimes-factors}}\,({\it{v\/}})\index{itimes-factors}, {\rm{itimes-factors}}\,({\it{w\/}})\index{itimes-factors})\index{bagint}, \\ 
{\it{a\/}})\-)\index{itimes-list}, \\ 
{\tt{0}})\-\index{ilessp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{ilessp}}\,(\=\+{\tt{0}}, \\ 
{\rm{itimes-list}}\,({\rm{eval\$}}\,(\=\+{\tt{'}}{\tt{list}}, \\ 
{\rm{bagint}}\,(\=\+{\rm{itimes-factors}}\,({\it{v\/}})\index{itimes-factors}, \\ 
{\rm{itimes-factors}}\,({\it{w\/}})\index{itimes-factors})\-\index{bagint}, \\ 
{\it{a\/}})\-)\index{itimes-list})\-\index{ilessp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+($\neg$ {\rm{ilessp}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{v\/}}, {\it{a\/}}), {\rm{eval\$}}\,({\bf{t}}, {\it{w\/}}, {\it{a\/}}))\index{ilessp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{ilessp}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{w\/}}, {\it{a\/}}), {\rm{eval\$}}\,({\bf{t}}, {\it{v\/}}, {\it{a\/}}))\index{ilessp}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ilessp-trichotomy; name this event `ilessp-trichotomy-off1'.\index{ilessp-trichotomy-off1}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-itimes-ilessp-factors \\ \index{correctness-of-cancel-itimes-ile!ssp-factors}
{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{cancel-itimes-ilessp-factors}}\,({\it{x\/}})\index{cancel-itimes-ilessp-factors}, {\it{a\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-count-listp-cdr; name this event `lessp-count-listp-cdr-on'.\index{lessp-count-listp-cdr-on}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{disjoin-equalities-with-0} \\  
\=\+{\rm{disjoin-equalities-with-0}}\,({\it{factors\/}})\index{disjoin-equalities-with-0} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\rm{cdr}}\,({\it{factors\/}})) \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{or}}, \\ 
{\rm{cons}}\,({\tt{'}}{\tt{equal}}, {\rm{cons}}\,({\rm{list}}\,({\tt{'}}{\tt{fix-int}}, {\rm{car}}\,({\it{factors\/}})), {\tt{'}}{\tt{(}}{\tt{'}}{\tt{0}}{\tt{)}})), \\ 
{\rm{disjoin-equalities-with-0}}\,({\rm{cdr}}\,({\it{factors\/}}))\index{disjoin-equalities-with-0})\- \\ 
{\bf else }{\rm{cons}}\,({\tt{'}}{\tt{equal}}, {\rm{cons}}\,({\rm{list}}\,({\tt{'}}{\tt{fix-int}}, {\rm{car}}\,({\it{factors\/}})), {\tt{'}}{\tt{(}}{\tt{'}}{\tt{0}}{\tt{)}}))$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable lessp-count-listp-cdr; name this event `lessp-count-listp-cdr-off1'.\index{lessp-count-listp-cdr-off1}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{cancel-factors-0} \\  
\=\+{\rm{cancel-factors-0}}\,({\it{x\/}})\index{cancel-factors-0} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{equal}} \\ 
{\bf then }\=\+{\bf if }{\rm{cadr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{'}}{\tt{0}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{cdr}}\,({\rm{itimes-factors}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-factors})) \\ 
{\bf then }{\rm{disjoin-equalities-with-0}}\,({\rm{itimes-factors}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-factors})\index{disjoin-equalities-with-0} \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{caddr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{'}}{\tt{0}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{cdr}}\,({\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors})) \\ 
{\bf then }{\rm{disjoin-equalities-with-0}}\,({\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors})\index{disjoin-equalities-with-0} \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{some-eval\$s-to-0} \\  
\=\+{\rm{some-eval\$s-to-0}}\,({\it{x\/}}, {\it{a\/}})\index{some-eval\$s-to-0} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+({\rm{fix-int}}\,({\rm{eval\$}}\,({\bf{t}}, {\rm{car}}\,({\it{x\/}}), {\it{a\/}}))\index{fix-int} $=$ {\tt{0}}) \\ 
$\vee$$\;\;\;\;${\rm{some-eval\$s-to-0}}\,({\rm{cdr}}\,({\it{x\/}}), {\it{a\/}})\index{some-eval\$s-to-0}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-disjoin-equalities-with-0 \\ \index{eval\$-disjoin-equalities-with-!0}
\=\+{\rm{listp}}\,({\it{lst\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{disjoin-equalities-with-0}}\,({\it{lst\/}})\index{disjoin-equalities-with-0}, {\it{a\/}}) \\ 
$=$$\;\;\;\;${\rm{some-eval\$s-to-0}}\,({\it{lst\/}}, {\it{a\/}})\index{some-eval\$s-to-0})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  some-eval\$s-to-0-append \\ \index{some-eval\$s-to-0-append}
\=\+{\rm{some-eval\$s-to-0}}\,({\rm{append}}\,({\it{x\/}}, {\it{y\/}}), {\it{a\/}})\index{some-eval\$s-to-0} \\ 
$=$$\;\;\;\;$({\rm{some-eval\$s-to-0}}\,({\it{x\/}}, {\it{a\/}})\index{some-eval\$s-to-0} $\vee$ {\rm{some-eval\$s-to-0}}\,({\it{y\/}}, {\it{a\/}})\index{some-eval\$s-to-0})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  some-eval\$s-to-0-eliminator \\ \index{some-eval\$s-to-0-eliminator}
{\rm{some-eval\$s-to-0}}\,({\it{x\/}}, {\it{a\/}})\index{some-eval\$s-to-0} $=$ ({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{itimes-list} $=$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  listp-cdr-factors-implies-integerp \\ \index{listp-cdr-factors-implies-intege!rp}
{\rm{listp}}\,({\rm{cdr}}\,({\rm{itimes-factors}}\,({\it{v\/}})\index{itimes-factors})) $\rightarrow$ {\rm{integerp}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{v\/}}, {\it{a\/}}))\index{integerp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-factors-0 \\ \index{correctness-of-cancel-factors-0}
{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{cancel-factors-0}}\,({\it{x\/}})\index{cancel-factors-0}, {\it{a\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-count-listp-cdr; name this event `lessp-count-listp-cdr-on1'.\index{lessp-count-listp-cdr-on1}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{conjoin-inequalities-with-0} \\  
\=\+{\rm{conjoin-inequalities-with-0}}\,({\it{factors\/}}, {\it{parity\/}})\index{conjoin-inequalities-with-0} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\rm{cdr}}\,({\it{factors\/}})) \\ 
{\bf then }\=\+{\bf if }{\it{parity\/}} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{or}}, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{and}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{ilessp}}, {\tt{'}}{\tt{'}}{\tt{0}}, {\rm{car}}\,({\it{factors\/}})), \\ 
{\rm{conjoin-inequalities-with-0}}\,({\rm{cdr}}\,({\it{factors\/}}), {\bf{t}})\index{conjoin-inequalities-with-0})\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{and}}, \\ 
{\rm{cons}}\,({\tt{'}}{\tt{ilessp}}, {\rm{cons}}\,({\rm{car}}\,({\it{factors\/}}), {\tt{'}}{\tt{(}}{\tt{'}}{\tt{0}}{\tt{)}})), \\ 
{\rm{conjoin-inequalities-with-0}}\,({\rm{cdr}}\,({\it{factors\/}}), {\bf{f}})\index{conjoin-inequalities-with-0})\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\tt{'}}{\tt{or}}, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{and}}, \\ 
{\rm{cons}}\,({\tt{'}}{\tt{ilessp}}, {\rm{cons}}\,({\rm{car}}\,({\it{factors\/}}), {\tt{'}}{\tt{(}}{\tt{'}}{\tt{0}}{\tt{)}})), \\ 
{\rm{conjoin-inequalities-with-0}}\,({\rm{cdr}}\,({\it{factors\/}}), {\bf{t}})\index{conjoin-inequalities-with-0})\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{and}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{ilessp}}, {\tt{'}}{\tt{'}}{\tt{0}}, {\rm{car}}\,({\it{factors\/}})), \\ 
{\rm{conjoin-inequalities-with-0}}\,({\rm{cdr}}\,({\it{factors\/}}), {\bf{f}})\index{conjoin-inequalities-with-0})\-)\-$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{parity\/}}$\;\;${\bf then }{\rm{list}}\,({\tt{'}}{\tt{ilessp}}, {\tt{'}}{\tt{'}}{\tt{0}}, {\rm{car}}\,({\it{factors\/}})) \\ 
{\bf else }{\rm{cons}}\,({\tt{'}}{\tt{ilessp}}, {\rm{cons}}\,({\rm{car}}\,({\it{factors\/}}), {\tt{'}}{\tt{(}}{\tt{'}}{\tt{0}}{\tt{)}}))$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable lessp-count-listp-cdr; name this event `lessp-count-listp-cdr-off2'.\index{lessp-count-listp-cdr-off2}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{cancel-factors-ilessp-0} \\  
\=\+{\rm{cancel-factors-ilessp-0}}\,({\it{x\/}})\index{cancel-factors-ilessp-0} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{ilessp}} \\ 
{\bf then }\=\+{\bf if }{\rm{cadr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{'}}{\tt{0}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{cdr}}\,({\rm{itimes-factors}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-factors})) \\ 
{\bf then }{\rm{conjoin-inequalities-with-0}}\,(\=\+{\rm{itimes-factors}}\,({\rm{caddr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\bf{t}})\-\index{conjoin-inequalities-with-0} \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{caddr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{'}}{\tt{0}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{cdr}}\,({\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors})) \\ 
{\bf then }{\rm{conjoin-inequalities-with-0}}\,(\=\+{\rm{itimes-factors}}\,({\rm{cadr}}\,({\it{x\/}}))\index{itimes-factors}, \\ 
{\bf{f}})\-\index{conjoin-inequalities-with-0} \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  conjoin-inequalities-with-0-eliminator \\ \index{conjoin-inequalities-with-0-eli!minator}
\=\+{\rm{listp}}\,({\it{x\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{eval\$}}\,({\bf{t}}, {\rm{conjoin-inequalities-with-0}}\,({\it{x\/}}, {\it{parity\/}})\index{conjoin-inequalities-with-0}, {\it{a\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\rm{ilessp}}\,({\tt{0}}, {\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{itimes-list})\index{ilessp} \\ 
{\bf else }{\rm{ilessp}}\,({\rm{itimes-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{itimes-list}, {\tt{0}})\index{ilessp}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-factors-ilessp-0 \\ \index{correctness-of-cancel-factors-i!lessp-0}
{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{cancel-factors-ilessp-0}}\,({\it{x\/}})\index{cancel-factors-ilessp-0}, {\it{a\/}})
\end{tabbing}


\noindent{\sc Event}:   Enable equal-itimes-list-eval\$-list-delete-new-1; name this event `equal-itimes-list-eval\$-list-delete-new-1-off'.\index{equal-itimes-list-eval\$-list-de!lete-new-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-itimes-list-eval\$-list-delete-new-2; name this event `equal-itimes-list-eval\$-list-delete-new-2-off'.\index{equal-itimes-list-eval\$-list-de!lete-new-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-itimes-list-eval\$-list-delete; name this event `itimes-itimes-list-eval\$-list-delete-off'.\index{itimes-itimes-list-eval\$-list-!delete-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-itimes-list-eval\$-list-bagdiff; name this event `equal-itimes-list-eval\$-list-bagdiff-off'.\index{equal-itimes-list-eval\$-list-b!agdiff-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-list-eval\$-factors-lemma; name this event `itimes-list-eval\$-factors-lemma-off'.\index{itimes-list-eval\$-factors-lemm!a-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-list-eval\$-factors-lemma-prime; name this event `itimes-list-eval\$-factors-lemma-prime-off'.\index{itimes-list-eval\$-factors-lemm!a-prime-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-list-eval\$-factors; name this event `itimes-list-eval\$-factors-off'.\index{itimes-list-eval\$-factors-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-or-itimes-term-integerp-eval\$; name this event `iplus-or-itimes-term-integerp-eval\$-off'.\index{iplus-or-itimes-term-integerp-ev!al\$-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-list-bagint-0; name this event `eval\$-list-bagint-0-off'.\index{eval\$-list-bagint-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-list-bagint-0-implies-equal; name this event `eval\$-list-bagint-0-implies-equal-off'.\index{eval\$-list-bagint-0-implies-eq!ual-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable izerop-ilessp-0-relationship; name this event `izerop-ilessp-0-relationship-off1'.\index{izerop-ilessp-0-relationship-of!f1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-itimes-list-eval\$-list-delete-helper-1; name this event `ilessp-itimes-list-eval\$-list-delete-helper-1-off'.\index{ilessp-itimes-list-eval\$-list-!delete-helper-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-itimes-list-eval\$-list-delete-helper-2; name this event `ilessp-itimes-list-eval\$-list-delete-helper-2-off'.\index{ilessp-itimes-list-eval\$-list-!delete-helper-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-itimes-list-eval\$-list-delete; name this event `ilessp-itimes-list-eval\$-list-delete-off'.\index{ilessp-itimes-list-eval\$-list-!delete-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-itimes-list-eval\$-list-delete-prime-helper-1; name this event `ilessp-itimes-list-eval\$-list-delete-prime-helper-1-off'.\index{ilessp-itimes-list-eval\$-list-!delete-prime-helper-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-itimes-list-eval\$-list-delete-prime-helper-2; name this event `ilessp-itimes-list-eval\$-list-delete-prime-helper-2-off'.\index{ilessp-itimes-list-eval\$-list-!delete-prime-helper-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-itimes-list-eval\$-list-delete-prime; name this event `ilessp-itimes-list-eval\$-list-delete-prime-off'.\index{ilessp-itimes-list-eval\$-list-!delete-prime-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-0-itimes; name this event `ilessp-0-itimes-off'.\index{ilessp-0-itimes-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-itimes-0; name this event `ilessp-itimes-0-off'.\index{ilessp-itimes-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable listp-cdr-factors-implies-integerp; name this event `listp-cdr-factors-implies-integerp-off'.\index{listp-cdr-factors-implies-intege!rp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-itimes; name this event `correctness-of-cancel-itimes-off'.\index{correctness-of-cancel-itimes-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-itimes-ilessp; name this event `correctness-of-cancel-itimes-ilessp-off'.\index{correctness-of-cancel-itimes-ile!ssp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable not-integerp-implies-not-equal-iplus; name this event `not-integerp-implies-not-equal-iplus-off'.\index{not-integerp-implies-not-equal-ip!lus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable not-integerp-implies-not-equal-itimes; name this event `not-integerp-implies-not-equal-itimes-off'.\index{not-integerp-implies-not-equal-iti!mes-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable subbagp-subsetp; name this event `subbagp-subsetp-off'.\index{subbagp-subsetp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-list-bagint-0-implies-equal-for-ilessp; name this event `eval\$-list-bagint-0-implies-equal-for-ilessp-off'.\index{eval\$-list-bagint-0-implies-eq!ual-for-ilessp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{split-out-ineg-terms} \\  
\=\+{\rm{split-out-ineg-terms}}\,({\it{x\/}})\index{split-out-ineg-terms} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{car}}\,({\it{x\/}})) \\ 
{\bf then }\=\+{\bf if }{\rm{caar}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{ineg}} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{car}}\,({\rm{split-out-ineg-terms}}\,({\rm{cdr}}\,({\it{x\/}}))\index{split-out-ineg-terms}), \\ 
{\rm{cons}}\,({\rm{cadar}}\,({\it{x\/}}), {\rm{cdr}}\,({\rm{split-out-ineg-terms}}\,({\rm{cdr}}\,({\it{x\/}}))\index{split-out-ineg-terms})))\- \\ 
{\bf elseif }\=\+({\rm{caar}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{quote}}) \\ 
$\wedge$$\;\;\;\;${\rm{negativep}}\,({\rm{cadar}}\,({\it{x\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{negative-guts}}\,({\rm{cadar}}\,({\it{x\/}})) $\not=$ {\tt{0}})\- \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{car}}\,({\rm{split-out-ineg-terms}}\,({\rm{cdr}}\,({\it{x\/}}))\index{split-out-ineg-terms}), \\ 
{\rm{cons}}\,(\=\+{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\rm{negative-guts}}\,({\rm{cadar}}\,({\it{x\/}}))), \\ 
{\rm{cdr}}\,({\rm{split-out-ineg-terms}}\,({\rm{cdr}}\,({\it{x\/}}))\index{split-out-ineg-terms}))\-)\- \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{car}}\,({\it{x\/}}), \\ 
{\rm{car}}\,({\rm{split-out-ineg-terms}}\,({\rm{cdr}}\,({\it{x\/}}))\index{split-out-ineg-terms}))\-, \\ 
{\rm{cdr}}\,({\rm{split-out-ineg-terms}}\,({\rm{cdr}}\,({\it{x\/}}))\index{split-out-ineg-terms}))\-$\;${\bf  endif}\- \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{cons}}\,({\rm{car}}\,({\it{x\/}}), {\rm{car}}\,({\rm{split-out-ineg-terms}}\,({\rm{cdr}}\,({\it{x\/}}))\index{split-out-ineg-terms})), \\ 
{\rm{cdr}}\,({\rm{split-out-ineg-terms}}\,({\rm{cdr}}\,({\it{x\/}}))\index{split-out-ineg-terms}))\-$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{remove-inegs} \\  
\=\+{\rm{remove-inegs}}\,({\it{x\/}}, {\it{y\/}})\index{remove-inegs} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\rm{listp}}\,({\rm{cdr}}\,({\rm{split-out-ineg-terms}}\,({\it{x\/}})\index{split-out-ineg-terms})) \\ 
$\vee$$\;\;\;\;${\rm{listp}}\,({\rm{cdr}}\,({\rm{split-out-ineg-terms}}\,({\it{y\/}})\index{split-out-ineg-terms}))\- \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{append}}\,(\=\+{\rm{cdr}}\,({\rm{split-out-ineg-terms}}\,({\it{y\/}})\index{split-out-ineg-terms}), \\ 
{\rm{car}}\,({\rm{split-out-ineg-terms}}\,({\it{x\/}})\index{split-out-ineg-terms}))\-, \\ 
{\rm{append}}\,(\=\+{\rm{cdr}}\,({\rm{split-out-ineg-terms}}\,({\it{x\/}})\index{split-out-ineg-terms}), \\ 
{\rm{car}}\,({\rm{split-out-ineg-terms}}\,({\it{y\/}})\index{split-out-ineg-terms}))\-)\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{iplus-or-ineg-term} \\  
\=\+{\rm{iplus-or-ineg-term}}\,({\it{x\/}})\index{iplus-or-ineg-term} \\ 
$=$$\;\;\;\;$({\rm{listp}}\,({\it{x\/}}) $\wedge$ (({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{ineg}}) $\vee$ ({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{iplus}})))\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{make-cancel-ineg-terms-equality} \\  
\=\+{\rm{make-cancel-ineg-terms-equality}}\,({\it{x\/}})\index{make-cancel-ineg-terms-equality} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{remove-inegs}}\,({\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, {\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\index{remove-inegs} \\ 
{\bf then }\=\+{\bf if }{\rm{iplus-or-ineg-term}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-or-ineg-term} \\ 
{\bf then }\=\+{\bf if }{\rm{iplus-or-ineg-term}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-or-ineg-term} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{integerp}}, {\rm{caddr}}\,({\it{x\/}})), \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\-$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{iplus-or-ineg-term}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-or-ineg-term} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{integerp}}, {\rm{cadr}}\,({\it{x\/}})), \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cancel-ineg-terms-from-equality} \\  
\=\+{\rm{cancel-ineg-terms-from-equality}}\,({\it{x\/}})\index{cancel-ineg-terms-from-equality} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) $\wedge$ ({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{equal}}) \\ 
{\bf then }{\rm{make-cancel-ineg-terms-equality}}\,({\it{x\/}})\index{make-cancel-ineg-terms-equality} \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cancel-ineg-terms-from-equality!-expanded} \\  
\=\+{\rm{cancel-ineg-terms-from-equality-expanded}}\,({\it{x\/}})\index{cancel-ineg-terms-from-equality!-expanded} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{equal}} \\ 
{\bf then }\=\+{\bf if }{\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{cadr}}\,({\it{x\/}})) \\ 
{\bf then }\=\+{\bf case on }{\rm{caadr}}\,({\it{x\/}}): \\ 
{\bf case = }{\it{ineg\/}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{caddr}}\,({\it{x\/}})) \\ 
{\bf then }\=\+{\bf case on }{\rm{caaddr}}\,({\it{x\/}}): \\ 
{\bf case = }{\it{ineg\/}} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\- \\ 
{\bf case = }{\it{iplus\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\- \\ 
{\bf otherwise }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{integerp}}, \\ 
{\rm{caddr}}\,({\it{x\/}}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\-$\;${\bf  endcase}\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{integerp}}, {\rm{caddr}}\,({\it{x\/}})), \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\-$\;${\bf  endif}\- \\ 
{\bf case = }{\it{iplus\/}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\rm{listp}}\,({\rm{caddr}}\,({\it{x\/}})) \\ 
{\bf then }\=\+{\bf case on }{\rm{caaddr}}\,({\it{x\/}}): \\ 
{\bf case = }{\it{ineg\/}} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\- \\ 
{\bf case = }{\it{iplus\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\- \\ 
{\bf otherwise }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{integerp}}, \\ 
{\rm{caddr}}\,({\it{x\/}}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\-$\;${\bf  endcase}\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{integerp}}, {\rm{caddr}}\,({\it{x\/}})), \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\-$\;${\bf  endif}\- \\ 
{\bf otherwise }\=\+{\bf if }{\rm{listp}}\,({\rm{caddr}}\,({\it{x\/}})) \\ 
{\bf then }\=\+{\bf case on }{\rm{caaddr}}\,({\it{x\/}}): \\ 
{\bf case = }{\it{ineg\/}} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{integerp}}, \\ 
{\rm{cadr}}\,({\it{x\/}}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\- \\ 
{\bf case = }{\it{iplus\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{integerp}}, \\ 
{\rm{cadr}}\,({\it{x\/}}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\- \\ 
{\bf otherwise }{\it{x\/}}$\;${\bf  endcase}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-$\;${\bf  endcase}\- \\ 
{\bf elseif }{\rm{listp}}\,({\rm{caddr}}\,({\it{x\/}})) \\ 
{\bf then }\=\+{\bf case on }{\rm{caaddr}}\,({\it{x\/}}): \\ 
{\bf case = }{\it{ineg\/}} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{integerp}}, {\rm{cadr}}\,({\it{x\/}})), \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\- \\ 
{\bf case = }{\it{iplus\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{if}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{integerp}}, {\rm{cadr}}\,({\it{x\/}})), \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{equal}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{quote}}, {\bf{f}}))\- \\ 
{\bf otherwise }{\it{x\/}}$\;${\bf  endcase}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  cancel-ineg-terms-from-equality-cancel-ineg-terms-from-equality-expanded \\ \index{cancel-ineg-terms-from-equality!-cancel-ineg-terms-from-equality-expanded}
\=\+{\rm{cancel-ineg-terms-from-equality-expanded}}\,({\it{x\/}})\index{cancel-ineg-terms-from-equality!-expanded} \\ 
$=$$\;\;\;\;${\rm{cancel-ineg-terms-from-equality}}\,({\it{x\/}})\index{cancel-ineg-terms-from-equality}\-
\end{tabbing}


\noindent{\sc Event}:   Enable cancel-ineg-terms-from-equality-expanded; name this event `cancel-ineg-terms-from-equality-expanded-off'.\index{cancel-ineg-terms-from-equality!-expanded-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  integerp-eval\$-iplus-or-ineg-term \\ \index{integerp-eval\$-iplus-or-ineg-te!rm}
{\rm{iplus-or-ineg-term}}\,({\it{x\/}})\index{iplus-or-ineg-term} $\rightarrow$ {\rm{integerp}}\,({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}))\index{integerp}
\end{tabbing}


\noindent{\sc Event}:   Enable iplus-or-ineg-term; name this event `iplus-or-ineg-term-off'.\index{iplus-or-ineg-term-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  eval\$-iplus-list-car-remove-inegs \\ \index{eval\$-iplus-list-car-remove-ine!gs}
\=\+{\rm{remove-inegs}}\,({\it{x\/}}, {\it{y\/}})\index{remove-inegs} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{iplus-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{car}}\,({\rm{remove-inegs}}\,({\it{x\/}}, {\it{y\/}})\index{remove-inegs}), {\it{a\/}}))\index{iplus-list} \\ 
$=$$\;\;\;\;${\rm{iplus}}\,(\=\+{\rm{iplus-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{car}}\,({\rm{split-out-ineg-terms}}\,({\it{x\/}})\index{split-out-ineg-terms}), {\it{a\/}}))\index{iplus-list}, \\ 
{\rm{iplus-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{cdr}}\,({\rm{split-out-ineg-terms}}\,({\it{y\/}})\index{split-out-ineg-terms}), {\it{a\/}}))\index{iplus-list})\-\index{iplus})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-iplus-list-cdr-remove-inegs \\ \index{eval\$-iplus-list-cdr-remove-ine!gs}
\=\+{\rm{remove-inegs}}\,({\it{x\/}}, {\it{y\/}})\index{remove-inegs} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{iplus-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{cdr}}\,({\rm{remove-inegs}}\,({\it{x\/}}, {\it{y\/}})\index{remove-inegs}), {\it{a\/}}))\index{iplus-list} \\ 
$=$$\;\;\;\;${\rm{iplus}}\,(\=\+{\rm{iplus-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{car}}\,({\rm{split-out-ineg-terms}}\,({\it{y\/}})\index{split-out-ineg-terms}), {\it{a\/}}))\index{iplus-list}, \\ 
{\rm{iplus-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{cdr}}\,({\rm{split-out-ineg-terms}}\,({\it{x\/}})\index{split-out-ineg-terms}), {\it{a\/}}))\index{iplus-list})\-\index{iplus})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  minus-ineg \\ \index{minus-ineg}
(({\it{x\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{x\/}} $\not=$ {\tt{0}})) $\rightarrow$ (($-$ {\it{x\/}}) $=$ {\rm{ineg}}\,({\it{x\/}})\index{ineg})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-list-eval\$-car-split-out-ineg-terms \\ \index{iplus-list-eval\$-car-split-out!-ineg-terms}
\=\+{\rm{iplus-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{car}}\,({\rm{split-out-ineg-terms}}\,({\it{x\/}})\index{split-out-ineg-terms}), {\it{a\/}}))\index{iplus-list} \\ 
$=$$\;\;\;\;${\rm{iplus}}\,(\=\+{\rm{iplus-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\it{x\/}}, {\it{a\/}}))\index{iplus-list}, \\ 
{\rm{iplus-list}}\,({\rm{eval\$}}\,({\tt{'}}{\tt{list}}, {\rm{cdr}}\,({\rm{split-out-ineg-terms}}\,({\it{x\/}})\index{split-out-ineg-terms}), {\it{a\/}}))\index{iplus-list})\-\index{iplus}\-
\end{tabbing}


\noindent{\sc Event}:   Enable remove-inegs; name this event `remove-inegs-off'.\index{remove-inegs-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-ineg-terms-from-equality \\ \index{correctness-of-cancel-ineg-term!s-from-equality}
{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{cancel-ineg-terms-from-equality-expanded}}\,({\it{x\/}})\index{cancel-ineg-terms-from-equality!-expanded}, {\it{a\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{make-cancel-ineg-terms-inequalit!y} \\  
\=\+{\rm{make-cancel-ineg-terms-inequality}}\,({\it{x\/}})\index{make-cancel-ineg-terms-inequalit!y} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{remove-inegs}}\,({\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, {\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\index{remove-inegs} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{ilessp}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cancel-ineg-terms-from-inequalit!y} \\  
\=\+{\rm{cancel-ineg-terms-from-inequality}}\,({\it{x\/}})\index{cancel-ineg-terms-from-inequalit!y} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) $\wedge$ ({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{ilessp}}) \\ 
{\bf then }\=\+{\bf if }{\rm{iplus-or-ineg-term}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-or-ineg-term} \\ 
{\bf then }{\rm{make-cancel-ineg-terms-inequality}}\,({\it{x\/}})\index{make-cancel-ineg-terms-inequalit!y} \\ 
{\bf elseif }{\rm{iplus-or-ineg-term}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-or-ineg-term} \\ 
{\bf then }{\rm{make-cancel-ineg-terms-inequality}}\,({\it{x\/}})\index{make-cancel-ineg-terms-inequalit!y} \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cancel-ineg-terms-from-inequalit!y-expanded} \\  
\=\+{\rm{cancel-ineg-terms-from-inequality-expanded}}\,({\it{x\/}})\index{cancel-ineg-terms-from-inequalit!y-expanded} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{ilessp}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{cadr}}\,({\it{x\/}})) \\ 
{\bf then }\=\+{\bf case on }{\rm{caadr}}\,({\it{x\/}}): \\ 
{\bf case = }{\it{ineg\/}} \\ 
{\bf then }\=\+{\bf if }{\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{ilessp}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf case = }{\it{iplus\/}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{ilessp}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf otherwise }\=\+{\bf if }{\rm{listp}}\,({\rm{caddr}}\,({\it{x\/}})) \\ 
{\bf then }\=\+{\bf case on }{\rm{caaddr}}\,({\it{x\/}}): \\ 
{\bf case = }{\it{ineg\/}} \\ 
{\bf then }\=\+{\bf if }{\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{ilessp}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf case = }{\it{iplus\/}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{ilessp}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf otherwise }{\it{x\/}}$\;${\bf  endcase}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-$\;${\bf  endcase}\- \\ 
{\bf elseif }{\rm{listp}}\,({\rm{caddr}}\,({\it{x\/}})) \\ 
{\bf then }\=\+{\bf case on }{\rm{caaddr}}\,({\it{x\/}}): \\ 
{\bf case = }{\it{ineg\/}} \\ 
{\bf then }\=\+{\bf if }{\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{ilessp}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf case = }{\it{iplus\/}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs} \\ 
{\bf then }{\rm{list}}\,(\=\+{\tt{'}}{\tt{ilessp}}, \\ 
{\rm{iplus-tree}}\,({\rm{car}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree}, \\ 
{\rm{iplus-tree}}\,({\rm{cdr}}\,({\rm{remove-inegs}}\,(\=\+{\rm{iplus-fringe}}\,({\rm{cadr}}\,({\it{x\/}}))\index{iplus-fringe}, \\ 
{\rm{iplus-fringe}}\,({\rm{caddr}}\,({\it{x\/}}))\index{iplus-fringe})\-\index{remove-inegs}))\index{iplus-tree})\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf otherwise }{\it{x\/}}$\;${\bf  endcase}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  cancel-ineg-terms-from-inequality-cancel-ineg-terms-from-inequality-expanded \\ \index{cancel-ineg-terms-from-inequalit!y-cancel-ineg-terms-from-inequality-expanded}
\=\+{\rm{cancel-ineg-terms-from-inequality-expanded}}\,({\it{x\/}})\index{cancel-ineg-terms-from-inequalit!y-expanded} \\ 
$=$$\;\;\;\;${\rm{cancel-ineg-terms-from-inequality}}\,({\it{x\/}})\index{cancel-ineg-terms-from-inequalit!y}\-
\end{tabbing}


\noindent{\sc Event}:   Enable cancel-ineg-terms-from-inequality-expanded; name this event `cancel-ineg-terms-from-inequality-expanded-off'.\index{cancel-ineg-terms-from-inequalit!y-expanded-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-cancel-ineg-terms-from-inequality \\ \index{correctness-of-cancel-ineg-term!s-from-inequality}
{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{a\/}}) $=$ {\rm{eval\$}}\,({\bf{t}}, {\rm{cancel-ineg-terms-from-inequality-expanded}}\,({\it{x\/}})\index{cancel-ineg-terms-from-inequalit!y-expanded}, {\it{a\/}})
\end{tabbing}


\noindent{\sc Event}:   Enable minus-ineg; name this event `minus-ineg-off'.\index{minus-ineg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-eval\$-iplus-or-ineg-term; name this event `integerp-eval\$-iplus-or-ineg-term-off'.\index{integerp-eval\$-iplus-or-ineg-te!rm-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plus-iplus \\ \index{plus-iplus}
(({\it{i\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{j\/}} $\in\;${\bf{N}}${}$)) $\rightarrow$ (({\it{i\/}} $+$ {\it{j\/}}) $=$ {\rm{iplus}}\,({\it{i\/}}, {\it{j\/}})\index{iplus})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-constants \\ \index{iplus-constants}
{\rm{iplus}}\,($1\;+$ {\it{i\/}}, {\rm{iplus}}\,($1\;+$ {\it{j\/}}, {\it{x\/}})\index{iplus})\index{iplus} $=$ {\rm{iplus}}\,(($1\;+$ {\it{i\/}}) $+$ ($1\;+$ {\it{j\/}}), {\it{x\/}})\index{iplus}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  numberp-is-integerp \\ \index{numberp-is-integerp}
({\it{w\/}} $\in\;${\bf{N}}${}$) $\rightarrow$ {\rm{integerp}}\,({\it{w\/}})\index{integerp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  difference-idifference \\ \index{difference-idifference}
\=\+(\=\+({\it{x\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$({\it{y\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{y\/}} $<$ {\it{x\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$(({\it{y\/}} $-$ {\it{x\/}}) $=$ {\rm{idifference}}\,({\it{y\/}}, {\it{x\/}})\index{idifference})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  cancel-constants-equal-lemma \\ \index{cancel-constants-equal-lemma}
\=\+(({\it{m\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{n\/}} $\in\;${\bf{N}}${}$)) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{iplus}}\,({\it{m\/}}, {\it{x\/}})\index{iplus} $=$ {\rm{iplus}}\,({\it{n\/}}, {\it{y\/}})\index{iplus}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{m\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\rm{fix-int}}\,({\it{x\/}})\index{fix-int} $=$ {\rm{iplus}}\,({\it{n\/}} $-$ {\it{m\/}}, {\it{y\/}})\index{iplus} \\ 
{\bf else }{\rm{iplus}}\,({\it{m\/}} $-$ {\it{n\/}}, {\it{x\/}})\index{iplus} $=$ {\rm{fix-int}}\,({\it{y\/}})\index{fix-int}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  cancel-constants-equal \\ \index{cancel-constants-equal}
\=\+({\rm{iplus}}\,($1\;+$ {\it{i\/}}, {\it{x\/}})\index{iplus} $=$ {\rm{iplus}}\,($1\;+$ {\it{j\/}}, {\it{y\/}})\index{iplus}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{i\/}} $<$ {\it{j\/}}$\;\;${\bf then }{\rm{fix-int}}\,({\it{x\/}})\index{fix-int} $=$ {\rm{iplus}}\,({\it{j\/}} $-$ {\it{i\/}}, {\it{y\/}})\index{iplus} \\ 
{\bf else }{\rm{iplus}}\,({\it{i\/}} $-$ {\it{j\/}}, {\it{x\/}})\index{iplus} $=$ {\rm{fix-int}}\,({\it{y\/}})\index{fix-int}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ilessp-add1 \\ \index{ilessp-add1}
({\it{y\/}} $\in\;${\bf{N}}${}$) $\rightarrow$ ({\rm{ilessp}}\,({\it{x\/}}, $1\;+$ {\it{y\/}})\index{ilessp} $=$ ($\neg$ {\rm{ilessp}}\,({\it{y\/}}, {\it{x\/}})\index{ilessp}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ilessp-add1-iplus \\ \index{ilessp-add1-iplus}
({\it{y\/}} $\in\;${\bf{N}}${}$) $\rightarrow$ ({\rm{ilessp}}\,({\it{x\/}}, {\rm{iplus}}\,($1\;+$ {\it{y\/}}, {\it{z\/}})\index{iplus})\index{ilessp} $=$ ($\neg$ {\rm{ilessp}}\,({\rm{iplus}}\,({\it{y\/}}, {\it{z\/}})\index{iplus}, {\it{x\/}})\index{ilessp}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  cancel-constants-ilessp-lemma-1 \\ \index{cancel-constants-ilessp-lemma-1}
\=\+(({\it{m\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{n\/}} $\in\;${\bf{N}}${}$)) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{ilessp}}\,({\rm{iplus}}\,({\it{m\/}}, {\it{x\/}})\index{iplus}, {\rm{iplus}}\,({\it{n\/}}, {\it{y\/}})\index{iplus})\index{ilessp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{m\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\rm{ilessp}}\,({\it{x\/}}, {\rm{iplus}}\,({\it{n\/}} $-$ {\it{m\/}}, {\it{y\/}})\index{iplus})\index{ilessp} \\ 
{\bf else }{\rm{ilessp}}\,({\rm{iplus}}\,({\it{m\/}} $-$ {\it{n\/}}, {\it{x\/}})\index{iplus}, {\it{y\/}})\index{ilessp}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  cancel-constants-ilessp-lemma-2 \\ \index{cancel-constants-ilessp-lemma-2}
\=\+(({\it{m\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{n\/}} $\in\;${\bf{N}}${}$)) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{ilessp}}\,({\rm{iplus}}\,({\it{m\/}}, {\it{x\/}})\index{iplus}, {\rm{iplus}}\,({\it{n\/}}, {\it{y\/}})\index{iplus})\index{ilessp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{m\/}} $<$ {\it{n\/}}$\;\;${\bf then }$\neg$ {\rm{ilessp}}\,({\rm{iplus}}\,(({\it{n\/}} $-$ {\it{m\/}}) $-\;1$, {\it{y\/}})\index{iplus}, {\it{x\/}})\index{ilessp} \\ 
{\bf else }{\rm{ilessp}}\,({\rm{iplus}}\,({\it{m\/}} $-$ {\it{n\/}}, {\it{x\/}})\index{iplus}, {\it{y\/}})\index{ilessp}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  cancel-constants-ilessp \\ \index{cancel-constants-ilessp}
\=\+{\rm{ilessp}}\,({\rm{iplus}}\,($1\;+$ {\it{i\/}}, {\it{x\/}})\index{iplus}, {\rm{iplus}}\,($1\;+$ {\it{j\/}}, {\it{y\/}})\index{iplus})\index{ilessp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{i\/}} $<$ {\it{j\/}}$\;\;${\bf then }$\neg$ {\rm{ilessp}}\,({\rm{iplus}}\,(({\it{j\/}} $-$ {\it{i\/}}) $-\;1$, {\it{y\/}})\index{iplus}, {\it{x\/}})\index{ilessp} \\ 
{\bf else }{\rm{ilessp}}\,({\rm{iplus}}\,({\it{i\/}} $-$ {\it{j\/}}, {\it{x\/}})\index{iplus}, {\it{y\/}})\index{ilessp}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable plus-iplus; name this event `plus-iplus-off'.\index{plus-iplus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable numberp-is-integerp; name this event `numberp-is-integerp-off'.\index{numberp-is-integerp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable difference-idifference; name this event `difference-idifference-off'.\index{difference-idifference-off}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{integers}} to consist of the following events: ileq,
idifference,
integerp-fix-int,
integerp-iplus,
integerp-idifference,
integerp-ineg,
integerp-iabs,
integerp-itimes,
fix-int-remover,
fix-int-fix-int,
fix-int-iplus,
fix-int-idifference,
fix-int-ineg,
fix-int-iabs,
fix-int-itimes,
ineg-iplus,
ineg-ineg,
ineg-fix-int,
ineg-of-non-integerp,
ineg-0,
iplus-left-id,
iplus-right-id,
iplus-0-left,
iplus-0-right,
commutativity2-of-iplus,
commutativity-of-iplus,
associativity-of-iplus,
iplus-cancellation-1,
iplus-cancellation-2,
iplus-ineg1,
iplus-ineg2,
iplus-fix-int1,
iplus-fix-int2,
idifference-fix-int1,
idifference-fix-int2,
iplus-list,
eval\$-list-append,
iplus-list-append,
iplus-ineg3,
iplus-ineg4,
correctness-of-cancel-iplus,
ilessp-fix-int-1,
ilessp-fix-int-2,
iplus-cancellation-1-for-ilessp,
iplus-cancellation-2-for-ilessp,
correctness-of-cancel-iplus-ilessp,
itimes-0-left,
itimes-0-right,
itimes-fix-int1,
itimes-fix-int2,
commutativity-of-itimes,
itimes-distributes-over-iplus-proof,
itimes-distributes-over-iplus,
commutativity2-of-itimes,
associativity-of-itimes,
equal-itimes-0,
equal-itimes-1,
equal-itimes-minus-1,
itimes-1-arg1,
quotient-remainder-uniqueness,
division-theorem,
itimes-ineg-1,
itimes-ineg-2,
itimes-cancellation-1,
itimes-cancellation-2,
itimes-cancellation-3,
integerp-iquotient,
integerp-iremainder,
integerp-idiv,
integerp-imod,
integerp-iquo,
integerp-irem,
iquotient-fix-int1,
iquotient-fix-int2,
iremainder-fix-int1,
iremainder-fix-int2,
idiv-fix-int1,
idiv-fix-int2,
imod-fix-int1,
imod-fix-int2,
iquo-fix-int1,
iquo-fix-int2,
irem-fix-int1,
irem-fix-int2,
fix-int-iquotient,
fix-int-iremainder,
fix-int-idiv,
fix-int-imod,
fix-int-iquo,
fix-int-irem,
itimes-list,
itimes-list-append,
member-append,
equal-fix-int,
subsetp,
correctness-of-cancel-itimes,
correctness-of-cancel-itimes-ilessp,
ilessp-strict,
eval\$-list-cons,
eval\$-list-nlistp,
eval\$-litatom,
eval\$-quote,
eval\$-other,
iplus-x-y-ineg-x,
correctness-of-cancel-ineg,
integerp-iplus-list,
eval\$-iplus-list-delete,
eval\$-iplus-list-bagdiff,
itimes-tree-ineg,
itimes-factors,
itimes--1,
equal-ineg-ineg,
ilessp-ineg-ineg,
fix-int-eval\$-itimes-tree-rec,
eval\$-itimes-tree-ineg,
ineg-eval\$-itimes-tree-ineg,
iplus-eval\$-itimes-tree-ineg,
itimes-eval\$-itimes-tree-ineg,
iplus-or-itimes-term,
cancel-itimes-factors,
cancel-itimes-factors-expanded,
cancel-itimes-factors-expanded-cancel-itimes-factors,
membership-of-0-implies-itimes-list-is-0,
member-0-eval\$-list,
correctness-of-cancel-itimes-factors,
cancel-itimes-ilessp-factors,
bagint-singleton,
ilessp-itimes-list-eval\$-list-bagdiff,
ilessp-itimes-list-eval\$-list-bagdiff-corollary-1,
member-0-itimes-factors-yields-0,
member-0-itimes-factors-yields-0-ilessp-consequence-1,
member-0-itimes-factors-yields-0-ilessp-consequence-2,
ilessp-itimes-list-eval\$-list-bagdiff-corollary-2,
correctness-of-cancel-itimes-ilessp-factors,
disjoin-equalities-with-0,
cancel-factors-0,
some-eval\$s-to-0,
eval\$-disjoin-equalities-with-0,
some-eval\$s-to-0-append,
some-eval\$s-to-0-eliminator,
correctness-of-cancel-factors-0,
conjoin-inequalities-with-0,
cancel-factors-ilessp-0,
split-out-ineg-terms,
correctness-of-cancel-ineg-terms-from-equality,
correctness-of-cancel-ineg-terms-from-inequality,
iplus-constants,
cancel-constants-equal,
ilessp-add1,
ilessp-add1-iplus,
cancel-constants-ilessp.\index{integers}

\addvspace{18pt}


\noindent{\sc Event}:   Disable eval\$; name this event `eval\$-on'.\index{eval\$-on}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{math-theory}} to consist of the following events: cancel-constants-ilessp,
cancel-constants-ilessp-lemma-2,
cancel-constants-ilessp-lemma-1,
ilessp-add1-iplus,
ilessp-add1,
cancel-constants-equal,
cancel-constants-equal-lemma,
iplus-constants,
correctness-of-cancel-ineg-terms-from-inequality,
cancel-ineg-terms-from-inequality-cancel-ineg-terms-from-inequality-expanded,
*1*cancel-ineg-terms-from-inequality-expanded,
cancel-ineg-terms-from-inequality,
*1*cancel-ineg-terms-from-inequality,
make-cancel-ineg-terms-inequality,
*1*make-cancel-ineg-terms-inequality,
correctness-of-cancel-ineg-terms-from-equality,
iplus-list-eval\$-car-split-out-ineg-terms,
eval\$-iplus-list-cdr-remove-inegs,
eval\$-iplus-list-car-remove-inegs,
cancel-ineg-terms-from-equality-cancel-ineg-terms-from-equality-expanded,
*1*cancel-ineg-terms-from-equality-expanded,
cancel-ineg-terms-from-equality,
*1*cancel-ineg-terms-from-equality,
make-cancel-ineg-terms-equality,
*1*make-cancel-ineg-terms-equality,
*1*iplus-or-ineg-term,
*1*remove-inegs,
split-out-ineg-terms,
*1*split-out-ineg-terms,
correctness-of-cancel-factors-ilessp-0,
conjoin-inequalities-with-0-eliminator,
cancel-factors-ilessp-0,
*1*cancel-factors-ilessp-0,
conjoin-inequalities-with-0,
*1*conjoin-inequalities-with-0,
correctness-of-cancel-factors-0,
some-eval\$s-to-0-eliminator,
some-eval\$s-to-0-append,
eval\$-disjoin-equalities-with-0,
some-eval\$s-to-0,
*1*some-eval\$s-to-0,
cancel-factors-0,
*1*cancel-factors-0,
disjoin-equalities-with-0,
*1*disjoin-equalities-with-0,
correctness-of-cancel-itimes-ilessp-factors,
equal-fix-int-to-ilessp,
eval\$-list-bagint-0-implies-equal-for-ilessp-lemma,
eval\$-list-bagint-0-for-ilessp,
member-0-itimes-factors-yields-0-ilessp-consequence-2,
member-0-itimes-factors-yields-0-ilessp-consequence-1,
member-0-itimes-factors-yields-0,
ilessp-itimes-list-eval\$-list-bagdiff-corollary-2,
ilessp-zero-implies-not-equal,
ilessp-itimes-list-eval\$-list-bagdiff-corollary-1,
zero-ilessp-implies-not-equal,
ilessp-itimes-list-eval\$-list-bagdiff,
bagint-singleton,
cancel-itimes-ilessp-factors,
*1*cancel-itimes-ilessp-factors,
correctness-of-cancel-itimes-factors,
member-0-eval\$-list,
membership-of-0-implies-itimes-list-is-0,
cancel-itimes-factors-expanded-cancel-itimes-factors,
*1*cancel-itimes-factors-expanded,
cancel-itimes-factors,
*1*cancel-itimes-factors,
*1*iplus-or-itimes-term,
itimes-eval\$-itimes-tree-ineg,
iplus-eval\$-itimes-tree-ineg,
ineg-eval\$-itimes-tree-ineg,
eval\$-itimes-tree-ineg,
fix-int-eval\$-itimes-tree-rec,
ilessp-ineg-ineg,
equal-ineg-ineg,
itimes--1,
itimes-factors,
*1*itimes-factors,
*1*itimes-tree-ineg,
ilessp-strict,
ilessp-itimes-right-negative,
ilessp-itimes-right-positive,
cancel-itimes-ilessp,
*1*cancel-itimes-ilessp,
*1*make-cancel-itimes-inequality,
*1*itimes-tree-no-fix-int,
subsetp,
*1*subsetp,
equal-fix-int,
member-append,
itimes-list-append,
cancel-itimes,
*1*cancel-itimes,
*1*make-cancel-itimes-equality,
integerp-itimes-list,
itimes-list,
*1*itimes-list,
*1*itimes-tree,
itimes-tree-rec,
*1*itimes-tree-rec,
itimes-fringe,
*1*itimes-fringe,
fix-int-irem,
fix-int-iquo,
fix-int-imod,
fix-int-idiv,
fix-int-iremainder,
fix-int-iquotient,
irem-fix-int2,
irem-fix-int1,
iquo-fix-int2,
iquo-fix-int1,
imod-fix-int2,
imod-fix-int1,
idiv-fix-int2,
idiv-fix-int1,
iremainder-fix-int2,
iremainder-fix-int1,
iquotient-fix-int2,
iquotient-fix-int1,
integerp-irem,
integerp-iquo,
integerp-imod,
integerp-idiv,
integerp-iremainder,
integerp-iquotient,
itimes-cancellation-3,
itimes-cancellation-2,
itimes-cancellation-1,
itimes-ineg-2,
itimes-ineg-1,
iquo-irem-uniqueness,
division-theorem-for-truncate-to-zero,
division-theorem-for-truncate-to-zero-part3,
division-theorem-for-truncate-to-zero-part2,
division-theorem-for-truncate-to-zero-part1,
idiv-imod-uniqueness,
division-theorem-for-truncate-to-neginf,
division-theorem-for-truncate-to-neginf-part3,
division-theorem-for-truncate-to-neginf-part2,
division-theorem-for-truncate-to-neginf-part1,
iquotient-iremainder-uniqueness,
division-theorem,
division-theorem-part3,
division-theorem-part2,
division-theorem-part1,
quotient-remainder-uniqueness,
itimes-1-arg1,
equal-itimes-minus-1,
equal-itimes-1,
equal-itimes-0,
associativity-of-itimes,
commutativity2-of-itimes,
itimes-distributes-over-iplus,
itimes-distributes-over-iplus-proof,
commutativity-of-itimes,
itimes-fix-int2,
itimes-fix-int1,
itimes-0-right,
itimes-0-left,
correctness-of-cancel-iplus-ilessp,
cancel-iplus-ilessp,
*1*cancel-iplus-ilessp,
*1*iplus-tree-no-fix-int,
iplus-cancellation-2-for-ilessp,
iplus-cancellation-1-for-ilessp,
cancel-iplus-ilessp-1,
*1*cancel-iplus-ilessp-1,
*1*make-cancel-iplus-inequality-1,
ilessp-fix-int-2,
ilessp-fix-int-1,
correctness-of-cancel-iplus,
iplus-ineg7,
iplus-list-append,
eval\$-iplus-list-delete,
*1*cancel-iplus,
eval\$-list-append,
integerp-iplus-list,
iplus-list,
*1*iplus-list,
*1*iplus-tree,
iplus-tree-rec,
*1*iplus-tree-rec,
iplus-fringe,
*1*iplus-fringe,
correctness-of-cancel-ineg,
iplus-x-y-ineg-x,
iplus-ineg4,
iplus-ineg3,
eval\$-cancel-ineg-aux-is-its-fn,
eval\$-cancel-ineg-aux-fn,
*1*eval\$-cancel-ineg-aux-fn,
eval\$-other,
eval\$-litatom,
eval\$-list-nlistp,
eval\$-list-cons,
cancel-ineg,
*1*cancel-ineg,
cancel-ineg-aux,
*1*cancel-ineg-aux,
idifference-fix-int2,
idifference-fix-int1,
iplus-fix-int2,
iplus-fix-int1,
iplus-ineg2,
iplus-ineg1,
iplus-cancellation-2,
iplus-cancellation-1,
associativity-of-iplus,
commutativity-of-iplus,
commutativity2-of-iplus,
iplus-0-right,
iplus-0-left,
ineg-0,
ineg-fix-int,
ineg-ineg,
ineg-iplus,
fix-int-itimes,
fix-int-iabs,
fix-int-ineg,
fix-int-idifference,
fix-int-iplus,
fix-int-fix-int,
fix-int-remover,
integerp-itimes,
integerp-iabs,
integerp-ineg,
integerp-idifference,
integerp-iplus,
integerp-fix-int,
*1*irem,
*1*iquo,
*1*imod,
*1*idiv,
*1*iremainder,
*1*iquotient,
*1*itimes,
*1*iabs,
idifference,
*1*idifference,
*1*ineg,
*1*iplus,
ileq,
*1*ileq,
*1*ilessp,
izerop,
*1*izerop,
*1*fix-int,
*1*integerp,
gcd-idempotence,
gcd-x-x,
commutativity2-of-gcd,
commutativity2-of-gcd-zero-case,
associativity-of-gcd,
associativity-of-gcd-zero-case,
common-divisor-divides-gcd,
gcd-is-the-greatest,
distributivity-of-times-over-gcd,
distributivity-of-times-over-gcd-proof,
remainder-gcd,
gcd-plus-instance,
gcd-plus,
gcd-plus-proof,
gcd-plus-instance-temp,
gcd-plus-instance-temp-proof,
lessp-gcd,
equal-gcd-0,
gcd-1,
gcd-0,
single-number-induction,
*1*single-number-induction,
commutativity-of-gcd,
log-exp,
log-times-exp,
log-times-exp-proof,
log-times,
log-times-proof,
log-quotient-exp,
log-quotient-times,
log-quotient-times-proof,
log-quotient,
leq-log-log,
double-log-induction,
*1*double-log-induction,
log-1,
log-0,
equal-log-0,
exp-difference,
equal-exp-1,
equal-exp-0,
exp-exp,
exp-times,
exp-0-arg2,
exp-1-arg1,
exp-0-arg1,
exp-plus,
exp-add1,
exp-zero,
quotient-exp,
remainder-exp-exp,
double-number-induction,
*1*double-number-induction,
remainder-exp,
gcd,
*1*gcd,
log,
*1*log,
exp,
*1*exp,
correctness-of-cancel-quotient-times,
cancel-quotient-times,
*1*cancel-quotient-times,
lessp-quotient,
quotient-x-x,
quotient-1-arg1,
quotient-1-arg1-casesplit,
quotient-1-arg2,
leq-quotient,
quotient-quotient,
quotient-plus-times-times-instance,
quotient-plus-times-times,
quotient-plus-times-times-proof,
quotient-plus-fact,
quotient-remainder-instance,
quotient-remainder,
quotient-remainder-times,
quotient-difference3,
quotient-difference2,
quotient-lessp-arg1,
quotient-difference1,
quotient-times-times-proof,
quotient-times-instance,
quotient-times,
quotient-times-proof,
quotient-times-instance-temp-proof,
quotient-plus,
quotient-plus-proof,
quotient-sub1,
equal-quotient-0,
quotient-add1,
quotient-zero,
quotient-of-non-number,
quotient-noop,
transitivity-of-divides,
remainder-x-x,
remainder-1-arg2,
remainder-1-arg1,
remainder-remainder,
remainder-plus-times-times-instance,
remainder-plus-times-times,
remainder-plus-times-times-proof,
remainder-plus-fact,
remainder-difference2,
double-remainder-induction,
*1*double-remainder-induction,
remainder-difference1,
remainder-times2-instance,
remainder-times2,
remainder-times2-proof,
remainder-times-times-proof,
remainder-times1-instance,
remainder-times1-instance-proof,
remainder-times1,
remainder-times1-proof,
equal-remainder-plus-remainder-proof,
equal-remainder-plus-0,
equal-remainder-plus-0-proof,
remainder-plus,
remainder-plus-proof,
remainder-add1,
remainder-quotient-elim,
remainder-zero,
remainder-of-non-number,
remainder-noop,
lessp-remainder,
correctness-of-cancel-equal-times,
cancel-equal-times,
*1*cancel-equal-times,
correctness-of-cancel-lessp-times,
cancel-lessp-times,
*1*cancel-lessp-times,
infer-equality-from-not-lessp,
lessp-times-arg1,
eval\$-equal,
and-not-zerop-tree,
*1*and-not-zerop-tree,
or-zerop-tree,
*1*or-zerop-tree,
times-fringe,
*1*times-fringe,
times-tree,
*1*times-tree,
lessp-1-times,
lessp-plus-times2,
lessp-plus-times1,
lessp-plus-times-proof,
lessp-times-cancellation-proof,
lessp-times3,
lessp-times3-proof2,
lessp-times3-proof1,
lessp-times2,
lessp-times2-proof,
lessp-times1,
lessp-times1-proof,
times-1-arg1,
times-quotient,
times-quotient-proof,
times-distributes-over-difference,
times-distributes-over-difference-proof,
associativity-of-times,
commutativity2-of-times,
times-distributes-over-plus,
times-distributes-over-plus-proof,
commutativity-of-times,
times-add1,
times-zero,
equal-sub1-0,
equal-times-1,
equal-times-0,
correctness-of-cancel-lessp-plus,
cancel-lessp-plus,
*1*cancel-lessp-plus,
difference-x-x,
difference-difference-arg2,
difference-difference-arg1,
difference-sub1-arg2,
difference-add1-arg2,
difference-leq-arg1,
difference-elim,
correctness-of-cancel-difference-plus,
cancel-difference-plus,
*1*cancel-difference-plus,
correctness-of-cancel-equal-plus,
cancel-equal-plus,
*1*cancel-equal-plus,
eval\$-quote,
plus-tree,
*1*plus-tree,
plus-fringe,
*1*plus-fringe,
diff-diff-arg2,
diff-diff-arg1,
difference-plus-plus-cancellation-proof,
difference-plus-cancellation-proof,
plus-difference-arg2,
plus-difference-arg1,
associativity-of-plus,
plus-add1-arg2,
plus-add1-arg1,
plus-zero-arg2,
commutativity2-of-plus,
commutativity-of-plus,
equal-difference-0,
equal-plus-0,
member-bagint,
occurrences-bagdiff,
occurrences-bagint,
subbagp-bagint2,
subbagp-bagint1,
subbagp-cdr2,
subbagp-cdr1,
subbagp-delete,
bagdiff-delete,
member-bagdiff,
occurrences-delete,
member-delete-implies-membership,
member-delete,
member-non-list,
equal-occurrences-zero,
delete-delete,
delete-non-member,
subbagp,
*1*subbagp,
occurrences,
*1*occurrences,
bagint,
*1*bagint,
bagdiff,
*1*bagdiff,
delete,
*1*delete.\index{math-theory}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-constants-ilessp; name this event `cancel-constants-ilessp-off'.\index{cancel-constants-ilessp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-constants-ilessp-lemma-2; name this event `cancel-constants-ilessp-lemma-2-off'.\index{cancel-constants-ilessp-lemma-2!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-constants-ilessp-lemma-1; name this event `cancel-constants-ilessp-lemma-1-off'.\index{cancel-constants-ilessp-lemma-1!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-add1-iplus; name this event `ilessp-add1-iplus-off'.\index{ilessp-add1-iplus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-add1; name this event `ilessp-add1-off'.\index{ilessp-add1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-constants-equal; name this event `cancel-constants-equal-off'.\index{cancel-constants-equal-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-constants-equal-lemma; name this event `cancel-constants-equal-lemma-off'.\index{cancel-constants-equal-lemma-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-constants; name this event `iplus-constants-off'.\index{iplus-constants-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-ineg-terms-from-inequality; name this event `correctness-of-cancel-ineg-terms-from-inequality-off'.\index{correctness-of-cancel-ineg-term!s-from-inequality-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-ineg-terms-from-inequality-cancel-ineg-terms-from-inequality-expanded; name this event `cancel-ineg-terms-from-inequality-cancel-ineg-terms-from-inequality-expanded-off'.\index{cancel-ineg-terms-from-inequalit!y-cancel-ineg-terms-from-inequality-expanded-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-ineg-terms-from-inequality-expanded; name this event `g*1*cancel-ineg-terms-from-inequality-expanded-off'.\index{g*1*cancel-ineg-terms-from-ineq!uality-expanded-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-ineg-terms-from-inequality; name this event `cancel-ineg-terms-from-inequality-off'.\index{cancel-ineg-terms-from-inequalit!y-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-ineg-terms-from-inequality; name this event `g*1*cancel-ineg-terms-from-inequality-off'.\index{g*1*cancel-ineg-terms-from-ineq!uality-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable make-cancel-ineg-terms-inequality; name this event `make-cancel-ineg-terms-inequality-off'.\index{make-cancel-ineg-terms-inequalit!y-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*make-cancel-ineg-terms-inequality; name this event `g*1*make-cancel-ineg-terms-inequality-off'.\index{g*1*make-cancel-ineg-terms-ineq!uality-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-ineg-terms-from-equality; name this event `correctness-of-cancel-ineg-terms-from-equality-off'.\index{correctness-of-cancel-ineg-term!s-from-equality-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-list-eval\$-car-split-out-ineg-terms; name this event `iplus-list-eval\$-car-split-out-ineg-terms-off'.\index{iplus-list-eval\$-car-split-out!-ineg-terms-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-iplus-list-cdr-remove-inegs; name this event `eval\$-iplus-list-cdr-remove-inegs-off'.\index{eval\$-iplus-list-cdr-remove-ine!gs-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-iplus-list-car-remove-inegs; name this event `eval\$-iplus-list-car-remove-inegs-off'.\index{eval\$-iplus-list-car-remove-ine!gs-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-ineg-terms-from-equality-cancel-ineg-terms-from-equality-expanded; name this event `cancel-ineg-terms-from-equality-cancel-ineg-terms-from-equality-expanded-off'.\index{cancel-ineg-terms-from-equality!-cancel-ineg-terms-from-equality-expanded-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-ineg-terms-from-equality-expanded; name this event `g*1*cancel-ineg-terms-from-equality-expanded-off'.\index{g*1*cancel-ineg-terms-from-equa!lity-expanded-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-ineg-terms-from-equality; name this event `cancel-ineg-terms-from-equality-off'.\index{cancel-ineg-terms-from-equality!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-ineg-terms-from-equality; name this event `g*1*cancel-ineg-terms-from-equality-off'.\index{g*1*cancel-ineg-terms-from-equa!lity-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable make-cancel-ineg-terms-equality; name this event `make-cancel-ineg-terms-equality-off'.\index{make-cancel-ineg-terms-equality!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*make-cancel-ineg-terms-equality; name this event `g*1*make-cancel-ineg-terms-equality-off'.\index{g*1*make-cancel-ineg-terms-equa!lity-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iplus-or-ineg-term; name this event `g*1*iplus-or-ineg-term-off'.\index{g*1*iplus-or-ineg-term-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*remove-inegs; name this event `g*1*remove-inegs-off'.\index{g*1*remove-inegs-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable split-out-ineg-terms; name this event `split-out-ineg-terms-off'.\index{split-out-ineg-terms-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*split-out-ineg-terms; name this event `g*1*split-out-ineg-terms-off'.\index{g*1*split-out-ineg-terms-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-factors-ilessp-0; name this event `correctness-of-cancel-factors-ilessp-0-off'.\index{correctness-of-cancel-factors-i!lessp-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable conjoin-inequalities-with-0-eliminator; name this event `conjoin-inequalities-with-0-eliminator-off'.\index{conjoin-inequalities-with-0-eli!minator-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-factors-ilessp-0; name this event `cancel-factors-ilessp-0-off'.\index{cancel-factors-ilessp-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-factors-ilessp-0; name this event `g*1*cancel-factors-ilessp-0-off'.\index{g*1*cancel-factors-ilessp-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable conjoin-inequalities-with-0; name this event `conjoin-inequalities-with-0-off'.\index{conjoin-inequalities-with-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*conjoin-inequalities-with-0; name this event `g*1*conjoin-inequalities-with-0-off'.\index{g*1*conjoin-inequalities-with-0!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-factors-0; name this event `correctness-of-cancel-factors-0-off'.\index{correctness-of-cancel-factors-0!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable some-eval\$s-to-0-eliminator; name this event `some-eval\$s-to-0-eliminator-off'.\index{some-eval\$s-to-0-eliminator-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable some-eval\$s-to-0-append; name this event `some-eval\$s-to-0-append-off'.\index{some-eval\$s-to-0-append-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-disjoin-equalities-with-0; name this event `eval\$-disjoin-equalities-with-0-off'.\index{eval\$-disjoin-equalities-with-!0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable some-eval\$s-to-0; name this event `some-eval\$s-to-0-off'.\index{some-eval\$s-to-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*some-eval\$s-to-0; name this event `g*1*some-eval\$s-to-0-off'.\index{g*1*some-eval\$s-to-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-factors-0; name this event `cancel-factors-0-off'.\index{cancel-factors-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-factors-0; name this event `g*1*cancel-factors-0-off'.\index{g*1*cancel-factors-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable disjoin-equalities-with-0; name this event `disjoin-equalities-with-0-off'.\index{disjoin-equalities-with-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*disjoin-equalities-with-0; name this event `g*1*disjoin-equalities-with-0-off'.\index{g*1*disjoin-equalities-with-0-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-itimes-ilessp-factors; name this event `correctness-of-cancel-itimes-ilessp-factors-off'.\index{correctness-of-cancel-itimes-ile!ssp-factors-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-fix-int-to-ilessp; name this event `equal-fix-int-to-ilessp-off'.\index{equal-fix-int-to-ilessp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-list-bagint-0-implies-equal-for-ilessp-lemma; name this event `eval\$-list-bagint-0-implies-equal-for-ilessp-lemma-off'.\index{eval\$-list-bagint-0-implies-eq!ual-for-ilessp-lemma-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-list-bagint-0-for-ilessp; name this event `eval\$-list-bagint-0-for-ilessp-off'.\index{eval\$-list-bagint-0-for-ilessp!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable member-0-itimes-factors-yields-0-ilessp-consequence-2; name this event `member-0-itimes-factors-yields-0-ilessp-consequence-2-off'.\index{member-0-itimes-factors-yields-!0-ilessp-consequence-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable member-0-itimes-factors-yields-0-ilessp-consequence-1; name this event `member-0-itimes-factors-yields-0-ilessp-consequence-1-off'.\index{member-0-itimes-factors-yields-!0-ilessp-consequence-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable member-0-itimes-factors-yields-0; name this event `member-0-itimes-factors-yields-0-off'.\index{member-0-itimes-factors-yields-!0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-itimes-list-eval\$-list-bagdiff-corollary-2; name this event `ilessp-itimes-list-eval\$-list-bagdiff-corollary-2-off'.\index{ilessp-itimes-list-eval\$-list-!bagdiff-corollary-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-zero-implies-not-equal; name this event `ilessp-zero-implies-not-equal-off'.\index{ilessp-zero-implies-not-equal-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-itimes-list-eval\$-list-bagdiff-corollary-1; name this event `ilessp-itimes-list-eval\$-list-bagdiff-corollary-1-off'.\index{ilessp-itimes-list-eval\$-list-!bagdiff-corollary-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable zero-ilessp-implies-not-equal; name this event `zero-ilessp-implies-not-equal-off'.\index{zero-ilessp-implies-not-equal-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-itimes-list-eval\$-list-bagdiff; name this event `ilessp-itimes-list-eval\$-list-bagdiff-off'.\index{ilessp-itimes-list-eval\$-list-!bagdiff-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable bagint-singleton; name this event `bagint-singleton-off'.\index{bagint-singleton-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-itimes-ilessp-factors; name this event `cancel-itimes-ilessp-factors-off'.\index{cancel-itimes-ilessp-factors-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-itimes-ilessp-factors; name this event `g*1*cancel-itimes-ilessp-factors-off'.\index{g*1*cancel-itimes-ilessp-factor!s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-itimes-factors; name this event `correctness-of-cancel-itimes-factors-off'.\index{correctness-of-cancel-itimes-fa!ctors-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable member-0-eval\$-list; name this event `member-0-eval\$-list-off'.\index{member-0-eval\$-list-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable membership-of-0-implies-itimes-list-is-0; name this event `membership-of-0-implies-itimes-list-is-0-off'.\index{membership-of-0-implies-itimes-!list-is-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-itimes-factors-expanded-cancel-itimes-factors; name this event `cancel-itimes-factors-expanded-cancel-itimes-factors-off'.\index{cancel-itimes-factors-expanded-!cancel-itimes-factors-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-itimes-factors-expanded; name this event `g*1*cancel-itimes-factors-expanded-off'.\index{g*1*cancel-itimes-factors-expan!ded-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-itimes-factors; name this event `cancel-itimes-factors-off'.\index{cancel-itimes-factors-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-itimes-factors; name this event `g*1*cancel-itimes-factors-off'.\index{g*1*cancel-itimes-factors-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iplus-or-itimes-term; name this event `g*1*iplus-or-itimes-term-off'.\index{g*1*iplus-or-itimes-term-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-eval\$-itimes-tree-ineg; name this event `itimes-eval\$-itimes-tree-ineg-off'.\index{itimes-eval\$-itimes-tree-ineg-!off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-eval\$-itimes-tree-ineg; name this event `iplus-eval\$-itimes-tree-ineg-off'.\index{iplus-eval\$-itimes-tree-ineg-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ineg-eval\$-itimes-tree-ineg; name this event `ineg-eval\$-itimes-tree-ineg-off'.\index{ineg-eval\$-itimes-tree-ineg-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-itimes-tree-ineg; name this event `eval\$-itimes-tree-ineg-off'.\index{eval\$-itimes-tree-ineg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-eval\$-itimes-tree-rec; name this event `fix-int-eval\$-itimes-tree-rec-off'.\index{fix-int-eval\$-itimes-tree-rec-!off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-ineg-ineg; name this event `ilessp-ineg-ineg-off'.\index{ilessp-ineg-ineg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-ineg-ineg; name this event `equal-ineg-ineg-off'.\index{equal-ineg-ineg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes--1; name this event `itimes--1-off'.\index{itimes--1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-factors; name this event `itimes-factors-off'.\index{itimes-factors-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*itimes-factors; name this event `g*1*itimes-factors-off'.\index{g*1*itimes-factors-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*itimes-tree-ineg; name this event `g*1*itimes-tree-ineg-off'.\index{g*1*itimes-tree-ineg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-strict; name this event `ilessp-strict-off'.\index{ilessp-strict-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-itimes-right-negative; name this event `ilessp-itimes-right-negative-off'.\index{ilessp-itimes-right-negative-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-itimes-right-positive; name this event `ilessp-itimes-right-positive-off'.\index{ilessp-itimes-right-positive-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-itimes-ilessp; name this event `cancel-itimes-ilessp-off'.\index{cancel-itimes-ilessp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-itimes-ilessp; name this event `g*1*cancel-itimes-ilessp-off'.\index{g*1*cancel-itimes-ilessp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*make-cancel-itimes-inequality; name this event `g*1*make-cancel-itimes-inequality-off'.\index{g*1*make-cancel-itimes-inequalit!y-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*itimes-tree-no-fix-int; name this event `g*1*itimes-tree-no-fix-int-off'.\index{g*1*itimes-tree-no-fix-int-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable subsetp; name this event `subsetp-off'.\index{subsetp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*subsetp; name this event `g*1*subsetp-off'.\index{g*1*subsetp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-fix-int; name this event `equal-fix-int-off'.\index{equal-fix-int-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable member-append; name this event `member-append-off'.\index{member-append-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-list-append; name this event `itimes-list-append-off'.\index{itimes-list-append-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-itimes; name this event `cancel-itimes-off'.\index{cancel-itimes-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-itimes; name this event `g*1*cancel-itimes-off'.\index{g*1*cancel-itimes-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*make-cancel-itimes-equality; name this event `g*1*make-cancel-itimes-equality-off'.\index{g*1*make-cancel-itimes-equality!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-itimes-list; name this event `integerp-itimes-list-off'.\index{integerp-itimes-list-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-list; name this event `itimes-list-off'.\index{itimes-list-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*itimes-list; name this event `g*1*itimes-list-off'.\index{g*1*itimes-list-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*itimes-tree; name this event `g*1*itimes-tree-off'.\index{g*1*itimes-tree-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-tree-rec; name this event `itimes-tree-rec-off'.\index{itimes-tree-rec-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*itimes-tree-rec; name this event `g*1*itimes-tree-rec-off'.\index{g*1*itimes-tree-rec-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-fringe; name this event `itimes-fringe-off'.\index{itimes-fringe-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*itimes-fringe; name this event `g*1*itimes-fringe-off'.\index{g*1*itimes-fringe-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-irem; name this event `fix-int-irem-off'.\index{fix-int-irem-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-iquo; name this event `fix-int-iquo-off'.\index{fix-int-iquo-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-imod; name this event `fix-int-imod-off'.\index{fix-int-imod-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-idiv; name this event `fix-int-idiv-off'.\index{fix-int-idiv-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-iremainder; name this event `fix-int-iremainder-off'.\index{fix-int-iremainder-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-iquotient; name this event `fix-int-iquotient-off'.\index{fix-int-iquotient-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable irem-fix-int2; name this event `irem-fix-int2-off'.\index{irem-fix-int2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable irem-fix-int1; name this event `irem-fix-int1-off'.\index{irem-fix-int1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iquo-fix-int2; name this event `iquo-fix-int2-off'.\index{iquo-fix-int2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iquo-fix-int1; name this event `iquo-fix-int1-off'.\index{iquo-fix-int1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable imod-fix-int2; name this event `imod-fix-int2-off'.\index{imod-fix-int2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable imod-fix-int1; name this event `imod-fix-int1-off'.\index{imod-fix-int1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable idiv-fix-int2; name this event `idiv-fix-int2-off'.\index{idiv-fix-int2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable idiv-fix-int1; name this event `idiv-fix-int1-off'.\index{idiv-fix-int1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iremainder-fix-int2; name this event `iremainder-fix-int2-off'.\index{iremainder-fix-int2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iremainder-fix-int1; name this event `iremainder-fix-int1-off'.\index{iremainder-fix-int1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iquotient-fix-int2; name this event `iquotient-fix-int2-off'.\index{iquotient-fix-int2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iquotient-fix-int1; name this event `iquotient-fix-int1-off'.\index{iquotient-fix-int1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-irem; name this event `integerp-irem-off'.\index{integerp-irem-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-iquo; name this event `integerp-iquo-off'.\index{integerp-iquo-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-imod; name this event `integerp-imod-off'.\index{integerp-imod-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-idiv; name this event `integerp-idiv-off'.\index{integerp-idiv-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-iremainder; name this event `integerp-iremainder-off'.\index{integerp-iremainder-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-iquotient; name this event `integerp-iquotient-off'.\index{integerp-iquotient-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-cancellation-3; name this event `itimes-cancellation-3-off'.\index{itimes-cancellation-3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-cancellation-2; name this event `itimes-cancellation-2-off'.\index{itimes-cancellation-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-cancellation-1; name this event `itimes-cancellation-1-off'.\index{itimes-cancellation-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-ineg-2; name this event `itimes-ineg-2-off'.\index{itimes-ineg-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-ineg-1; name this event `itimes-ineg-1-off'.\index{itimes-ineg-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iquo-irem-uniqueness; name this event `iquo-irem-uniqueness-off'.\index{iquo-irem-uniqueness-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-for-truncate-to-zero; name this event `division-theorem-for-truncate-to-zero-off'.\index{division-theorem-for-truncate-t!o-zero-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-for-truncate-to-zero-part3; name this event `division-theorem-for-truncate-to-zero-part3-off'.\index{division-theorem-for-truncate-t!o-zero-part3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-for-truncate-to-zero-part2; name this event `division-theorem-for-truncate-to-zero-part2-off'.\index{division-theorem-for-truncate-t!o-zero-part2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-for-truncate-to-zero-part1; name this event `division-theorem-for-truncate-to-zero-part1-off'.\index{division-theorem-for-truncate-t!o-zero-part1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable idiv-imod-uniqueness; name this event `idiv-imod-uniqueness-off'.\index{idiv-imod-uniqueness-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-for-truncate-to-neginf; name this event `division-theorem-for-truncate-to-neginf-off'.\index{division-theorem-for-truncate-t!o-neginf-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-for-truncate-to-neginf-part3; name this event `division-theorem-for-truncate-to-neginf-part3-off'.\index{division-theorem-for-truncate-t!o-neginf-part3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-for-truncate-to-neginf-part2; name this event `division-theorem-for-truncate-to-neginf-part2-off'.\index{division-theorem-for-truncate-t!o-neginf-part2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-for-truncate-to-neginf-part1; name this event `division-theorem-for-truncate-to-neginf-part1-off'.\index{division-theorem-for-truncate-t!o-neginf-part1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iquotient-iremainder-uniqueness; name this event `iquotient-iremainder-uniqueness-off'.\index{iquotient-iremainder-uniqueness!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem; name this event `division-theorem-off'.\index{division-theorem-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-part3; name this event `division-theorem-part3-off'.\index{division-theorem-part3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-part2; name this event `division-theorem-part2-off'.\index{division-theorem-part2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-part1; name this event `division-theorem-part1-off'.\index{division-theorem-part1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-remainder-uniqueness; name this event `quotient-remainder-uniqueness-off'.\index{quotient-remainder-uniqueness-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-1-arg1; name this event `itimes-1-arg1-off'.\index{itimes-1-arg1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-itimes-minus-1; name this event `equal-itimes-minus-1-off'.\index{equal-itimes-minus-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-itimes-1; name this event `equal-itimes-1-off'.\index{equal-itimes-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-itimes-0; name this event `equal-itimes-0-off'.\index{equal-itimes-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable associativity-of-itimes; name this event `associativity-of-itimes-off'.\index{associativity-of-itimes-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity2-of-itimes; name this event `commutativity2-of-itimes-off'.\index{commutativity2-of-itimes-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-distributes-over-iplus; name this event `itimes-distributes-over-iplus-off'.\index{itimes-distributes-over-iplus-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-distributes-over-iplus-proof; name this event `itimes-distributes-over-iplus-proof-off'.\index{itimes-distributes-over-iplus-p!roof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity-of-itimes; name this event `commutativity-of-itimes-off'.\index{commutativity-of-itimes-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-fix-int2; name this event `itimes-fix-int2-off'.\index{itimes-fix-int2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-fix-int1; name this event `itimes-fix-int1-off'.\index{itimes-fix-int1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-0-right; name this event `itimes-0-right-off'.\index{itimes-0-right-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-0-left; name this event `itimes-0-left-off'.\index{itimes-0-left-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-iplus-ilessp; name this event `correctness-of-cancel-iplus-ilessp-off'.\index{correctness-of-cancel-iplus-ile!ssp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-iplus-ilessp; name this event `cancel-iplus-ilessp-off'.\index{cancel-iplus-ilessp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-iplus-ilessp; name this event `g*1*cancel-iplus-ilessp-off'.\index{g*1*cancel-iplus-ilessp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iplus-tree-no-fix-int; name this event `g*1*iplus-tree-no-fix-int-off'.\index{g*1*iplus-tree-no-fix-int-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-cancellation-2-for-ilessp; name this event `iplus-cancellation-2-for-ilessp-off'.\index{iplus-cancellation-2-for-ilessp!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-cancellation-1-for-ilessp; name this event `iplus-cancellation-1-for-ilessp-off'.\index{iplus-cancellation-1-for-ilessp!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-iplus-ilessp-1; name this event `cancel-iplus-ilessp-1-off'.\index{cancel-iplus-ilessp-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-iplus-ilessp-1; name this event `g*1*cancel-iplus-ilessp-1-off'.\index{g*1*cancel-iplus-ilessp-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*make-cancel-iplus-inequality-1; name this event `g*1*make-cancel-iplus-inequality-1-off'.\index{g*1*make-cancel-iplus-inequalit!y-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-fix-int-2; name this event `ilessp-fix-int-2-off'.\index{ilessp-fix-int-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-fix-int-1; name this event `ilessp-fix-int-1-off'.\index{ilessp-fix-int-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-iplus; name this event `correctness-of-cancel-iplus-off'.\index{correctness-of-cancel-iplus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-ineg7; name this event `iplus-ineg7-off'.\index{iplus-ineg7-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-list-append; name this event `iplus-list-append-off'.\index{iplus-list-append-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-iplus-list-delete; name this event `eval\$-iplus-list-delete-off'.\index{eval\$-iplus-list-delete-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-iplus; name this event `g*1*cancel-iplus-off'.\index{g*1*cancel-iplus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-list-append; name this event `eval\$-list-append-off'.\index{eval\$-list-append-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-iplus-list; name this event `integerp-iplus-list-off'.\index{integerp-iplus-list-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-list; name this event `iplus-list-off'.\index{iplus-list-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iplus-list; name this event `g*1*iplus-list-off'.\index{g*1*iplus-list-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iplus-tree; name this event `g*1*iplus-tree-off'.\index{g*1*iplus-tree-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-tree-rec; name this event `iplus-tree-rec-off'.\index{iplus-tree-rec-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iplus-tree-rec; name this event `g*1*iplus-tree-rec-off'.\index{g*1*iplus-tree-rec-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-fringe; name this event `iplus-fringe-off'.\index{iplus-fringe-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iplus-fringe; name this event `g*1*iplus-fringe-off'.\index{g*1*iplus-fringe-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-ineg; name this event `correctness-of-cancel-ineg-off'.\index{correctness-of-cancel-ineg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-x-y-ineg-x; name this event `iplus-x-y-ineg-x-off'.\index{iplus-x-y-ineg-x-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-ineg4; name this event `iplus-ineg4-off'.\index{iplus-ineg4-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-ineg3; name this event `iplus-ineg3-off'.\index{iplus-ineg3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-cancel-ineg-aux-is-its-fn; name this event `eval\$-cancel-ineg-aux-is-its-fn-off'.\index{eval\$-cancel-ineg-aux-is-its-f!n-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-cancel-ineg-aux-fn; name this event `eval\$-cancel-ineg-aux-fn-off'.\index{eval\$-cancel-ineg-aux-fn-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*eval\$-cancel-ineg-aux-fn; name this event `g*1*eval\$-cancel-ineg-aux-fn-off'.\index{g*1*eval\$-cancel-ineg-aux-fn-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-other; name this event `eval\$-other-off'.\index{eval\$-other-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-litatom; name this event `eval\$-litatom-off'.\index{eval\$-litatom-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-list-nlistp; name this event `eval\$-list-nlistp-off'.\index{eval\$-list-nlistp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-list-cons; name this event `eval\$-list-cons-off'.\index{eval\$-list-cons-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-ineg; name this event `cancel-ineg-off'.\index{cancel-ineg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-ineg; name this event `g*1*cancel-ineg-off'.\index{g*1*cancel-ineg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-ineg-aux; name this event `cancel-ineg-aux-off'.\index{cancel-ineg-aux-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-ineg-aux; name this event `g*1*cancel-ineg-aux-off'.\index{g*1*cancel-ineg-aux-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable idifference-fix-int2; name this event `idifference-fix-int2-off'.\index{idifference-fix-int2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable idifference-fix-int1; name this event `idifference-fix-int1-off'.\index{idifference-fix-int1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-fix-int2; name this event `iplus-fix-int2-off'.\index{iplus-fix-int2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-fix-int1; name this event `iplus-fix-int1-off'.\index{iplus-fix-int1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-ineg2; name this event `iplus-ineg2-off'.\index{iplus-ineg2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-ineg1; name this event `iplus-ineg1-off'.\index{iplus-ineg1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-cancellation-2; name this event `iplus-cancellation-2-off'.\index{iplus-cancellation-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-cancellation-1; name this event `iplus-cancellation-1-off'.\index{iplus-cancellation-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable associativity-of-iplus; name this event `associativity-of-iplus-off'.\index{associativity-of-iplus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity-of-iplus; name this event `commutativity-of-iplus-off'.\index{commutativity-of-iplus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity2-of-iplus; name this event `commutativity2-of-iplus-off'.\index{commutativity2-of-iplus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-0-right; name this event `iplus-0-right-off'.\index{iplus-0-right-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-0-left; name this event `iplus-0-left-off'.\index{iplus-0-left-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ineg-0; name this event `ineg-0-off'.\index{ineg-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ineg-fix-int; name this event `ineg-fix-int-off'.\index{ineg-fix-int-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ineg-ineg; name this event `ineg-ineg-off'.\index{ineg-ineg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ineg-iplus; name this event `ineg-iplus-off'.\index{ineg-iplus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-itimes; name this event `fix-int-itimes-off'.\index{fix-int-itimes-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-iabs; name this event `fix-int-iabs-off'.\index{fix-int-iabs-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-ineg; name this event `fix-int-ineg-off'.\index{fix-int-ineg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-idifference; name this event `fix-int-idifference-off'.\index{fix-int-idifference-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-iplus; name this event `fix-int-iplus-off'.\index{fix-int-iplus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-fix-int; name this event `fix-int-fix-int-off'.\index{fix-int-fix-int-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-remover; name this event `fix-int-remover-off'.\index{fix-int-remover-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-itimes; name this event `integerp-itimes-off'.\index{integerp-itimes-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-iabs; name this event `integerp-iabs-off'.\index{integerp-iabs-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-ineg; name this event `integerp-ineg-off'.\index{integerp-ineg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-idifference; name this event `integerp-idifference-off'.\index{integerp-idifference-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-iplus; name this event `integerp-iplus-off'.\index{integerp-iplus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-fix-int; name this event `integerp-fix-int-off'.\index{integerp-fix-int-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*irem; name this event `g*1*irem-off'.\index{g*1*irem-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iquo; name this event `g*1*iquo-off'.\index{g*1*iquo-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*imod; name this event `g*1*imod-off'.\index{g*1*imod-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*idiv; name this event `g*1*idiv-off'.\index{g*1*idiv-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iremainder; name this event `g*1*iremainder-off'.\index{g*1*iremainder-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iquotient; name this event `g*1*iquotient-off'.\index{g*1*iquotient-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*itimes; name this event `g*1*itimes-off'.\index{g*1*itimes-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iabs; name this event `g*1*iabs-off'.\index{g*1*iabs-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable idifference; name this event `idifference-off'.\index{idifference-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*idifference; name this event `g*1*idifference-off'.\index{g*1*idifference-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*ineg; name this event `g*1*ineg-off'.\index{g*1*ineg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iplus; name this event `g*1*iplus-off'.\index{g*1*iplus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ileq; name this event `ileq-off'.\index{ileq-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*ileq; name this event `g*1*ileq-off'.\index{g*1*ileq-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*ilessp; name this event `g*1*ilessp-off'.\index{g*1*ilessp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable izerop; name this event `izerop-off'.\index{izerop-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*izerop; name this event `g*1*izerop-off'.\index{g*1*izerop-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*fix-int; name this event `g*1*fix-int-off'.\index{g*1*fix-int-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*integerp; name this event `g*1*integerp-off'.\index{g*1*integerp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd-idempotence; name this event `gcd-idempotence-off'.\index{gcd-idempotence-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd-x-x; name this event `gcd-x-x-off'.\index{gcd-x-x-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity2-of-gcd; name this event `commutativity2-of-gcd-off'.\index{commutativity2-of-gcd-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity2-of-gcd-zero-case; name this event `commutativity2-of-gcd-zero-case-off'.\index{commutativity2-of-gcd-zero-case!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable associativity-of-gcd; name this event `associativity-of-gcd-off'.\index{associativity-of-gcd-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable associativity-of-gcd-zero-case; name this event `associativity-of-gcd-zero-case-off'.\index{associativity-of-gcd-zero-case-!off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable common-divisor-divides-gcd; name this event `common-divisor-divides-gcd-off'.\index{common-divisor-divides-gcd-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd-is-the-greatest; name this event `gcd-is-the-greatest-off'.\index{gcd-is-the-greatest-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable distributivity-of-times-over-gcd; name this event `distributivity-of-times-over-gcd-off'.\index{distributivity-of-times-over-gc!d-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable distributivity-of-times-over-gcd-proof; name this event `distributivity-of-times-over-gcd-proof-off'.\index{distributivity-of-times-over-gc!d-proof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-gcd; name this event `remainder-gcd-off'.\index{remainder-gcd-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd-plus-instance; name this event `gcd-plus-instance-off'.\index{gcd-plus-instance-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd-plus; name this event `gcd-plus-off'.\index{gcd-plus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd-plus-proof; name this event `gcd-plus-proof-off'.\index{gcd-plus-proof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd-plus-instance-temp; name this event `gcd-plus-instance-temp-off'.\index{gcd-plus-instance-temp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd-plus-instance-temp-proof; name this event `gcd-plus-instance-temp-proof-off'.\index{gcd-plus-instance-temp-proof-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-gcd; name this event `lessp-gcd-off'.\index{lessp-gcd-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-gcd-0; name this event `equal-gcd-0-off'.\index{equal-gcd-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd-1; name this event `gcd-1-off'.\index{gcd-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd-0; name this event `gcd-0-off'.\index{gcd-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable single-number-induction; name this event `single-number-induction-off'.\index{single-number-induction-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*single-number-induction; name this event `g*1*single-number-induction-off'.\index{g*1*single-number-induction-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity-of-gcd; name this event `commutativity-of-gcd-off'.\index{commutativity-of-gcd-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-exp; name this event `log-exp-off'.\index{log-exp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-times-exp; name this event `log-times-exp-off'.\index{log-times-exp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-times-exp-proof; name this event `log-times-exp-proof-off'.\index{log-times-exp-proof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-times; name this event `log-times-off'.\index{log-times-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-times-proof; name this event `log-times-proof-off'.\index{log-times-proof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-quotient-exp; name this event `log-quotient-exp-off'.\index{log-quotient-exp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-quotient-times; name this event `log-quotient-times-off'.\index{log-quotient-times-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-quotient-times-proof; name this event `log-quotient-times-proof-off'.\index{log-quotient-times-proof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-quotient; name this event `log-quotient-off'.\index{log-quotient-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable leq-log-log; name this event `leq-log-log-off'.\index{leq-log-log-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable double-log-induction; name this event `double-log-induction-off'.\index{double-log-induction-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*double-log-induction; name this event `g*1*double-log-induction-off'.\index{g*1*double-log-induction-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-1; name this event `log-1-off'.\index{log-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-0; name this event `log-0-off'.\index{log-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-log-0; name this event `equal-log-0-off'.\index{equal-log-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable exp-difference; name this event `exp-difference-off'.\index{exp-difference-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-exp-1; name this event `equal-exp-1-off'.\index{equal-exp-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-exp-0; name this event `equal-exp-0-off'.\index{equal-exp-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable exp-exp; name this event `exp-exp-off'.\index{exp-exp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable exp-times; name this event `exp-times-off'.\index{exp-times-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable exp-0-arg2; name this event `exp-0-arg2-off'.\index{exp-0-arg2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable exp-1-arg1; name this event `exp-1-arg1-off'.\index{exp-1-arg1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable exp-0-arg1; name this event `exp-0-arg1-off'.\index{exp-0-arg1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable exp-plus; name this event `exp-plus-off'.\index{exp-plus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable exp-add1; name this event `exp-add1-off'.\index{exp-add1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable exp-zero; name this event `exp-zero-off'.\index{exp-zero-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-exp; name this event `quotient-exp-off'.\index{quotient-exp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-exp-exp; name this event `remainder-exp-exp-off'.\index{remainder-exp-exp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable double-number-induction; name this event `double-number-induction-off'.\index{double-number-induction-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*double-number-induction; name this event `g*1*double-number-induction-off'.\index{g*1*double-number-induction-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-exp; name this event `remainder-exp-off'.\index{remainder-exp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd; name this event `gcd-off'.\index{gcd-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*gcd; name this event `g*1*gcd-off'.\index{g*1*gcd-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log; name this event `log-off'.\index{log-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*log; name this event `g*1*log-off'.\index{g*1*log-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable exp; name this event `exp-off'.\index{exp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*exp; name this event `g*1*exp-off'.\index{g*1*exp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-quotient-times; name this event `correctness-of-cancel-quotient-times-off'.\index{correctness-of-cancel-quotient-ti!mes-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-quotient-times; name this event `cancel-quotient-times-off'.\index{cancel-quotient-times-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-quotient-times; name this event `g*1*cancel-quotient-times-off'.\index{g*1*cancel-quotient-times-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-quotient; name this event `lessp-quotient-off'.\index{lessp-quotient-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-x-x; name this event `quotient-x-x-off'.\index{quotient-x-x-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-1-arg1; name this event `quotient-1-arg1-off'.\index{quotient-1-arg1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-1-arg1-casesplit; name this event `quotient-1-arg1-casesplit-off'.\index{quotient-1-arg1-casesplit-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-1-arg2; name this event `quotient-1-arg2-off'.\index{quotient-1-arg2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable leq-quotient; name this event `leq-quotient-off'.\index{leq-quotient-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-quotient; name this event `quotient-quotient-off'.\index{quotient-quotient-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-plus-times-times-instance; name this event `quotient-plus-times-times-instance-off'.\index{quotient-plus-times-times-insta!nce-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-plus-times-times; name this event `quotient-plus-times-times-off'.\index{quotient-plus-times-times-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-plus-times-times-proof; name this event `quotient-plus-times-times-proof-off'.\index{quotient-plus-times-times-proof!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-plus-fact; name this event `quotient-plus-fact-off'.\index{quotient-plus-fact-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-remainder-instance; name this event `quotient-remainder-instance-off'.\index{quotient-remainder-instance-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-remainder; name this event `quotient-remainder-off'.\index{quotient-remainder-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-remainder-times; name this event `quotient-remainder-times-off'.\index{quotient-remainder-times-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-difference3; name this event `quotient-difference3-off'.\index{quotient-difference3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-difference2; name this event `quotient-difference2-off'.\index{quotient-difference2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-lessp-arg1; name this event `quotient-lessp-arg1-off'.\index{quotient-lessp-arg1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-difference1; name this event `quotient-difference1-off'.\index{quotient-difference1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-times-times-proof; name this event `quotient-times-times-proof-off'.\index{quotient-times-times-proof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-times-instance; name this event `quotient-times-instance-off'.\index{quotient-times-instance-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-times; name this event `quotient-times-off'.\index{quotient-times-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-times-proof; name this event `quotient-times-proof-off'.\index{quotient-times-proof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-times-instance-temp-proof; name this event `quotient-times-instance-temp-proof-off'.\index{quotient-times-instance-temp-pr!oof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-plus; name this event `quotient-plus-off'.\index{quotient-plus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-plus-proof; name this event `quotient-plus-proof-off'.\index{quotient-plus-proof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-sub1; name this event `quotient-sub1-off'.\index{quotient-sub1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-quotient-0; name this event `equal-quotient-0-off'.\index{equal-quotient-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-add1; name this event `quotient-add1-off'.\index{quotient-add1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-zero; name this event `quotient-zero-off'.\index{quotient-zero-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-of-non-number; name this event `quotient-of-non-number-off'.\index{quotient-of-non-number-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-noop; name this event `quotient-noop-off'.\index{quotient-noop-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable transitivity-of-divides; name this event `transitivity-of-divides-off'.\index{transitivity-of-divides-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-x-x; name this event `remainder-x-x-off'.\index{remainder-x-x-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-1-arg2; name this event `remainder-1-arg2-off'.\index{remainder-1-arg2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-1-arg1; name this event `remainder-1-arg1-off'.\index{remainder-1-arg1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-remainder; name this event `remainder-remainder-off'.\index{remainder-remainder-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-plus-times-times-instance; name this event `remainder-plus-times-times-instance-off'.\index{remainder-plus-times-times-inst!ance-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-plus-times-times; name this event `remainder-plus-times-times-off'.\index{remainder-plus-times-times-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-plus-times-times-proof; name this event `remainder-plus-times-times-proof-off'.\index{remainder-plus-times-times-proo!f-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-plus-fact; name this event `remainder-plus-fact-off'.\index{remainder-plus-fact-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-difference2; name this event `remainder-difference2-off'.\index{remainder-difference2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable double-remainder-induction; name this event `double-remainder-induction-off'.\index{double-remainder-induction-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*double-remainder-induction; name this event `g*1*double-remainder-induction-off'.\index{g*1*double-remainder-induction-!off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-difference1; name this event `remainder-difference1-off'.\index{remainder-difference1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-times2-instance; name this event `remainder-times2-instance-off'.\index{remainder-times2-instance-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-times2; name this event `remainder-times2-off'.\index{remainder-times2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-times2-proof; name this event `remainder-times2-proof-off'.\index{remainder-times2-proof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-times-times-proof; name this event `remainder-times-times-proof-off'.\index{remainder-times-times-proof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-times1-instance; name this event `remainder-times1-instance-off'.\index{remainder-times1-instance-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-times1-instance-proof; name this event `remainder-times1-instance-proof-off'.\index{remainder-times1-instance-proof!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-times1; name this event `remainder-times1-off'.\index{remainder-times1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-times1-proof; name this event `remainder-times1-proof-off'.\index{remainder-times1-proof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-remainder-plus-remainder-proof; name this event `equal-remainder-plus-remainder-proof-off'.\index{equal-remainder-plus-remainder-p!roof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-remainder-plus-0; name this event `equal-remainder-plus-0-off'.\index{equal-remainder-plus-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-remainder-plus-0-proof; name this event `equal-remainder-plus-0-proof-off'.\index{equal-remainder-plus-0-proof-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-plus; name this event `remainder-plus-off'.\index{remainder-plus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-plus-proof; name this event `remainder-plus-proof-off'.\index{remainder-plus-proof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-add1; name this event `remainder-add1-off'.\index{remainder-add1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-quotient-elim; name this event `remainder-quotient-elim-off'.\index{remainder-quotient-elim-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-zero; name this event `remainder-zero-off'.\index{remainder-zero-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-of-non-number; name this event `remainder-of-non-number-off'.\index{remainder-of-non-number-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-noop; name this event `remainder-noop-off'.\index{remainder-noop-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-remainder; name this event `lessp-remainder-off'.\index{lessp-remainder-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-equal-times; name this event `correctness-of-cancel-equal-times-off'.\index{correctness-of-cancel-equal-time!s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-equal-times; name this event `cancel-equal-times-off'.\index{cancel-equal-times-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-equal-times; name this event `g*1*cancel-equal-times-off'.\index{g*1*cancel-equal-times-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-lessp-times; name this event `correctness-of-cancel-lessp-times-off'.\index{correctness-of-cancel-lessp-time!s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-lessp-times; name this event `cancel-lessp-times-off'.\index{cancel-lessp-times-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-lessp-times; name this event `g*1*cancel-lessp-times-off'.\index{g*1*cancel-lessp-times-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable infer-equality-from-not-lessp; name this event `infer-equality-from-not-lessp-off'.\index{infer-equality-from-not-lessp-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-times-arg1; name this event `lessp-times-arg1-off'.\index{lessp-times-arg1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-equal; name this event `eval\$-equal-off1'.\index{eval\$-equal-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable and-not-zerop-tree; name this event `and-not-zerop-tree-off'.\index{and-not-zerop-tree-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*and-not-zerop-tree; name this event `g*1*and-not-zerop-tree-off'.\index{g*1*and-not-zerop-tree-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable or-zerop-tree; name this event `or-zerop-tree-off'.\index{or-zerop-tree-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*or-zerop-tree; name this event `g*1*or-zerop-tree-off'.\index{g*1*or-zerop-tree-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-fringe; name this event `times-fringe-off'.\index{times-fringe-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*times-fringe; name this event `g*1*times-fringe-off'.\index{g*1*times-fringe-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-tree; name this event `times-tree-off'.\index{times-tree-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*times-tree; name this event `g*1*times-tree-off'.\index{g*1*times-tree-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-1-times; name this event `lessp-1-times-off'.\index{lessp-1-times-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-plus-times2; name this event `lessp-plus-times2-off'.\index{lessp-plus-times2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-plus-times1; name this event `lessp-plus-times1-off'.\index{lessp-plus-times1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-plus-times-proof; name this event `lessp-plus-times-proof-off'.\index{lessp-plus-times-proof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-times-cancellation-proof; name this event `lessp-times-cancellation-proof-off'.\index{lessp-times-cancellation-proof-!off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-times3; name this event `lessp-times3-off'.\index{lessp-times3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-times3-proof2; name this event `lessp-times3-proof2-off'.\index{lessp-times3-proof2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-times3-proof1; name this event `lessp-times3-proof1-off'.\index{lessp-times3-proof1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-times2; name this event `lessp-times2-off'.\index{lessp-times2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-times2-proof; name this event `lessp-times2-proof-off'.\index{lessp-times2-proof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-times1; name this event `lessp-times1-off'.\index{lessp-times1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-times1-proof; name this event `lessp-times1-proof-off'.\index{lessp-times1-proof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-1-arg1; name this event `times-1-arg1-off'.\index{times-1-arg1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-quotient; name this event `times-quotient-off'.\index{times-quotient-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-quotient-proof; name this event `times-quotient-proof-off'.\index{times-quotient-proof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-distributes-over-difference; name this event `times-distributes-over-difference-off'.\index{times-distributes-over-differen!ce-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-distributes-over-difference-proof; name this event `times-distributes-over-difference-proof-off'.\index{times-distributes-over-differen!ce-proof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable associativity-of-times; name this event `associativity-of-times-off'.\index{associativity-of-times-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity2-of-times; name this event `commutativity2-of-times-off'.\index{commutativity2-of-times-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-distributes-over-plus; name this event `times-distributes-over-plus-off'.\index{times-distributes-over-plus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-distributes-over-plus-proof; name this event `times-distributes-over-plus-proof-off'.\index{times-distributes-over-plus-pro!of-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity-of-times; name this event `commutativity-of-times-off'.\index{commutativity-of-times-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-add1; name this event `times-add1-off'.\index{times-add1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-zero; name this event `times-zero-off'.\index{times-zero-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-sub1-0; name this event `equal-sub1-0-off'.\index{equal-sub1-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-times-1; name this event `equal-times-1-off'.\index{equal-times-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-times-0; name this event `equal-times-0-off'.\index{equal-times-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-lessp-plus; name this event `correctness-of-cancel-lessp-plus-off'.\index{correctness-of-cancel-lessp-plu!s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-lessp-plus; name this event `cancel-lessp-plus-off'.\index{cancel-lessp-plus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-lessp-plus; name this event `g*1*cancel-lessp-plus-off'.\index{g*1*cancel-lessp-plus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable difference-x-x; name this event `difference-x-x-off'.\index{difference-x-x-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable difference-difference-arg2; name this event `difference-difference-arg2-off'.\index{difference-difference-arg2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable difference-difference-arg1; name this event `difference-difference-arg1-off'.\index{difference-difference-arg1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable difference-sub1-arg2; name this event `difference-sub1-arg2-off'.\index{difference-sub1-arg2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable difference-add1-arg2; name this event `difference-add1-arg2-off'.\index{difference-add1-arg2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable difference-leq-arg1; name this event `difference-leq-arg1-off'.\index{difference-leq-arg1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable difference-elim; name this event `difference-elim-off'.\index{difference-elim-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-difference-plus; name this event `correctness-of-cancel-difference-plus-off'.\index{correctness-of-cancel-difference!-plus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-difference-plus; name this event `cancel-difference-plus-off'.\index{cancel-difference-plus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-difference-plus; name this event `g*1*cancel-difference-plus-off'.\index{g*1*cancel-difference-plus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-equal-plus; name this event `correctness-of-cancel-equal-plus-off'.\index{correctness-of-cancel-equal-plu!s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-equal-plus; name this event `cancel-equal-plus-off'.\index{cancel-equal-plus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-equal-plus; name this event `g*1*cancel-equal-plus-off'.\index{g*1*cancel-equal-plus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-quote; name this event `eval\$-quote-off1'.\index{eval\$-quote-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable plus-tree; name this event `plus-tree-off'.\index{plus-tree-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*plus-tree; name this event `g*1*plus-tree-off'.\index{g*1*plus-tree-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable plus-fringe; name this event `plus-fringe-off'.\index{plus-fringe-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*plus-fringe; name this event `g*1*plus-fringe-off'.\index{g*1*plus-fringe-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable diff-diff-arg2; name this event `diff-diff-arg2-off'.\index{diff-diff-arg2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable diff-diff-arg1; name this event `diff-diff-arg1-off'.\index{diff-diff-arg1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable difference-plus-plus-cancellation-proof; name this event `difference-plus-plus-cancellation-proof-off'.\index{difference-plus-plus-cancellati!on-proof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable difference-plus-cancellation-proof; name this event `difference-plus-cancellation-proof-off'.\index{difference-plus-cancellation-pr!oof-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable plus-difference-arg2; name this event `plus-difference-arg2-off'.\index{plus-difference-arg2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable plus-difference-arg1; name this event `plus-difference-arg1-off'.\index{plus-difference-arg1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable associativity-of-plus; name this event `associativity-of-plus-off'.\index{associativity-of-plus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable plus-add1-arg2; name this event `plus-add1-arg2-off'.\index{plus-add1-arg2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable plus-add1-arg1; name this event `plus-add1-arg1-off'.\index{plus-add1-arg1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable plus-zero-arg2; name this event `plus-zero-arg2-off'.\index{plus-zero-arg2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity2-of-plus; name this event `commutativity2-of-plus-off'.\index{commutativity2-of-plus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity-of-plus; name this event `commutativity-of-plus-off'.\index{commutativity-of-plus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-difference-0; name this event `equal-difference-0-off'.\index{equal-difference-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-plus-0; name this event `equal-plus-0-off'.\index{equal-plus-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable member-bagint; name this event `member-bagint-off'.\index{member-bagint-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable occurrences-bagdiff; name this event `occurrences-bagdiff-off'.\index{occurrences-bagdiff-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable occurrences-bagint; name this event `occurrences-bagint-off'.\index{occurrences-bagint-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable subbagp-bagint2; name this event `subbagp-bagint2-off'.\index{subbagp-bagint2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable subbagp-bagint1; name this event `subbagp-bagint1-off'.\index{subbagp-bagint1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable subbagp-cdr2; name this event `subbagp-cdr2-off'.\index{subbagp-cdr2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable subbagp-cdr1; name this event `subbagp-cdr1-off'.\index{subbagp-cdr1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable subbagp-delete; name this event `subbagp-delete-off'.\index{subbagp-delete-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable bagdiff-delete; name this event `bagdiff-delete-off'.\index{bagdiff-delete-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable member-bagdiff; name this event `member-bagdiff-off'.\index{member-bagdiff-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable occurrences-delete; name this event `occurrences-delete-off'.\index{occurrences-delete-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable member-delete-implies-membership; name this event `member-delete-implies-membership-off'.\index{member-delete-implies-membership!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable member-delete; name this event `member-delete-off'.\index{member-delete-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable member-non-list; name this event `member-non-list-off'.\index{member-non-list-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-occurrences-zero; name this event `equal-occurrences-zero-off'.\index{equal-occurrences-zero-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable delete-delete; name this event `delete-delete-off'.\index{delete-delete-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable delete-non-member; name this event `delete-non-member-off'.\index{delete-non-member-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable subbagp; name this event `subbagp-off'.\index{subbagp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*subbagp; name this event `g*1*subbagp-off'.\index{g*1*subbagp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable occurrences; name this event `occurrences-off'.\index{occurrences-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*occurrences; name this event `g*1*occurrences-off'.\index{g*1*occurrences-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable bagint; name this event `bagint-off'.\index{bagint-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*bagint; name this event `g*1*bagint-off'.\index{g*1*bagint-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable bagdiff; name this event `bagdiff-off'.\index{bagdiff-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*bagdiff; name this event `g*1*bagdiff-off'.\index{g*1*bagdiff-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable delete; name this event `delete-off'.\index{delete-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*delete; name this event `g*1*delete-off'.\index{g*1*delete-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{if*} \\  
\=\+{\rm{if*}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{if*} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}}$\;\;${\bf then }{\it{b\/}} \\ 
{\bf else }{\it{c\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable if*; name this event `if*-off'.\index{if*-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{or*}$\;\;$
{\rm{or*}}\,({\it{a\/}}, {\it{b\/}})\index{or*} $=$ {\rm{if*}}\,({\it{a\/}}, {\bf{t}}, {\rm{if*}}\,({\it{b\/}}, {\bf{t}}, {\bf{f}})\index{if*})\index{if*}
\end{tabbing}


\noindent{\sc Event}:   Enable or*; name this event `or*-off'.\index{or*-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{and*}$\;\;$
{\rm{and*}}\,({\it{a\/}}, {\it{b\/}})\index{and*} $=$ {\rm{if*}}\,({\it{a\/}}, {\rm{if*}}\,({\it{b\/}}, {\bf{t}}, {\bf{f}})\index{if*}, {\bf{f}})\index{if*}
\end{tabbing}


\noindent{\sc Event}:   Enable and*; name this event `and*-off'.\index{and*-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{not*}$\;\;$
{\rm{not*}}\,({\it{a\/}})\index{not*} $=$ {\rm{if*}}\,({\it{a\/}}, {\bf{f}}, {\bf{t}})\index{if*}
\end{tabbing}


\noindent{\sc Event}:   Enable not*; name this event `not*-off'.\index{not*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{prop*-theory}} to consist of the following events: or*,
and*,
not*.\index{prop*-theory}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  simplify-if* \\ \index{simplify-if*}
({\it{c\/}} $\rightarrow$ ({\rm{if*}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{if*} $=$ {\it{a\/}})) $\wedge$ (($\neg$ {\it{c\/}}) $\rightarrow$ ({\rm{if*}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{if*} $=$ {\it{b\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  if*-c-x-x \\ \index{if*-c-x-x}
{\rm{if*}}\,({\it{c\/}}, {\it{x\/}}, {\it{x\/}})\index{if*} $=$ {\it{x\/}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  if*-cons \\ \index{if*-cons}
{\rm{if*}}\,({\it{a\/}}, {\rm{cons}}\,({\it{b\/}}, {\it{c\/}}), {\rm{cons}}\,({\it{d\/}}, {\it{e\/}}))\index{if*} $=$ {\rm{cons}}\,({\rm{if*}}\,({\it{a\/}}, {\it{b\/}}, {\it{d\/}})\index{if*}, {\rm{if*}}\,({\it{a\/}}, {\it{c\/}}, {\it{e\/}})\index{if*})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-not* \\ \index{rewrite-not*}
({\it{x\/}} $\rightarrow$ ({\rm{not*}}\,({\it{x\/}})\index{not*} $=$ {\bf{f}})) $\wedge$ (($\neg$ {\it{x\/}}) $\rightarrow$ ({\rm{not*}}\,({\it{x\/}})\index{not*} $=$ {\bf{t}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-and* \\ \index{rewrite-and*}
\=\+({\rm{and*}}\,({\bf{f}}, {\it{x\/}})\index{and*} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$({\rm{and*}}\,({\it{x\/}}, {\bf{f}})\index{and*} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$({\it{y\/}} $\rightarrow$ (({\rm{and*}}\,({\it{y\/}}, {\it{x\/}})\index{and*} $=$ {\rm{if*}}\,({\it{x\/}}, {\bf{t}}, {\bf{f}})\index{if*}) $\wedge$ ({\rm{and*}}\,({\it{x\/}}, {\it{y\/}})\index{and*} $=$ {\rm{if*}}\,({\it{x\/}}, {\bf{t}}, {\bf{f}})\index{if*})))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-or* \\ \index{rewrite-or*}
\=\+({\rm{or*}}\,({\bf{f}}, {\it{x\/}})\index{or*} $=$ {\rm{if*}}\,({\it{x\/}}, {\bf{t}}, {\bf{f}})\index{if*}) \\ 
$\wedge$$\;\;\;\;$({\rm{or*}}\,({\it{x\/}}, {\bf{f}})\index{or*} $=$ {\rm{if*}}\,({\it{x\/}}, {\bf{t}}, {\bf{f}})\index{if*}) \\ 
$\wedge$$\;\;\;\;$({\it{y\/}} $\rightarrow$ (({\rm{or*}}\,({\it{y\/}}, {\it{x\/}})\index{or*} $=$ {\bf{t}}) $\wedge$ ({\rm{or*}}\,({\it{x\/}}, {\it{y\/}})\index{or*} $=$ {\bf{t}})))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  expand-*-connectives \\ \index{expand-*-connectives}
\=\+(\=\+{\rm{if*}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{if*} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{c\/}}$\;\;${\bf then }{\it{a\/}} \\ 
{\bf else }{\it{b\/}}$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{or*}}\,({\it{a\/}}, {\it{b\/}})\index{or*} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\it{b\/}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{and*}}\,({\it{a\/}}, {\it{b\/}})\index{and*} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} \\ 
{\bf then }\=\+{\bf if }{\it{b\/}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{not*}}\,({\it{a\/}})\index{not*} $=$ ($\neg$ {\it{a\/}}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable expand-*-connectives; name this event `expand-*-connectives-off'.\index{expand-*-connectives-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  car-cdr-if-cons \\ \index{car-cdr-if-cons}
\=\+(\=\+{\rm{car}}\,(\=\+{\bf if }{\it{x\/}}$\;\;${\bf then }{\rm{cons}}\,({\it{a\/}}, {\it{b\/}}) \\ 
{\bf else }{\rm{cons}}\,({\it{c\/}}, {\it{d\/}})$\;${\bf  endif}\-) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}}$\;\;${\bf then }{\it{a\/}} \\ 
{\bf else }{\it{c\/}}$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cdr}}\,(\=\+{\bf if }{\it{x\/}}$\;\;${\bf then }{\rm{cons}}\,({\it{a\/}}, {\it{b\/}}) \\ 
{\bf else }{\rm{cons}}\,({\it{c\/}}, {\it{d\/}})$\;${\bf  endif}\-) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}}$\;\;${\bf then }{\it{b\/}} \\ 
{\bf else }{\it{d\/}}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  our-car-cdr-elim \\ \index{our-car-cdr-elim}
({\it{l\/}} $=$ {\rm{cons}}\,({\rm{car}}\,({\it{l\/}}), {\it{x\/}})) $=$ ({\rm{listp}}\,({\it{l\/}}) $\wedge$ ({\it{x\/}} $=$ {\rm{cdr}}\,({\it{l\/}})))
\end{tabbing}


\noindent{\sc Event}:   Enable our-car-cdr-elim; name this event `our-car-cdr-elim-off'.\index{our-car-cdr-elim-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable plus; name this event `plus-off'.\index{plus-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plus-0 \\ \index{plus-0}
\=\+(({\it{zero\/}} $\simeq {\tt{0}}$) $\rightarrow$ (({\it{x\/}} $+$ {\it{zero\/}}) $=$ {\rm{fix}}\,({\it{x\/}}))) \\ 
$\wedge$$\;\;\;\;$(({\it{zero\/}} $\simeq {\tt{0}}$) $\rightarrow$ (({\it{zero\/}} $+$ {\it{x\/}}) $=$ {\rm{fix}}\,({\it{x\/}})))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plus-add1 \\ \index{plus-add1}
\=\+((($1\;+$ {\it{x\/}}) $+$ {\it{y\/}}) $=$ ($1\;+$ ({\it{x\/}} $+$ {\it{y\/}}))) \\ 
$\wedge$$\;\;\;\;$(({\it{x\/}} $+$ ($1\;+$ {\it{y\/}})) $=$ ($1\;+$ ({\it{x\/}} $+$ {\it{y\/}})))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plus-bottom \\ \index{plus-bottom}
(({\it{a\/}} $+$ {\it{b\/}}) $=$ {\tt{0}}) $=$ (({\it{a\/}} $\simeq {\tt{0}}$) $\wedge$ ({\it{b\/}} $\simeq {\tt{0}}$))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plus-add1-sub1 \\ \index{plus-add1-sub1}
\=\+(({\it{n\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ ((({\it{n\/}} $-\;1$) $+$ ($1\;+$ {\it{m\/}})) $=$ ({\it{n\/}} $+$ {\it{m\/}}))) \\ 
$\wedge$$\;\;\;\;$(({\it{n\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ ((($1\;+$ {\it{m\/}}) $+$ ({\it{n\/}} $-\;1$)) $=$ ({\it{m\/}} $+$ {\it{n\/}})))\-
\end{tabbing}


\noindent{\sc Event}:   Enable difference; name this event `difference-off'.\index{difference-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-x-1 \\ \index{difference-x-1}
({\it{x\/}} $-$ {\tt{1}}) $=$ ({\it{x\/}} $-\;1$)
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  our-difference-x-x \\ \index{our-difference-x-x}
({\it{x\/}} $-$ {\it{x\/}}) $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  our-equal-difference-0 \\ \index{our-equal-difference-0}
\=\+(({\it{x\/}} $-$ {\it{y\/}}) $=$ {\tt{0}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{y\/}} $<$ {\it{x\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  difference-0 \\ \index{difference-0}
({\it{z\/}} $\simeq {\tt{0}}$) $\rightarrow$ (({\it{x\/}} $-$ {\it{z\/}}) $=$ {\rm{fix}}\,({\it{x\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  difference-add1-add1 \\ \index{difference-add1-add1}
(($1\;+$ {\it{x\/}}) $-$ ($1\;+$ {\it{y\/}})) $=$ ({\it{x\/}} $-$ {\it{y\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  not-lessp-difference \\ \index{not-lessp-difference}
({\it{x\/}} $<$ ({\it{x\/}} $-$ {\it{y\/}})) $=$ {\bf{f}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-difference=0 \\ \index{lessp-difference=0}
\=\+\=\+{\bf if }{\it{y\/}} $<$ {\it{x\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$(({\it{x\/}} $-$ {\it{y\/}}) $=$ {\tt{0}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  times-bottom \\ \index{times-bottom}
(({\it{x\/}} $*$ {\it{y\/}}) $=$ {\tt{0}}) $=$ (({\it{x\/}} $\simeq {\tt{0}}$) $\vee$ ({\it{y\/}} $\simeq {\tt{0}}$))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  times-1 \\ \index{times-1}
(({\it{a\/}} $*$ {\tt{1}}) $=$ {\rm{fix}}\,({\it{a\/}})) $\wedge$ (({\tt{1}} $*$ {\it{a\/}}) $=$ {\rm{fix}}\,({\it{a\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  times-add1-again \\ \index{times-add1-again}
({\it{a\/}} $*$ ($1\;+$ {\it{b\/}})) $=$ ({\it{a\/}} $+$ ({\it{a\/}} $*$ {\it{b\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  times-commutes \\ \index{times-commutes}
({\it{a\/}} $*$ {\it{b\/}}) $=$ ({\it{b\/}} $*$ {\it{a\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-lessp \\ \index{quotient-lessp}
(({\tt{1}} $<$ {\it{base\/}}) $\wedge$ ({\it{n\/}} $\not\simeq {\tt{0}}$)) $\rightarrow$ (({\it{n\/}} $\div$ {\it{base\/}}) $<$ {\it{n\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  zerop-quotient \\ \index{zerop-quotient}
(({\it{n\/}} $\div$ {\it{m\/}}) $=$ {\tt{0}}) $=$ (({\it{n\/}} $\simeq {\tt{0}}$) $\vee$ ({\it{m\/}} $\simeq {\tt{0}}$) $\vee$ ({\it{n\/}} $<$ {\it{m\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-x-x \\ \index{lessp-x-x}
({\it{x\/}} $<$ {\it{x\/}}) $=$ {\bf{f}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-sub1-x-y-crock \\ \index{lessp-sub1-x-y-crock}
({\it{x\/}} $=$ {\it{y\/}}) $\rightarrow$ ((({\it{x\/}} $-\;1$) $<$ {\it{y\/}}) $=$ ({\it{x\/}} $\not\simeq {\tt{0}}$))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-sub1-x-x \\ \index{lessp-sub1-x-x}
(({\it{x\/}} $-\;1$) $<$ {\it{x\/}}) $=$ ({\it{x\/}} $\not\simeq {\tt{0}}$)
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-x-1 \\ \index{lessp-x-1}
({\it{x\/}} $<$ {\tt{1}}) $=$ ({\it{x\/}} $\simeq {\tt{0}}$)
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  leq-lessp-difference \\ \index{leq-lessp-difference}
\=\+(\=\+\=\+{\bf if }{\it{y\/}} $<$ {\it{x\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$({\it{z\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$({\it{y\/}} $\not\simeq {\tt{0}}$))\- \\ 
$\rightarrow$$\;\;\;\;$((({\it{x\/}} $-$ {\it{z\/}}) $<$ {\it{y\/}}) $=$ {\bf{t}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable append; name this event `append-off'.\index{append-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{append5} \\  
{\rm{append5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{append5} $=$ {\rm{append}}\,({\it{a\/}}, {\rm{append}}\,({\it{b\/}}, {\rm{append}}\,({\it{c\/}}, {\rm{append}}\,({\it{d\/}}, {\it{e\/}}))))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{append6} \\  
\=\+{\rm{append6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{append6} \\ 
$=$$\;\;\;\;${\rm{append}}\,({\it{a\/}}, {\rm{append}}\,({\it{b\/}}, {\rm{append}}\,({\it{c\/}}, {\rm{append}}\,({\it{d\/}}, {\rm{append}}\,({\it{e\/}}, {\it{g\/}})))))\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{append7} \\  
\=\+{\rm{append7}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}})\index{append7} \\ 
$=$$\;\;\;\;${\rm{append}}\,({\it{a\/}}, {\rm{append}}\,({\it{b\/}}, {\rm{append}}\,({\it{c\/}}, {\rm{append}}\,({\it{d\/}}, {\rm{append}}\,({\it{e\/}}, {\rm{append}}\,({\it{g\/}}, {\it{h\/}}))))))\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{append8} \\  
\=\+{\rm{append8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{append8} \\ 
$=$$\;\;\;\;${\rm{append}}\,(\=\+{\it{a\/}}, \\ 
{\rm{append}}\,({\it{b\/}}, {\rm{append}}\,({\it{c\/}}, {\rm{append}}\,({\it{d\/}}, {\rm{append}}\,({\it{e\/}}, {\rm{append}}\,({\it{g\/}}, {\rm{append}}\,({\it{h\/}}, {\it{i\/}})))))))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  append-nlistp \\ \index{append-nlistp}
({\it{a\/}} $\simeq\;${{\bf{nil}}}${}$) $\rightarrow$ ({\rm{append}}\,({\it{a\/}}, {\it{b\/}}) $=$ {\it{b\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  append-cons \\ \index{append-cons}
{\rm{append}}\,({\rm{cons}}\,({\it{a\/}}, {\it{b\/}}), {\it{c\/}}) $=$ {\rm{cons}}\,({\it{a\/}}, {\rm{append}}\,({\it{b\/}}, {\it{c\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  our-member-append \\ \index{our-member-append}
({\it{a\/}} $\in$ {\rm{append}}\,({\it{b\/}}, {\it{c\/}})) $=$ (({\it{a\/}} $\in$ {\it{b\/}}) $\vee$ ({\it{a\/}} $\in$ {\it{c\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  associativity-of-append \\ \index{associativity-of-append}
{\rm{append}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}), {\it{c\/}}) $=$ {\rm{append}}\,({\it{a\/}}, {\rm{append}}\,({\it{b\/}}, {\it{c\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-append-x-x \\ \index{equal-append-x-x}
({\rm{append}}\,({\it{a\/}}, {\it{b\/}}) $=$ {\rm{append}}\,({\it{a\/}}, {\it{c\/}})) $=$ ({\it{b\/}} $=$ {\it{c\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{properp} \\  
\=\+{\rm{properp}}\,({\it{l\/}})\index{properp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}})$\;\;${\bf then }{\rm{properp}}\,({\rm{cdr}}\,({\it{l\/}}))\index{properp} \\ 
{\bf else }{\it{l\/}} $=$ {\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable properp; name this event `properp-off'.\index{properp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  properp-if \\ \index{properp-if}
\=\+({\rm{properp}}\,({\it{a\/}})\index{properp} $\wedge$ {\rm{properp}}\,({\it{b\/}})\index{properp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{properp}}\,(\=\+{\bf if }{\it{c\/}}$\;\;${\bf then }{\it{a\/}} \\ 
{\bf else }{\it{b\/}}$\;${\bf  endif}\-)\index{properp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-nlistp \\ \index{properp-nlistp}
({\it{l\/}} $\simeq\;${{\bf{nil}}}${}$) $\rightarrow$ ({\rm{properp}}\,({\it{l\/}})\index{properp} $=$ ({\it{l\/}} $=$ {\bf{nil}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-cons \\ \index{properp-cons}
{\rm{properp}}\,({\rm{cons}}\,({\it{x\/}}, {\it{y\/}}))\index{properp} $=$ {\rm{properp}}\,({\it{y\/}})\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-append \\ \index{properp-append}
{\rm{properp}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{properp} $=$ {\rm{properp}}\,({\it{b\/}})\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-append-nil \\ \index{properp-append-nil}
{\rm{properp}}\,({\it{a\/}})\index{properp} $\rightarrow$ ({\rm{append}}\,({\it{a\/}}, {\bf{nil}}) $=$ {\it{a\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-if* \\ \index{properp-if*}
({\rm{properp}}\,({\it{a\/}})\index{properp} $\wedge$ {\rm{properp}}\,({\it{b\/}})\index{properp}) $\rightarrow$ {\rm{properp}}\,({\rm{if*}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{if*})\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{position} \\  
\=\+{\rm{position}}\,({\it{x\/}}, {\it{l\/}})\index{position} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{l\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{f}} \\ 
{\bf elseif }{\it{x\/}} $=$ {\rm{car}}\,({\it{l\/}})$\;\;${\bf then }{\tt{0}} \\ 
{\bf elseif }{\rm{position}}\,({\it{x\/}}, {\rm{cdr}}\,({\it{l\/}}))\index{position}$\;\;${\bf then }$1\;+$ {\rm{position}}\,({\it{x\/}}, {\rm{cdr}}\,({\it{l\/}}))\index{position} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable position; name this event `position-off'.\index{position-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  member==$>$position \\ \index{member==$>$position}
({\it{x\/}} $\in$ {\it{l\/}}) $\rightarrow$ {\rm{position}}\,({\it{x\/}}, {\it{l\/}})\index{position}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{length} \\  
\=\+{\rm{length}}\,({\it{l\/}})\index{length} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}})$\;\;${\bf then }$1\;+$ {\rm{length}}\,({\rm{cdr}}\,({\it{l\/}}))\index{length} \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable length; name this event `length-off'.\index{length-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-nlistp \\ \index{length-nlistp}
({\it{l\/}} $\simeq\;${{\bf{nil}}}${}$) $\rightarrow$ ({\rm{length}}\,({\it{l\/}})\index{length} $=$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-bottom \\ \index{length-bottom}
({\rm{length}}\,({\it{x\/}})\index{length} $=$ {\tt{0}}) $=$ ({\it{x\/}} $\simeq\;${{\bf{nil}}}${}$)
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-1 \\ \index{length-1}
({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\tt{1}}) $=$ ({\rm{listp}}\,({\it{a\/}}) $\wedge$ ({\rm{cdr}}\,({\it{a\/}}) $\simeq\;${{\bf{nil}}}${}$))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-cons \\ \index{length-cons}
{\rm{length}}\,({\rm{cons}}\,({\it{x\/}}, {\it{y\/}}))\index{length} $=$ ($1\;+$ {\rm{length}}\,({\it{y\/}})\index{length})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-append \\ \index{length-append}
{\rm{length}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{length} $=$ ({\rm{length}}\,({\it{a\/}})\index{length} $+$ {\rm{length}}\,({\it{b\/}})\index{length})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-cdr-lemmas \\ \index{length-cdr-lemmas}
\=\+(({\rm{length}}\,({\rm{cdr}}\,({\it{x\/}}))\index{length} $=$ {\rm{length}}\,({\it{x\/}})\index{length}) $=$ ({\it{x\/}} $\simeq\;${{\bf{nil}}}${}$)) \\ 
$\wedge$$\;\;\;\;$(({\rm{length}}\,({\rm{cdr}}\,({\it{x\/}}))\index{length} $<$ {\rm{length}}\,({\it{x\/}})\index{length}) $=$ {\rm{listp}}\,({\it{x\/}}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-length-add1 \\ \index{equal-length-add1}
({\rm{length}}\,({\it{x\/}})\index{length} $=$ ($1\;+$ {\it{y\/}})) $=$ ({\rm{listp}}\,({\it{x\/}}) $\wedge$ ({\rm{length}}\,({\rm{cdr}}\,({\it{x\/}}))\index{length} $=$ {\rm{fix}}\,({\it{y\/}})))
\end{tabbing}


\noindent{\sc Event}:   Enable equal-length-add1; name this event `equal-length-add1-off'.\index{equal-length-add1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-cdr \\ \index{length-cdr}
({\rm{length}}\,({\rm{cdr}}\,({\it{v\/}}))\index{length} $=$ ({\rm{length}}\,({\it{v\/}})\index{length} $-\;1$)) $=$ {\bf{t}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-length-cdr \\ \index{equal-length-cdr}
({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{length}}\,({\it{b\/}})\index{length}) $\rightarrow$ (({\rm{length}}\,({\rm{cdr}}\,({\it{a\/}}))\index{length} $=$ {\rm{length}}\,({\rm{cdr}}\,({\it{b\/}}))\index{length}) $=$ {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-if \\ \index{length-if}
\=\+({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{length}}\,({\it{b\/}})\index{length}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{length}}\,(\=\+{\bf if }{\it{c\/}}$\;\;${\bf then }{\it{a\/}} \\ 
{\bf else }{\it{b\/}}$\;${\bf  endif}\-)\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\it{a\/}})\index{length})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-if* \\ \index{length-if*}
({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{length}}\,({\it{b\/}})\index{length}) $\rightarrow$ ({\rm{length}}\,({\rm{if*}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{if*})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{rev1} \\  
\=\+{\rm{rev1}}\,({\it{x\/}}, {\it{sponge\/}})\index{rev1} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{sponge\/}} \\ 
{\bf else }{\rm{rev1}}\,({\rm{cdr}}\,({\it{x\/}}), {\rm{cons}}\,({\rm{car}}\,({\it{x\/}}), {\it{sponge\/}}))\index{rev1}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable rev1; name this event `rev1-off'.\index{rev1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{reverse}$\;\;$
{\rm{reverse}}\,({\it{x\/}})\index{reverse} $=$ {\rm{rev1}}\,({\it{x\/}}, {\bf{nil}})\index{rev1}
\end{tabbing}


\noindent{\sc Event}:   Enable reverse; name this event `reverse-off'.\index{reverse-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-rev1 \\ \index{length-rev1}
{\rm{length}}\,({\rm{rev1}}\,({\it{x\/}}, {\it{sponge\/}})\index{rev1})\index{length} $=$ ({\rm{length}}\,({\it{x\/}})\index{length} $+$ {\rm{length}}\,({\it{sponge\/}})\index{length})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-reverse \\ \index{length-reverse}
{\rm{length}}\,({\rm{reverse}}\,({\it{x\/}})\index{reverse})\index{length} $=$ {\rm{length}}\,({\it{x\/}})\index{length}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{delete*} \\  
\=\+{\rm{delete*}}\,({\it{x\/}}, {\it{l\/}})\index{delete*} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{l\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{l\/}} \\ 
{\bf elseif }{\it{x\/}} $=$ {\rm{car}}\,({\it{l\/}})$\;\;${\bf then }{\rm{delete*}}\,({\it{x\/}}, {\rm{cdr}}\,({\it{l\/}}))\index{delete*} \\ 
{\bf else }{\rm{cons}}\,({\rm{car}}\,({\it{l\/}}), {\rm{delete*}}\,({\it{x\/}}, {\rm{cdr}}\,({\it{l\/}}))\index{delete*})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable delete*; name this event `delete*-off'.\index{delete*-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{subset} \\  
\=\+{\rm{subset}}\,({\it{l1\/}}, {\it{l2\/}})\index{subset} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{l1\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }({\rm{car}}\,({\it{l1\/}}) $\in$ {\it{l2\/}}) $\wedge$ {\rm{subset}}\,({\rm{cdr}}\,({\it{l1\/}}), {\it{l2\/}})\index{subset}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable subset; name this event `subset-off'.\index{subset-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  subset-nlistp \\ \index{subset-nlistp}
({\it{x\/}} $\simeq\;${{\bf{nil}}}${}$) $\rightarrow$ {\rm{subset}}\,({\it{x\/}}, {\it{y\/}})\index{subset}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  subset-cons \\ \index{subset-cons}
{\rm{subset}}\,({\rm{cons}}\,({\it{x\/}}, {\it{y\/}}), {\it{z\/}})\index{subset} $=$ (({\it{x\/}} $\in$ {\it{z\/}}) $\wedge$ {\rm{subset}}\,({\it{y\/}}, {\it{z\/}})\index{subset})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  subset-x-cons-y-z \\ \index{subset-x-cons-y-z}
\=\+{\rm{subset}}\,({\it{x\/}}, {\rm{cons}}\,({\it{y\/}}, {\it{z\/}}))\index{subset} \\ 
$=$$\;\;\;\;$({\rm{subset}}\,({\it{x\/}}, {\it{z\/}})\index{subset} $\vee$ (({\it{y\/}} $\in$ {\it{x\/}}) $\wedge$ {\rm{subset}}\,({\rm{delete*}}\,({\it{y\/}}, {\it{x\/}})\index{delete*}, {\it{z\/}})\index{subset}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  subset-append \\ \index{subset-append}
({\rm{subset}}\,({\it{a\/}}, {\it{b\/}})\index{subset} $\vee$ {\rm{subset}}\,({\it{a\/}}, {\it{c\/}})\index{subset}) $\rightarrow$ {\rm{subset}}\,({\it{a\/}}, {\rm{append}}\,({\it{b\/}}, {\it{c\/}}))\index{subset}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  subset-x-x \\ \index{subset-x-x}
{\rm{subset}}\,({\it{x\/}}, {\it{x\/}})\index{subset}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{disjoint} \\  
\=\+{\rm{disjoint}}\,({\it{l1\/}}, {\it{l2\/}})\index{disjoint} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{l1\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }({\rm{car}}\,({\it{l1\/}}) $\not\in$ {\it{l2\/}}) $\wedge$ {\rm{disjoint}}\,({\rm{cdr}}\,({\it{l1\/}}), {\it{l2\/}})\index{disjoint}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable disjoint; name this event `disjoint-off'.\index{disjoint-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  disjoint-nlistp \\ \index{disjoint-nlistp}
(({\it{x\/}} $\simeq\;${{\bf{nil}}}${}$) $\vee$ ({\it{y\/}} $\simeq\;${{\bf{nil}}}${}$)) $\rightarrow$ {\rm{disjoint}}\,({\it{x\/}}, {\it{y\/}})\index{disjoint}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  disjoint-cons \\ \index{disjoint-cons}
\=\+({\rm{disjoint}}\,({\rm{cons}}\,({\it{x\/}}, {\it{y\/}}), {\it{z\/}})\index{disjoint} $=$ (({\it{x\/}} $\not\in$ {\it{z\/}}) $\wedge$ {\rm{disjoint}}\,({\it{y\/}}, {\it{z\/}})\index{disjoint})) \\ 
$\wedge$$\;\;\;\;$({\rm{disjoint}}\,({\it{z\/}}, {\rm{cons}}\,({\it{x\/}}, {\it{y\/}}))\index{disjoint} $=$ (({\it{x\/}} $\not\in$ {\it{z\/}}) $\wedge$ {\rm{disjoint}}\,({\it{z\/}}, {\it{y\/}})\index{disjoint}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  disjoint-append \\ \index{disjoint-append}
\=\+({\rm{disjoint}}\,({\it{x\/}}, {\rm{append}}\,({\it{y\/}}, {\it{z\/}}))\index{disjoint} $=$ ({\rm{disjoint}}\,({\it{x\/}}, {\it{y\/}})\index{disjoint} $\wedge$ {\rm{disjoint}}\,({\it{x\/}}, {\it{z\/}})\index{disjoint})) \\ 
$\wedge$$\;\;\;\;$({\rm{disjoint}}\,({\rm{append}}\,({\it{y\/}}, {\it{z\/}}), {\it{x\/}})\index{disjoint} $=$ ({\rm{disjoint}}\,({\it{y\/}}, {\it{x\/}})\index{disjoint} $\wedge$ {\rm{disjoint}}\,({\it{z\/}}, {\it{x\/}})\index{disjoint}))\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{duplicates?} \\  
\=\+{\rm{duplicates?}}\,({\it{l\/}})\index{duplicates?} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{l\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }({\rm{car}}\,({\it{l\/}}) $\in$ {\rm{cdr}}\,({\it{l\/}})) $\vee$ {\rm{duplicates?}}\,({\rm{cdr}}\,({\it{l\/}}))\index{duplicates?}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable duplicates?; name this event `duplicates?-off'.\index{duplicates?-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  duplicates?-cons \\ \index{duplicates?-cons}
{\rm{duplicates?}}\,({\rm{cons}}\,({\it{x\/}}, {\it{y\/}}))\index{duplicates?} $=$ (({\it{x\/}} $\in$ {\it{y\/}}) $\vee$ {\rm{duplicates?}}\,({\it{y\/}})\index{duplicates?})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  duplicates-append \\ \index{duplicates-append}
\=\+{\rm{duplicates?}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{duplicates?} \\ 
$=$$\;\;\;\;$({\rm{duplicates?}}\,({\it{a\/}})\index{duplicates?} $\vee$ {\rm{duplicates?}}\,({\it{b\/}})\index{duplicates?} $\vee$ ($\neg$ {\rm{disjoint}}\,({\it{a\/}}, {\it{b\/}})\index{disjoint}))\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{firstn} \\  
\=\+{\rm{firstn}}\,({\it{n\/}}, {\it{l\/}})\index{firstn} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}}) \\ 
{\bf then }\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{car}}\,({\it{l\/}}), {\rm{firstn}}\,({\it{n\/}} $-\;1$, {\rm{cdr}}\,({\it{l\/}}))\index{firstn})$\;${\bf  endif}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable firstn; name this event `firstn-off'.\index{firstn-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-firstn \\ \index{length-firstn}
\=\+{\rm{length}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{l\/}})\index{firstn})\index{length} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ {\it{n\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-$\;\;${\bf then }{\rm{fix}}\,({\it{n\/}}) \\ 
{\bf else }{\rm{length}}\,({\it{l\/}})\index{length}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-firstn1 \\ \index{length-firstn1}
\=\+\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ {\it{n\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{length}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{l\/}})\index{firstn})\index{length} $=$ {\rm{fix}}\,({\it{n\/}}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-firstn2 \\ \index{length-firstn2}
\=\+($\neg$ \=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ {\it{n\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-) \\ 
$\rightarrow$$\;\;\;\;$({\rm{length}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{l\/}})\index{firstn})\index{length} $=$ {\rm{length}}\,({\it{l\/}})\index{length})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  car-firstn \\ \index{car-firstn}
\=\+{\rm{car}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{a\/}})\index{firstn}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{a\/}}) $\wedge$ ({\it{n\/}} $\not\simeq {\tt{0}}$)$\;\;${\bf then }{\rm{car}}\,({\it{a\/}}) \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  not-member-firstn \\ \index{not-member-firstn}
({\it{x\/}} $\not\in$ {\it{y\/}}) $\rightarrow$ ({\it{x\/}} $\not\in$ {\rm{firstn}}\,({\it{n\/}}, {\it{y\/}})\index{firstn})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  not-duplicates?-firstn \\ \index{not-duplicates?-firstn}
($\neg$ {\rm{duplicates?}}\,({\it{x\/}})\index{duplicates?}) $\rightarrow$ ($\neg$ {\rm{duplicates?}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{x\/}})\index{firstn})\index{duplicates?})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  subset-firstn \\ \index{subset-firstn}
{\rm{subset}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{l\/}})\index{firstn}, {\it{l\/}})\index{subset}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  firstn-bottom \\ \index{firstn-bottom}
({\rm{firstn}}\,({\it{n\/}}, {\it{l\/}})\index{firstn} $=$ {\bf{nil}}) $=$ (({\it{l\/}} $\simeq\;${{\bf{nil}}}${}$) $\vee$ ({\it{n\/}} $\simeq {\tt{0}}$))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  disjoint-firstn \\ \index{disjoint-firstn}
{\rm{disjoint}}\,({\it{x\/}}, {\it{y\/}})\index{disjoint} $\rightarrow$ {\rm{disjoint}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{x\/}})\index{firstn}, {\it{y\/}})\index{disjoint}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  disjoint-firstn1 \\ \index{disjoint-firstn1}
{\rm{disjoint}}\,({\it{y\/}}, {\it{x\/}})\index{disjoint} $\rightarrow$ {\rm{disjoint}}\,({\it{y\/}}, {\rm{firstn}}\,({\it{n\/}}, {\it{x\/}})\index{firstn})\index{disjoint}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-firstn \\ \index{properp-firstn}
{\rm{properp}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{l\/}})\index{firstn})\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  firstn-append \\ \index{firstn-append}
{\rm{firstn}}\,({\it{n\/}}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{firstn} $=$ {\rm{append}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{a\/}})\index{firstn}, {\rm{firstn}}\,({\it{n\/}} $-$ {\rm{length}}\,({\it{a\/}})\index{length}, {\it{b\/}})\index{firstn})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{restn} \\  
\=\+{\rm{restn}}\,({\it{n\/}}, {\it{l\/}})\index{restn} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}}) \\ 
{\bf then }\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\it{l\/}} \\ 
{\bf else }{\rm{restn}}\,({\it{n\/}} $-\;1$, {\rm{cdr}}\,({\it{l\/}}))\index{restn}$\;${\bf  endif}\- \\ 
{\bf else }{\it{l\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable restn; name this event `restn-off'.\index{restn-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-restn \\ \index{length-restn}
{\rm{length}}\,({\rm{restn}}\,({\it{n\/}}, {\it{l\/}})\index{restn})\index{length} $=$ ({\rm{length}}\,({\it{l\/}})\index{length} $-$ {\it{n\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  not-duplicates?-restn \\ \index{not-duplicates?-restn}
($\neg$ {\rm{duplicates?}}\,({\it{x\/}})\index{duplicates?}) $\rightarrow$ ($\neg$ {\rm{duplicates?}}\,({\rm{restn}}\,({\it{n\/}}, {\it{x\/}})\index{restn})\index{duplicates?})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  not-member-restn \\ \index{not-member-restn}
({\it{x\/}} $\not\in$ {\it{y\/}}) $\rightarrow$ ({\it{x\/}} $\not\in$ {\rm{restn}}\,({\it{n\/}}, {\it{y\/}})\index{restn})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  subset-restn \\ \index{subset-restn}
{\rm{subset}}\,({\rm{restn}}\,({\it{n\/}}, {\it{l\/}})\index{restn}, {\it{l\/}})\index{subset}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  disjoint-restn \\ \index{disjoint-restn}
{\rm{disjoint}}\,({\it{x\/}}, {\it{y\/}})\index{disjoint} $\rightarrow$ {\rm{disjoint}}\,({\rm{restn}}\,({\it{n\/}}, {\it{x\/}})\index{restn}, {\it{y\/}})\index{disjoint}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  disjoint-restn1 \\ \index{disjoint-restn1}
{\rm{disjoint}}\,({\it{y\/}}, {\it{x\/}})\index{disjoint} $\rightarrow$ {\rm{disjoint}}\,({\it{y\/}}, {\rm{restn}}\,({\it{n\/}}, {\it{x\/}})\index{restn})\index{disjoint}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-restn \\ \index{properp-restn}
{\rm{properp}}\,({\rm{restn}}\,({\it{n\/}}, {\it{l\/}})\index{restn})\index{properp} $=$ {\rm{properp}}\,({\it{l\/}})\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  restn-append \\ \index{restn-append}
{\rm{restn}}\,({\it{n\/}}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{restn} $=$ {\rm{append}}\,({\rm{restn}}\,({\it{n\/}}, {\it{a\/}})\index{restn}, {\rm{restn}}\,({\it{n\/}} $-$ {\rm{length}}\,({\it{a\/}})\index{length}, {\it{b\/}})\index{restn})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  too-many-restns \\ \index{too-many-restns}
\=\+(\=\+{\rm{properp}}\,({\it{l\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{restn}}\,({\it{n\/}}, {\it{l\/}})\index{restn} $=$ {\bf{nil}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  cdr-restn \\ \index{cdr-restn}
({\it{n\/}} $<$ {\rm{length}}\,({\it{v\/}})\index{length}) $\rightarrow$ ({\rm{cdr}}\,({\rm{restn}}\,({\it{n\/}}, {\it{v\/}})\index{restn}) $=$ {\rm{restn}}\,($1\;+$ {\it{n\/}}, {\it{v\/}})\index{restn})
\end{tabbing}


\noindent{\sc Event}:   Enable cdr-restn; name this event `cdr-restn-off'.\index{cdr-restn-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  disjoint-firstn-restn-lemmas \\ \index{disjoint-firstn-restn-lemmas}
\=\+({\rm{disjoint}}\,({\it{x\/}}, {\it{y\/}})\index{disjoint} $\rightarrow$ {\rm{disjoint}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{x\/}})\index{firstn}, {\rm{firstn}}\,({\it{m\/}}, {\it{y\/}})\index{firstn})\index{disjoint}) \\ 
$\wedge$$\;\;\;\;$({\rm{disjoint}}\,({\it{x\/}}, {\it{y\/}})\index{disjoint} $\rightarrow$ {\rm{disjoint}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{x\/}})\index{firstn}, {\rm{restn}}\,({\it{m\/}}, {\it{y\/}})\index{restn})\index{disjoint}) \\ 
$\wedge$$\;\;\;\;$({\rm{disjoint}}\,({\it{x\/}}, {\it{y\/}})\index{disjoint} $\rightarrow$ {\rm{disjoint}}\,({\rm{restn}}\,({\it{n\/}}, {\it{x\/}})\index{restn}, {\rm{firstn}}\,({\it{m\/}}, {\it{y\/}})\index{firstn})\index{disjoint}) \\ 
$\wedge$$\;\;\;\;$({\rm{disjoint}}\,({\it{x\/}}, {\it{y\/}})\index{disjoint} $\rightarrow$ {\rm{disjoint}}\,({\rm{restn}}\,({\it{n\/}}, {\it{x\/}})\index{restn}, {\rm{restn}}\,({\it{m\/}}, {\it{y\/}})\index{restn})\index{disjoint})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  no-duplicates-disjoint-firstn-restn \\ \index{no-duplicates-disjoint-firstn-re!stn}
\=\+(($\neg$ {\rm{duplicates?}}\,({\it{x\/}})\index{duplicates?}) $\rightarrow$ {\rm{disjoint}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{x\/}})\index{firstn}, {\rm{restn}}\,({\it{n\/}}, {\it{x\/}})\index{restn})\index{disjoint}) \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{duplicates?}}\,({\it{x\/}})\index{duplicates?}) $\rightarrow$ {\rm{disjoint}}\,({\rm{restn}}\,({\it{n\/}}, {\it{x\/}})\index{restn}, {\rm{firstn}}\,({\it{n\/}}, {\it{x\/}})\index{firstn})\index{disjoint})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  append-firstn-restn \\ \index{append-firstn-restn}
{\rm{append}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{l\/}})\index{firstn}, {\rm{restn}}\,({\it{n\/}}, {\it{l\/}})\index{restn}) $=$ {\it{l\/}}
\end{tabbing}


\noindent{\sc Event}:   Enable pairlist; name this event `pairlist-off'.\index{pairlist-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  pairlist-nlistp \\ \index{pairlist-nlistp}
({\it{a\/}} $\simeq\;${{\bf{nil}}}${}$) $\rightarrow$ ({\rm{pairlist}}\,({\it{a\/}}, {\it{b\/}}) $=$ {\bf{nil}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  pairlist-cons \\ \index{pairlist-cons}
{\rm{pairlist}}\,({\rm{cons}}\,({\it{x\/}}, {\it{y\/}}), {\it{z\/}}) $=$ {\rm{cons}}\,({\rm{cons}}\,({\it{x\/}}, {\rm{car}}\,({\it{z\/}})), {\rm{pairlist}}\,({\it{y\/}}, {\rm{cdr}}\,({\it{z\/}})))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  pairlist-append \\ \index{pairlist-append}
\=\+({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{length}}\,({\it{c\/}})\index{length}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{pairlist}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}), {\rm{append}}\,({\it{c\/}}, {\it{d\/}})) \\ 
$=$$\;\;\;\;${\rm{append}}\,({\rm{pairlist}}\,({\it{a\/}}, {\it{c\/}}), {\rm{pairlist}}\,({\it{b\/}}, {\it{d\/}})))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-pairlist \\ \index{properp-pairlist}
{\rm{properp}}\,({\rm{pairlist}}\,({\it{x\/}}, {\it{y\/}}))\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  pairlists-are-equal-when-their-2nd-lists-are-nlistp \\ \index{pairlists-are-equal-when-their-!2nd-lists-are-nlistp}
(({\it{l1\/}} $\simeq\;${{\bf{nil}}}${}$) $\wedge$ ({\it{l2\/}} $\simeq\;${{\bf{nil}}}${}$)) $\rightarrow$ (({\rm{pairlist}}\,({\it{a\/}}, {\it{l1\/}}) $=$ {\rm{pairlist}}\,({\it{a\/}}, {\it{l2\/}})) $=$ {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{nth} \\  
\=\+{\rm{nth}}\,({\it{n\/}}, {\it{list\/}})\index{nth} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\rm{car}}\,({\it{list\/}}) \\ 
{\bf else }{\rm{nth}}\,({\it{n\/}} $-\;1$, {\rm{cdr}}\,({\it{list\/}}))\index{nth}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable nth; name this event `nth-off'.\index{nth-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-nth \\ \index{open-nth}
\=\+(({\it{n\/}} $\simeq {\tt{0}}$) $\rightarrow$ ({\rm{nth}}\,({\it{n\/}}, {\it{list\/}})\index{nth} $=$ {\rm{car}}\,({\it{list\/}}))) \\ 
$\wedge$$\;\;\;\;$(({\it{n\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ ({\rm{nth}}\,({\it{n\/}}, {\it{list\/}})\index{nth} $=$ {\rm{nth}}\,({\it{n\/}} $-\;1$, {\rm{cdr}}\,({\it{list\/}}))\index{nth}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable open-nth; name this event `open-nth-off'.\index{open-nth-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  nth-if \\ \index{nth-if}
\=\+{\rm{nth}}\,(\=\+{\it{n\/}}, \\ 
\=\+{\bf if }{\it{a\/}}$\;\;${\bf then }{\it{b\/}} \\ 
{\bf else }{\it{c\/}}$\;${\bf  endif}\-)\-\index{nth} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}}$\;\;${\bf then }{\rm{nth}}\,({\it{n\/}}, {\it{b\/}})\index{nth} \\ 
{\bf else }{\rm{nth}}\,({\it{n\/}}, {\it{c\/}})\index{nth}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable nth-if; name this event `nth-if-off'.\index{nth-if-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  nth-restn \\ \index{nth-restn}
{\rm{nth}}\,({\it{n\/}}, {\it{v\/}})\index{nth} $=$ {\rm{car}}\,({\rm{restn}}\,({\it{n\/}}, {\it{v\/}})\index{restn})
\end{tabbing}


\noindent{\sc Event}:   Enable nth-restn; name this event `nth-restn-off'.\index{nth-restn-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  nth-append \\ \index{nth-append}
({\it{n\/}} $<$ {\rm{length}}\,({\it{a\/}})\index{length}) $\rightarrow$ ({\rm{nth}}\,({\it{n\/}}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{nth} $=$ {\rm{nth}}\,({\it{n\/}}, {\it{a\/}})\index{nth})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  nth-append-too \\ \index{nth-append-too}
\=\+\=\+{\bf if }{\it{n\/}} $<$ {\rm{length}}\,({\it{a\/}})\index{length}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{nth}}\,({\it{n\/}}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{nth} $=$ {\rm{nth}}\,({\it{n\/}} $-$ {\rm{length}}\,({\it{a\/}})\index{length}, {\it{b\/}})\index{nth})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{nthcdr} \\  
\=\+{\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\it{l\/}} \\ 
{\bf else }{\rm{nthcdr}}\,({\it{n\/}} $-\;1$, {\rm{cdr}}\,({\it{l\/}}))\index{nthcdr}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable nthcdr; name this event `nthcdr-off'.\index{nthcdr-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-nthcdr \\ \index{open-nthcdr}
\=\+(({\it{n\/}} $\simeq {\tt{0}}$) $\rightarrow$ ({\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr} $=$ {\it{l\/}})) \\ 
$\wedge$$\;\;\;\;$(({\it{n\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ ({\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr} $=$ {\rm{nthcdr}}\,({\it{n\/}} $-\;1$, {\rm{cdr}}\,({\it{l\/}}))\index{nthcdr}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-as-null-nthcdr \\ \index{properp-as-null-nthcdr}
{\rm{properp}}\,({\it{l\/}})\index{properp} $=$ ({\rm{nthcdr}}\,({\rm{length}}\,({\it{l\/}})\index{length}, {\it{l\/}})\index{nthcdr} $=$ {\bf{nil}})
\end{tabbing}


\noindent{\sc Event}:   Enable properp-as-null-nthcdr; name this event `properp-as-null-nthcdr-off'.\index{properp-as-null-nthcdr-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cdr-nthcdr \\ \index{cdr-nthcdr}
{\rm{cdr}}\,({\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr}) $=$ {\rm{nthcdr}}\,($1\;+$ {\it{n\/}}, {\it{l\/}})\index{nthcdr}
\end{tabbing}


\noindent{\sc Event}:   Enable cdr-nthcdr; name this event `cdr-nthcdr-off'.\index{cdr-nthcdr-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  listp-nthcdr \\ \index{listp-nthcdr}
{\rm{listp}}\,({\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr}) $=$ ({\it{n\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{subrange} \\  
\=\+{\rm{subrange}}\,({\it{l\/}}, {\it{n\/}}, {\it{m\/}})\index{subrange} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{m\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\bf{nil}} \\ 
{\bf elseif }{\it{n\/}} $\simeq {\tt{0}}$ \\ 
{\bf then }\=\+{\bf if }{\it{m\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\rm{list}}\,({\rm{car}}\,({\it{l\/}})) \\ 
{\bf else }{\rm{cons}}\,({\rm{car}}\,({\it{l\/}}), {\rm{subrange}}\,({\rm{cdr}}\,({\it{l\/}}), {\tt{0}}, {\it{m\/}} $-\;1$)\index{subrange})$\;${\bf  endif}\- \\ 
{\bf else }{\rm{subrange}}\,({\rm{cdr}}\,({\it{l\/}}), {\it{n\/}} $-\;1$, {\it{m\/}} $-\;1$)\index{subrange}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable subrange; name this event `subrange-off'.\index{subrange-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  properp-subrange \\ \index{properp-subrange}
{\rm{properp}}\,({\rm{subrange}}\,({\it{v\/}}, {\it{n\/}}, {\it{m\/}})\index{subrange})\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  subrange-cons \\ \index{subrange-cons}
\=\+{\rm{subrange}}\,({\rm{cons}}\,({\it{car\/}}, {\it{cdr\/}}), {\it{n\/}}, {\it{m\/}})\index{subrange} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{m\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\bf{nil}} \\ 
{\bf elseif }{\it{n\/}} $\simeq {\tt{0}}$ \\ 
{\bf then }\=\+{\bf if }{\it{m\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\rm{list}}\,({\it{car\/}}) \\ 
{\bf else }{\rm{cons}}\,({\it{car\/}}, {\rm{subrange}}\,({\it{cdr\/}}, {\tt{0}}, {\it{m\/}} $-\;1$)\index{subrange})$\;${\bf  endif}\- \\ 
{\bf else }{\rm{subrange}}\,({\it{cdr\/}}, {\it{n\/}} $-\;1$, {\it{m\/}} $-\;1$)\index{subrange}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable subrange-cons; name this event `subrange-cons-off'.\index{subrange-cons-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-subrange \\ \index{length-subrange}
\=\+{\rm{length}}\,({\rm{subrange}}\,({\it{l\/}}, {\it{n\/}}, {\it{m\/}})\index{subrange})\index{length} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{m\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }$1\;+$ ({\it{m\/}} $-$ {\it{n\/}})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  subrange-append-right \\ \index{subrange-append-right}
\=\+(\=\+({\it{m\/}} $\not<$ {\it{n\/}}) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $<$ {\rm{length}}\,({\it{a\/}})\index{length}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{subrange}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}), {\it{n\/}}, {\it{m\/}})\index{subrange} \\ 
$=$$\;\;\;\;${\rm{subrange}}\,({\it{b\/}}, {\it{n\/}} $-$ {\rm{length}}\,({\it{a\/}})\index{length}, {\it{m\/}} $-$ {\rm{length}}\,({\it{a\/}})\index{length})\index{subrange})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  subrange-append-left \\ \index{subrange-append-left}
\=\+(({\it{m\/}} $\not<$ {\it{n\/}}) $\wedge$ ({\it{n\/}} $<$ {\rm{length}}\,({\it{a\/}})\index{length}) $\wedge$ ({\it{m\/}} $<$ {\rm{length}}\,({\it{a\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{subrange}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}), {\it{n\/}}, {\it{m\/}})\index{subrange} $=$ {\rm{subrange}}\,({\it{a\/}}, {\it{n\/}}, {\it{m\/}})\index{subrange})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  subrange-0 \\ \index{subrange-0}
\=\+(({\it{m\/}} $=$ ({\rm{length}}\,({\it{a\/}})\index{length} $-\;1$)) $\wedge$ {\rm{properp}}\,({\it{a\/}})\index{properp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$({\rm{subrange}}\,({\it{a\/}}, {\tt{0}}, {\it{m\/}})\index{subrange} $=$ {\it{a\/}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  listp-subrange \\ \index{listp-subrange}
{\rm{listp}}\,({\rm{subrange}}\,({\it{l\/}}, {\it{n\/}}, {\it{m\/}})\index{subrange}) $=$ ({\it{m\/}} $\not<$ {\it{n\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  subset-subrange \\ \index{subset-subrange}
({\it{n\/}} $<$ {\rm{length}}\,({\it{v\/}})\index{length}) $\rightarrow$ {\rm{subset}}\,({\rm{subrange}}\,({\it{v\/}}, {\it{m\/}}, {\it{n\/}})\index{subrange}, {\it{v\/}})\index{subset}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  not-member-subrange \\ \index{not-member-subrange}
(({\it{n\/}} $<$ {\rm{length}}\,({\it{v\/}})\index{length}) $\wedge$ ({\it{x\/}} $\not\in$ {\it{v\/}})) $\rightarrow$ ({\it{x\/}} $\not\in$ {\rm{subrange}}\,({\it{v\/}}, {\it{m\/}}, {\it{n\/}})\index{subrange})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  disjoint-subrange \\ \index{disjoint-subrange}
\=\+({\rm{disjoint}}\,({\it{x\/}}, {\it{y\/}})\index{disjoint} $\wedge$ ({\it{m\/}} $<$ {\rm{length}}\,({\it{y\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{disjoint}}\,({\it{x\/}}, {\rm{subrange}}\,({\it{y\/}}, {\it{n\/}}, {\it{m\/}})\index{subrange})\index{disjoint} $\wedge$ {\rm{disjoint}}\,({\rm{subrange}}\,({\it{y\/}}, {\it{n\/}}, {\it{m\/}})\index{subrange}, {\it{x\/}})\index{disjoint})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  open-subrange \\ \index{open-subrange}
\=\+(({\it{m\/}} $<$ {\it{n\/}}) $\rightarrow$ ({\rm{subrange}}\,({\it{l\/}}, {\it{n\/}}, {\it{m\/}})\index{subrange} $=$ {\bf{nil}})) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\it{m\/}} $\not<$ {\it{n\/}}) $\wedge$ ({\it{n\/}} $\simeq {\tt{0}}$) $\wedge$ ({\it{m\/}} $\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$({\rm{subrange}}\,({\it{l\/}}, {\it{n\/}}, {\it{m\/}})\index{subrange} $=$ {\rm{list}}\,({\rm{car}}\,({\it{l\/}}))))\- \\ 
$\wedge$$\;\;\;\;$(\=\+(({\it{m\/}} $\not<$ {\it{n\/}}) $\wedge$ ({\it{n\/}} $\simeq {\tt{0}}$) $\wedge$ ({\it{m\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$({\rm{subrange}}\,({\it{l\/}}, {\it{n\/}}, {\it{m\/}})\index{subrange} $=$ {\rm{cons}}\,({\rm{car}}\,({\it{l\/}}), {\rm{subrange}}\,({\rm{cdr}}\,({\it{l\/}}), {\tt{0}}, {\it{m\/}} $-\;1$)\index{subrange})))\- \\ 
$\wedge$$\;\;\;\;$(\=\+(({\it{m\/}} $\not<$ {\it{n\/}}) $\wedge$ ({\it{n\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$({\rm{subrange}}\,({\it{l\/}}, {\it{n\/}}, {\it{m\/}})\index{subrange} $=$ {\rm{subrange}}\,({\rm{cdr}}\,({\it{l\/}}), {\it{n\/}} $-\;1$, {\it{m\/}} $-\;1$)\index{subrange}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable open-subrange; name this event `open-subrange-off'.\index{open-subrange-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{update-nth} \\  
\=\+{\rm{update-nth}}\,({\it{n\/}}, {\it{lst\/}}, {\it{value\/}})\index{update-nth} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{lst\/}}) \\ 
{\bf then }\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\rm{cons}}\,({\it{value\/}}, {\rm{cdr}}\,({\it{lst\/}})) \\ 
{\bf else }{\rm{cons}}\,({\rm{car}}\,({\it{lst\/}}), {\rm{update-nth}}\,({\it{n\/}} $-\;1$, {\rm{cdr}}\,({\it{lst\/}}), {\it{value\/}})\index{update-nth})$\;${\bf  endif}\- \\ 
{\bf else }{\it{lst\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable update-nth; name this event `update-nth-off'.\index{update-nth-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{make-list} \\  
\=\+{\rm{make-list}}\,({\it{n\/}}, {\it{value\/}})\index{make-list} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\it{value\/}}, {\rm{make-list}}\,({\it{n\/}} $-\;1$, {\it{value\/}})\index{make-list})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable make-list; name this event `make-list-off'.\index{make-list-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-make-list \\ \index{open-make-list}
\=\+(({\it{n\/}} $\simeq {\tt{0}}$) $\rightarrow$ ({\rm{make-list}}\,({\it{n\/}}, {\it{x\/}})\index{make-list} $=$ {\bf{nil}})) \\ 
$\wedge$$\;\;\;\;$(({\it{n\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ ({\rm{make-list}}\,({\it{n\/}}, {\it{x\/}})\index{make-list} $=$ {\rm{cons}}\,({\it{x\/}}, {\rm{make-list}}\,({\it{n\/}} $-\;1$, {\it{x\/}})\index{make-list})))\-
\end{tabbing}


\noindent{\sc Event}:   Enable open-make-list; name this event `open-make-list-off'.\index{open-make-list-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-make-list \\ \index{length-make-list}
{\rm{length}}\,({\rm{make-list}}\,({\it{n\/}}, {\it{value\/}})\index{make-list})\index{length} $=$ {\rm{fix}}\,({\it{n\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  make-list-append \\ \index{make-list-append}
{\rm{append}}\,({\rm{make-list}}\,({\it{n\/}}, {\it{value\/}})\index{make-list}, {\rm{make-list}}\,({\it{m\/}}, {\it{value\/}})\index{make-list}) $=$ {\rm{make-list}}\,({\it{n\/}} $+$ {\it{m\/}}, {\it{value\/}})\index{make-list}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-make-list \\ \index{properp-make-list}
{\rm{properp}}\,({\rm{make-list}}\,({\it{n\/}}, {\it{value\/}})\index{make-list})\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  firstn-make-list \\ \index{firstn-make-list}
\=\+\=\+{\bf if }{\it{m\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{firstn}}\,({\it{n\/}}, {\rm{make-list}}\,({\it{m\/}}, {\it{v\/}})\index{make-list})\index{firstn} $=$ {\rm{make-list}}\,({\it{n\/}}, {\it{v\/}})\index{make-list})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tree-size} \\  
\=\+{\rm{tree-size}}\,({\it{tree\/}})\index{tree-size} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\tt{1}} \\ 
{\bf else }{\rm{tree-size}}\,({\rm{car}}\,({\it{tree\/}}))\index{tree-size} $+$ {\rm{tree-size}}\,({\rm{cdr}}\,({\it{tree\/}}))\index{tree-size}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tree-size; name this event `tree-size-off'.\index{tree-size-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tree-size-nlistp \\ \index{tree-size-nlistp}
({\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$) $\rightarrow$ ({\rm{tree-size}}\,({\it{tree\/}})\index{tree-size} $=$ {\tt{1}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  not-equal-tree-size-tree-0 \\ \index{not-equal-tree-size-tree-0}
{\rm{tree-size}}\,({\it{tree\/}})\index{tree-size} $\not=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tree-size-1-crock \\ \index{tree-size-1-crock}
{\tt{1}} $\not=$ {\rm{tree-size}}\,({\rm{cons}}\,({\it{a\/}}, {\it{b\/}}))\index{tree-size}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  a-helpful-lemma-for-tree-inductions \\ \index{a-helpful-lemma-for-tree-inducti!ons}
\=\+({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{length}}\,({\it{a\/}})\index{length} $<$ {\rm{tree-size}}\,({\rm{car}}\,({\it{tree\/}}))\index{tree-size}) $=$ {\bf{f}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tree-size-lemmas \\ \index{tree-size-lemmas}
\=\+(\=\+({\rm{listp}}\,({\it{tree\/}}) $\wedge$ ({\it{size\/}} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})) \\ 
$\rightarrow$$\;\;\;\;$(({\it{size\/}} $-$ {\rm{tree-size}}\,({\rm{car}}\,({\it{tree\/}}))\index{tree-size}) $=$ {\rm{tree-size}}\,({\rm{cdr}}\,({\it{tree\/}}))\index{tree-size}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{listp}}\,({\it{tree\/}}) $\wedge$ ({\it{size\/}} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})) \\ 
$\rightarrow$$\;\;\;\;$(({\it{size\/}} $-$ {\rm{tree-size}}\,({\rm{cdr}}\,({\it{tree\/}}))\index{tree-size}) $=$ {\rm{tree-size}}\,({\rm{car}}\,({\it{tree\/}}))\index{tree-size}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  make-list-append-tree-crock \\ \index{make-list-append-tree-crock}
\=\+{\rm{listp}}\,({\it{tree\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{make-list}}\,({\rm{tree-size}}\,({\rm{car}}\,({\it{tree\/}}))\index{tree-size} $+$ {\rm{tree-size}}\,({\rm{cdr}}\,({\it{tree\/}}))\index{tree-size}, {\it{value\/}})\index{make-list} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}, {\it{value\/}})\index{make-list})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable make-list-append-tree-crock; name this event `make-list-append-tree-crock-off'.\index{make-list-append-tree-crock-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tfirstn} \\  
{\rm{tfirstn}}\,({\it{list\/}}, {\it{tree\/}})\index{tfirstn} $=$ {\rm{firstn}}\,({\rm{tree-size}}\,({\rm{car}}\,({\it{tree\/}}))\index{tree-size}, {\it{list\/}})\index{firstn}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{trestn} \\  
{\rm{trestn}}\,({\it{list\/}}, {\it{tree\/}})\index{trestn} $=$ {\rm{restn}}\,({\rm{tree-size}}\,({\rm{car}}\,({\it{tree\/}}))\index{tree-size}, {\it{list\/}})\index{restn}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tree-height} \\  
\=\+{\rm{tree-height}}\,({\it{tree\/}})\index{tree-height} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\tt{1}} \\ 
{\bf else }$1\;+$ {\rm{max}}\,({\rm{tree-height}}\,({\rm{car}}\,({\it{tree\/}}))\index{tree-height}, {\rm{tree-height}}\,({\rm{cdr}}\,({\it{tree\/}}))\index{tree-height})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tree-height; name this event `tree-height-off'.\index{tree-height-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{make-tree} \\  
\=\+{\rm{make-tree}}\,({\it{n\/}})\index{make-tree} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf elseif }{\it{n\/}} $=$ {\tt{1}}$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }{\rm{cons}}\,({\rm{make-tree}}\,({\it{n\/}} $\div$ {\tt{2}})\index{make-tree}, {\rm{make-tree}}\,({\it{n\/}} $-$ ({\it{n\/}} $\div$ {\tt{2}}))\index{make-tree})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable make-tree; name this event `make-tree-off'.\index{make-tree-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tree-size-make-tree \\ \index{tree-size-make-tree}
({\it{n\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ ({\rm{tree-size}}\,({\rm{make-tree}}\,({\it{n\/}})\index{make-tree})\index{tree-size} $=$ {\it{n\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  listp-make-tree \\ \index{listp-make-tree}
\=\+{\rm{listp}}\,({\rm{make-tree}}\,({\it{n\/}})\index{make-tree}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $<$ {\tt{2}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  list-rewrite-4 \\ \index{list-rewrite-4}
\=\+({\rm{properp}}\,({\it{a\/}})\index{properp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\tt{4}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{list}}\,({\rm{car}}\,({\it{a\/}}), {\rm{cadr}}\,({\it{a\/}}), {\rm{caddr}}\,({\it{a\/}}), {\rm{cadddr}}\,({\it{a\/}})) $=$ {\it{a\/}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable list-rewrite-4; name this event `list-rewrite-4-off'.\index{list-rewrite-4-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  list-elim-4 \\ \index{list-elim-4}
\=\+({\it{l\/}} $=$ {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})) \\ 
$=$$\;\;\;\;$(\=\+({\rm{car}}\,({\it{l\/}}) $=$ {\it{a\/}}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadr}}\,({\it{l\/}}) $=$ {\it{b\/}}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\it{l\/}}) $=$ {\it{c\/}}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadddr}}\,({\it{l\/}}) $=$ {\it{d\/}}) \\ 
$\wedge$$\;\;\;\;$({\rm{cddddr}}\,({\it{l\/}}) $=$ {\bf{nil}}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable list-elim-4; name this event `list-elim-4-off'.\index{list-elim-4-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{list-as-collected-nth} \\  
\=\+{\rm{list-as-collected-nth}}\,({\it{l\/}}, {\it{length\/}}, {\it{n\/}})\index{list-as-collected-nth} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{length\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{nth}}\,({\it{n\/}}, {\it{l\/}})\index{nth}, {\rm{list-as-collected-nth}}\,({\it{l\/}}, {\it{length\/}} $-\;1$, $1\;+$ {\it{n\/}})\index{list-as-collected-nth})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable list-as-collected-nth; name this event `list-as-collected-nth-off'.\index{list-as-collected-nth-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-list-as-collected-nth \\ \index{open-list-as-collected-nth}
\=\+(({\it{length\/}} $\simeq {\tt{0}}$) $\rightarrow$ ({\rm{list-as-collected-nth}}\,({\it{l\/}}, {\it{length\/}}, {\it{n\/}})\index{list-as-collected-nth} $=$ {\bf{nil}})) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{length\/}} $\not\simeq {\tt{0}}$) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{list-as-collected-nth}}\,({\it{l\/}}, {\it{length\/}}, {\it{n\/}})\index{list-as-collected-nth} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{nth}}\,({\it{n\/}}, {\it{l\/}})\index{nth}, \\ 
{\rm{list-as-collected-nth}}\,({\it{l\/}}, {\it{length\/}} $-\;1$, $1\;+$ {\it{n\/}})\index{list-as-collected-nth})\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-length-4-as-collected-nth \\ \index{equal-length-4-as-collected-nth}
\=\+(({\rm{length}}\,({\it{l\/}})\index{length} $=$ {\tt{4}}) $\wedge$ {\rm{properp}}\,({\it{l\/}})\index{properp}) \\ 
$\rightarrow$$\;\;\;\;$({\it{l\/}} $=$ {\rm{list-as-collected-nth}}\,({\it{l\/}}, {\tt{4}}, {\tt{0}})\index{list-as-collected-nth})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-length-32-as-collected-nth \\ \index{equal-length-32-as-collected-nt!h}
\=\+(({\rm{length}}\,({\it{l\/}})\index{length} $=$ {\tt{32}}) $\wedge$ {\rm{properp}}\,({\it{l\/}})\index{properp}) \\ 
$\rightarrow$$\;\;\;\;$({\it{l\/}} $=$ {\rm{list-as-collected-nth}}\,({\it{l\/}}, {\tt{32}}, {\tt{0}})\index{list-as-collected-nth})\-
\end{tabbing}


\noindent{\sc Event}:   Add the shell {\it{index\/}}\index{index}, with recognizer function symbol {\it{indexp\/}} and 2 accessors: {\it{i-name\/}}, with type restriction (one-of numberp litatom) and default value zero; {\it{i-num\/}}, with type restriction (one-of numberp) and default value zero.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{lnfix} \\  
\=\+{\rm{lnfix}}\,({\it{x\/}})\index{lnfix} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{x\/}} $\in\;${\bf{N}}${}$) $\vee$ {\rm{litatom}}\,({\it{x\/}})$\;\;${\bf then }{\it{x\/}} \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{indices} \\  
\=\+{\rm{indices}}\,({\it{name\/}}, {\it{from\/}}, {\it{n\/}})\index{indices} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{index}}\,({\it{name\/}}, {\it{from\/}})\index{index}, {\rm{indices}}\,({\it{name\/}}, $1\;+$ {\it{from\/}}, {\it{n\/}} $-\;1$)\index{indices})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable indices; name this event `indices-off'.\index{indices-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  indices-zerop \\ \index{indices-zerop}
({\it{n\/}} $\simeq {\tt{0}}$) $\rightarrow$ ({\rm{indices}}\,({\it{name\/}}, {\it{from\/}}, {\it{n\/}})\index{indices} $=$ {\bf{nil}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  open-indices \\ \index{open-indices}
\=\+({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{indices}}\,({\it{name\/}}, {\it{from\/}}, {\it{n\/}})\index{indices} \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\rm{index}}\,({\it{name\/}}, {\it{from\/}})\index{index}, {\rm{indices}}\,({\it{name\/}}, $1\;+$ {\it{from\/}}, {\it{n\/}} $-\;1$)\index{indices}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  indices-as-append \\ \index{indices-as-append}
\=\+({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{indices}}\,({\it{name\/}}, {\it{from\/}}, {\it{n\/}})\index{indices} \\ 
$=$$\;\;\;\;${\rm{append}}\,(\=\+{\rm{indices}}\,({\it{name\/}}, {\it{from\/}}, {\it{n\/}} $-\;1$)\index{indices}, \\ 
{\rm{list}}\,({\rm{index}}\,({\it{name\/}}, ({\it{n\/}} $-\;1$) $+$ {\it{from\/}})\index{index}))\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable indices-as-append; name this event `indices-as-append-off'.\index{indices-as-append-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-indices \\ \index{length-indices}
{\rm{length}}\,({\rm{indices}}\,({\it{name\/}}, {\it{from\/}}, {\it{n\/}})\index{indices})\index{length} $=$ {\rm{fix}}\,({\it{n\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  listp-indices \\ \index{listp-indices}
{\rm{listp}}\,({\rm{indices}}\,({\it{name\/}}, {\it{from\/}}, {\it{n\/}})\index{indices}) $=$ ({\it{n\/}} $\not\simeq {\tt{0}}$)
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-indices \\ \index{properp-indices}
{\rm{properp}}\,({\rm{indices}}\,({\it{name\/}}, {\it{from\/}}, {\it{n\/}})\index{indices})\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  member-indices \\ \index{member-indices}
\=\+({\it{x\/}} $\in$ {\rm{indices}}\,({\it{name\/}}, {\it{from\/}}, {\it{n\/}})\index{indices}) \\ 
$=$$\;\;\;\;$(\=\+({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{indexp}}\,({\it{x\/}})\index{indexp} \\ 
$\wedge$$\;\;\;\;$({\rm{i-name}}\,({\it{x\/}})\index{i-name} $=$ {\rm{lnfix}}\,({\it{name\/}})\index{lnfix}) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{i-num}}\,({\it{x\/}})\index{i-num} $<$ {\it{from\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$({\rm{i-num}}\,({\it{x\/}})\index{i-num} $<$ ({\it{from\/}} $+$ {\it{n\/}})))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  disjoint-indices-different-names \\ \index{disjoint-indices-different-name!s}
\=\+({\rm{lnfix}}\,({\it{name1\/}})\index{lnfix} $\not=$ {\rm{lnfix}}\,({\it{name2\/}})\index{lnfix}) \\ 
$\rightarrow$$\;\;\;\;${\rm{disjoint}}\,({\rm{indices}}\,({\it{name1\/}}, {\it{from1\/}}, {\it{n1\/}})\index{indices}, {\rm{indices}}\,({\it{name2\/}}, {\it{from2\/}}, {\it{n2\/}})\index{indices})\index{disjoint}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  no-duplicates-in-indices \\ \index{no-duplicates-in-indices}
$\neg$ {\rm{duplicates?}}\,({\rm{indices}}\,({\it{name\/}}, {\it{from\/}}, {\it{n\/}})\index{indices})\index{duplicates?}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  position-name-indices \\ \index{position-name-indices}
\=\+({\it{index\/}} $\in$ {\rm{indices}}\,({\it{name\/}}, {\it{from\/}}, {\it{n\/}})\index{indices}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{position}}\,({\it{index\/}}, {\rm{indices}}\,({\it{name\/}}, {\it{from\/}}, {\it{n\/}})\index{indices})\index{position} $=$ ({\rm{i-num}}\,({\it{index\/}})\index{i-num} $-$ {\it{from\/}}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  nth-indices \\ \index{nth-indices}
({\it{n\/}} $<$ {\it{m\/}}) $\rightarrow$ ({\rm{nth}}\,({\it{n\/}}, {\rm{indices}}\,({\it{name\/}}, {\it{from\/}}, {\it{m\/}})\index{indices})\index{nth} $=$ {\rm{index}}\,({\it{name\/}}, {\it{n\/}} $+$ {\it{from\/}})\index{index})
\end{tabbing}


\noindent{\sc Event}:   Enable nth-indices; name this event `nth-indices-off'.\index{nth-indices-off}

\addvspace{18pt}


\noindent{\sc Event}:   Add the shell {\it{x\/}}\index{x}, with recognizer function symbol {\it{xp\/}} and no accessors.

\addvspace{18pt}


\noindent{\sc Event}:   Add the shell {\it{z\/}}\index{z}, with recognizer function symbol {\it{zp\/}} and no accessors.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{boolp}$\;\;$
{\rm{boolp}}\,({\it{x\/}})\index{boolp} $=$ (({\it{x\/}} $=$ {\bf{t}}) $\vee$ ({\it{x\/}} $=$ {\bf{f}}))
\end{tabbing}


\noindent{\sc Event}:   Enable boolp; name this event `boolp-off'.\index{boolp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  prove-boolp \\ \index{prove-boolp}
({\rm{truep}}\,({\it{x\/}}) $\vee$ {\rm{falsep}}\,({\it{x\/}})) $\rightarrow$ {\rm{boolp}}\,({\it{x\/}})\index{boolp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  boolp-lemmas \\ \index{boolp-lemmas}
\=\+{\rm{boolp}}\,({\bf{t}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\bf{f}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\rm{boolp}}\,({\it{b\/}})\index{boolp} $\rightarrow$ (({\it{b\/}} $=$ {\bf{t}}) $=$ {\it{b\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{boolp}}\,({\it{b\/}})\index{boolp} $\rightarrow$ (({\it{b\/}} $=$ {\bf{f}}) $=$ ($\neg$ {\it{b\/}})))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  boolp-implies-not-equal-z \\ \index{boolp-implies-not-equal-z}
{\rm{boolp}}\,({\it{x\/}})\index{boolp} $\rightarrow$ ({\it{x\/}} $\not=$ {\sc{z}}\index{z})
\end{tabbing}


\noindent{\sc Event}:   Enable boolp-implies-not-equal-z; name this event `boolp-implies-not-equal-z-off'.\index{boolp-implies-not-equal-z-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{boolfix} \\  
\=\+{\rm{boolfix}}\,({\it{x\/}})\index{boolfix} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{threep}$\;\;$
{\rm{threep}}\,({\it{x\/}})\index{threep} $=$ (({\it{x\/}} $=$ {\bf{t}}) $\vee$ ({\it{x\/}} $=$ {\bf{f}}) $\vee$ ({\it{x\/}} $=$ {\sc{x}}\index{x}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{threefix} \\  
\=\+{\rm{threefix}}\,({\it{x\/}})\index{threefix} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{boolp}}\,({\it{x\/}})\index{boolp}$\;\;${\bf then }{\it{x\/}} \\ 
{\bf else }{\sc{x}}\index{x}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  threefix-idempotent \\ \index{threefix-idempotent}
{\rm{threefix}}\,({\rm{threefix}}\,({\it{x\/}})\index{threefix})\index{threefix} $=$ {\rm{threefix}}\,({\it{x\/}})\index{threefix}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  threefix=x \\ \index{threefix=x}
({\sc{x}}\index{x} $=$ {\rm{threefix}}\,({\it{x\/}})\index{threefix}) $=$ ($\neg$ {\rm{boolp}}\,({\it{x\/}})\index{boolp})
\end{tabbing}


\noindent{\sc Event}:   Enable threefix=x; name this event `threefix=x-off'.\index{threefix=x-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fourp} \\  
{\rm{fourp}}\,({\it{x\/}})\index{fourp} $=$ (({\it{x\/}} $=$ {\bf{t}}) $\vee$ ({\bf{f}} $=$ {\it{x\/}}) $\vee$ ({\it{x\/}} $=$ {\sc{x}}\index{x}) $\vee$ ({\it{x\/}} $=$ {\sc{z}}\index{z}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fourfix} \\  
\=\+{\rm{fourfix}}\,({\it{x\/}})\index{fourfix} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{fourp}}\,({\it{x\/}})\index{fourp}$\;\;${\bf then }{\it{x\/}} \\ 
{\bf else }{\sc{x}}\index{x}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{bvp} \\  
\=\+{\rm{bvp}}\,({\it{x\/}})\index{bvp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{x\/}} $=$ {\bf{nil}} \\ 
{\bf else }{\rm{boolp}}\,({\rm{car}}\,({\it{x\/}}))\index{boolp} $\wedge$ {\rm{bvp}}\,({\rm{cdr}}\,({\it{x\/}}))\index{bvp}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable bvp; name this event `bvp-off'.\index{bvp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  bvp-nlistp \\ \index{bvp-nlistp}
({\it{x\/}} $\simeq\;${{\bf{nil}}}${}$) $\rightarrow$ ({\rm{bvp}}\,({\it{x\/}})\index{bvp} $=$ ({\it{x\/}} $=$ {\bf{nil}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-cons \\ \index{bvp-cons}
{\rm{bvp}}\,({\rm{cons}}\,({\it{x\/}}, {\it{y\/}}))\index{bvp} $=$ ({\rm{boolp}}\,({\it{x\/}})\index{boolp} $\wedge$ {\rm{bvp}}\,({\it{y\/}})\index{bvp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-firstn \\ \index{bvp-firstn}
{\rm{bvp}}\,({\it{x\/}})\index{bvp} $\rightarrow$ {\rm{bvp}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{x\/}})\index{firstn})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-restn \\ \index{bvp-restn}
{\rm{bvp}}\,({\it{x\/}})\index{bvp} $\rightarrow$ {\rm{bvp}}\,({\rm{restn}}\,({\it{n\/}}, {\it{x\/}})\index{restn})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-append \\ \index{bvp-append}
{\rm{bvp}}\,({\it{a\/}})\index{bvp} $\rightarrow$ ({\rm{bvp}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{bvp} $=$ {\rm{bvp}}\,({\it{b\/}})\index{bvp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-is-properp \\ \index{bvp-is-properp}
{\rm{bvp}}\,({\it{v\/}})\index{bvp} $\rightarrow$ {\rm{properp}}\,({\it{v\/}})\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-make-list \\ \index{bvp-make-list}
{\rm{bvp}}\,({\rm{make-list}}\,({\it{n\/}}, {\it{v\/}})\index{make-list})\index{bvp} $=$ (({\it{n\/}} $\simeq {\tt{0}}$) $\vee$ {\rm{boolp}}\,({\it{v\/}})\index{boolp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-nthcdr \\ \index{bvp-nthcdr}
\=\+(\=\+{\rm{bvp}}\,({\it{l\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ {\it{n\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{bvp}}\,({\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr})\index{bvp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-if \\ \index{bvp-if}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ {\rm{bvp}}\,({\it{b\/}})\index{bvp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{bvp}}\,(\=\+{\bf if }{\it{c\/}}$\;\;${\bf then }{\it{a\/}} \\ 
{\bf else }{\it{b\/}}$\;${\bf  endif}\-)\index{bvp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-if* \\ \index{bvp-if*}
({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ {\rm{bvp}}\,({\it{b\/}})\index{bvp}) $\rightarrow$ {\rm{bvp}}\,({\rm{if*}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{if*})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{bv2p} \\  
{\rm{bv2p}}\,({\it{x\/}}, {\it{y\/}})\index{bv2p} $=$ ({\rm{bvp}}\,({\it{x\/}})\index{bvp} $\wedge$ {\rm{bvp}}\,({\it{y\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{x\/}})\index{length} $=$ {\rm{length}}\,({\it{y\/}})\index{length}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{bvp-length} \\  
\=\+{\rm{bvp-length}}\,({\it{bvp\/}}, {\it{n\/}})\index{bvp-length} \\ 
$=$$\;\;\;\;$(\=\+{\rm{bvp}}\,({\it{bvp\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{bvp\/}})\index{length} $<$ {\it{n\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable bvp-length; name this event `bvp-length-off'.\index{bvp-length-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  bvp-length-cdr \\ \index{bvp-length-cdr}
{\rm{bvp-length}}\,({\it{x\/}}, $1\;+$ {\it{n\/}})\index{bvp-length} $\rightarrow$ {\rm{bvp-length}}\,({\rm{cdr}}\,({\it{x\/}}), {\it{n\/}})\index{bvp-length}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  boolfix-car-x=x \\ \index{boolfix-car-x=x}
{\rm{bvp-length}}\,({\it{x\/}}, {\tt{1}})\index{bvp-length} $\rightarrow$ ({\rm{boolfix}}\,({\rm{car}}\,({\it{x\/}}))\index{boolfix} $=$ {\rm{car}}\,({\it{x\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  boolp-car-x \\ \index{boolp-car-x}
{\rm{bvp-length}}\,({\it{x\/}}, {\tt{1}})\index{bvp-length} $\rightarrow$ {\rm{boolp}}\,({\rm{car}}\,({\it{x\/}}))\index{boolp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-length-restn \\ \index{bvp-length-restn}
\=\+{\rm{bvp}}\,({\it{bvp\/}})\index{bvp} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{bvp-length}}\,({\rm{restn}}\,({\it{n\/}}, {\it{bvp\/}})\index{restn}, {\it{m\/}})\index{bvp-length} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\rm{length}}\,({\it{bvp\/}})\index{length} $-$ {\it{n\/}}) $<$ {\it{m\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  show-that-nth=t \\ \index{show-that-nth=t}
({\rm{nth}}\,({\it{n\/}}, {\it{a\/}})\index{nth} $\wedge$ {\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\it{n\/}} $<$ {\rm{length}}\,({\it{a\/}})\index{length})) $\rightarrow$ ({\rm{nth}}\,({\it{n\/}}, {\it{a\/}})\index{nth} $=$ {\bf{t}})
\end{tabbing}


\noindent{\sc Event}:   Enable show-that-nth=t; name this event `show-that-nth=t-off'.\index{show-that-nth=t-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  boolp-nth \\ \index{boolp-nth}
{\rm{bvp}}\,({\it{a\/}})\index{bvp} $\rightarrow$ ({\rm{boolp}}\,({\rm{nth}}\,({\it{n\/}}, {\it{a\/}})\index{nth})\index{boolp} $=$ ({\it{n\/}} $<$ {\rm{length}}\,({\it{a\/}})\index{length}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  another-way-to-look-at-boolp-nth \\ \index{another-way-to-look-at-boolp-nt!h}
\=\+({\rm{bvp}}\,({\it{v\/}})\index{bvp} $\wedge$ ({\it{n\/}} $<$ {\rm{length}}\,({\it{v\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+\=\+{\bf if }{\rm{nth}}\,({\it{n\/}}, {\it{v\/}})\index{nth}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
$=$$\;\;\;\;${\rm{nth}}\,({\it{n\/}}, {\it{v\/}})\index{nth})\- \\ 
$=$$\;\;\;\;${\bf{t}})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{xor} \\  
\=\+{\rm{xor}}\,({\it{a\/}}, {\it{b\/}})\index{xor} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} \\ 
{\bf then }\=\+{\bf if }{\it{b\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{b\/}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-buf} \\  
\=\+{\rm{b-buf}}\,({\it{x\/}})\index{b-buf} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-not}$\;\;$
{\rm{b-not}}\,({\it{x\/}})\index{b-not} $=$ ($\neg$ {\it{x\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-nand}$\;\;$
{\rm{b-nand}}\,({\it{a\/}}, {\it{b\/}})\index{b-nand} $=$ ($\neg$ ({\it{a\/}} $\wedge$ {\it{b\/}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-nand3}$\;\;$
{\rm{b-nand3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{b-nand3} $=$ ($\neg$ ({\it{a\/}} $\wedge$ {\it{b\/}} $\wedge$ {\it{c\/}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-nand4}$\;\;$
{\rm{b-nand4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{b-nand4} $=$ ($\neg$ ({\it{a\/}} $\wedge$ {\it{b\/}} $\wedge$ {\it{c\/}} $\wedge$ {\it{d\/}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-nand5} \\  
{\rm{b-nand5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{b-nand5} $=$ ($\neg$ ({\it{a\/}} $\wedge$ {\it{b\/}} $\wedge$ {\it{c\/}} $\wedge$ {\it{d\/}} $\wedge$ {\it{e\/}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-nand6} \\  
{\rm{b-nand6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{b-nand6} $=$ ($\neg$ ({\it{a\/}} $\wedge$ {\it{b\/}} $\wedge$ {\it{c\/}} $\wedge$ {\it{d\/}} $\wedge$ {\it{e\/}} $\wedge$ {\it{g\/}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-nand8} \\  
\=\+{\rm{b-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{b-nand8} \\ 
$=$$\;\;\;\;$($\neg$ ({\it{a\/}} $\wedge$ {\it{b\/}} $\wedge$ {\it{c\/}} $\wedge$ {\it{d\/}} $\wedge$ {\it{e\/}} $\wedge$ {\it{g\/}} $\wedge$ {\it{h\/}} $\wedge$ {\it{i\/}}))\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-or}$\;\;$
{\rm{b-or}}\,({\it{a\/}}, {\it{b\/}})\index{b-or} $=$ ({\it{a\/}} $\vee$ {\it{b\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-or3}$\;\;$
{\rm{b-or3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{b-or3} $=$ ({\it{a\/}} $\vee$ {\it{b\/}} $\vee$ {\it{c\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-or4}$\;\;$
{\rm{b-or4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{b-or4} $=$ ({\it{a\/}} $\vee$ {\it{b\/}} $\vee$ {\it{c\/}} $\vee$ {\it{d\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-xor} \\  
\=\+{\rm{b-xor}}\,({\it{x\/}}, {\it{y\/}})\index{b-xor} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} \\ 
{\bf then }\=\+{\bf if }{\it{y\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{y\/}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-xor3}$\;\;$
{\rm{b-xor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{b-xor3} $=$ {\rm{b-xor}}\,({\rm{b-xor}}\,({\it{a\/}}, {\it{b\/}})\index{b-xor}, {\it{c\/}})\index{b-xor}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-equv} \\  
\=\+{\rm{b-equv}}\,({\it{x\/}}, {\it{y\/}})\index{b-equv} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} \\ 
{\bf then }\=\+{\bf if }{\it{y\/}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{y\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-equv3}$\;\;$
{\rm{b-equv3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{b-equv3} $=$ {\rm{b-equv}}\,({\it{a\/}}, {\rm{b-xor}}\,({\it{b\/}}, {\it{c\/}})\index{b-xor})\index{b-equv}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-and}$\;\;$
{\rm{b-and}}\,({\it{a\/}}, {\it{b\/}})\index{b-and} $=$ ({\it{a\/}} $\wedge$ {\it{b\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-and3}$\;\;$
{\rm{b-and3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{b-and3} $=$ ({\it{a\/}} $\wedge$ {\it{b\/}} $\wedge$ {\it{c\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-and4}$\;\;$
{\rm{b-and4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{b-and4} $=$ ({\it{a\/}} $\wedge$ {\it{b\/}} $\wedge$ {\it{c\/}} $\wedge$ {\it{d\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-nor}$\;\;$
{\rm{b-nor}}\,({\it{a\/}}, {\it{b\/}})\index{b-nor} $=$ ($\neg$ ({\it{a\/}} $\vee$ {\it{b\/}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-nor3}$\;\;$
{\rm{b-nor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{b-nor3} $=$ ($\neg$ ({\it{a\/}} $\vee$ {\it{b\/}} $\vee$ {\it{c\/}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-nor4}$\;\;$
{\rm{b-nor4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{b-nor4} $=$ ($\neg$ ({\it{a\/}} $\vee$ {\it{b\/}} $\vee$ {\it{c\/}} $\vee$ {\it{d\/}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-nor5} \\  
{\rm{b-nor5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{b-nor5} $=$ ($\neg$ ({\it{a\/}} $\vee$ {\it{b\/}} $\vee$ {\it{c\/}} $\vee$ {\it{d\/}} $\vee$ {\it{e\/}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-nor6} \\  
{\rm{b-nor6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{b-nor6} $=$ ($\neg$ ({\it{a\/}} $\vee$ {\it{b\/}} $\vee$ {\it{c\/}} $\vee$ {\it{d\/}} $\vee$ {\it{e\/}} $\vee$ {\it{g\/}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-nor8} \\  
\=\+{\rm{b-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{b-nor8} \\ 
$=$$\;\;\;\;$($\neg$ ({\it{a\/}} $\vee$ {\it{b\/}} $\vee$ {\it{c\/}} $\vee$ {\it{d\/}} $\vee$ {\it{e\/}} $\vee$ {\it{g\/}} $\vee$ {\it{h\/}} $\vee$ {\it{i\/}}))\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-if} \\  
\=\+{\rm{b-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{b-if} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{c\/}} \\ 
{\bf then }\=\+{\bf if }{\it{a\/}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{b\/}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  open-b-xor \\ \index{open-b-xor}
\=\+{\rm{b-xor}}\,({\it{a\/}}, {\it{b\/}})\index{b-xor} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} \\ 
{\bf then }\=\+{\bf if }{\it{b\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{b\/}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  open-b-xor3 \\ \index{open-b-xor3}
{\rm{b-xor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{b-xor3} $=$ {\rm{b-xor}}\,({\it{a\/}}, {\rm{b-xor}}\,({\it{b\/}}, {\it{c\/}})\index{b-xor})\index{b-xor}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  open-b-equv \\ \index{open-b-equv}
\=\+{\rm{b-equv}}\,({\it{a\/}}, {\it{b\/}})\index{b-equv} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} \\ 
{\bf then }\=\+{\bf if }{\it{b\/}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{b\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  open-b-equv3 \\ \index{open-b-equv3}
{\rm{b-equv3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{b-equv3} $=$ {\rm{b-equv}}\,({\it{a\/}}, {\rm{b-xor}}\,({\it{b\/}}, {\it{c\/}})\index{b-xor})\index{b-equv}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-and-rewrite \\ \index{b-and-rewrite}
($\neg$ {\rm{b-and}}\,({\bf{f}}, {\it{x\/}})\index{b-and}) $\wedge$ ($\neg$ {\rm{b-and}}\,({\it{x\/}}, {\bf{f}})\index{b-and}) $\wedge$ (({\it{x\/}} $\wedge$ {\it{y\/}}) $\rightarrow$ {\rm{b-and}}\,({\it{x\/}}, {\it{y\/}})\index{b-and})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-buf-x=x \\ \index{b-buf-x=x}
{\rm{boolp}}\,({\it{x\/}})\index{boolp} $\rightarrow$ ({\rm{b-buf}}\,({\it{x\/}})\index{b-buf} $=$ {\it{x\/}})
\end{tabbing}


\noindent{\sc Event}:   Let us define the theory {\it{b-gates}} to consist of the following events: b-buf,
b-not,
b-nand,
b-nand3,
b-nand4,
b-nand5,
b-nand6,
b-nand8,
b-or,
b-or3,
b-or4,
b-xor,
b-xor3,
b-equv,
b-equv3,
b-and,
b-and3,
b-and4,
b-nor,
b-nor3,
b-nor4,
b-nor5,
b-nor6,
b-nor8,
b-if,
open-b-xor,
open-b-xor3,
open-b-equv,
open-b-equv3,
b-and-rewrite,
b-buf-x=x.\index{b-gates}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  boolp-b-gates \\ \index{boolp-b-gates}
\=\+{\rm{boolp}}\,({\rm{b-buf}}\,({\it{x\/}})\index{b-buf})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-not}}\,({\it{x\/}})\index{b-not})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-nand}}\,({\it{a\/}}, {\it{b\/}})\index{b-nand})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-nand3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{b-nand3})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-nand4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{b-nand4})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-nand5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{b-nand5})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-nand6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{b-nand6})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{b-nand8})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-or}}\,({\it{a\/}}, {\it{b\/}})\index{b-or})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-or3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{b-or3})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-or4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{b-or4})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-xor}}\,({\it{x\/}}, {\it{y\/}})\index{b-xor})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-xor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{b-xor3})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-equv}}\,({\it{x\/}}, {\it{y\/}})\index{b-equv})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-equv3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{b-equv3})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-and}}\,({\it{a\/}}, {\it{b\/}})\index{b-and})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-and3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{b-and3})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-and4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{b-and4})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-nor}}\,({\it{a\/}}, {\it{b\/}})\index{b-nor})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-nor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{b-nor3})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-nor4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{b-nor4})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-nor5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{b-nor5})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-nor6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{b-nor6})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{b-nor8})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{b-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{b-if})\index{boolp}\-
\end{tabbing}


\noindent{\sc Event}:   Enable boolp-b-gates; name this event `boolp-b-gates-off'.\index{boolp-b-gates-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{id}$\;\;$
{\rm{id}}\,({\it{x\/}})\index{id} $=$ {\it{x\/}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ao2}$\;\;$
{\rm{ao2}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{ao2} $=$ {\rm{b-nor}}\,({\rm{b-and}}\,({\it{a\/}}, {\it{b\/}})\index{b-and}, {\rm{b-and}}\,({\it{c\/}}, {\it{d\/}})\index{b-and})\index{b-nor}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ao4}$\;\;$
{\rm{ao4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{ao4} $=$ {\rm{b-nand}}\,({\rm{b-or}}\,({\it{a\/}}, {\it{b\/}})\index{b-or}, {\rm{b-or}}\,({\it{c\/}}, {\it{d\/}})\index{b-or})\index{b-nand}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ao6}$\;\;$
{\rm{ao6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{ao6} $=$ {\rm{b-nor}}\,({\rm{b-and}}\,({\it{a\/}}, {\it{b\/}})\index{b-and}, {\it{c\/}})\index{b-nor}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ao7}$\;\;$
{\rm{ao7}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{ao7} $=$ {\rm{b-nand}}\,({\rm{b-or}}\,({\it{a\/}}, {\it{b\/}})\index{b-or}, {\it{c\/}})\index{b-nand}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{vss}$\;\;$
{\sc{vss}}\index{vss} $=$ {\bf{f}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{vdd}$\;\;$
{\sc{vdd}}\index{vdd} $=$ {\bf{t}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-buf} \\  
\=\+{\rm{v-buf}}\,({\it{x\/}})\index{v-buf} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{b-buf}}\,({\rm{car}}\,({\it{x\/}}))\index{b-buf}, {\rm{v-buf}}\,({\rm{cdr}}\,({\it{x\/}}))\index{v-buf})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-buf; name this event `v-buf-off'.\index{v-buf-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-not} \\  
\=\+{\rm{v-not}}\,({\it{x\/}})\index{v-not} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{x\/}}))\index{b-not}, {\rm{v-not}}\,({\rm{cdr}}\,({\it{x\/}}))\index{v-not})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-not; name this event `v-not-off'.\index{v-not-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-and} \\  
\=\+{\rm{v-and}}\,({\it{x\/}}, {\it{y\/}})\index{v-and} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{b-and}}\,({\rm{car}}\,({\it{x\/}}), {\rm{car}}\,({\it{y\/}}))\index{b-and}, {\rm{v-and}}\,({\rm{cdr}}\,({\it{x\/}}), {\rm{cdr}}\,({\it{y\/}}))\index{v-and})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-and; name this event `v-and-off'.\index{v-and-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-or} \\  
\=\+{\rm{v-or}}\,({\it{x\/}}, {\it{y\/}})\index{v-or} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{b-or}}\,({\rm{car}}\,({\it{x\/}}), {\rm{car}}\,({\it{y\/}}))\index{b-or}, {\rm{v-or}}\,({\rm{cdr}}\,({\it{x\/}}), {\rm{cdr}}\,({\it{y\/}}))\index{v-or})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-or; name this event `v-or-off'.\index{v-or-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-xor} \\  
\=\+{\rm{v-xor}}\,({\it{x\/}}, {\it{y\/}})\index{v-xor} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{b-xor}}\,({\rm{car}}\,({\it{x\/}}), {\rm{car}}\,({\it{y\/}}))\index{b-xor}, {\rm{v-xor}}\,({\rm{cdr}}\,({\it{x\/}}), {\rm{cdr}}\,({\it{y\/}}))\index{v-xor})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-xor; name this event `v-xor-off'.\index{v-xor-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-shift-right} \\  
\=\+{\rm{v-shift-right}}\,({\it{a\/}}, {\it{si\/}})\index{v-shift-right} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{append}}\,({\rm{v-buf}}\,({\rm{cdr}}\,({\it{a\/}}))\index{v-buf}, {\rm{list}}\,({\rm{boolfix}}\,({\it{si\/}})\index{boolfix}))$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-shift-right; name this event `v-shift-right-off'.\index{v-shift-right-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-lsr}$\;\;$
{\rm{v-lsr}}\,({\it{a\/}})\index{v-lsr} $=$ {\rm{v-shift-right}}\,({\it{a\/}}, {\bf{f}})\index{v-shift-right}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-ror}$\;\;$
{\rm{v-ror}}\,({\it{a\/}}, {\it{si\/}})\index{v-ror} $=$ {\rm{v-shift-right}}\,({\it{a\/}}, {\it{si\/}})\index{v-shift-right}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-asr}$\;\;$
{\rm{v-asr}}\,({\it{a\/}})\index{v-asr} $=$ {\rm{v-shift-right}}\,({\it{a\/}}, {\rm{nth}}\,({\rm{length}}\,({\it{a\/}})\index{length} $-\;1$, {\it{a\/}})\index{nth})\index{v-shift-right}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-if} \\  
\=\+{\rm{v-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-if} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+\=\+{\bf if }\=\+{\bf if }{\it{c\/}}$\;\;${\bf then }{\rm{car}}\,({\it{a\/}}) \\ 
{\bf else }{\rm{car}}\,({\it{b\/}})$\;${\bf  endif}\-$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-, \\ 
{\rm{v-if}}\,({\it{c\/}}, {\rm{cdr}}\,({\it{a\/}}), {\rm{cdr}}\,({\it{b\/}}))\index{v-if})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-if; name this event `v-if-off'.\index{v-if-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  bvp-v-buf \\ \index{bvp-v-buf}
{\rm{bvp}}\,({\rm{v-buf}}\,({\it{a\/}})\index{v-buf})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-v-not \\ \index{bvp-v-not}
{\rm{bvp}}\,({\rm{v-not}}\,({\it{a\/}})\index{v-not})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-v-and \\ \index{bvp-v-and}
{\rm{bvp}}\,({\rm{v-and}}\,({\it{a\/}}, {\it{b\/}})\index{v-and})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-v-or \\ \index{bvp-v-or}
{\rm{bvp}}\,({\rm{v-or}}\,({\it{a\/}}, {\it{b\/}})\index{v-or})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-v-xor \\ \index{bvp-v-xor}
{\rm{bvp}}\,({\rm{v-xor}}\,({\it{a\/}}, {\it{b\/}})\index{v-xor})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-v-shift-right \\ \index{bvp-v-shift-right}
{\rm{bvp}}\,({\rm{v-shift-right}}\,({\it{a\/}}, {\it{si\/}})\index{v-shift-right})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-v-lsr \\ \index{bvp-v-lsr}
{\rm{bvp}}\,({\rm{v-lsr}}\,({\it{a\/}})\index{v-lsr})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-v-asr \\ \index{bvp-v-asr}
{\rm{bvp}}\,({\rm{v-asr}}\,({\it{a\/}})\index{v-asr})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-v-ror \\ \index{bvp-v-ror}
{\rm{bvp}}\,({\rm{v-ror}}\,({\it{a\/}}, {\it{c\/}})\index{v-ror})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-v-if \\ \index{bvp-v-if}
{\rm{bvp}}\,({\rm{v-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-if})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-v-buf \\ \index{length-v-buf}
{\rm{length}}\,({\rm{v-buf}}\,({\it{a\/}})\index{v-buf})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-v-not \\ \index{length-v-not}
{\rm{length}}\,({\rm{v-not}}\,({\it{a\/}})\index{v-not})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-v-and \\ \index{length-v-and}
{\rm{length}}\,({\rm{v-and}}\,({\it{a\/}}, {\it{b\/}})\index{v-and})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-v-or \\ \index{length-v-or}
{\rm{length}}\,({\rm{v-or}}\,({\it{a\/}}, {\it{b\/}})\index{v-or})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-v-xor \\ \index{length-v-xor}
{\rm{length}}\,({\rm{v-xor}}\,({\it{a\/}}, {\it{b\/}})\index{v-xor})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-v-shift-right \\ \index{length-v-shift-right}
{\rm{length}}\,({\rm{v-shift-right}}\,({\it{a\/}}, {\it{b\/}})\index{v-shift-right})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-v-lsr \\ \index{length-v-lsr}
{\rm{length}}\,({\rm{v-lsr}}\,({\it{a\/}})\index{v-lsr})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-v-asr \\ \index{length-v-asr}
{\rm{length}}\,({\rm{v-asr}}\,({\it{a\/}})\index{v-asr})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-v-ror \\ \index{length-v-ror}
{\rm{length}}\,({\rm{v-ror}}\,({\it{a\/}}, {\it{b\/}})\index{v-ror})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-v-if \\ \index{length-v-if}
{\rm{length}}\,({\rm{v-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-if})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-and-append-help \\ \index{v-and-append-help}
\=\+({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{length}}\,({\it{b\/}})\index{length}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{append}}\,({\rm{v-and}}\,({\it{a\/}}, {\it{b\/}})\index{v-and}, {\rm{v-and}}\,({\it{d\/}}, {\it{e\/}})\index{v-and}) $=$ {\rm{v-and}}\,({\rm{append}}\,({\it{a\/}}, {\it{d\/}}), {\rm{append}}\,({\it{b\/}}, {\it{e\/}}))\index{v-and})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-or-append-help \\ \index{v-or-append-help}
\=\+({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{length}}\,({\it{b\/}})\index{length}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{append}}\,({\rm{v-or}}\,({\it{a\/}}, {\it{b\/}})\index{v-or}, {\rm{v-or}}\,({\it{d\/}}, {\it{e\/}})\index{v-or}) $=$ {\rm{v-or}}\,({\rm{append}}\,({\it{a\/}}, {\it{d\/}}), {\rm{append}}\,({\it{b\/}}, {\it{e\/}}))\index{v-or})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-xor-append-help \\ \index{v-xor-append-help}
\=\+({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{length}}\,({\it{b\/}})\index{length}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{append}}\,({\rm{v-xor}}\,({\it{a\/}}, {\it{b\/}})\index{v-xor}, {\rm{v-xor}}\,({\it{d\/}}, {\it{e\/}})\index{v-xor}) $=$ {\rm{v-xor}}\,({\rm{append}}\,({\it{a\/}}, {\it{d\/}}), {\rm{append}}\,({\it{b\/}}, {\it{e\/}}))\index{v-xor})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-not-append-help \\ \index{v-not-append-help}
{\rm{append}}\,({\rm{v-not}}\,({\it{a\/}})\index{v-not}, {\rm{v-not}}\,({\it{b\/}})\index{v-not}) $=$ {\rm{v-not}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{v-not}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-buf-append-help \\ \index{v-buf-append-help}
{\rm{append}}\,({\rm{v-buf}}\,({\it{a\/}})\index{v-buf}, {\rm{v-buf}}\,({\it{b\/}})\index{v-buf}) $=$ {\rm{v-buf}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{v-buf}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-if-append-help \\ \index{v-if-append-help}
\=\+({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{length}}\,({\it{b\/}})\index{length}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{append}}\,({\rm{v-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-if}, {\rm{v-if}}\,({\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{v-if}) $=$ {\rm{v-if}}\,({\it{c\/}}, {\rm{append}}\,({\it{a\/}}, {\it{d\/}}), {\rm{append}}\,({\it{b\/}}, {\it{e\/}}))\index{v-if})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-if-c-congruence \\ \index{v-if-c-congruence}
{\it{c\/}} $\rightarrow$ (({\rm{v-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-if} $=$ {\rm{v-if}}\,({\bf{t}}, {\it{a\/}}, {\it{b\/}})\index{v-if}) $=$ {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-not-firstn \\ \index{v-not-firstn}
{\rm{v-not}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{l\/}})\index{firstn})\index{v-not} $=$ {\rm{firstn}}\,({\it{n\/}}, {\rm{v-not}}\,({\it{l\/}})\index{v-not})\index{firstn}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-not-restn \\ \index{v-not-restn}
{\rm{v-not}}\,({\rm{restn}}\,({\it{n\/}}, {\it{l\/}})\index{restn})\index{v-not} $=$ {\rm{restn}}\,({\it{n\/}}, {\rm{v-not}}\,({\it{l\/}})\index{v-not})\index{restn}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  firstn-v-not \\ \index{firstn-v-not}
{\rm{firstn}}\,({\it{n\/}}, {\rm{v-not}}\,({\it{l\/}})\index{v-not})\index{firstn} $=$ {\rm{v-not}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{l\/}})\index{firstn})\index{v-not}
\end{tabbing}


\noindent{\sc Event}:   Enable firstn-v-not; name this event `firstn-v-not-off'.\index{firstn-v-not-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  restn-v-not \\ \index{restn-v-not}
{\rm{restn}}\,({\it{n\/}}, {\rm{v-not}}\,({\it{l\/}})\index{v-not})\index{restn} $=$ {\rm{v-not}}\,({\rm{restn}}\,({\it{n\/}}, {\it{l\/}})\index{restn})\index{v-not}
\end{tabbing}


\noindent{\sc Event}:   Enable restn-v-not; name this event `restn-v-not-off'.\index{restn-v-not-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-not-inverts-all \\ \index{v-not-inverts-all}
({\it{n\/}} $<$ {\rm{length}}\,({\it{bvp\/}})\index{length}) $\rightarrow$ ({\rm{nth}}\,({\it{n\/}}, {\rm{v-not}}\,({\it{bvp\/}})\index{v-not})\index{nth} $=$ {\rm{b-not}}\,({\rm{nth}}\,({\it{n\/}}, {\it{bvp\/}})\index{nth})\index{b-not})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-or-make-list-f \\ \index{v-or-make-list-f}
({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\it{n\/}})) $\rightarrow$ ({\rm{v-or}}\,({\rm{make-list}}\,({\it{n\/}}, {\bf{f}})\index{make-list}, {\it{a\/}})\index{v-or} $=$ {\it{a\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-to-nat} \\  
\=\+{\rm{v-to-nat}}\,({\it{v\/}})\index{v-to-nat} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{v\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }\=\+\=\+{\bf if }{\rm{car}}\,({\it{v\/}})$\;\;${\bf then }{\tt{1}} \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\- \\ 
$+$$\;\;\;\;$({\tt{2}} $*$ {\rm{v-to-nat}}\,({\rm{cdr}}\,({\it{v\/}}))\index{v-to-nat})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-to-nat; name this event `v-to-nat-off'.\index{v-to-nat-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{nat-to-v} \\  
\=\+{\rm{nat-to-v}}\,({\it{x\/}}, {\it{n\/}})\index{nat-to-v} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(({\it{x\/}} ${}${\bf{mod}}${}$ {\tt{2}}) $\not\simeq {\tt{0}}$, {\rm{nat-to-v}}\,({\it{x\/}} $\div$ {\tt{2}}, {\it{n\/}} $-\;1$)\index{nat-to-v})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable nat-to-v; name this event `nat-to-v-off'.\index{nat-to-v-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  firstn-nat-to-v \\ \index{firstn-nat-to-v}
\=\+\=\+{\bf if }{\it{m\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{firstn}}\,({\it{n\/}}, {\rm{nat-to-v}}\,({\it{nat\/}}, {\it{m\/}})\index{nat-to-v})\index{firstn} $=$ {\rm{nat-to-v}}\,({\it{nat\/}}, {\it{n\/}})\index{nat-to-v})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  restn-nat-to-v-0-hack \\ \index{restn-nat-to-v-0-hack}
\=\+\=\+{\bf if }{\it{m\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{restn}}\,({\it{n\/}}, {\rm{nat-to-v}}\,({\tt{0}}, {\it{m\/}})\index{nat-to-v})\index{restn} $=$ {\rm{nat-to-v}}\,({\tt{0}}, {\it{m\/}} $-$ {\it{n\/}})\index{nat-to-v})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-nat-to-v \\ \index{length-nat-to-v}
{\rm{length}}\,({\rm{nat-to-v}}\,({\it{n\/}}, {\it{length\/}})\index{nat-to-v})\index{length} $=$ {\rm{fix}}\,({\it{length\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-nat-to-v \\ \index{bvp-nat-to-v}
{\rm{bvp}}\,({\rm{nat-to-v}}\,({\it{n\/}}, {\it{length\/}})\index{nat-to-v})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  car-nat-to-v-0-is-f \\ \index{car-nat-to-v-0-is-f}
({\it{n\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ ($\neg$ {\rm{car}}\,({\rm{nat-to-v}}\,({\tt{0}}, {\it{n\/}})\index{nat-to-v}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  any-of-nat-to-v-0-is-f \\ \index{any-of-nat-to-v-0-is-f}
({\it{n\/}} $<$ {\it{m\/}}) $\rightarrow$ ($\neg$ {\rm{nth}}\,({\it{n\/}}, {\rm{nat-to-v}}\,({\tt{0}}, {\it{m\/}})\index{nat-to-v})\index{nth})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-nth}$\;\;$
{\rm{v-nth}}\,({\it{v-n\/}}, {\it{lst\/}})\index{v-nth} $=$ {\rm{nth}}\,({\rm{v-to-nat}}\,({\it{v-n\/}})\index{v-to-nat}, {\it{lst\/}})\index{nth}
\end{tabbing}


\noindent{\sc Event}:   Enable v-nth; name this event `v-nth-off'.\index{v-nth-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{update-v-nth} \\  
{\rm{update-v-nth}}\,({\it{v-n\/}}, {\it{lst\/}}, {\it{value\/}})\index{update-v-nth} $=$ {\rm{update-nth}}\,({\rm{v-to-nat}}\,({\it{v-n\/}})\index{v-to-nat}, {\it{lst\/}}, {\it{value\/}})\index{update-nth}
\end{tabbing}


\noindent{\sc Event}:   Enable update-v-nth; name this event `update-v-nth-off'.\index{update-v-nth-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-nzerop} \\  
\=\+{\rm{v-nzerop}}\,({\it{x\/}})\index{v-nzerop} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\rm{car}}\,({\it{x\/}}) $\vee$ {\rm{v-nzerop}}\,({\rm{cdr}}\,({\it{x\/}}))\index{v-nzerop}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-nzerop; name this event `v-nzerop-off'.\index{v-nzerop-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-zerop}$\;\;$
{\rm{v-zerop}}\,({\it{x\/}})\index{v-zerop} $=$ ($\neg$ {\rm{v-nzerop}}\,({\it{x\/}})\index{v-nzerop})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-nzerop-as-or-crock \\ \index{v-nzerop-as-or-crock}
\=\+({\rm{v-nzerop}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{a\/}})\index{firstn})\index{v-nzerop} $\rightarrow$ {\rm{v-nzerop}}\,({\it{a\/}})\index{v-nzerop}) \\ 
$\wedge$$\;\;\;\;$({\rm{v-nzerop}}\,({\rm{restn}}\,({\it{n\/}}, {\it{a\/}})\index{restn})\index{v-nzerop} $\rightarrow$ {\rm{v-nzerop}}\,({\it{a\/}})\index{v-nzerop})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  not-v-nzerop-as-and-crock \\ \index{not-v-nzerop-as-and-crock}
\=\+(($\neg$ {\rm{v-nzerop}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{a\/}})\index{firstn})\index{v-nzerop}) $\wedge$ ($\neg$ {\rm{v-nzerop}}\,({\rm{restn}}\,({\it{n\/}}, {\it{a\/}})\index{restn})\index{v-nzerop})) \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{v-nzerop}}\,({\it{a\/}})\index{v-nzerop})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  not-v-nzerop-v-xor-x-x \\ \index{not-v-nzerop-v-xor-x-x}
$\neg$ {\rm{v-nzerop}}\,({\rm{v-xor}}\,({\it{x\/}}, {\it{x\/}})\index{v-xor})\index{v-nzerop}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-xor-nzerop=not-equal \\ \index{v-xor-nzerop=not-equal}
{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\rightarrow$ ({\rm{v-nzerop}}\,({\rm{v-xor}}\,({\it{a\/}}, {\it{b\/}})\index{v-xor})\index{v-nzerop} $=$ ({\it{a\/}} $\not=$ {\it{b\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-zerop-make-list-f \\ \index{v-zerop-make-list-f}
{\rm{v-zerop}}\,({\rm{make-list}}\,({\it{n\/}}, {\bf{f}})\index{make-list})\index{v-zerop} $=$ {\bf{t}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  not-v-nzerop-all-f \\ \index{not-v-nzerop-all-f}
$\neg$ {\rm{v-nzerop}}\,({\rm{make-list}}\,({\it{n\/}}, {\bf{f}})\index{make-list})\index{v-nzerop}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-negp} \\  
\=\+{\rm{v-negp}}\,({\it{x\/}})\index{v-negp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{f}} \\ 
{\bf elseif }{\rm{cdr}}\,({\it{x\/}}) $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{car}}\,({\it{x\/}}) \\ 
{\bf else }{\rm{v-negp}}\,({\rm{cdr}}\,({\it{x\/}}))\index{v-negp}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-negp; name this event `v-negp-off'.\index{v-negp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  boolp-v-negp \\ \index{boolp-v-negp}
{\rm{bvp}}\,({\it{v\/}})\index{bvp} $\rightarrow$ {\rm{boolp}}\,({\rm{v-negp}}\,({\it{v\/}})\index{v-negp})\index{boolp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-negp-as-nth \\ \index{v-negp-as-nth}
({\rm{length}}\,({\it{bv\/}})\index{length} $\not=$ {\tt{0}}) $\rightarrow$ ({\rm{v-negp}}\,({\it{bv\/}})\index{v-negp} $=$ {\rm{nth}}\,({\rm{length}}\,({\it{bv\/}})\index{length} $-\;1$, {\it{bv\/}})\index{nth})
\end{tabbing}


\noindent{\sc Event}:   Enable v-negp-as-nth; name this event `v-negp-as-nth-off'.\index{v-negp-as-nth-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{sign-extend} \\  
\=\+{\rm{sign-extend}}\,({\it{v\/}}, {\it{n\/}})\index{sign-extend} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf elseif }{\it{v\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{make-list}}\,({\it{n\/}}, {\bf{f}})\index{make-list} \\ 
{\bf elseif }{\rm{cdr}}\,({\it{v\/}}) $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }{\rm{cons}}\,({\rm{boolfix}}\,({\rm{car}}\,({\it{v\/}}))\index{boolfix}, {\rm{make-list}}\,({\it{n\/}} $-\;1$, {\rm{boolfix}}\,({\rm{car}}\,({\it{v\/}}))\index{boolfix})\index{make-list}) \\ 
{\bf else }{\rm{cons}}\,({\rm{boolfix}}\,({\rm{car}}\,({\it{v\/}}))\index{boolfix}, {\rm{sign-extend}}\,({\rm{cdr}}\,({\it{v\/}}), {\it{n\/}} $-\;1$)\index{sign-extend})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable sign-extend; name this event `sign-extend-off'.\index{sign-extend-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-sign-extend \\ \index{length-sign-extend}
{\rm{length}}\,({\rm{sign-extend}}\,({\it{v\/}}, {\it{n\/}})\index{sign-extend})\index{length} $=$ {\rm{fix}}\,({\it{n\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-sign-extend \\ \index{bvp-sign-extend}
{\rm{bvp}}\,({\rm{sign-extend}}\,({\it{v\/}}, {\it{n\/}})\index{sign-extend})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  sign-extend-as-append \\ \index{sign-extend-as-append}
\=\+(\=\+{\rm{bvp}}\,({\it{v\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $<$ {\rm{length}}\,({\it{v\/}})\index{length}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{v\/}})\index{length} $\not=$ {\tt{0}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{sign-extend}}\,({\it{v\/}}, {\it{n\/}})\index{sign-extend} \\ 
$=$$\;\;\;\;${\rm{append}}\,({\it{v\/}}, {\rm{make-list}}\,({\it{n\/}} $-$ {\rm{length}}\,({\it{v\/}})\index{length}, {\rm{nth}}\,({\rm{length}}\,({\it{v\/}})\index{length} $-\;1$, {\it{v\/}})\index{nth})\index{make-list}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable sign-extend-as-append; name this event `sign-extend-as-append-off'.\index{sign-extend-as-append-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-adder} \\  
\=\+{\rm{v-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{list}}\,({\rm{boolfix}}\,({\it{c\/}})\index{boolfix}) \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{b-xor3}}\,({\it{c\/}}, {\rm{car}}\,({\it{a\/}}), {\rm{car}}\,({\it{b\/}}))\index{b-xor3}, \\ 
{\rm{v-adder}}\,(\=\+{\rm{b-or}}\,(\=\+{\rm{b-and}}\,({\rm{car}}\,({\it{a\/}}), {\rm{car}}\,({\it{b\/}}))\index{b-and}, \\ 
{\rm{b-or}}\,({\rm{b-and}}\,({\rm{car}}\,({\it{a\/}}), {\it{c\/}})\index{b-and}, {\rm{b-and}}\,({\rm{car}}\,({\it{b\/}}), {\it{c\/}})\index{b-and})\index{b-or})\-\index{b-or}, \\ 
{\rm{cdr}}\,({\it{a\/}}), \\ 
{\rm{cdr}}\,({\it{b\/}}))\-\index{v-adder})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-adder; name this event `v-adder-off'.\index{v-adder-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-adder-output} \\  
{\rm{v-adder-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder-output} $=$ {\rm{firstn}}\,({\rm{length}}\,({\it{a\/}})\index{length}, {\rm{v-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder})\index{firstn}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-adder-carry-out} \\  
{\rm{v-adder-carry-out}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder-carry-out} $=$ {\rm{nth}}\,({\rm{length}}\,({\it{a\/}})\index{length}, {\rm{v-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder})\index{nth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-adder-overflowp} \\  
\=\+{\rm{v-adder-overflowp}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder-overflowp} \\ 
$=$$\;\;\;\;${\rm{b-and}}\,(\=\+{\rm{b-equv}}\,({\rm{nth}}\,({\rm{length}}\,({\it{a\/}})\index{length} $-\;1$, {\it{a\/}})\index{nth}, {\rm{nth}}\,({\rm{length}}\,({\it{b\/}})\index{length} $-\;1$, {\it{b\/}})\index{nth})\index{b-equv}, \\ 
{\rm{b-xor}}\,(\=\+{\rm{nth}}\,({\rm{length}}\,({\it{a\/}})\index{length} $-\;1$, {\it{a\/}})\index{nth}, \\ 
{\rm{nth}}\,({\rm{length}}\,({\it{a\/}})\index{length} $-\;1$, {\rm{v-adder-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder-output})\index{nth})\-\index{b-xor})\-\index{b-and}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-subtracter-output} \\  
{\rm{v-subtracter-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-subtracter-output} $=$ {\rm{v-adder-output}}\,({\rm{b-not}}\,({\it{c\/}})\index{b-not}, {\rm{v-not}}\,({\it{a\/}})\index{v-not}, {\it{b\/}})\index{v-adder-output}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-subtracter-carry-out} \\  
\=\+{\rm{v-subtracter-carry-out}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-subtracter-carry-out} \\ 
$=$$\;\;\;\;${\rm{b-not}}\,({\rm{v-adder-carry-out}}\,({\rm{b-not}}\,({\it{c\/}})\index{b-not}, {\rm{v-not}}\,({\it{a\/}})\index{v-not}, {\it{b\/}})\index{v-adder-carry-out})\index{b-not}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-subtracter-overflowp} \\  
{\rm{v-subtracter-overflowp}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-subtracter-overflowp} $=$ {\rm{v-adder-overflowp}}\,({\rm{b-not}}\,({\it{c\/}})\index{b-not}, {\rm{v-not}}\,({\it{a\/}})\index{v-not}, {\it{b\/}})\index{v-adder-overflowp}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-inc} \\  
{\rm{v-inc}}\,({\it{x\/}})\index{v-inc} $=$ {\rm{v-adder-output}}\,({\bf{t}}, {\it{x\/}}, {\rm{nat-to-v}}\,({\tt{0}}, {\rm{length}}\,({\it{x\/}})\index{length})\index{nat-to-v})\index{v-adder-output}
\end{tabbing}


\noindent{\sc Event}:   Enable v-inc; name this event `v-inc-off'.\index{v-inc-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-dec} \\  
{\rm{v-dec}}\,({\it{x\/}})\index{v-dec} $=$ {\rm{v-subtracter-output}}\,({\bf{t}}, {\rm{nat-to-v}}\,({\tt{0}}, {\rm{length}}\,({\it{x\/}})\index{length})\index{nat-to-v}, {\it{x\/}})\index{v-subtracter-output}
\end{tabbing}


\noindent{\sc Event}:   Enable v-dec; name this event `v-dec-off'.\index{v-dec-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-of-v-adder \\ \index{length-of-v-adder}
{\rm{length}}\,({\rm{v-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder})\index{length} $=$ ($1\;+$ {\rm{length}}\,({\it{a\/}})\index{length})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-v-adder \\ \index{bvp-v-adder}
{\rm{bvp}}\,({\rm{v-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-of-v-adder-output \\ \index{length-of-v-adder-output}
{\rm{length}}\,({\rm{v-adder-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder-output})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-of-v-subtracter-output \\ \index{length-of-v-subtracter-output}
{\rm{length}}\,({\rm{v-subtracter-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-subtracter-output})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-length-v-inc-v-dec \\ \index{bvp-length-v-inc-v-dec}
\=\+{\rm{bvp}}\,({\rm{v-inc}}\,({\it{x\/}})\index{v-inc})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{v-dec}}\,({\it{x\/}})\index{v-dec})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{v-inc}}\,({\it{x\/}})\index{v-inc})\index{length} $=$ {\rm{length}}\,({\it{x\/}})\index{length}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{v-dec}}\,({\it{x\/}})\index{v-dec})\index{length} $=$ {\rm{length}}\,({\it{x\/}})\index{length})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-buf-works \\ \index{v-buf-works}
{\rm{bvp}}\,({\it{x\/}})\index{bvp} $\rightarrow$ ({\rm{v-buf}}\,({\it{x\/}})\index{v-buf} $=$ {\it{x\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-if-works \\ \index{v-if-works}
\=\+{\rm{bv2p}}\,({\it{x\/}}, {\it{y\/}})\index{bv2p} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-if}}\,({\it{c\/}}, {\it{x\/}}, {\it{y\/}})\index{v-if} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{c\/}}$\;\;${\bf then }{\it{x\/}} \\ 
{\bf else }{\it{y\/}}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-adder-works \\ \index{v-adder-works}
\=\+{\rm{bv2p}}\,({\it{x\/}}, {\it{y\/}})\index{bv2p} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-to-nat}}\,({\rm{v-adder}}\,({\it{c\/}}, {\it{x\/}}, {\it{y\/}})\index{v-adder})\index{v-to-nat} \\ 
$=$$\;\;\;\;$(\=\+\=\+{\bf if }{\it{c\/}}$\;\;${\bf then }{\tt{1}} \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\- \\ 
$+$$\;\;\;\;${\rm{v-to-nat}}\,({\it{x\/}})\index{v-to-nat} \\ 
$+$$\;\;\;\;${\rm{v-to-nat}}\,({\it{y\/}})\index{v-to-nat})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-threefix} \\  
\=\+{\rm{v-threefix}}\,({\it{v\/}})\index{v-threefix} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{v\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{threefix}}\,({\rm{car}}\,({\it{v\/}}))\index{threefix}, {\rm{v-threefix}}\,({\rm{cdr}}\,({\it{v\/}}))\index{v-threefix})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-threefix; name this event `v-threefix-off'.\index{v-threefix-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-v-threefix \\ \index{open-v-threefix}
\=\+(({\it{v\/}} $\simeq\;${{\bf{nil}}}${}$) $\rightarrow$ ({\rm{v-threefix}}\,({\it{v\/}})\index{v-threefix} $=$ {\bf{nil}})) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{listp}}\,({\it{v\/}}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{v-threefix}}\,({\it{v\/}})\index{v-threefix} $=$ {\rm{cons}}\,({\rm{threefix}}\,({\rm{car}}\,({\it{v\/}}))\index{threefix}, {\rm{v-threefix}}\,({\rm{cdr}}\,({\it{v\/}}))\index{v-threefix})))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-threefix-bvp \\ \index{v-threefix-bvp}
{\rm{bvp}}\,({\it{v\/}})\index{bvp} $\rightarrow$ ({\rm{v-threefix}}\,({\it{v\/}})\index{v-threefix} $=$ {\it{v\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-v-threefix \\ \index{properp-v-threefix}
{\rm{properp}}\,({\rm{v-threefix}}\,({\it{x\/}})\index{v-threefix})\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-v-threefix \\ \index{length-v-threefix}
{\rm{length}}\,({\rm{v-threefix}}\,({\it{x\/}})\index{v-threefix})\index{length} $=$ {\rm{length}}\,({\it{x\/}})\index{length}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  append-v-threefix \\ \index{append-v-threefix}
{\rm{append}}\,({\rm{v-threefix}}\,({\it{a\/}})\index{v-threefix}, {\rm{v-threefix}}\,({\it{b\/}})\index{v-threefix}) $=$ {\rm{v-threefix}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{v-threefix}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-threefix-append \\ \index{v-threefix-append}
{\rm{v-threefix}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{v-threefix} $=$ {\rm{append}}\,({\rm{v-threefix}}\,({\it{a\/}})\index{v-threefix}, {\rm{v-threefix}}\,({\it{b\/}})\index{v-threefix})
\end{tabbing}


\noindent{\sc Event}:   Enable v-threefix-append; name this event `v-threefix-append-off'.\index{v-threefix-append-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-threefix-idempotence \\ \index{v-threefix-idempotence}
{\rm{v-threefix}}\,({\rm{v-threefix}}\,({\it{x\/}})\index{v-threefix})\index{v-threefix} $=$ {\rm{v-threefix}}\,({\it{x\/}})\index{v-threefix}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-v-threefix \\ \index{bvp-v-threefix}
{\rm{properp}}\,({\it{v\/}})\index{properp} $\rightarrow$ ({\rm{bvp}}\,({\rm{v-threefix}}\,({\it{v\/}})\index{v-threefix})\index{bvp} $=$ {\rm{bvp}}\,({\it{v\/}})\index{bvp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-threefix-make-list-x \\ \index{v-threefix-make-list-x}
{\rm{v-threefix}}\,({\rm{make-list}}\,({\it{n\/}}, {\sc{x}}\index{x})\index{make-list})\index{v-threefix} $=$ {\rm{make-list}}\,({\it{n\/}}, {\sc{x}}\index{x})\index{make-list}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-fourfix} \\  
\=\+{\rm{v-fourfix}}\,({\it{v\/}})\index{v-fourfix} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{v\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{fourfix}}\,({\rm{car}}\,({\it{v\/}}))\index{fourfix}, {\rm{v-fourfix}}\,({\rm{cdr}}\,({\it{v\/}}))\index{v-fourfix})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-fourfix; name this event `v-fourfix-off'.\index{v-fourfix-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  bvp-v-fourfix \\ \index{bvp-v-fourfix}
{\rm{bvp}}\,({\it{v\/}})\index{bvp} $\rightarrow$ ({\rm{v-fourfix}}\,({\it{v\/}})\index{v-fourfix} $=$ {\it{v\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-fourfix-make-list \\ \index{v-fourfix-make-list}
\=\+(({\it{x\/}} $=$ {\bf{t}}) $\vee$ ({\it{x\/}} $=$ {\bf{f}}) $\vee$ ({\it{x\/}} $=$ {\sc{x}}\index{x}) $\vee$ ({\it{x\/}} $=$ {\sc{z}}\index{z})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{v-fourfix}}\,({\rm{make-list}}\,({\it{n\/}}, {\it{x\/}})\index{make-list})\index{v-fourfix} $=$ {\rm{make-list}}\,({\it{n\/}}, {\it{x\/}})\index{make-list})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-threefix-v-fourfix \\ \index{v-threefix-v-fourfix}
{\rm{v-threefix}}\,({\rm{v-fourfix}}\,({\it{v\/}})\index{v-fourfix})\index{v-threefix} $=$ {\rm{v-threefix}}\,({\it{v\/}})\index{v-threefix}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-iff} \\  
\=\+{\rm{v-iff}}\,({\it{a\/}}, {\it{b\/}})\index{v-iff} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }({\rm{car}}\,({\it{a\/}}) $\leftrightarrow$ {\rm{car}}\,({\it{b\/}})) $\wedge$ {\rm{v-iff}}\,({\rm{cdr}}\,({\it{a\/}}), {\rm{cdr}}\,({\it{b\/}}))\index{v-iff}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-iff; name this event `v-iff-off'.\index{v-iff-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-iff-x-x \\ \index{v-iff-x-x}
{\rm{v-iff}}\,({\it{x\/}}, {\it{x\/}})\index{v-iff}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-iff-rev1 \\ \index{v-iff-rev1}
\=\+(({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{length}}\,({\it{b\/}})\index{length}) $\wedge$ ({\rm{length}}\,({\it{x\/}})\index{length} $=$ {\rm{length}}\,({\it{y\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{v-iff}}\,({\rm{rev1}}\,({\it{a\/}}, {\it{x\/}})\index{rev1}, {\rm{rev1}}\,({\it{b\/}}, {\it{y\/}})\index{rev1})\index{v-iff} $=$ ({\rm{v-iff}}\,({\it{a\/}}, {\it{b\/}})\index{v-iff} $\wedge$ {\rm{v-iff}}\,({\it{x\/}}, {\it{y\/}})\index{v-iff}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-iff-reverse \\ \index{v-iff-reverse}
({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{length}}\,({\it{b\/}})\index{length}) $\rightarrow$ ({\rm{v-iff}}\,({\rm{reverse}}\,({\it{a\/}})\index{reverse}, {\rm{reverse}}\,({\it{b\/}})\index{reverse})\index{v-iff} $=$ {\rm{v-iff}}\,({\it{a\/}}, {\it{b\/}})\index{v-iff})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-iff=equal \\ \index{v-iff=equal}
{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\rightarrow$ ({\rm{v-iff}}\,({\it{a\/}}, {\it{b\/}})\index{v-iff} $=$ ({\it{a\/}} $=$ {\it{b\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-subrange \\ \index{bvp-subrange}
({\rm{bvp}}\,({\it{v\/}})\index{bvp} $\wedge$ ({\it{n\/}} $<$ {\rm{length}}\,({\it{v\/}})\index{length})) $\rightarrow$ {\rm{bvp}}\,({\rm{subrange}}\,({\it{v\/}}, {\it{m\/}}, {\it{n\/}})\index{subrange})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  boolp-if* \\ \index{boolp-if*}
({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp}) $\rightarrow$ {\rm{boolp}}\,({\rm{if*}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{if*})\index{boolp}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{value} \\  
\=\+{\rm{value}}\,({\it{name\/}}, {\it{alist\/}})\index{value} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{alist\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{car}}\,({\it{alist\/}})) \\ 
{\bf then }\=\+{\bf if }{\rm{caar}}\,({\it{alist\/}}) $=$ {\it{name\/}}$\;\;${\bf then }{\rm{cdar}}\,({\it{alist\/}}) \\ 
{\bf else }{\rm{value}}\,({\it{name\/}}, {\rm{cdr}}\,({\it{alist\/}}))\index{value}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{value}}\,({\it{name\/}}, {\rm{cdr}}\,({\it{alist\/}}))\index{value}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable value; name this event `value-off'.\index{value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-value} \\  
\=\+{\rm{collect-value}}\,({\it{args\/}}, {\it{alist\/}})\index{collect-value} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{args\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{value}}\,({\rm{car}}\,({\it{args\/}}), {\it{alist\/}})\index{value}, {\rm{collect-value}}\,({\rm{cdr}}\,({\it{args\/}}), {\it{alist\/}})\index{collect-value})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-value; name this event `collect-value-off'.\index{collect-value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-value \\ \index{rewrite-value}
\=\+{\rm{value}}\,({\it{a\/}}, {\rm{cons}}\,({\rm{cons}}\,({\it{b\/}}, {\it{c\/}}), {\it{d\/}}))\index{value} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $=$ {\it{b\/}}$\;\;${\bf then }{\it{c\/}} \\ 
{\bf else }{\rm{value}}\,({\it{a\/}}, {\it{d\/}})\index{value}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-value-4x \\ \index{rewrite-value-4x}
\=\+{\rm{value}}\,({\it{a\/}}, {\rm{cons}}\,({\rm{cons}}\,({\it{b\/}}, {\it{c\/}}), {\rm{cons}}\,({\rm{cons}}\,({\it{d\/}}, {\it{e\/}}), {\rm{cons}}\,({\rm{cons}}\,({\it{g\/}}, {\it{h\/}}), {\rm{cons}}\,({\rm{cons}}\,({\it{i\/}}, {\it{j\/}}), {\it{k\/}})))))\index{value} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $=$ {\it{b\/}}$\;\;${\bf then }{\it{c\/}} \\ 
{\bf elseif }{\it{a\/}} $=$ {\it{d\/}}$\;\;${\bf then }{\it{e\/}} \\ 
{\bf elseif }{\it{a\/}} $=$ {\it{g\/}}$\;\;${\bf then }{\it{h\/}} \\ 
{\bf elseif }{\it{a\/}} $=$ {\it{i\/}}$\;\;${\bf then }{\it{j\/}} \\ 
{\bf else }{\rm{value}}\,({\it{a\/}}, {\it{k\/}})\index{value}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  value-append-pairlist \\ \index{value-append-pairlist}
\=\+{\rm{value}}\,({\it{a\/}}, {\rm{append}}\,({\rm{pairlist}}\,({\it{b\/}}, {\it{c\/}}), {\it{d\/}}))\index{value} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $\in$ {\it{b\/}}$\;\;${\bf then }{\rm{value}}\,({\it{a\/}}, {\rm{pairlist}}\,({\it{b\/}}, {\it{c\/}}))\index{value} \\ 
{\bf else }{\rm{value}}\,({\it{a\/}}, {\it{d\/}})\index{value}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  value-pairlist \\ \index{value-pairlist}
\=\+({\it{name\/}} $\in$ {\it{names\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{value}}\,({\it{name\/}}, {\rm{pairlist}}\,({\it{names\/}}, {\it{values\/}}))\index{value} \\ 
$=$$\;\;\;\;${\rm{car}}\,({\rm{restn}}\,({\rm{position}}\,({\it{name\/}}, {\it{names\/}})\index{position}, {\it{values\/}})\index{restn}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable value-pairlist; name this event `value-pairlist-off'.\index{value-pairlist-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  value-indices-hack \\ \index{value-indices-hack}
\=\+(\=\+({\it{the-name\/}} $\in$ {\rm{indices}}\,({\it{name\/}}, {\it{n\/}}, {\it{m\/}})\index{indices}) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{values\/}})\index{length} $<$ {\it{m\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{value}}\,({\it{the-name\/}}, {\rm{pairlist}}\,({\rm{indices}}\,({\it{name\/}}, {\it{n\/}}, {\it{m\/}})\index{indices}, {\it{values\/}}))\index{value} \\ 
$=$$\;\;\;\;${\rm{nth}}\,({\rm{i-num}}\,({\it{the-name\/}})\index{i-num} $-$ {\it{n\/}}, {\it{values\/}})\index{nth})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  collect-value-nlistp \\ \index{collect-value-nlistp}
({\it{args\/}} $\simeq\;${{\bf{nil}}}${}$) $\rightarrow$ ({\rm{collect-value}}\,({\it{args\/}}, {\it{alist\/}})\index{collect-value} $=$ {\bf{nil}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  listp-collect-value \\ \index{listp-collect-value}
{\rm{listp}}\,({\rm{collect-value}}\,({\it{args\/}}, {\it{alist\/}})\index{collect-value}) $=$ {\rm{listp}}\,({\it{args\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  collect-value-append \\ \index{collect-value-append}
\=\+{\rm{collect-value}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}), {\it{alist\/}})\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{append}}\,({\rm{collect-value}}\,({\it{a\/}}, {\it{alist\/}})\index{collect-value}, {\rm{collect-value}}\,({\it{b\/}}, {\it{alist\/}})\index{collect-value})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-collect-value \\ \index{length-collect-value}
{\rm{length}}\,({\rm{collect-value}}\,({\it{args\/}}, {\it{alist\/}})\index{collect-value})\index{length} $=$ {\rm{length}}\,({\it{args\/}})\index{length}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  collect-value-append-pairlist-when-subset \\ \index{collect-value-append-pairlist-w!hen-subset}
\=\+{\rm{subset}}\,({\it{args1\/}}, {\it{args2\/}})\index{subset} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,({\it{args1\/}}, {\rm{append}}\,({\rm{pairlist}}\,({\it{args2\/}}, {\it{answer\/}}), {\it{x\/}}))\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{collect-value}}\,({\it{args1\/}}, {\rm{pairlist}}\,({\it{args2\/}}, {\it{answer\/}}))\index{collect-value})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  collect-value-append-pairlist-when-disjoint \\ \index{collect-value-append-pairlist-w!hen-disjoint}
\=\+{\rm{disjoint}}\,({\it{args1\/}}, {\it{args2\/}})\index{disjoint} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,({\it{args1\/}}, {\rm{append}}\,({\rm{pairlist}}\,({\it{args2\/}}, {\it{a\/}}), {\it{b\/}}))\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{collect-value}}\,({\it{args1\/}}, {\it{b\/}})\index{collect-value})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  collect-value-disjoint-pairlist \\ \index{collect-value-disjoint-pairlist}
\=\+({\it{a\/}} $\not\in$ {\it{args\/}}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{collect-value}}\,({\it{args\/}}, {\rm{cons}}\,({\rm{cons}}\,({\it{a\/}}, {\it{b\/}}), {\it{c\/}}))\index{collect-value} $=$ {\rm{collect-value}}\,({\it{args\/}}, {\it{c\/}})\index{collect-value})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  collect-value-litatom-indices-speedup \\ \index{collect-value-litatom-indices-spee!dup}
\=\+{\rm{litatom}}\,({\it{a\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,({\rm{indices}}\,({\it{name\/}}, {\it{from\/}}, {\it{to\/}})\index{indices}, {\rm{cons}}\,({\rm{cons}}\,({\it{a\/}}, {\it{b\/}}), {\it{c\/}}))\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{collect-value}}\,({\rm{indices}}\,({\it{name\/}}, {\it{from\/}}, {\it{to\/}})\index{indices}, {\it{c\/}})\index{collect-value})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-collect-value-promote-alists \\ \index{equal-collect-value-promote-ali!sts}
\=\+({\it{alist1\/}} $=$ {\it{alist2\/}}) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{collect-value}}\,({\it{args\/}}, {\it{alist1\/}})\index{collect-value} $=$ {\rm{collect-value}}\,({\it{args\/}}, {\it{alist2\/}})\index{collect-value}) $=$ {\bf{t}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  collect-value-firstn \\ \index{collect-value-firstn}
\=\+($\neg$ {\rm{duplicates?}}\,({\it{args\/}})\index{duplicates?}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{args\/}})\index{firstn}, {\rm{pairlist}}\,({\it{args\/}}, {\it{answer\/}}))\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{collect-value}}\,(\=\+{\rm{firstn}}\,({\it{n\/}}, {\it{args\/}})\index{firstn}, \\ 
{\rm{pairlist}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{args\/}})\index{firstn}, {\rm{firstn}}\,({\it{n\/}}, {\it{answer\/}})\index{firstn}))\-\index{collect-value})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  collect-value-restn \\ \index{collect-value-restn}
\=\+($\neg$ {\rm{duplicates?}}\,({\it{args\/}})\index{duplicates?}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,({\rm{restn}}\,({\it{n\/}}, {\it{args\/}})\index{restn}, {\rm{pairlist}}\,({\it{args\/}}, {\it{answer\/}}))\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{collect-value}}\,(\=\+{\rm{restn}}\,({\it{n\/}}, {\it{args\/}})\index{restn}, \\ 
{\rm{pairlist}}\,({\rm{restn}}\,({\it{n\/}}, {\it{args\/}})\index{restn}, {\rm{restn}}\,({\it{n\/}}, {\it{answer\/}})\index{restn}))\-\index{collect-value})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  collect-value-cons \\ \index{collect-value-cons}
\=\+{\rm{collect-value}}\,({\rm{cons}}\,({\it{a\/}}, {\it{b\/}}), {\it{alist\/}})\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\rm{value}}\,({\it{a\/}}, {\it{alist\/}})\index{value}, {\rm{collect-value}}\,({\it{b\/}}, {\it{alist\/}})\index{collect-value})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  singleton-collect-value \\ \index{singleton-collect-value}
\=\+({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\tt{1}}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{collect-value}}\,({\it{a\/}}, {\it{alist\/}})\index{collect-value} $=$ {\rm{list}}\,({\rm{value}}\,({\rm{car}}\,({\it{a\/}}), {\it{alist\/}})\index{value}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-collect-value \\ \index{properp-collect-value}
{\rm{properp}}\,({\rm{collect-value}}\,({\it{args\/}}, {\it{alist\/}})\index{collect-value})\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  collect-value-args-pairlist-args \\ \index{collect-value-args-pairlist-arg!s}
\=\+(\=\+($\neg$ {\rm{duplicates?}}\,({\it{args\/}})\index{duplicates?}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{args\/}})\index{length} $=$ {\rm{length}}\,({\it{list\/}})\index{length}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{list\/}})\index{properp})\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{collect-value}}\,({\it{args\/}}, {\rm{pairlist}}\,({\it{args\/}}, {\it{list\/}}))\index{collect-value} $=$ {\it{list\/}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  collect-value-splitting-crock-helper \\ \index{collect-value-splitting-crock-he!lper}
\=\+{\rm{collect-value}}\,({\rm{append}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{l\/}})\index{firstn}, {\rm{restn}}\,({\it{n\/}}, {\it{l\/}})\index{restn}), {\it{alist\/}})\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{append}}\,(\=\+{\rm{collect-value}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{l\/}})\index{firstn}, {\it{alist\/}})\index{collect-value}, \\ 
{\rm{collect-value}}\,({\rm{restn}}\,({\it{n\/}}, {\it{l\/}})\index{restn}, {\it{alist\/}})\index{collect-value})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  collect-value-splitting-crock \\ \index{collect-value-splitting-crock}
\=\+{\rm{collect-value}}\,({\it{l\/}}, {\it{alist\/}})\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{append}}\,(\=\+{\rm{collect-value}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{l\/}})\index{firstn}, {\it{alist\/}})\index{collect-value}, \\ 
{\rm{collect-value}}\,({\rm{restn}}\,({\it{n\/}}, {\it{l\/}})\index{restn}, {\it{alist\/}})\index{collect-value})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  collect-value-make-list \\ \index{collect-value-make-list}
{\rm{collect-value}}\,({\rm{make-list}}\,({\it{n\/}}, {\it{name\/}})\index{make-list}, {\it{alist\/}})\index{collect-value} $=$ {\rm{make-list}}\,({\it{n\/}}, {\rm{value}}\,({\it{name\/}}, {\it{alist\/}})\index{value})\index{make-list}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cdr-cdr-sub1-sub1-induction} \\  
\=\+{\rm{cdr-cdr-sub1-sub1-induction}}\,({\it{l1\/}}, {\it{n\/}}, {\it{m\/}}, {\it{l2\/}})\index{cdr-cdr-sub1-sub1-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{m\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\it{n\/}} $\simeq {\tt{0}}$ \\ 
{\bf then }\=\+{\bf if }{\it{m\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{cdr-cdr-sub1-sub1-induction}}\,({\rm{cdr}}\,({\it{l1\/}}), {\tt{0}}, {\it{m\/}} $-\;1$, {\rm{cdr}}\,({\it{l2\/}}))\index{cdr-cdr-sub1-sub1-induction}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{cdr-cdr-sub1-sub1-induction}}\,({\rm{cdr}}\,({\it{l1\/}}), {\it{n\/}} $-\;1$, {\it{m\/}} $-\;1$, {\rm{cdr}}\,({\it{l2\/}}))\index{cdr-cdr-sub1-sub1-induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  collect-value-subrange-args-pairlist-args \\ \index{collect-value-subrange-args-pai!rlist-args}
\=\+(\=\+($\neg$ {\rm{duplicates?}}\,({\it{args\/}})\index{duplicates?}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{args\/}})\index{length} $=$ {\rm{length}}\,({\it{list\/}})\index{length}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{list\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $<$ {\rm{length}}\,({\it{args\/}})\index{length}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,({\rm{subrange}}\,({\it{args\/}}, {\it{m\/}}, {\it{n\/}})\index{subrange}, {\rm{pairlist}}\,({\it{args\/}}, {\it{list\/}}))\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{subrange}}\,({\it{list\/}}, {\it{m\/}}, {\it{n\/}})\index{subrange})\-\-
\end{tabbing}


\noindent{\sc Event}:   Add the shell {\it{rom\/}}\index{rom}, with recognizer function symbol {\it{romp\/}} and 1 accessor: {\it{rom-guts\/}}, with type restriction (none-of) and default value zero.

\addvspace{18pt}


\noindent{\sc Event}:   Add the shell {\it{ram\/}}\index{ram}, with recognizer function symbol {\it{ramp\/}} and 1 accessor: {\it{ram-guts\/}}, with type restriction (none-of) and default value zero.

\addvspace{18pt}


\noindent{\sc Event}:   Add the shell {\it{stub\/}}\index{stub}, with recognizer function symbol {\it{stubp\/}} and 1 accessor: {\it{stub-guts\/}}, with type restriction (none-of) and default value zero.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{memory-properp} \\  
\=\+{\rm{memory-properp}}\,({\it{n\/}}, {\it{width\/}}, {\it{mem\/}})\index{memory-properp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{stubp}}\,({\it{mem\/}})\index{stubp} \\ 
{\bf then }{\rm{properp}}\,({\rm{stub-guts}}\,({\it{mem\/}})\index{stub-guts})\index{properp} $\wedge$ ({\rm{length}}\,({\rm{stub-guts}}\,({\it{mem\/}})\index{stub-guts})\index{length} $=$ {\it{width\/}}) \\ 
{\bf elseif }{\it{n\/}} $\simeq {\tt{0}}$ \\ 
{\bf then }\=\+{\bf if }{\rm{ramp}}\,({\it{mem\/}})\index{ramp} \\ 
{\bf then }\=\+{\rm{properp}}\,({\rm{ram-guts}}\,({\it{mem\/}})\index{ram-guts})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{ram-guts}}\,({\it{mem\/}})\index{ram-guts})\index{length} $=$ {\it{width\/}})\- \\ 
{\bf elseif }{\rm{romp}}\,({\it{mem\/}})\index{romp} \\ 
{\bf then }\=\+{\rm{properp}}\,({\rm{rom-guts}}\,({\it{mem\/}})\index{rom-guts})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{rom-guts}}\,({\it{mem\/}})\index{rom-guts})\index{length} $=$ {\it{width\/}})\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }\=\+{\rm{listp}}\,({\it{mem\/}}) \\ 
$\wedge$$\;\;\;\;${\rm{memory-properp}}\,({\it{n\/}} $-\;1$, {\it{width\/}}, {\rm{car}}\,({\it{mem\/}}))\index{memory-properp} \\ 
$\wedge$$\;\;\;\;${\rm{memory-properp}}\,({\it{n\/}} $-\;1$, {\it{width\/}}, {\rm{cdr}}\,({\it{mem\/}}))\index{memory-properp}\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable memory-properp; name this event `memory-properp-off'.\index{memory-properp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{memory-okp} \\  
\=\+{\rm{memory-okp}}\,({\it{n\/}}, {\it{width\/}}, {\it{mem\/}})\index{memory-okp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{stubp}}\,({\it{mem\/}})\index{stubp} \\ 
{\bf then }{\rm{bvp}}\,({\rm{stub-guts}}\,({\it{mem\/}})\index{stub-guts})\index{bvp} $\wedge$ ({\rm{length}}\,({\rm{stub-guts}}\,({\it{mem\/}})\index{stub-guts})\index{length} $=$ {\it{width\/}}) \\ 
{\bf elseif }{\it{n\/}} $\simeq {\tt{0}}$ \\ 
{\bf then }\=\+{\bf if }{\rm{ramp}}\,({\it{mem\/}})\index{ramp} \\ 
{\bf then }{\rm{bvp}}\,({\rm{ram-guts}}\,({\it{mem\/}})\index{ram-guts})\index{bvp} $\wedge$ ({\rm{length}}\,({\rm{ram-guts}}\,({\it{mem\/}})\index{ram-guts})\index{length} $=$ {\it{width\/}}) \\ 
{\bf elseif }{\rm{romp}}\,({\it{mem\/}})\index{romp} \\ 
{\bf then }{\rm{bvp}}\,({\rm{rom-guts}}\,({\it{mem\/}})\index{rom-guts})\index{bvp} $\wedge$ ({\rm{length}}\,({\rm{rom-guts}}\,({\it{mem\/}})\index{rom-guts})\index{length} $=$ {\it{width\/}}) \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }\=\+{\rm{listp}}\,({\it{mem\/}}) \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\it{n\/}} $-\;1$, {\it{width\/}}, {\rm{car}}\,({\it{mem\/}}))\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\it{n\/}} $-\;1$, {\it{width\/}}, {\rm{cdr}}\,({\it{mem\/}}))\index{memory-okp}\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable memory-okp; name this event `memory-okp-off'.\index{memory-okp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{read-mem1} \\  
\=\+{\rm{read-mem1}}\,({\it{v-addr\/}}, {\it{mem\/}})\index{read-mem1} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{stubp}}\,({\it{mem\/}})\index{stubp}$\;\;${\bf then }{\rm{stub-guts}}\,({\it{mem\/}})\index{stub-guts} \\ 
{\bf elseif }{\it{v-addr\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }\=\+{\bf if }{\rm{ramp}}\,({\it{mem\/}})\index{ramp}$\;\;${\bf then }{\rm{ram-guts}}\,({\it{mem\/}})\index{ram-guts} \\ 
{\bf elseif }{\rm{romp}}\,({\it{mem\/}})\index{romp}$\;\;${\bf then }{\rm{rom-guts}}\,({\it{mem\/}})\index{rom-guts} \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{mem\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf elseif }{\rm{car}}\,({\it{v-addr\/}})$\;\;${\bf then }{\rm{read-mem1}}\,({\rm{cdr}}\,({\it{v-addr\/}}), {\rm{cdr}}\,({\it{mem\/}}))\index{read-mem1} \\ 
{\bf else }{\rm{read-mem1}}\,({\rm{cdr}}\,({\it{v-addr\/}}), {\rm{car}}\,({\it{mem\/}}))\index{read-mem1}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable read-mem1; name this event `read-mem1-off'.\index{read-mem1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{read-mem} \\  
{\rm{read-mem}}\,({\it{v-addr\/}}, {\it{mem\/}})\index{read-mem} $=$ {\rm{read-mem1}}\,({\rm{reverse}}\,({\it{v-addr\/}})\index{reverse}, {\it{mem\/}})\index{read-mem1}
\end{tabbing}


\noindent{\sc Event}:   Enable read-mem; name this event `read-mem-off'.\index{read-mem-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{write-mem1} \\  
\=\+{\rm{write-mem1}}\,({\it{v-addr\/}}, {\it{mem\/}}, {\it{value\/}})\index{write-mem1} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{stubp}}\,({\it{mem\/}})\index{stubp}$\;\;${\bf then }{\it{mem\/}} \\ 
{\bf elseif }{\it{v-addr\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }\=\+{\bf if }{\rm{ramp}}\,({\it{mem\/}})\index{ramp}$\;\;${\bf then }{\rm{ram}}\,({\it{value\/}})\index{ram} \\ 
{\bf else }{\it{mem\/}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{mem\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{mem\/}} \\ 
{\bf elseif }{\rm{car}}\,({\it{v-addr\/}}) \\ 
{\bf then }{\rm{cons}}\,({\rm{car}}\,({\it{mem\/}}), {\rm{write-mem1}}\,({\rm{cdr}}\,({\it{v-addr\/}}), {\rm{cdr}}\,({\it{mem\/}}), {\it{value\/}})\index{write-mem1}) \\ 
{\bf else }{\rm{cons}}\,({\rm{write-mem1}}\,({\rm{cdr}}\,({\it{v-addr\/}}), {\rm{car}}\,({\it{mem\/}}), {\it{value\/}})\index{write-mem1}, {\rm{cdr}}\,({\it{mem\/}}))$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable write-mem1; name this event `write-mem1-off'.\index{write-mem1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{write-mem} \\  
{\rm{write-mem}}\,({\it{v-addr\/}}, {\it{mem\/}}, {\it{value\/}})\index{write-mem} $=$ {\rm{write-mem1}}\,({\rm{reverse}}\,({\it{v-addr\/}})\index{reverse}, {\it{mem\/}}, {\it{value\/}})\index{write-mem1}
\end{tabbing}


\noindent{\sc Event}:   Enable write-mem; name this event `write-mem-off'.\index{write-mem-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ramp-mem1} \\  
\=\+{\rm{ramp-mem1}}\,({\it{v-addr\/}}, {\it{mem\/}})\index{ramp-mem1} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{stubp}}\,({\it{mem\/}})\index{stubp}$\;\;${\bf then }{\bf{f}} \\ 
{\bf elseif }{\it{v-addr\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{ramp}}\,({\it{mem\/}})\index{ramp} \\ 
{\bf elseif }{\it{mem\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{f}} \\ 
{\bf elseif }{\rm{car}}\,({\it{v-addr\/}})$\;\;${\bf then }{\rm{ramp-mem1}}\,({\rm{cdr}}\,({\it{v-addr\/}}), {\rm{cdr}}\,({\it{mem\/}}))\index{ramp-mem1} \\ 
{\bf else }{\rm{ramp-mem1}}\,({\rm{cdr}}\,({\it{v-addr\/}}), {\rm{car}}\,({\it{mem\/}}))\index{ramp-mem1}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ramp-mem1; name this event `ramp-mem1-off'.\index{ramp-mem1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ramp-mem} \\  
{\rm{ramp-mem}}\,({\it{v-addr\/}}, {\it{mem\/}})\index{ramp-mem} $=$ {\rm{ramp-mem1}}\,({\rm{reverse}}\,({\it{v-addr\/}})\index{reverse}, {\it{mem\/}})\index{ramp-mem1}
\end{tabbing}


\noindent{\sc Event}:   Enable ramp-mem; name this event `ramp-mem-off'.\index{ramp-mem-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{all-ramp-mem} \\  
\=\+{\rm{all-ramp-mem}}\,({\it{n\/}}, {\it{mem\/}})\index{all-ramp-mem} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{stubp}}\,({\it{mem\/}})\index{stubp}$\;\;${\bf then }{\bf{f}} \\ 
{\bf elseif }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\rm{ramp}}\,({\it{mem\/}})\index{ramp} \\ 
{\bf elseif }{\it{mem\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }\=\+{\rm{all-ramp-mem}}\,({\it{n\/}} $-\;1$, {\rm{car}}\,({\it{mem\/}}))\index{all-ramp-mem} \\ 
$\wedge$$\;\;\;\;${\rm{all-ramp-mem}}\,({\it{n\/}} $-\;1$, {\rm{cdr}}\,({\it{mem\/}}))\index{all-ramp-mem}\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable all-ramp-mem; name this event `all-ramp-mem-off'.\index{all-ramp-mem-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{constant-ram} \\  
\=\+{\rm{constant-ram}}\,({\it{mem\/}}, {\it{value\/}})\index{constant-ram} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{ramp}}\,({\it{mem\/}})\index{ramp}$\;\;${\bf then }{\rm{ram}}\,({\it{value\/}})\index{ram} \\ 
{\bf elseif }{\it{mem\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{mem\/}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{constant-ram}}\,({\rm{car}}\,({\it{mem\/}}), {\it{value\/}})\index{constant-ram}, \\ 
{\rm{constant-ram}}\,({\rm{cdr}}\,({\it{mem\/}}), {\it{value\/}})\index{constant-ram})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable constant-ram; name this event `constant-ram-off'.\index{constant-ram-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  memory-properp-if \\ \index{memory-properp-if}
\=\+({\rm{memory-properp}}\,({\it{n\/}}, {\it{width\/}}, {\it{a\/}})\index{memory-properp} $\wedge$ {\rm{memory-properp}}\,({\it{n\/}}, {\it{width\/}}, {\it{b\/}})\index{memory-properp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{memory-properp}}\,(\=\+{\it{n\/}}, \\ 
{\it{width\/}}, \\ 
\=\+{\bf if }{\it{c\/}}$\;\;${\bf then }{\it{a\/}} \\ 
{\bf else }{\it{b\/}}$\;${\bf  endif}\-)\-\index{memory-properp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  memory-okp-if \\ \index{memory-okp-if}
\=\+({\rm{memory-okp}}\,({\it{n\/}}, {\it{width\/}}, {\it{a\/}})\index{memory-okp} $\wedge$ {\rm{memory-okp}}\,({\it{n\/}}, {\it{width\/}}, {\it{b\/}})\index{memory-okp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{memory-okp}}\,(\=\+{\it{n\/}}, \\ 
{\it{width\/}}, \\ 
\=\+{\bf if }{\it{c\/}}$\;\;${\bf then }{\it{a\/}} \\ 
{\bf else }{\it{b\/}}$\;${\bf  endif}\-)\-\index{memory-okp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  memory-properp-constant-ram \\ \index{memory-properp-constant-ram}
\=\+(\=\+{\rm{memory-properp}}\,({\it{n\/}}, {\it{width\/}}, {\it{mem\/}})\index{memory-properp} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{value\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\it{width\/}} $=$ {\rm{length}}\,({\it{value\/}})\index{length}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{memory-properp}}\,({\it{n\/}}, {\it{width\/}}, {\rm{constant-ram}}\,({\it{mem\/}}, {\it{value\/}})\index{constant-ram})\index{memory-properp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  memory-properp-after-write-mem1 \\ \index{memory-properp-after-write-mem1}
\=\+(\=\+{\rm{memory-properp}}\,({\it{n\/}}, {\it{width\/}}, {\it{mem\/}})\index{memory-properp} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{value\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\it{width\/}} $=$ {\rm{length}}\,({\it{value\/}})\index{length}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $=$ {\rm{length}}\,({\it{v-addr\/}})\index{length}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{memory-properp}}\,({\it{n\/}}, {\it{width\/}}, {\rm{write-mem1}}\,({\it{v-addr\/}}, {\it{mem\/}}, {\it{value\/}})\index{write-mem1})\index{memory-properp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  memory-properp-after-write-mem \\ \index{memory-properp-after-write-mem}
\=\+(\=\+{\rm{memory-properp}}\,({\it{n\/}}, {\it{width\/}}, {\it{mem\/}})\index{memory-properp} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{value\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\it{width\/}} $=$ {\rm{length}}\,({\it{value\/}})\index{length}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $=$ {\rm{length}}\,({\it{v-addr\/}})\index{length}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{memory-properp}}\,({\it{n\/}}, {\it{width\/}}, {\rm{write-mem}}\,({\it{v-addr\/}}, {\it{mem\/}}, {\it{value\/}})\index{write-mem})\index{memory-properp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  memory-okp-after-write-mem1 \\ \index{memory-okp-after-write-mem1}
\=\+(\=\+{\rm{memory-okp}}\,({\it{n\/}}, {\it{width\/}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{value\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\it{width\/}} $=$ {\rm{length}}\,({\it{value\/}})\index{length}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $=$ {\rm{length}}\,({\it{v-addr\/}})\index{length}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{memory-okp}}\,({\it{n\/}}, {\it{width\/}}, {\rm{write-mem1}}\,({\it{v-addr\/}}, {\it{mem\/}}, {\it{value\/}})\index{write-mem1})\index{memory-okp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  memory-okp-after-write-mem \\ \index{memory-okp-after-write-mem}
\=\+(\=\+{\rm{memory-okp}}\,({\it{n\/}}, {\it{width\/}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{value\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\it{width\/}} $=$ {\rm{length}}\,({\it{value\/}})\index{length}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $=$ {\rm{length}}\,({\it{v-addr\/}})\index{length}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{memory-okp}}\,({\it{n\/}}, {\it{width\/}}, {\rm{write-mem}}\,({\it{v-addr\/}}, {\it{mem\/}}, {\it{value\/}})\index{write-mem})\index{memory-okp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-iff-v-addr1-v-addr2-read-mem1-write-mem1 \\ \index{v-iff-v-addr1-v-addr2-read-mem1!-write-mem1}
\=\+(\=\+{\rm{v-iff}}\,({\it{v-addr1\/}}, {\it{v-addr2\/}})\index{v-iff} \\ 
$\wedge$$\;\;\;\;${\rm{ramp-mem1}}\,({\it{v-addr2\/}}, {\it{mem\/}})\index{ramp-mem1} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{v-addr1\/}})\index{length} $=$ {\rm{length}}\,({\it{v-addr2\/}})\index{length}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{read-mem1}}\,({\it{v-addr1\/}}, {\rm{write-mem1}}\,({\it{v-addr2\/}}, {\it{mem\/}}, {\it{value\/}})\index{write-mem1})\index{read-mem1} $=$ {\it{value\/}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-iff-v-addr1-v-addr2-read-mem1-write-mem1-not-ram \\ \index{v-iff-v-addr1-v-addr2-read-mem1!-write-mem1-not-ram}
\=\+(($\neg$ {\rm{ramp-mem1}}\,({\it{v-addr2\/}}, {\it{mem\/}})\index{ramp-mem1}) $\wedge$ ({\rm{length}}\,({\it{v-addr1\/}})\index{length} $=$ {\rm{length}}\,({\it{v-addr2\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{read-mem1}}\,({\it{v-addr1\/}}, {\rm{write-mem1}}\,({\it{v-addr2\/}}, {\it{mem\/}}, {\it{value\/}})\index{write-mem1})\index{read-mem1} \\ 
$=$$\;\;\;\;${\rm{read-mem1}}\,({\it{v-addr1\/}}, {\it{mem\/}})\index{read-mem1})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  not-v-iff-v-addr1-v-addr2-read-mem1-write-mem1 \\ \index{not-v-iff-v-addr1-v-addr2-read-!mem1-write-mem1}
\=\+($\neg$ {\rm{v-iff}}\,({\it{v-addr1\/}}, {\it{v-addr2\/}})\index{v-iff}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{read-mem1}}\,({\it{v-addr1\/}}, {\rm{write-mem1}}\,({\it{v-addr2\/}}, {\it{mem\/}}, {\it{value\/}})\index{write-mem1})\index{read-mem1} \\ 
$=$$\;\;\;\;${\rm{read-mem1}}\,({\it{v-addr1\/}}, {\it{mem\/}})\index{read-mem1})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  read-mem-write-mem \\ \index{read-mem-write-mem}
\=\+({\rm{length}}\,({\it{v-addr1\/}})\index{length} $=$ {\rm{length}}\,({\it{v-addr2\/}})\index{length}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{read-mem}}\,({\it{v-addr1\/}}, {\rm{write-mem}}\,({\it{v-addr2\/}}, {\it{mem\/}}, {\it{value\/}})\index{write-mem})\index{read-mem} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{v-iff}}\,({\it{v-addr1\/}}, {\it{v-addr2\/}})\index{v-iff} $\wedge$ {\rm{ramp-mem}}\,({\it{v-addr2\/}}, {\it{mem\/}})\index{ramp-mem} \\ 
{\bf then }{\it{value\/}} \\ 
{\bf else }{\rm{read-mem}}\,({\it{v-addr1\/}}, {\it{mem\/}})\index{read-mem}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-read-mem1 \\ \index{properp-read-mem1}
\=\+{\rm{memory-properp}}\,({\rm{length}}\,({\it{v-addr\/}})\index{length}, {\it{size\/}}, {\it{mem\/}})\index{memory-properp} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{properp}}\,({\rm{read-mem1}}\,({\it{v-addr\/}}, {\it{mem\/}})\index{read-mem1})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{read-mem1}}\,({\it{v-addr\/}}, {\it{mem\/}})\index{read-mem1})\index{length} $=$ {\it{size\/}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-read-mem \\ \index{properp-read-mem}
\=\+{\rm{memory-properp}}\,({\rm{length}}\,({\rm{reverse}}\,({\it{v-addr\/}})\index{reverse})\index{length}, {\it{size\/}}, {\it{mem\/}})\index{memory-properp} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{properp}}\,({\rm{read-mem}}\,({\it{v-addr\/}}, {\it{mem\/}})\index{read-mem})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{read-mem}}\,({\it{v-addr\/}}, {\it{mem\/}})\index{read-mem})\index{length} $=$ {\it{size\/}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-read-mem-32 \\ \index{properp-read-mem-32}
\=\+{\rm{memory-properp}}\,({\rm{length}}\,({\it{v-addr\/}})\index{length}, {\tt{32}}, {\it{mem\/}})\index{memory-properp} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{properp}}\,({\rm{read-mem}}\,({\it{v-addr\/}}, {\it{mem\/}})\index{read-mem})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{read-mem}}\,({\it{v-addr\/}}, {\it{mem\/}})\index{read-mem})\index{length} $=$ {\tt{32}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-read-mem1 \\ \index{bvp-read-mem1}
\=\+{\rm{memory-okp}}\,({\rm{length}}\,({\it{v-addr\/}})\index{length}, {\it{size\/}}, {\it{mem\/}})\index{memory-okp} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{bvp}}\,({\rm{read-mem1}}\,({\it{v-addr\/}}, {\it{mem\/}})\index{read-mem1})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{read-mem1}}\,({\it{v-addr\/}}, {\it{mem\/}})\index{read-mem1})\index{length} $=$ {\it{size\/}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-read-mem \\ \index{bvp-read-mem}
\=\+{\rm{memory-okp}}\,({\rm{length}}\,({\rm{reverse}}\,({\it{v-addr\/}})\index{reverse})\index{length}, {\it{size\/}}, {\it{mem\/}})\index{memory-okp} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{bvp}}\,({\rm{read-mem}}\,({\it{v-addr\/}}, {\it{mem\/}})\index{read-mem})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{read-mem}}\,({\it{v-addr\/}}, {\it{mem\/}})\index{read-mem})\index{length} $=$ {\it{size\/}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-read-mem-32 \\ \index{bvp-read-mem-32}
\=\+{\rm{memory-okp}}\,({\rm{length}}\,({\it{v-addr\/}})\index{length}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\rightarrow$$\;\;\;\;$({\rm{bvp}}\,({\rm{read-mem}}\,({\it{v-addr\/}}, {\it{mem\/}})\index{read-mem})\index{bvp} $\wedge$ ({\rm{length}}\,({\rm{read-mem}}\,({\it{v-addr\/}}, {\it{mem\/}})\index{read-mem})\index{length} $=$ {\tt{32}}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  all-ramp-mem-$>$ramp-mem1 \\ \index{all-ramp-mem-$>$ramp-mem1}
{\rm{all-ramp-mem}}\,({\rm{length}}\,({\it{v-addr\/}})\index{length}, {\it{mem\/}})\index{all-ramp-mem} $\rightarrow$ {\rm{ramp-mem1}}\,({\it{v-addr\/}}, {\it{mem\/}})\index{ramp-mem1}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  all-ramp-mem-$>$ramp-mem \\ \index{all-ramp-mem-$>$ramp-mem}
{\rm{all-ramp-mem}}\,({\rm{length}}\,({\it{v-addr\/}})\index{length}, {\it{mem\/}})\index{all-ramp-mem} $\rightarrow$ {\rm{ramp-mem}}\,({\it{v-addr\/}}, {\it{mem\/}})\index{ramp-mem}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  all-ramp-mem-after-write-mem1 \\ \index{all-ramp-mem-after-write-mem1}
\=\+({\rm{all-ramp-mem}}\,({\it{n\/}}, {\it{mem\/}})\index{all-ramp-mem} $\wedge$ ({\it{n\/}} $=$ {\rm{length}}\,({\it{v-addr\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;${\rm{all-ramp-mem}}\,({\it{n\/}}, {\rm{write-mem1}}\,({\it{v-addr\/}}, {\it{mem\/}}, {\it{value\/}})\index{write-mem1})\index{all-ramp-mem}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  all-ramp-mem-after-write-mem \\ \index{all-ramp-mem-after-write-mem}
\=\+({\rm{all-ramp-mem}}\,({\it{n\/}}, {\it{mem\/}})\index{all-ramp-mem} $\wedge$ ({\it{n\/}} $=$ {\rm{length}}\,({\it{v-addr\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;${\rm{all-ramp-mem}}\,({\it{n\/}}, {\rm{write-mem}}\,({\it{v-addr\/}}, {\it{mem\/}}, {\it{value\/}})\index{write-mem})\index{all-ramp-mem}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  all-ramp-mem-constant-ram \\ \index{all-ramp-mem-constant-ram}
{\rm{all-ramp-mem}}\,({\it{n\/}}, {\rm{constant-ram}}\,({\it{mem\/}}, {\it{value\/}})\index{constant-ram})\index{all-ramp-mem} $=$ {\rm{all-ramp-mem}}\,({\it{n\/}}, {\it{mem\/}})\index{all-ramp-mem}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  memory-okp==$>$memory-properp \\ \index{memory-okp==$>$memory-properp}
{\rm{memory-okp}}\,({\it{n\/}}, {\it{m\/}}, {\it{mem\/}})\index{memory-okp} $\rightarrow$ {\rm{memory-properp}}\,({\it{n\/}}, {\it{m\/}}, {\it{mem\/}})\index{memory-properp}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{dual-port-ram-value} \\  
\=\+{\rm{dual-port-ram-value}}\,({\it{bits\/}}, {\it{address-lines\/}}, {\it{args\/}}, {\it{state\/}})\index{dual-port-ram-value} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+($\neg$ {\rm{bvp}}\,({\rm{subrange}}\,({\it{args\/}}, {\tt{0}}, {\it{address-lines\/}} $-\;1$)\index{subrange})\index{bvp}) \\ 
$\vee$$\;\;\;\;$(\=\+({\rm{nth}}\,({\tt{2}} $*$ {\it{address-lines\/}}, {\it{args\/}})\index{nth} $\not=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{bvp}}\,({\rm{subrange}}\,(\=\+{\it{args\/}}, \\ 
{\it{address-lines\/}}, \\ 
({\tt{2}} $*$ {\it{address-lines\/}}) $-\;1$)\-\index{subrange})\index{bvp}) \\ 
$\vee$$\;\;\;\;$(\=\+{\rm{subrange}}\,({\it{args\/}}, {\tt{0}}, {\it{address-lines\/}} $-\;1$)\index{subrange} \\ 
$=$$\;\;\;\;${\rm{subrange}}\,(\=\+{\it{args\/}}, \\ 
{\it{address-lines\/}}, \\ 
({\tt{2}} $*$ {\it{address-lines\/}}) $-\;1$)\-\index{subrange})\-)\-)\-\- \\ 
{\bf then }{\rm{make-list}}\,({\it{bits\/}}, {\sc{x}}\index{x})\index{make-list} \\ 
{\bf elseif }\=\+{\rm{properp}}\,({\rm{read-mem}}\,({\rm{subrange}}\,({\it{args\/}}, {\tt{0}}, {\it{address-lines\/}} $-\;1$)\index{subrange}, {\it{state\/}})\index{read-mem})\index{properp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{length}}\,({\rm{read-mem}}\,(\=\+{\rm{subrange}}\,({\it{args\/}}, {\tt{0}}, {\it{address-lines\/}} $-\;1$)\index{subrange}, \\ 
{\it{state\/}})\-\index{read-mem})\index{length} \\ 
$=$$\;\;\;\;${\it{bits\/}})\-\- \\ 
{\bf then }{\rm{read-mem}}\,({\rm{subrange}}\,({\it{args\/}}, {\tt{0}}, {\it{address-lines\/}} $-\;1$)\index{subrange}, {\it{state\/}})\index{read-mem} \\ 
{\bf else }{\rm{make-list}}\,({\it{bits\/}}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{dual-port-ram-state} \\  
\=\+{\rm{dual-port-ram-state}}\,({\it{bits\/}}, {\it{address-lines\/}}, {\it{args\/}}, {\it{state\/}})\index{dual-port-ram-state} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{nth}}\,({\tt{2}} $*$ {\it{address-lines\/}}, {\it{args\/}})\index{nth} $=$ {\bf{t}}$\;\;${\bf then }{\it{state\/}} \\ 
{\bf elseif }$\neg$ {\rm{bvp}}\,({\rm{subrange}}\,({\it{args\/}}, {\it{address-lines\/}}, ({\tt{2}} $*$ {\it{address-lines\/}}) $-\;1$)\index{subrange})\index{bvp} \\ 
{\bf then }{\rm{constant-ram}}\,({\it{state\/}}, {\rm{make-list}}\,({\it{bits\/}}, {\sc{x}}\index{x})\index{make-list})\index{constant-ram} \\ 
{\bf elseif }{\rm{nth}}\,({\tt{2}} $*$ {\it{address-lines\/}}, {\it{args\/}})\index{nth} $=$ {\bf{f}} \\ 
{\bf then }{\rm{write-mem}}\,(\=\+{\rm{subrange}}\,({\it{args\/}}, {\it{address-lines\/}}, ({\tt{2}} $*$ {\it{address-lines\/}}) $-\;1$)\index{subrange}, \\ 
{\it{state\/}}, \\ 
{\rm{subrange}}\,(\=\+{\it{args\/}}, \\ 
$1\;+$ ({\tt{2}} $*$ {\it{address-lines\/}}), \\ 
({\tt{2}} $*$ {\it{address-lines\/}}) $+$ {\it{bits\/}})\-\index{subrange})\-\index{write-mem} \\ 
{\bf else }{\rm{write-mem}}\,(\=\+{\rm{subrange}}\,(\=\+{\it{args\/}}, \\ 
{\it{address-lines\/}}, \\ 
({\tt{2}} $*$ {\it{address-lines\/}}) $-\;1$)\-\index{subrange}, \\ 
{\it{state\/}}, \\ 
{\rm{make-list}}\,({\it{bits\/}}, {\sc{x}}\index{x})\index{make-list})\-\index{write-mem}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-length-dual-port-ram-value \\ \index{properp-length-dual-port-ram-va!lue}
\=\+{\rm{properp}}\,({\rm{dual-port-ram-value}}\,({\it{bits\/}}, {\it{address-lines\/}}, {\it{args\/}}, {\it{state\/}})\index{dual-port-ram-value})\index{properp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{length}}\,({\rm{dual-port-ram-value}}\,({\it{bits\/}}, {\it{address-lines\/}}, {\it{args\/}}, {\it{state\/}})\index{dual-port-ram-value})\index{length} \\ 
$=$$\;\;\;\;${\rm{fix}}\,({\it{bits\/}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{next-memory-state} \\  
\=\+{\rm{next-memory-state}}\,({\it{state\/}}, {\it{strobe-\/}}, {\it{rw-\/}}, {\it{address\/}}, {\it{data\/}})\index{next-memory-state} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{boolp}}\,({\it{strobe-\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf case on }{\rm{cadr}}\,({\it{state\/}}): \\ 
{\bf case = }{\tt{0}} \\ 
{\bf then }\=\+{\bf if }{\it{strobe-\/}} \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}}$\;\;${\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf elseif }{\it{rw-\/}} \\ 
{\bf then }\=\+{\bf if }{\rm{cadddddr}}\,({\it{state\/}}) $\wedge$ {\rm{boolp}}\,({\rm{cadddddr}}\,({\it{state\/}}))\index{boolp} \\ 
{\bf then }\=\+{\bf if }\=\+{\rm{bvp}}\,({\it{address\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{caddddddr}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\it{address\/}} $=$ {\rm{caddddddr}}\,({\it{state\/}}))\- \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\tt{1}}, \\ 
{\rm{cdaddr}}\,({\it{state\/}}), \\ 
{\rm{caaddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{caaddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\tt{3}}, \\ 
{\rm{cdaddr}}\,({\it{state\/}}), \\ 
{\rm{caaddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{caaddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,(\=\+{\rm{length}}\,({\it{data\/}})\index{length}, \\ 
{\sc{x}}\index{x})\-\index{make-list}$\;${\bf  endif}\-)\-$\;${\bf  endif}\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-\index{constant-ram}, \\ 
{\tt{3}}, \\ 
{\rm{cdaddr}}\,({\it{state\/}}), \\ 
{\rm{caaddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{caaddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\-$\;${\bf  endif}\- \\ 
{\bf elseif }\=\+($\neg$ {\rm{cadddddr}}\,({\it{state\/}})) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{bvp}}\,({\it{address\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{caddddddr}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\it{address\/}} $=$ {\rm{caddddddr}}\,({\it{state\/}})))\- \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\it{data\/}} $=$ {\rm{cadddddddr}}\,({\it{state\/}}))\- \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\tt{2}}, \\ 
{\rm{cdaddr}}\,({\it{state\/}}), \\ 
{\rm{caaddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{caaddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}}$\;\;${\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,({\rm{car}}\,({\it{state\/}}), {\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{constant-ram}, \\ 
{\tt{3}}, \\ 
{\rm{cdaddr}}\,({\it{state\/}}), \\ 
{\rm{caaddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{caaddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\-$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{1}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\it{strobe-\/}} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-\index{constant-ram}, \\ 
{\tt{0}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\-$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{rw-\/}} \\ 
{\bf then }\=\+{\bf if }\=\+{\rm{bvp}}\,({\it{address\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{caddddddr}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\it{address\/}} $=$ {\rm{caddddddr}}\,({\it{state\/}}))\- \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\tt{1}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\rm{cadddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{cadddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\tt{3}}, \\ 
{\rm{cdaddr}}\,({\it{state\/}}), \\ 
{\rm{caaddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{caaddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\-$\;${\bf  endif}\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,({\rm{car}}\,({\it{state\/}}), {\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{constant-ram}, \\ 
{\tt{3}}, \\ 
{\rm{cdaddr}}\,({\it{state\/}}), \\ 
{\rm{caaddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{caaddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\-$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{2}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\it{strobe-\/}} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,({\rm{car}}\,({\it{state\/}}), {\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{constant-ram}, \\ 
{\tt{0}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf elseif }\=\+(\=\+{\rm{bvp}}\,({\it{address\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{caddddddr}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\it{address\/}} $=$ {\rm{caddddddr}}\,({\it{state\/}})))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{bvp}}\,({\it{data\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\it{data\/}} $=$ {\rm{cadddddddr}}\,({\it{state\/}})))\- \\ 
$\wedge$$\;\;\;\;$({\rm{cadddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$)\- \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{write-mem}}\,({\it{address\/}}, {\rm{car}}\,({\it{state\/}}), {\it{data\/}})\index{write-mem}, \\ 
{\tt{0}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-\index{constant-ram}, \\ 
{\tt{0}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\-$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{rw-\/}} \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,({\rm{car}}\,({\it{state\/}}), {\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{constant-ram}, \\ 
{\tt{3}}, \\ 
{\rm{cdaddr}}\,({\it{state\/}}), \\ 
{\rm{caaddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{caaddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}}$\;\;${\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf elseif }\=\+(\=\+{\rm{bvp}}\,({\it{address\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{caddddddr}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\it{address\/}} $=$ {\rm{caddddddr}}\,({\it{state\/}})))\- \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\it{data\/}} $=$ {\rm{cadddddddr}}\,({\it{state\/}}))\- \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\tt{2}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\rm{cadddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{cadddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}}$\;\;${\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,({\rm{car}}\,({\it{state\/}}), {\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{constant-ram}, \\ 
{\tt{3}}, \\ 
{\rm{cdaddr}}\,({\it{state\/}}), \\ 
{\rm{caaddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{caaddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\-$\;${\bf  endif}\- \\ 
{\bf otherwise }\=\+{\bf if }{\it{strobe-\/}} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-\index{constant-ram}, \\ 
{\tt{0}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,(\=\+{\rm{length}}\,({\it{data\/}})\index{length}, \\ 
{\sc{x}}\index{x})\-\index{make-list}$\;${\bf  endif}\-)\-$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{rw-\/}} \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\tt{3}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\rm{cadddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{cadddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-\index{constant-ram}, \\ 
{\tt{3}}, \\ 
{\rm{cdaddr}}\,({\it{state\/}}), \\ 
{\rm{caaddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{caaddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\-$\;${\bf  endif}\-$\;${\bf  endcase}\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,({\rm{car}}\,({\it{state\/}}), {\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{constant-ram}, \\ 
{\tt{0}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}}$\;\;${\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable next-memory-state; name this event `next-memory-state-off'.\index{next-memory-state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{memory-value} \\  
\=\+{\rm{memory-value}}\,({\it{state\/}}, {\it{strobe-\/}}, {\it{rw-\/}}, {\it{address\/}}, {\it{data\/}})\index{memory-value} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\rm{and*}}\,({\rm{boolp}}\,({\it{strobe-\/}})\index{boolp}, {\rm{boolp}}\,({\it{rw-\/}})\index{boolp})\index{and*}, \\ 
\=\+{\bf case on }{\rm{cadr}}\,({\it{state\/}}): \\ 
{\bf case = }{\tt{0}} \\ 
{\bf then }{\rm{if*}}\,(\=\+{\it{strobe-\/}}, \\ 
{\rm{cons}}\,({\sc{x}}\index{x}, {\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{z}}\index{z})\index{make-list}), \\ 
{\rm{cons}}\,(\=\+{\rm{if*}}\,({\rm{caaddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, {\bf{f}}, {\bf{t}})\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\it{rw-\/}}, \\ 
{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}, \\ 
{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{z}}\index{z})\index{make-list})\-\index{if*})\-)\-\index{if*} \\ 
{\bf case = }{\tt{1}} \\ 
{\bf $\;\;$then }{\rm{if*}}\,(\=\+{\it{strobe-\/}}, \\ 
{\rm{cons}}\,({\sc{x}}\index{x}, {\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{z}}\index{z})\index{make-list}), \\ 
{\rm{if*}}\,(\=\+{\it{rw-\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{and*}}\,(\=\+{\it{address\/}} $=$ {\rm{caddddddr}}\,({\it{state\/}}), \\ 
{\rm{and*}}\,({\rm{bvp}}\,({\it{address\/}})\index{bvp}, {\rm{bvp}}\,({\rm{caddddddr}}\,({\it{state\/}}))\index{bvp})\index{and*})\-\index{and*}, \\ 
{\rm{if*}}\,(\=\+{\rm{cadddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{if*}}\,(\=\+{\rm{caddddr}}\,({\it{state\/}}), \\ 
{\rm{read-mem}}\,({\it{address\/}}, {\rm{car}}\,({\it{state\/}}))\index{read-mem}, \\ 
{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list})\-\index{if*})\-, \\ 
{\rm{cons}}\,({\bf{t}}, {\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}))\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{cadddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}), \\ 
{\rm{cons}}\,({\bf{t}}, {\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}))\-\index{if*})\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{cadddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{z}}\index{z})\index{make-list}), \\ 
{\rm{cons}}\,({\bf{t}}, {\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{z}}\index{z})\index{make-list}))\-\index{if*})\-\index{if*})\-\index{if*} \\ 
{\bf case = }{\tt{2}} \\ 
{\bf $\;\;$then }{\rm{if*}}\,(\=\+{\it{strobe-\/}}, \\ 
{\rm{cons}}\,({\sc{x}}\index{x}, {\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{z}}\index{z})\index{make-list}), \\ 
{\rm{if*}}\,(\=\+{\rm{cadddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{z}}\index{z})\index{make-list}), \\ 
{\rm{cons}}\,({\bf{t}}, {\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{z}}\index{z})\index{make-list}))\-\index{if*})\-\index{if*} \\ 
{\bf otherwise }{\rm{if*}}\,(\=\+{\it{strobe-\/}}, \\ 
{\rm{cons}}\,({\sc{x}}\index{x}, {\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{z}}\index{z})\index{make-list}), \\ 
{\rm{if*}}\,(\=\+{\it{rw-\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{cadddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}), \\ 
{\rm{cons}}\,({\bf{t}}, {\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}))\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{cadddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{z}}\index{z})\index{make-list}), \\ 
{\rm{cons}}\,({\bf{t}}, {\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{z}}\index{z})\index{make-list}))\-\index{if*})\-\index{if*})\-\index{if*}$\;${\bf  endcase}\-, \\ 
{\rm{cons}}\,({\sc{x}}\index{x}, {\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}))\-\index{if*}\-
\end{tabbing}


\noindent{\sc Event}:   Enable memory-value; name this event `memory-value-off'.\index{memory-value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{mem-value} \\  
\=\+{\rm{mem-value}}\,({\it{args\/}}, {\it{state\/}})\index{mem-value} \\ 
$=$$\;\;\;\;${\rm{memory-value}}\,(\=\+{\it{state\/}}, \\ 
{\rm{cadr}}\,({\it{args\/}}), \\ 
{\rm{car}}\,({\it{args\/}}), \\ 
{\rm{subrange}}\,({\it{args\/}}, {\tt{2}}, {\tt{33}})\index{subrange}, \\ 
{\rm{subrange}}\,({\it{args\/}}, {\tt{34}}, {\tt{65}})\index{subrange})\-\index{memory-value}\-
\end{tabbing}


\noindent{\sc Event}:   Enable mem-value; name this event `mem-value-off'.\index{mem-value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{mem-state} \\  
\=\+{\rm{mem-state}}\,({\it{args\/}}, {\it{state\/}})\index{mem-state} \\ 
$=$$\;\;\;\;${\rm{next-memory-state}}\,(\=\+{\it{state\/}}, \\ 
{\rm{cadr}}\,({\it{args\/}}), \\ 
{\rm{car}}\,({\it{args\/}}), \\ 
{\rm{subrange}}\,({\it{args\/}}, {\tt{2}}, {\tt{33}})\index{subrange}, \\ 
{\rm{subrange}}\,({\it{args\/}}, {\tt{34}}, {\tt{65}})\index{subrange})\-\index{next-memory-state}\-
\end{tabbing}


\noindent{\sc Event}:   Enable mem-state; name this event `mem-state-off'.\index{mem-state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  properp-length-memory-value \\ \index{properp-length-memory-value}
\=\+(\=\+{\rm{memory-properp}}\,({\tt{32}}, {\tt{32}}, {\rm{car}}\,({\it{state\/}}))\index{memory-properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{address\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data\/}})\index{length} $=$ {\tt{32}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{properp}}\,({\rm{cdr}}\,({\rm{memory-value}}\,({\it{state\/}}, {\it{strobe\/}}, {\it{rw-\/}}, {\it{address\/}}, {\it{data\/}})\index{memory-value}))\index{properp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{length}}\,({\rm{cdr}}\,({\rm{memory-value}}\,({\it{state\/}}, {\it{strobe\/}}, {\it{rw-\/}}, {\it{address\/}}, {\it{data\/}})\index{memory-value}))\index{length} \\ 
$=$$\;\;\;\;${\tt{32}})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-memory-value \\ \index{equal-memory-value}
\=\+({\rm{length}}\,({\it{data1\/}})\index{length} $=$ {\rm{length}}\,({\it{data2\/}})\index{length}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{memory-value}}\,({\it{state\/}}, {\it{strobe\/}}, {\it{rw-\/}}, {\it{address\/}}, {\it{data1\/}})\index{memory-value} \\ 
$=$$\;\;\;\;${\rm{memory-value}}\,({\it{state\/}}, {\it{strobe\/}}, {\it{rw-\/}}, {\it{address\/}}, {\it{data2\/}})\index{memory-value})\- \\ 
$=$$\;\;\;\;${\bf{t}})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{next-memory-state\$induction} \\  
\=\+{\rm{next-memory-state\$induction}}\,({\it{state\/}}, {\it{strobe-\/}}, {\it{rw-\/}}, {\it{address\/}}, {\it{data\/}})\index{next-memory-state\$induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{boolp}}\,({\it{strobe-\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf case on }{\rm{cadr}}\,({\it{state\/}}): \\ 
{\bf case = }{\tt{0}} \\ 
{\bf then }\=\+{\bf if }{\it{strobe-\/}} \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}}$\;\;${\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf elseif }{\it{rw-\/}} \\ 
{\bf then }\=\+{\bf if }{\rm{cadddddr}}\,({\it{state\/}}) $\wedge$ {\rm{boolp}}\,({\rm{cadddddr}}\,({\it{state\/}}))\index{boolp} \\ 
{\bf then }\=\+{\bf if }\=\+{\rm{bvp}}\,({\it{address\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{caddddddr}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\it{address\/}} $=$ {\rm{caddddddr}}\,({\it{state\/}}))\- \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\tt{1}}, \\ 
{\rm{cdaddr}}\,({\it{state\/}}), \\ 
{\rm{caaddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{caaddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\tt{3}}, \\ 
{\rm{cdaddr}}\,({\it{state\/}}), \\ 
{\rm{caaddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{caaddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,(\=\+{\rm{length}}\,({\it{data\/}})\index{length}, \\ 
{\sc{x}}\index{x})\-\index{make-list}$\;${\bf  endif}\-)\-$\;${\bf  endif}\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-\index{constant-ram}, \\ 
{\tt{3}}, \\ 
{\rm{cdaddr}}\,({\it{state\/}}), \\ 
{\rm{caaddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{caaddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\-$\;${\bf  endif}\- \\ 
{\bf elseif }\=\+($\neg$ {\rm{cadddddr}}\,({\it{state\/}})) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{bvp}}\,({\it{address\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{caddddddr}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\it{address\/}} $=$ {\rm{caddddddr}}\,({\it{state\/}})))\- \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\it{data\/}} $=$ {\rm{cadddddddr}}\,({\it{state\/}}))\- \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\tt{2}}, \\ 
{\rm{cdaddr}}\,({\it{state\/}}), \\ 
{\rm{caaddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{caaddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}}$\;\;${\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,({\rm{car}}\,({\it{state\/}}), {\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{constant-ram}, \\ 
{\tt{3}}, \\ 
{\rm{cdaddr}}\,({\it{state\/}}), \\ 
{\rm{caaddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{caaddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\-$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{1}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\it{strobe-\/}} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-\index{constant-ram}, \\ 
{\tt{0}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\-$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{rw-\/}} \\ 
{\bf then }\=\+{\bf if }\=\+{\rm{bvp}}\,({\it{address\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{caddddddr}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\it{address\/}} $=$ {\rm{caddddddr}}\,({\it{state\/}}))\- \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\tt{1}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\rm{cadddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{cadddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\tt{3}}, \\ 
{\rm{cdaddr}}\,({\it{state\/}}), \\ 
{\rm{caaddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{caaddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\-$\;${\bf  endif}\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,({\rm{car}}\,({\it{state\/}}), {\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{constant-ram}, \\ 
{\tt{3}}, \\ 
{\rm{cdaddr}}\,({\it{state\/}}), \\ 
{\rm{caaddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{caaddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\-$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{2}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\it{strobe-\/}} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,({\rm{car}}\,({\it{state\/}}), {\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{constant-ram}, \\ 
{\tt{0}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf elseif }\=\+(\=\+{\rm{bvp}}\,({\it{address\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{caddddddr}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\it{address\/}} $=$ {\rm{caddddddr}}\,({\it{state\/}})))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{bvp}}\,({\it{data\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\it{data\/}} $=$ {\rm{cadddddddr}}\,({\it{state\/}})))\- \\ 
$\wedge$$\;\;\;\;$({\rm{cadddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$)\- \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{write-mem}}\,({\it{address\/}}, {\rm{car}}\,({\it{state\/}}), {\it{data\/}})\index{write-mem}, \\ 
{\tt{0}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-\index{constant-ram}, \\ 
{\tt{0}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\-$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{rw-\/}} \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,({\rm{car}}\,({\it{state\/}}), {\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{constant-ram}, \\ 
{\tt{3}}, \\ 
{\rm{cdaddr}}\,({\it{state\/}}), \\ 
{\rm{caaddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{caaddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}}$\;\;${\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf elseif }\=\+(\=\+{\rm{bvp}}\,({\it{address\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{caddddddr}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\it{address\/}} $=$ {\rm{caddddddr}}\,({\it{state\/}})))\- \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\it{data\/}} $=$ {\rm{cadddddddr}}\,({\it{state\/}}))\- \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\tt{2}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\rm{cadddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{cadddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}}$\;\;${\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,({\rm{car}}\,({\it{state\/}}), {\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{constant-ram}, \\ 
{\tt{3}}, \\ 
{\rm{cdaddr}}\,({\it{state\/}}), \\ 
{\rm{caaddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{caaddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\-$\;${\bf  endif}\- \\ 
{\bf otherwise }\=\+{\bf if }{\it{strobe-\/}} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-\index{constant-ram}, \\ 
{\tt{0}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,(\=\+{\rm{length}}\,({\it{data\/}})\index{length}, \\ 
{\sc{x}}\index{x})\-\index{make-list}$\;${\bf  endif}\-)\-$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{rw-\/}} \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\tt{3}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\rm{cadddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{cadddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-\index{constant-ram}, \\ 
{\tt{3}}, \\ 
{\rm{cdaddr}}\,({\it{state\/}}), \\ 
{\rm{caaddr}}\,({\it{state\/}}) $-\;1$, \\ 
{\rm{caaddr}}\,({\it{state\/}}) $\simeq {\tt{0}}$, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\-$\;${\bf  endif}\-$\;${\bf  endcase}\- \\ 
{\bf elseif }$\neg$ ({\rm{boolp}}\,({\it{strobe-\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{rw-\/}})\index{boolp}) \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{constant-ram}}\,({\rm{car}}\,({\it{state\/}}), {\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{constant-ram}, \\ 
{\tt{0}}, \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\rm{threefix}}\,({\it{rw-\/}})\index{threefix}, \\ 
{\rm{v-threefix}}\,({\it{address\/}})\index{v-threefix}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{rw-\/}}$\;\;${\bf then }{\rm{v-threefix}}\,({\rm{cadddddddr}}\,({\it{state\/}}))\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{data\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{data\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
{\bf else }{\rm{next-memory-state\$induction}}\,(\=\+{\it{state\/}} $-\;1$, \\ 
{\it{strobe-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{address\/}}, \\ 
{\it{data\/}})\-\index{next-memory-state\$induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-length-next-memory-state \\ \index{properp-length-next-memory-state}
\=\+{\rm{properp}}\,({\rm{next-memory-state}}\,({\it{state\/}}, {\it{strobe-\/}}, {\it{rw-\/}}, {\it{address\/}}, {\it{data\/}})\index{next-memory-state})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{next-memory-state}}\,({\it{state\/}}, {\it{strobe-\/}}, {\it{rw-\/}}, {\it{address\/}}, {\it{data\/}})\index{next-memory-state})\index{length} $=$ {\tt{8}})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fix-breadth-tree-stack} \\  
\=\+{\rm{fix-breadth-tree-stack}}\,({\it{stack\/}}, {\it{n\/}})\index{fix-breadth-tree-stack} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{stack\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{append}}\,({\rm{make-list}}\,({\it{n\/}}, {\bf{f}})\index{make-list}, {\rm{car}}\,({\it{stack\/}})), \\ 
{\rm{fix-breadth-tree-stack}}\,({\rm{cdr}}\,({\it{stack\/}}), {\tt{2}} $*$ {\it{n\/}})\index{fix-breadth-tree-stack})\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{breadth-tree} \\  
\=\+{\rm{breadth-tree}}\,({\it{tree\/}}, {\it{stack\/}}, {\it{n\/}})\index{breadth-tree} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
\=\+{\bf if }{\it{stack\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{make-list}}\,({\it{n\/}}, {\bf{f}})\index{make-list} \\ 
{\bf else }{\rm{car}}\,({\it{stack\/}})$\;${\bf  endif}\-)\-, \\ 
{\rm{fix-breadth-tree-stack}}\,({\rm{cdr}}\,({\it{stack\/}}), {\tt{2}})\index{fix-breadth-tree-stack})\- \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
\=\+{\bf if }{\it{stack\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{make-list}}\,({\it{n\/}}, {\bf{f}})\index{make-list} \\ 
{\bf else }{\rm{car}}\,({\it{stack\/}})$\;${\bf  endif}\-)\-, \\ 
{\rm{breadth-tree}}\,(\=\+{\rm{cdr}}\,({\it{tree\/}}), \\ 
{\rm{breadth-tree}}\,(\=\+{\rm{car}}\,({\it{tree\/}}), \\ 
{\rm{cdr}}\,({\it{stack\/}}), \\ 
{\tt{2}} $*$ {\it{n\/}})\-\index{breadth-tree}, \\ 
$1\;+$ ({\tt{2}} $*$ {\it{n\/}}))\-\index{breadth-tree})\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{collect-breadth-tree} \\  
\=\+{\rm{collect-breadth-tree}}\,({\it{stack\/}}, {\it{n\/}})\index{collect-breadth-tree} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{stack\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf elseif }{\rm{car}}\,({\it{stack\/}}) $=$ {\rm{make-list}}\,({\it{n\/}}, {\bf{t}})\index{make-list} \\ 
{\bf then }{\rm{cons}}\,({\bf{t}}, {\rm{collect-breadth-tree}}\,({\rm{cdr}}\,({\it{stack\/}}), {\tt{2}} $*$ {\it{n\/}})\index{collect-breadth-tree}) \\ 
{\bf else }{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{append}}\,(\=\+{\rm{car}}\,({\it{stack\/}}), \\ 
{\rm{collect-breadth-tree}}\,({\rm{cdr}}\,({\it{stack\/}}), {\tt{2}} $*$ {\it{n\/}})\index{collect-breadth-tree})\-)\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tree-number} \\  
\=\+{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number} \\ 
$=$$\;\;\;\;$(\=\+($1\;+$ {\rm{v-to-nat}}\,({\rm{collect-breadth-tree}}\,({\rm{breadth-tree}}\,({\it{tree\/}}, {\bf{nil}}, {\tt{0}})\index{breadth-tree}, {\tt{1}})\index{collect-breadth-tree})\index{v-to-nat}) \\ 
$\div$$\;\;\;\;${\tt{2}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tree-number; name this event `tree-number-off'.\index{tree-number-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{f-buf}$\;\;$
{\rm{f-buf}}\,({\it{a\/}})\index{f-buf} $=$ {\rm{threefix}}\,({\it{a\/}})\index{threefix}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-and} \\  
\=\+{\rm{f-and}}\,({\it{a\/}}, {\it{b\/}})\index{f-and} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{a\/}} $=$ {\bf{f}}) $\vee$ ({\it{b\/}} $=$ {\bf{f}})$\;\;${\bf then }{\bf{f}} \\ 
{\bf elseif }({\it{a\/}} $=$ {\bf{t}}) $\wedge$ ({\it{b\/}} $=$ {\bf{t}})$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\sc{x}}\index{x}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-and3}$\;\;$
{\rm{f-and3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-and3} $=$ {\rm{f-and}}\,({\it{a\/}}, {\rm{f-and}}\,({\it{b\/}}, {\it{c\/}})\index{f-and})\index{f-and}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-and4}$\;\;$
{\rm{f-and4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-and4} $=$ {\rm{f-and}}\,({\it{a\/}}, {\rm{f-and}}\,({\it{b\/}}, {\rm{f-and}}\,({\it{c\/}}, {\it{d\/}})\index{f-and})\index{f-and})\index{f-and}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-not} \\  
\=\+{\rm{f-not}}\,({\it{a\/}})\index{f-not} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{boolp}}\,({\it{a\/}})\index{boolp}$\;\;${\bf then }$\neg$ {\it{a\/}} \\ 
{\bf else }{\sc{x}}\index{x}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-nand}$\;\;$
{\rm{f-nand}}\,({\it{a\/}}, {\it{b\/}})\index{f-nand} $=$ {\rm{f-not}}\,({\rm{f-and}}\,({\it{a\/}}, {\it{b\/}})\index{f-and})\index{f-not}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-nand3}$\;\;$
{\rm{f-nand3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-nand3} $=$ {\rm{f-not}}\,({\rm{f-and}}\,({\it{a\/}}, {\rm{f-and}}\,({\it{b\/}}, {\it{c\/}})\index{f-and})\index{f-and})\index{f-not}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-nand4} \\  
{\rm{f-nand4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nand4} $=$ {\rm{f-not}}\,({\rm{f-and}}\,({\it{a\/}}, {\rm{f-and}}\,({\it{b\/}}, {\rm{f-and}}\,({\it{c\/}}, {\it{d\/}})\index{f-and})\index{f-and})\index{f-and})\index{f-not}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-nand5} \\  
{\rm{f-nand5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nand5} $=$ {\rm{f-not}}\,({\rm{f-and}}\,({\it{a\/}}, {\rm{f-and}}\,({\it{b\/}}, {\rm{f-and}}\,({\it{c\/}}, {\rm{f-and}}\,({\it{d\/}}, {\it{e\/}})\index{f-and})\index{f-and})\index{f-and})\index{f-and})\index{f-not}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-nand6} \\  
\=\+{\rm{f-nand6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nand6} \\ 
$=$$\;\;\;\;${\rm{f-not}}\,({\rm{f-and}}\,({\it{a\/}}, {\rm{f-and}}\,({\it{b\/}}, {\rm{f-and}}\,({\it{c\/}}, {\rm{f-and}}\,({\it{d\/}}, {\rm{f-and}}\,({\it{e\/}}, {\it{g\/}})\index{f-and})\index{f-and})\index{f-and})\index{f-and})\index{f-and})\index{f-not}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-nand8} \\  
\=\+{\rm{f-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nand8} \\ 
$=$$\;\;\;\;${\rm{f-not}}\,({\rm{f-and}}\,({\it{a\/}}, {\rm{f-and}}\,({\it{b\/}}, {\rm{f-and}}\,({\it{c\/}}, {\rm{f-and}}\,({\it{d\/}}, {\rm{f-and}}\,({\it{e\/}}, {\rm{f-and}}\,({\it{g\/}}, {\rm{f-and}}\,({\it{h\/}}, {\it{i\/}})\index{f-and})\index{f-and})\index{f-and})\index{f-and})\index{f-and})\index{f-and})\index{f-and})\index{f-not}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-or} \\  
\=\+{\rm{f-or}}\,({\it{a\/}}, {\it{b\/}})\index{f-or} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{a\/}} $=$ {\bf{t}}) $\vee$ ({\it{b\/}} $=$ {\bf{t}})$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }({\it{a\/}} $=$ {\bf{f}}) $\wedge$ ({\it{b\/}} $=$ {\bf{f}})$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\sc{x}}\index{x}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-or3}$\;\;$
{\rm{f-or3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-or3} $=$ {\rm{f-or}}\,({\it{a\/}}, {\rm{f-or}}\,({\it{b\/}}, {\it{c\/}})\index{f-or})\index{f-or}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-or4}$\;\;$
{\rm{f-or4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-or4} $=$ {\rm{f-or}}\,({\it{a\/}}, {\rm{f-or}}\,({\it{b\/}}, {\rm{f-or}}\,({\it{c\/}}, {\it{d\/}})\index{f-or})\index{f-or})\index{f-or}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-nor}$\;\;$
{\rm{f-nor}}\,({\it{a\/}}, {\it{b\/}})\index{f-nor} $=$ {\rm{f-not}}\,({\rm{f-or}}\,({\it{a\/}}, {\it{b\/}})\index{f-or})\index{f-not}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-nor3}$\;\;$
{\rm{f-nor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-nor3} $=$ {\rm{f-not}}\,({\rm{f-or}}\,({\it{a\/}}, {\rm{f-or}}\,({\it{b\/}}, {\it{c\/}})\index{f-or})\index{f-or})\index{f-not}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-nor4}$\;\;$
{\rm{f-nor4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nor4} $=$ {\rm{f-not}}\,({\rm{f-or}}\,({\it{a\/}}, {\rm{f-or}}\,({\it{b\/}}, {\rm{f-or}}\,({\it{c\/}}, {\it{d\/}})\index{f-or})\index{f-or})\index{f-or})\index{f-not}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-nor5} \\  
{\rm{f-nor5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nor5} $=$ {\rm{f-not}}\,({\rm{f-or}}\,({\it{a\/}}, {\rm{f-or}}\,({\it{b\/}}, {\rm{f-or}}\,({\it{c\/}}, {\rm{f-or}}\,({\it{d\/}}, {\it{e\/}})\index{f-or})\index{f-or})\index{f-or})\index{f-or})\index{f-not}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-nor6} \\  
{\rm{f-nor6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nor6} $=$ {\rm{f-not}}\,({\rm{f-or}}\,({\it{a\/}}, {\rm{f-or}}\,({\it{b\/}}, {\rm{f-or}}\,({\it{c\/}}, {\rm{f-or}}\,({\it{d\/}}, {\rm{f-or}}\,({\it{e\/}}, {\it{g\/}})\index{f-or})\index{f-or})\index{f-or})\index{f-or})\index{f-or})\index{f-not}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-nor8} \\  
\=\+{\rm{f-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nor8} \\ 
$=$$\;\;\;\;${\rm{f-not}}\,({\rm{f-or}}\,({\it{a\/}}, {\rm{f-or}}\,({\it{b\/}}, {\rm{f-or}}\,({\it{c\/}}, {\rm{f-or}}\,({\it{d\/}}, {\rm{f-or}}\,({\it{e\/}}, {\rm{f-or}}\,({\it{g\/}}, {\rm{f-or}}\,({\it{h\/}}, {\it{i\/}})\index{f-or})\index{f-or})\index{f-or})\index{f-or})\index{f-or})\index{f-or})\index{f-or})\index{f-not}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-xor} \\  
\=\+{\rm{f-xor}}\,({\it{a\/}}, {\it{b\/}})\index{f-xor} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $=$ {\bf{t}}$\;\;${\bf then }{\rm{f-not}}\,({\it{b\/}})\index{f-not} \\ 
{\bf elseif }{\it{a\/}} $=$ {\bf{f}}$\;\;${\bf then }{\rm{threefix}}\,({\it{b\/}})\index{threefix} \\ 
{\bf else }{\sc{x}}\index{x}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-xor3}$\;\;$
{\rm{f-xor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-xor3} $=$ {\rm{f-xor}}\,({\it{a\/}}, {\rm{f-xor}}\,({\it{b\/}}, {\it{c\/}})\index{f-xor})\index{f-xor}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-equv} \\  
\=\+{\rm{f-equv}}\,({\it{a\/}}, {\it{b\/}})\index{f-equv} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $=$ {\bf{t}}$\;\;${\bf then }{\rm{threefix}}\,({\it{b\/}})\index{threefix} \\ 
{\bf elseif }{\it{a\/}} $=$ {\bf{f}}$\;\;${\bf then }{\rm{f-not}}\,({\it{b\/}})\index{f-not} \\ 
{\bf else }{\sc{x}}\index{x}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-equv3}$\;\;$
{\rm{f-equv3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-equv3} $=$ {\rm{f-equv}}\,({\it{a\/}}, {\rm{f-xor}}\,({\it{b\/}}, {\it{c\/}})\index{f-xor})\index{f-equv}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-if} \\  
\=\+{\rm{f-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{f-if} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{c\/}} $=$ {\bf{t}}$\;\;${\bf then }{\rm{threefix}}\,({\it{a\/}})\index{threefix} \\ 
{\bf elseif }{\it{c\/}} $=$ {\bf{f}}$\;\;${\bf then }{\rm{threefix}}\,({\it{b\/}})\index{threefix} \\ 
{\bf else }{\sc{x}}\index{x}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ft-buf} \\  
\=\+{\rm{ft-buf}}\,({\it{c\/}}, {\it{a\/}})\index{ft-buf} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{c\/}} $=$ {\bf{t}}$\;\;${\bf then }{\rm{threefix}}\,({\it{a\/}})\index{threefix} \\ 
{\bf elseif }{\it{c\/}} $=$ {\bf{f}}$\;\;${\bf then }{\sc{z}}\index{z} \\ 
{\bf else }{\sc{x}}\index{x}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ft-wire} \\  
\=\+{\rm{ft-wire}}\,({\it{a\/}}, {\it{b\/}})\index{ft-wire} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $=$ {\it{b\/}}$\;\;${\bf then }{\rm{fourfix}}\,({\it{a\/}})\index{fourfix} \\ 
{\bf elseif }{\it{a\/}} $=$ {\sc{z}}\index{z}$\;\;${\bf then }{\rm{fourfix}}\,({\it{b\/}})\index{fourfix} \\ 
{\bf elseif }{\it{b\/}} $=$ {\sc{z}}\index{z}$\;\;${\bf then }{\rm{fourfix}}\,({\it{a\/}})\index{fourfix} \\ 
{\bf else }{\sc{x}}\index{x}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f-pullup} \\  
\=\+{\rm{f-pullup}}\,({\it{a\/}})\index{f-pullup} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $=$ {\sc{z}}\index{z}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{threefix}}\,({\it{a\/}})\index{threefix}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$ao2}$\;\;$
{\rm{f\$ao2}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f\$ao2} $=$ {\rm{f-nor}}\,({\rm{f-and}}\,({\it{a\/}}, {\it{b\/}})\index{f-and}, {\rm{f-and}}\,({\it{c\/}}, {\it{d\/}})\index{f-and})\index{f-nor}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  expand-f-functions \\ \index{expand-f-functions}
\=\+({\rm{f-buf}}\,({\it{a\/}})\index{f-buf} $=$ {\rm{threefix}}\,({\it{a\/}})\index{threefix}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{f-and}}\,({\it{a\/}}, {\it{b\/}})\index{f-and} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{a\/}} $=$ {\bf{f}}) $\vee$ ({\it{b\/}} $=$ {\bf{f}})$\;\;${\bf then }{\bf{f}} \\ 
{\bf elseif }({\it{a\/}} $=$ {\bf{t}}) $\wedge$ ({\it{b\/}} $=$ {\bf{t}})$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\sc{x}}\index{x}$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{f-and3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-and3} $=$ {\rm{f-and}}\,({\it{a\/}}, {\rm{f-and}}\,({\it{b\/}}, {\it{c\/}})\index{f-and})\index{f-and}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-and4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-and4} $=$ {\rm{f-and}}\,({\it{a\/}}, {\rm{f-and}}\,({\it{b\/}}, {\rm{f-and}}\,({\it{c\/}}, {\it{d\/}})\index{f-and})\index{f-and})\index{f-and}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{f-not}}\,({\it{a\/}})\index{f-not} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{boolp}}\,({\it{a\/}})\index{boolp}$\;\;${\bf then }$\neg$ {\it{a\/}} \\ 
{\bf else }{\sc{x}}\index{x}$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand}}\,({\it{a\/}}, {\it{b\/}})\index{f-nand} $=$ {\rm{f-not}}\,({\rm{f-and}}\,({\it{a\/}}, {\it{b\/}})\index{f-and})\index{f-not}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-nand3} $=$ {\rm{f-not}}\,({\rm{f-and}}\,({\it{a\/}}, {\rm{f-and}}\,({\it{b\/}}, {\it{c\/}})\index{f-and})\index{f-and})\index{f-not}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nand4} $=$ {\rm{f-not}}\,({\rm{f-and}}\,({\it{a\/}}, {\rm{f-and}}\,({\it{b\/}}, {\rm{f-and}}\,({\it{c\/}}, {\it{d\/}})\index{f-and})\index{f-and})\index{f-and})\index{f-not}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{f-or}}\,({\it{a\/}}, {\it{b\/}})\index{f-or} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{a\/}} $=$ {\bf{t}}) $\vee$ ({\it{b\/}} $=$ {\bf{t}})$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }({\it{a\/}} $=$ {\bf{f}}) $\wedge$ ({\it{b\/}} $=$ {\bf{f}})$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\sc{x}}\index{x}$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nand5} $=$ {\rm{f-not}}\,({\rm{f-and}}\,({\it{a\/}}, {\rm{f-and}}\,({\it{b\/}}, {\rm{f-and}}\,({\it{c\/}}, {\rm{f-and}}\,({\it{d\/}}, {\it{e\/}})\index{f-and})\index{f-and})\index{f-and})\index{f-and})\index{f-not}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{f-nand6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nand6} \\ 
$=$$\;\;\;\;${\rm{f-not}}\,({\rm{f-and}}\,({\it{a\/}}, {\rm{f-and}}\,({\it{b\/}}, {\rm{f-and}}\,({\it{c\/}}, {\rm{f-and}}\,({\it{d\/}}, {\rm{f-and}}\,({\it{e\/}}, {\it{g\/}})\index{f-and})\index{f-and})\index{f-and})\index{f-and})\index{f-and})\index{f-not})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{f-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nand8} \\ 
$=$$\;\;\;\;${\rm{f-not}}\,({\rm{f-and}}\,(\=\+{\it{a\/}}, \\ 
{\rm{f-and}}\,(\=\+{\it{b\/}}, \\ 
{\rm{f-and}}\,(\=\+{\it{c\/}}, \\ 
{\rm{f-and}}\,({\it{d\/}}, {\rm{f-and}}\,({\it{e\/}}, {\rm{f-and}}\,({\it{g\/}}, {\rm{f-and}}\,({\it{h\/}}, {\it{i\/}})\index{f-and})\index{f-and})\index{f-and})\index{f-and})\-\index{f-and})\-\index{f-and})\-\index{f-and})\index{f-not})\- \\ 
$\wedge$$\;\;\;\;$({\rm{f-or3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-or3} $=$ {\rm{f-or}}\,({\it{a\/}}, {\rm{f-or}}\,({\it{b\/}}, {\it{c\/}})\index{f-or})\index{f-or}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-or4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-or4} $=$ {\rm{f-or}}\,({\it{a\/}}, {\rm{f-or}}\,({\it{b\/}}, {\rm{f-or}}\,({\it{c\/}}, {\it{d\/}})\index{f-or})\index{f-or})\index{f-or}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor}}\,({\it{a\/}}, {\it{b\/}})\index{f-nor} $=$ {\rm{f-not}}\,({\rm{f-or}}\,({\it{a\/}}, {\it{b\/}})\index{f-or})\index{f-not}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-nor3} $=$ {\rm{f-not}}\,({\rm{f-or}}\,({\it{a\/}}, {\rm{f-or}}\,({\it{b\/}}, {\it{c\/}})\index{f-or})\index{f-or})\index{f-not}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nor4} $=$ {\rm{f-not}}\,({\rm{f-or}}\,({\it{a\/}}, {\rm{f-or}}\,({\it{b\/}}, {\rm{f-or}}\,({\it{c\/}}, {\it{d\/}})\index{f-or})\index{f-or})\index{f-or})\index{f-not}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nor5} $=$ {\rm{f-not}}\,({\rm{f-or}}\,({\it{a\/}}, {\rm{f-or}}\,({\it{b\/}}, {\rm{f-or}}\,({\it{c\/}}, {\rm{f-or}}\,({\it{d\/}}, {\it{e\/}})\index{f-or})\index{f-or})\index{f-or})\index{f-or})\index{f-not}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{f-nor6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nor6} \\ 
$=$$\;\;\;\;${\rm{f-not}}\,({\rm{f-or}}\,({\it{a\/}}, {\rm{f-or}}\,({\it{b\/}}, {\rm{f-or}}\,({\it{c\/}}, {\rm{f-or}}\,({\it{d\/}}, {\rm{f-or}}\,({\it{e\/}}, {\it{g\/}})\index{f-or})\index{f-or})\index{f-or})\index{f-or})\index{f-or})\index{f-not})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{f-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nor8} \\ 
$=$$\;\;\;\;${\rm{f-not}}\,({\rm{f-or}}\,(\=\+{\it{a\/}}, \\ 
{\rm{f-or}}\,({\it{b\/}}, {\rm{f-or}}\,({\it{c\/}}, {\rm{f-or}}\,({\it{d\/}}, {\rm{f-or}}\,({\it{e\/}}, {\rm{f-or}}\,({\it{g\/}}, {\rm{f-or}}\,({\it{h\/}}, {\it{i\/}})\index{f-or})\index{f-or})\index{f-or})\index{f-or})\index{f-or})\index{f-or})\-\index{f-or})\index{f-not})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{f-xor}}\,({\it{a\/}}, {\it{b\/}})\index{f-xor} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $=$ {\bf{t}}$\;\;${\bf then }{\rm{f-not}}\,({\it{b\/}})\index{f-not} \\ 
{\bf elseif }{\it{a\/}} $=$ {\bf{f}}$\;\;${\bf then }{\rm{threefix}}\,({\it{b\/}})\index{threefix} \\ 
{\bf else }{\sc{x}}\index{x}$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{f-xor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-xor3} $=$ {\rm{f-xor}}\,({\it{a\/}}, {\rm{f-xor}}\,({\it{b\/}}, {\it{c\/}})\index{f-xor})\index{f-xor}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{f-equv}}\,({\it{a\/}}, {\it{b\/}})\index{f-equv} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $=$ {\bf{t}}$\;\;${\bf then }{\rm{threefix}}\,({\it{b\/}})\index{threefix} \\ 
{\bf elseif }{\it{a\/}} $=$ {\bf{f}}$\;\;${\bf then }{\rm{f-not}}\,({\it{b\/}})\index{f-not} \\ 
{\bf else }{\sc{x}}\index{x}$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{f-equv3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-equv3} $=$ {\rm{f-equv}}\,({\it{a\/}}, {\rm{f-xor}}\,({\it{b\/}}, {\it{c\/}})\index{f-xor})\index{f-equv}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{f-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{f-if} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{c\/}} $=$ {\bf{t}}$\;\;${\bf then }{\rm{threefix}}\,({\it{a\/}})\index{threefix} \\ 
{\bf elseif }{\it{c\/}} $=$ {\bf{f}}$\;\;${\bf then }{\rm{threefix}}\,({\it{b\/}})\index{threefix} \\ 
{\bf else }{\sc{x}}\index{x}$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{ft-buf}}\,({\it{c\/}}, {\it{a\/}})\index{ft-buf} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{c\/}} $=$ {\bf{t}}$\;\;${\bf then }{\rm{threefix}}\,({\it{a\/}})\index{threefix} \\ 
{\bf elseif }{\it{c\/}} $=$ {\bf{f}}$\;\;${\bf then }{\sc{z}}\index{z} \\ 
{\bf else }{\sc{x}}\index{x}$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{ft-wire}}\,({\it{a\/}}, {\it{b\/}})\index{ft-wire} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $=$ {\it{b\/}}$\;\;${\bf then }{\rm{fourfix}}\,({\it{a\/}})\index{fourfix} \\ 
{\bf elseif }{\it{a\/}} $=$ {\sc{z}}\index{z}$\;\;${\bf then }{\rm{fourfix}}\,({\it{b\/}})\index{fourfix} \\ 
{\bf elseif }{\it{b\/}} $=$ {\sc{z}}\index{z}$\;\;${\bf then }{\rm{fourfix}}\,({\it{a\/}})\index{fourfix} \\ 
{\bf else }{\sc{x}}\index{x}$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{f-pullup}}\,({\it{a\/}})\index{f-pullup} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $=$ {\sc{z}}\index{z}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{threefix}}\,({\it{a\/}})\index{threefix}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable expand-f-functions; name this event `expand-f-functions-off'.\index{expand-f-functions-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f-buf-lemma \\ \index{f-buf-lemma}
{\rm{boolp}}\,({\it{x\/}})\index{boolp} $\rightarrow$ ({\rm{f-buf}}\,({\it{x\/}})\index{f-buf} $=$ {\it{x\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-and-rewrite \\ \index{f-and-rewrite}
\=\+($\neg$ {\rm{f-and}}\,({\bf{f}}, {\it{x\/}})\index{f-and}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{f-and}}\,({\it{x\/}}, {\bf{f}})\index{f-and}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-and}}\,({\it{x\/}}, {\bf{t}})\index{f-and} $=$ {\rm{f-buf}}\,({\it{x\/}})\index{f-buf}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-and}}\,({\bf{t}}, {\it{x\/}})\index{f-and} $=$ {\rm{f-buf}}\,({\it{x\/}})\index{f-buf}) \\ 
$\wedge$$\;\;\;\;$(({\it{x\/}} $\wedge$ {\it{y\/}} $\wedge$ {\rm{boolp}}\,({\it{x\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{y\/}})\index{boolp}) $\rightarrow$ ({\rm{f-and}}\,({\it{x\/}}, {\it{y\/}})\index{f-and} $=$ {\bf{t}}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-or-rewrite \\ \index{f-or-rewrite}
\=\+({\rm{f-or}}\,({\bf{f}}, {\bf{f}})\index{f-or} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$(({\it{x\/}} $\wedge$ {\rm{boolp}}\,({\it{x\/}})\index{boolp}) $\rightarrow$ ({\rm{f-or}}\,({\it{x\/}}, {\it{y\/}})\index{f-or} $=$ {\bf{t}})) \\ 
$\wedge$$\;\;\;\;$(({\it{x\/}} $\wedge$ {\rm{boolp}}\,({\it{x\/}})\index{boolp}) $\rightarrow$ ({\rm{f-or}}\,({\it{y\/}}, {\it{x\/}})\index{f-or} $=$ {\bf{t}}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-not-rewrite \\ \index{f-not-rewrite}
({\rm{f-not}}\,({\bf{t}})\index{f-not} $=$ {\bf{f}}) $\wedge$ ({\rm{f-not}}\,({\bf{f}})\index{f-not} $=$ {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ft-buf-rewrite \\ \index{ft-buf-rewrite}
\=\+({\rm{ft-buf}}\,({\bf{t}}, {\it{x\/}})\index{ft-buf} $=$ {\rm{threefix}}\,({\it{x\/}})\index{threefix}) \\ 
$\wedge$$\;\;\;\;$({\rm{ft-buf}}\,({\bf{f}}, {\it{x\/}})\index{ft-buf} $=$ {\sc{z}}\index{z}) \\ 
$\wedge$$\;\;\;\;$({\rm{ft-buf}}\,({\it{c\/}}, {\rm{threefix}}\,({\it{x\/}})\index{threefix})\index{ft-buf} $=$ {\rm{ft-buf}}\,({\it{c\/}}, {\it{x\/}})\index{ft-buf}) \\ 
$\wedge$$\;\;\;\;$({\rm{ft-buf}}\,({\sc{x}}\index{x}, {\it{x\/}})\index{ft-buf} $=$ {\sc{x}}\index{x})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-if-rewrite \\ \index{f-if-rewrite}
({\rm{f-if}}\,({\bf{t}}, {\it{a\/}}, {\it{b\/}})\index{f-if} $=$ {\rm{f-buf}}\,({\it{a\/}})\index{f-buf}) $\wedge$ ({\rm{f-if}}\,({\bf{f}}, {\it{a\/}}, {\it{b\/}})\index{f-if} $=$ {\rm{f-buf}}\,({\it{b\/}})\index{f-buf})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ft-wire-rewrite \\ \index{ft-wire-rewrite}
\=\+({\rm{ft-wire}}\,({\sc{x}}\index{x}, {\it{x\/}})\index{ft-wire} $=$ {\sc{x}}\index{x}) \\ 
$\wedge$$\;\;\;\;$({\rm{ft-wire}}\,({\it{x\/}}, {\sc{x}}\index{x})\index{ft-wire} $=$ {\sc{x}}\index{x}) \\ 
$\wedge$$\;\;\;\;$({\rm{ft-wire}}\,({\it{x\/}}, {\sc{z}}\index{z})\index{ft-wire} $=$ {\rm{fourfix}}\,({\it{x\/}})\index{fourfix}) \\ 
$\wedge$$\;\;\;\;$({\rm{ft-wire}}\,({\sc{z}}\index{z}, {\it{x\/}})\index{ft-wire} $=$ {\rm{fourfix}}\,({\it{x\/}})\index{fourfix})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-pullup-rewrite \\ \index{f-pullup-rewrite}
\=\+({\rm{f-pullup}}\,({\bf{t}})\index{f-pullup} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-pullup}}\,({\bf{f}})\index{f-pullup} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-pullup}}\,({\sc{x}}\index{x})\index{f-pullup} $=$ {\sc{x}}\index{x}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-pullup}}\,({\sc{z}}\index{z})\index{f-pullup} $=$ {\bf{t}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  threefix-help-lemma \\ \index{threefix-help-lemma}
\=\+({\rm{threefix}}\,({\bf{f}})\index{threefix} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$({\rm{threefix}}\,({\bf{t}})\index{threefix} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{threefix}}\,({\sc{x}}\index{x})\index{threefix} $=$ {\sc{x}}\index{x}) \\ 
$\wedge$$\;\;\;\;$({\rm{threefix}}\,({\rm{f-buf}}\,({\it{x\/}})\index{f-buf})\index{threefix} $=$ {\rm{threefix}}\,({\it{x\/}})\index{threefix}) \\ 
$\wedge$$\;\;\;\;$({\rm{threefix}}\,({\rm{f-not}}\,({\it{x\/}})\index{f-not})\index{threefix} $=$ {\rm{f-not}}\,({\it{x\/}})\index{f-not}) \\ 
$\wedge$$\;\;\;\;$({\rm{threefix}}\,({\rm{f-and}}\,({\it{x\/}}, {\it{y\/}})\index{f-and})\index{threefix} $=$ {\rm{f-and}}\,({\it{x\/}}, {\it{y\/}})\index{f-and}) \\ 
$\wedge$$\;\;\;\;$({\rm{threefix}}\,({\rm{f-or}}\,({\it{x\/}}, {\it{y\/}})\index{f-or})\index{threefix} $=$ {\rm{f-or}}\,({\it{x\/}}, {\it{y\/}})\index{f-or}) \\ 
$\wedge$$\;\;\;\;$({\rm{threefix}}\,({\rm{f-xor}}\,({\it{x\/}}, {\it{y\/}})\index{f-xor})\index{threefix} $=$ {\rm{f-xor}}\,({\it{x\/}}, {\it{y\/}})\index{f-xor}) \\ 
$\wedge$$\;\;\;\;$({\rm{threefix}}\,({\rm{f-equv}}\,({\it{x\/}}, {\it{y\/}})\index{f-equv})\index{threefix} $=$ {\rm{f-equv}}\,({\it{x\/}}, {\it{y\/}})\index{f-equv})\-
\end{tabbing}


\noindent{\sc Event}:   Enable threefix-help-lemma; name this event `threefix-help-lemma-off'.\index{threefix-help-lemma-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f-not-f-not=f-buf \\ \index{f-not-f-not=f-buf}
{\rm{f-not}}\,({\rm{f-not}}\,({\it{x\/}})\index{f-not})\index{f-not} $=$ {\rm{f-buf}}\,({\it{x\/}})\index{f-buf}
\end{tabbing}


\noindent{\sc Event}:   Enable f-not-f-not=f-buf; name this event `f-not-f-not=f-buf-off'.\index{f-not-f-not=f-buf-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f-buf-delete-lemmas \\ \index{f-buf-delete-lemmas}
\=\+({\rm{f-buf}}\,({\rm{f-buf}}\,({\it{a\/}})\index{f-buf})\index{f-buf} $=$ {\rm{f-buf}}\,({\it{a\/}})\index{f-buf}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-not}}\,({\it{a\/}})\index{f-not})\index{f-buf} $=$ {\rm{f-not}}\,({\it{a\/}})\index{f-not}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-nand}}\,({\it{a\/}}, {\it{b\/}})\index{f-nand})\index{f-buf} $=$ {\rm{f-nand}}\,({\it{a\/}}, {\it{b\/}})\index{f-nand}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-nand3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-nand3})\index{f-buf} $=$ {\rm{f-nand3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-nand3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-nand4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nand4})\index{f-buf} $=$ {\rm{f-nand4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nand4}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-nand5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nand5})\index{f-buf} $=$ {\rm{f-nand5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nand5}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-nand6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nand6})\index{f-buf} $=$ {\rm{f-nand6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nand6}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nand8})\index{f-buf} $=$ {\rm{f-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nand8}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-or}}\,({\it{a\/}}, {\it{b\/}})\index{f-or})\index{f-buf} $=$ {\rm{f-or}}\,({\it{a\/}}, {\it{b\/}})\index{f-or}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-or3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-or3})\index{f-buf} $=$ {\rm{f-or3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-or3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-or4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-or4})\index{f-buf} $=$ {\rm{f-or4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-or4}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-xor}}\,({\it{a\/}}, {\it{b\/}})\index{f-xor})\index{f-buf} $=$ {\rm{f-xor}}\,({\it{a\/}}, {\it{b\/}})\index{f-xor}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-xor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-xor3})\index{f-buf} $=$ {\rm{f-xor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-xor3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-equv}}\,({\it{a\/}}, {\it{b\/}})\index{f-equv})\index{f-buf} $=$ {\rm{f-equv}}\,({\it{a\/}}, {\it{b\/}})\index{f-equv}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-equv3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-equv3})\index{f-buf} $=$ {\rm{f-equv3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-equv3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-and}}\,({\it{a\/}}, {\it{b\/}})\index{f-and})\index{f-buf} $=$ {\rm{f-and}}\,({\it{a\/}}, {\it{b\/}})\index{f-and}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-and3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-and3})\index{f-buf} $=$ {\rm{f-and3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-and3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-and4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-and4})\index{f-buf} $=$ {\rm{f-and4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-and4}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-nor}}\,({\it{a\/}}, {\it{b\/}})\index{f-nor})\index{f-buf} $=$ {\rm{f-nor}}\,({\it{a\/}}, {\it{b\/}})\index{f-nor}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-nor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-nor3})\index{f-buf} $=$ {\rm{f-nor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-nor3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-nor4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nor4})\index{f-buf} $=$ {\rm{f-nor4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nor4}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-nor5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nor5})\index{f-buf} $=$ {\rm{f-nor5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nor5}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-nor6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nor6})\index{f-buf} $=$ {\rm{f-nor6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nor6}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nor8})\index{f-buf} $=$ {\rm{f-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nor8}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-buf}}\,({\rm{f-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{f-if})\index{f-buf} $=$ {\rm{f-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{f-if})\-
\end{tabbing}


\noindent{\sc Event}:   Enable f-buf-delete-lemmas; name this event `f-buf-delete-lemmas-off'.\index{f-buf-delete-lemmas-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f-gate-threefix-congruence-lemmas\$help \\ \index{f-gate-threefix-congruence-lemm!as\$help}
\=\+({\rm{f-buf}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix})\index{f-buf} $=$ {\rm{f-buf}}\,({\it{a\/}})\index{f-buf}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-not}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix})\index{f-not} $=$ {\rm{f-not}}\,({\it{a\/}})\index{f-not}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-or}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}})\index{f-or} $=$ {\rm{f-or}}\,({\it{a\/}}, {\it{b\/}})\index{f-or}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-or}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix})\index{f-or} $=$ {\rm{f-or}}\,({\it{a\/}}, {\it{b\/}})\index{f-or}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-xor}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}})\index{f-xor} $=$ {\rm{f-xor}}\,({\it{a\/}}, {\it{b\/}})\index{f-xor}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-xor}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix})\index{f-xor} $=$ {\rm{f-xor}}\,({\it{a\/}}, {\it{b\/}})\index{f-xor}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-equv}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}})\index{f-equv} $=$ {\rm{f-equv}}\,({\it{a\/}}, {\it{b\/}})\index{f-equv}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-equv}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix})\index{f-equv} $=$ {\rm{f-equv}}\,({\it{a\/}}, {\it{b\/}})\index{f-equv}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-and}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}})\index{f-and} $=$ {\rm{f-and}}\,({\it{a\/}}, {\it{b\/}})\index{f-and}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-and}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix})\index{f-and} $=$ {\rm{f-and}}\,({\it{a\/}}, {\it{b\/}})\index{f-and}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-if}}\,({\rm{threefix}}\,({\it{c\/}})\index{threefix}, {\it{a\/}}, {\it{b\/}})\index{f-if} $=$ {\rm{f-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{f-if}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-if}}\,({\it{c\/}}, {\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}})\index{f-if} $=$ {\rm{f-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{f-if}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-if}}\,({\it{c\/}}, {\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix})\index{f-if} $=$ {\rm{f-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{f-if})\-
\end{tabbing}


\noindent{\sc Event}:   Enable f-gate-threefix-congruence-lemmas\$help; name this event `f-gate-threefix-congruence-lemmas\$help-off'.\index{f-gate-threefix-congruence-lemm!as\$help-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f-gate-threefix-congruence-lemmas \\ \index{f-gate-threefix-congruence-lemm!as}
\=\+({\rm{f-buf}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix})\index{f-buf} $=$ {\rm{f-buf}}\,({\it{a\/}})\index{f-buf}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-not}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix})\index{f-not} $=$ {\rm{f-not}}\,({\it{a\/}})\index{f-not}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}})\index{f-nand} $=$ {\rm{f-nand}}\,({\it{a\/}}, {\it{b\/}})\index{f-nand}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix})\index{f-nand} $=$ {\rm{f-nand}}\,({\it{a\/}}, {\it{b\/}})\index{f-nand}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand3}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}}, {\it{c\/}})\index{f-nand3} $=$ {\rm{f-nand3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-nand3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand3}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}})\index{f-nand3} $=$ {\rm{f-nand3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-nand3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand3}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}})\index{f-nand3} $=$ {\rm{f-nand3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-nand3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand4}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nand4} $=$ {\rm{f-nand4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nand4}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand4}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}}, {\it{d\/}})\index{f-nand4} $=$ {\rm{f-nand4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nand4}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand4}}\,({\it{a\/}}, {\it{b\/}}, {\rm{threefix}}\,({\it{c\/}})\index{threefix}, {\it{d\/}})\index{f-nand4} $=$ {\rm{f-nand4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nand4}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\rm{threefix}}\,({\it{d\/}})\index{threefix})\index{f-nand4} $=$ {\rm{f-nand4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nand4}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand5}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nand5} $=$ {\rm{f-nand5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nand5}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand5}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nand5} $=$ {\rm{f-nand5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nand5}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand5}}\,({\it{a\/}}, {\it{b\/}}, {\rm{threefix}}\,({\it{c\/}})\index{threefix}, {\it{d\/}}, {\it{e\/}})\index{f-nand5} $=$ {\rm{f-nand5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nand5}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\rm{threefix}}\,({\it{d\/}})\index{threefix}, {\it{e\/}})\index{f-nand5} $=$ {\rm{f-nand5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nand5}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\rm{threefix}}\,({\it{e\/}})\index{threefix})\index{f-nand5} $=$ {\rm{f-nand5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nand5}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand6}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nand6} $=$ {\rm{f-nand6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nand6}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand6}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nand6} $=$ {\rm{f-nand6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nand6}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand6}}\,({\it{a\/}}, {\it{b\/}}, {\rm{threefix}}\,({\it{c\/}})\index{threefix}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nand6} $=$ {\rm{f-nand6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nand6}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\rm{threefix}}\,({\it{d\/}})\index{threefix}, {\it{e\/}}, {\it{g\/}})\index{f-nand6} $=$ {\rm{f-nand6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nand6}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\rm{threefix}}\,({\it{e\/}})\index{threefix}, {\it{g\/}})\index{f-nand6} $=$ {\rm{f-nand6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nand6}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\rm{threefix}}\,({\it{g\/}})\index{threefix})\index{f-nand6} $=$ {\rm{f-nand6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nand6}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand8}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nand8} $=$ {\rm{f-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nand8}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand8}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nand8} $=$ {\rm{f-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nand8}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\rm{threefix}}\,({\it{c\/}})\index{threefix}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nand8} $=$ {\rm{f-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nand8}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\rm{threefix}}\,({\it{d\/}})\index{threefix}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nand8} $=$ {\rm{f-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nand8}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\rm{threefix}}\,({\it{e\/}})\index{threefix}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nand8} $=$ {\rm{f-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nand8}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\rm{threefix}}\,({\it{g\/}})\index{threefix}, {\it{h\/}}, {\it{i\/}})\index{f-nand8} $=$ {\rm{f-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nand8}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\rm{threefix}}\,({\it{h\/}})\index{threefix}, {\it{i\/}})\index{f-nand8} $=$ {\rm{f-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nand8}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\rm{threefix}}\,({\it{i\/}})\index{threefix})\index{f-nand8} $=$ {\rm{f-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nand8}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-or}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}})\index{f-or} $=$ {\rm{f-or}}\,({\it{a\/}}, {\it{b\/}})\index{f-or}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-or}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix})\index{f-or} $=$ {\rm{f-or}}\,({\it{a\/}}, {\it{b\/}})\index{f-or}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-or3}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}}, {\it{c\/}})\index{f-or3} $=$ {\rm{f-or3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-or3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-or3}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}})\index{f-or3} $=$ {\rm{f-or3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-or3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-or3}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}})\index{f-or3} $=$ {\rm{f-or3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-or3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-or4}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-or4} $=$ {\rm{f-or4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-or4}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-or4}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}}, {\it{d\/}})\index{f-or4} $=$ {\rm{f-or4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-or4}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-or4}}\,({\it{a\/}}, {\it{b\/}}, {\rm{threefix}}\,({\it{c\/}})\index{threefix}, {\it{d\/}})\index{f-or4} $=$ {\rm{f-or4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-or4}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-or4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\rm{threefix}}\,({\it{d\/}})\index{threefix})\index{f-or4} $=$ {\rm{f-or4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-or4}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-xor}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}})\index{f-xor} $=$ {\rm{f-xor}}\,({\it{a\/}}, {\it{b\/}})\index{f-xor}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-xor}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix})\index{f-xor} $=$ {\rm{f-xor}}\,({\it{a\/}}, {\it{b\/}})\index{f-xor}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-xor3}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}}, {\it{c\/}})\index{f-xor3} $=$ {\rm{f-xor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-xor3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-xor3}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}})\index{f-xor3} $=$ {\rm{f-xor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-xor3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-xor3}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}})\index{f-xor3} $=$ {\rm{f-xor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-xor3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-equv}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}})\index{f-equv} $=$ {\rm{f-equv}}\,({\it{a\/}}, {\it{b\/}})\index{f-equv}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-equv}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix})\index{f-equv} $=$ {\rm{f-equv}}\,({\it{a\/}}, {\it{b\/}})\index{f-equv}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-equv3}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}}, {\it{c\/}})\index{f-equv3} $=$ {\rm{f-equv3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-equv3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-equv3}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}})\index{f-equv3} $=$ {\rm{f-equv3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-equv3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-equv3}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}})\index{f-equv3} $=$ {\rm{f-equv3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-equv3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-and}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}})\index{f-and} $=$ {\rm{f-and}}\,({\it{a\/}}, {\it{b\/}})\index{f-and}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-and}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix})\index{f-and} $=$ {\rm{f-and}}\,({\it{a\/}}, {\it{b\/}})\index{f-and}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-and3}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}}, {\it{c\/}})\index{f-and3} $=$ {\rm{f-and3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-and3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-and3}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}})\index{f-and3} $=$ {\rm{f-and3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-and3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-and3}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}})\index{f-and3} $=$ {\rm{f-and3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-and3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-and4}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-and4} $=$ {\rm{f-and4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-and4}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-and4}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}}, {\it{d\/}})\index{f-and4} $=$ {\rm{f-and4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-and4}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-and4}}\,({\it{a\/}}, {\it{b\/}}, {\rm{threefix}}\,({\it{c\/}})\index{threefix}, {\it{d\/}})\index{f-and4} $=$ {\rm{f-and4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-and4}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-and4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\rm{threefix}}\,({\it{d\/}})\index{threefix})\index{f-and4} $=$ {\rm{f-and4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-and4}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}})\index{f-nor} $=$ {\rm{f-nor}}\,({\it{a\/}}, {\it{b\/}})\index{f-nor}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix})\index{f-nor} $=$ {\rm{f-nor}}\,({\it{a\/}}, {\it{b\/}})\index{f-nor}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor3}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}}, {\it{c\/}})\index{f-nor3} $=$ {\rm{f-nor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-nor3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor3}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}})\index{f-nor3} $=$ {\rm{f-nor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-nor3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor3}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}})\index{f-nor3} $=$ {\rm{f-nor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-nor3}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor4}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nor4} $=$ {\rm{f-nor4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nor4}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor4}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}}, {\it{d\/}})\index{f-nor4} $=$ {\rm{f-nor4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nor4}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor4}}\,({\it{a\/}}, {\it{b\/}}, {\rm{threefix}}\,({\it{c\/}})\index{threefix}, {\it{d\/}})\index{f-nor4} $=$ {\rm{f-nor4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nor4}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\rm{threefix}}\,({\it{d\/}})\index{threefix})\index{f-nor4} $=$ {\rm{f-nor4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nor4}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor5}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nor5} $=$ {\rm{f-nor5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nor5}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor5}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nor5} $=$ {\rm{f-nor5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nor5}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor5}}\,({\it{a\/}}, {\it{b\/}}, {\rm{threefix}}\,({\it{c\/}})\index{threefix}, {\it{d\/}}, {\it{e\/}})\index{f-nor5} $=$ {\rm{f-nor5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nor5}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\rm{threefix}}\,({\it{d\/}})\index{threefix}, {\it{e\/}})\index{f-nor5} $=$ {\rm{f-nor5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nor5}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\rm{threefix}}\,({\it{e\/}})\index{threefix})\index{f-nor5} $=$ {\rm{f-nor5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nor5}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor6}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nor6} $=$ {\rm{f-nor6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nor6}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor6}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nor6} $=$ {\rm{f-nor6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nor6}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor6}}\,({\it{a\/}}, {\it{b\/}}, {\rm{threefix}}\,({\it{c\/}})\index{threefix}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nor6} $=$ {\rm{f-nor6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nor6}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\rm{threefix}}\,({\it{d\/}})\index{threefix}, {\it{e\/}}, {\it{g\/}})\index{f-nor6} $=$ {\rm{f-nor6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nor6}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\rm{threefix}}\,({\it{e\/}})\index{threefix}, {\it{g\/}})\index{f-nor6} $=$ {\rm{f-nor6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nor6}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\rm{threefix}}\,({\it{g\/}})\index{threefix})\index{f-nor6} $=$ {\rm{f-nor6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nor6}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor8}}\,({\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nor8} $=$ {\rm{f-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nor8}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor8}}\,({\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nor8} $=$ {\rm{f-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nor8}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\rm{threefix}}\,({\it{c\/}})\index{threefix}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nor8} $=$ {\rm{f-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nor8}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\rm{threefix}}\,({\it{d\/}})\index{threefix}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nor8} $=$ {\rm{f-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nor8}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\rm{threefix}}\,({\it{e\/}})\index{threefix}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nor8} $=$ {\rm{f-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nor8}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\rm{threefix}}\,({\it{g\/}})\index{threefix}, {\it{h\/}}, {\it{i\/}})\index{f-nor8} $=$ {\rm{f-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nor8}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\rm{threefix}}\,({\it{h\/}})\index{threefix}, {\it{i\/}})\index{f-nor8} $=$ {\rm{f-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nor8}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\rm{threefix}}\,({\it{i\/}})\index{threefix})\index{f-nor8} $=$ {\rm{f-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nor8}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-if}}\,({\rm{threefix}}\,({\it{c\/}})\index{threefix}, {\it{a\/}}, {\it{b\/}})\index{f-if} $=$ {\rm{f-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{f-if}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-if}}\,({\it{c\/}}, {\rm{threefix}}\,({\it{a\/}})\index{threefix}, {\it{b\/}})\index{f-if} $=$ {\rm{f-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{f-if}) \\ 
$\wedge$$\;\;\;\;$({\rm{f-if}}\,({\it{c\/}}, {\it{a\/}}, {\rm{threefix}}\,({\it{b\/}})\index{threefix})\index{f-if} $=$ {\rm{f-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{f-if})\-
\end{tabbing}


\noindent{\sc Event}:   Enable f-gate-threefix-congruence-lemmas; name this event `f-gate-threefix-congruence-lemmas-off'.\index{f-gate-threefix-congruence-lemm!as-off}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{f-gates}} to consist of the following events: f-buf,
f-not,
f-nand,
f-nand3,
f-nand4,
f-nand5,
f-nand6,
f-nand8,
f-or,
f-or3,
f-or4,
f-xor,
f-xor3,
f-equv,
f-equv3,
f-and,
f-and3,
f-and4,
f-nor,
f-nor3,
f-nor4,
f-nor5,
f-nor6,
f-nor8,
f-if,
ft-buf,
ft-wire,
f-pullup.\index{f-gates}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f-gates=b-gates \\ \index{f-gates=b-gates}
\=\+({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\rightarrow$ ({\rm{f-buf}}\,({\it{a\/}})\index{f-buf} $=$ {\rm{b-buf}}\,({\it{a\/}})\index{b-buf})) \\ 
$\wedge$$\;\;\;\;$({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\rightarrow$ ({\rm{f-not}}\,({\it{a\/}})\index{f-not} $=$ {\rm{b-not}}\,({\it{a\/}})\index{b-not})) \\ 
$\wedge$$\;\;\;\;$(({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp}) $\rightarrow$ ({\rm{f-nand}}\,({\it{a\/}}, {\it{b\/}})\index{f-nand} $=$ {\rm{b-nand}}\,({\it{a\/}}, {\it{b\/}})\index{b-nand})) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f-nand3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-nand3} $=$ {\rm{b-nand3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{b-nand3}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{d\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f-nand4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nand4} $=$ {\rm{b-nand4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{b-nand4}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{d\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{e\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f-nand5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nand5} $=$ {\rm{b-nand5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{b-nand5}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{boolp}}\,({\it{a\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{b\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{c\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{d\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{e\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{g\/}})\index{boolp})\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{f-nand6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nand6} $=$ {\rm{b-nand6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{b-nand6}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{boolp}}\,({\it{a\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{b\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{c\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{d\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{e\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{g\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{h\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{i\/}})\index{boolp})\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{f-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nand8} $=$ {\rm{b-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{b-nand8}))\- \\ 
$\wedge$$\;\;\;\;$(({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp}) $\rightarrow$ ({\rm{f-or}}\,({\it{a\/}}, {\it{b\/}})\index{f-or} $=$ {\rm{b-or}}\,({\it{a\/}}, {\it{b\/}})\index{b-or})) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f-or3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-or3} $=$ {\rm{b-or3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{b-or3}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{d\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f-or4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-or4} $=$ {\rm{b-or4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{b-or4}))\- \\ 
$\wedge$$\;\;\;\;$(({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp}) $\rightarrow$ ({\rm{f-xor}}\,({\it{a\/}}, {\it{b\/}})\index{f-xor} $=$ {\rm{b-xor}}\,({\it{a\/}}, {\it{b\/}})\index{b-xor})) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f-xor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-xor3} $=$ {\rm{b-xor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{b-xor3}))\- \\ 
$\wedge$$\;\;\;\;$(({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp}) $\rightarrow$ ({\rm{f-equv}}\,({\it{a\/}}, {\it{b\/}})\index{f-equv} $=$ {\rm{b-equv}}\,({\it{a\/}}, {\it{b\/}})\index{b-equv})) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f-equv3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-equv3} $=$ {\rm{b-equv3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{b-equv3}))\- \\ 
$\wedge$$\;\;\;\;$(({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp}) $\rightarrow$ ({\rm{f-and}}\,({\it{a\/}}, {\it{b\/}})\index{f-and} $=$ {\rm{b-and}}\,({\it{a\/}}, {\it{b\/}})\index{b-and})) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f-and3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-and3} $=$ {\rm{b-and3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{b-and3}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{d\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f-and4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-and4} $=$ {\rm{b-and4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{b-and4}))\- \\ 
$\wedge$$\;\;\;\;$(({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp}) $\rightarrow$ ({\rm{f-nor}}\,({\it{a\/}}, {\it{b\/}})\index{f-nor} $=$ {\rm{b-nor}}\,({\it{a\/}}, {\it{b\/}})\index{b-nor})) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f-nor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-nor3} $=$ {\rm{b-nor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{b-nor3}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{d\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f-nor4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nor4} $=$ {\rm{b-nor4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{b-nor4}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{d\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{e\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f-nor5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nor5} $=$ {\rm{b-nor5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{b-nor5}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{boolp}}\,({\it{a\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{b\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{c\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{d\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{e\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{g\/}})\index{boolp})\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{f-nor6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nor6} $=$ {\rm{b-nor6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{b-nor6}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{boolp}}\,({\it{a\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{b\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{c\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{d\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{e\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{g\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{h\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{i\/}})\index{boolp})\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{f-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nor8} $=$ {\rm{b-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{b-nor8}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{boolp}}\,({\it{c\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{f-if} $=$ {\rm{b-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{b-if}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fv-or} \\  
\=\+{\rm{fv-or}}\,({\it{a\/}}, {\it{b\/}})\index{fv-or} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{f-or}}\,({\rm{car}}\,({\it{a\/}}), {\rm{car}}\,({\it{b\/}}))\index{f-or}, {\rm{fv-or}}\,({\rm{cdr}}\,({\it{a\/}}), {\rm{cdr}}\,({\it{b\/}}))\index{fv-or})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fv-or; name this event `fv-or-off'.\index{fv-or-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  properp-length-fv-or \\ \index{properp-length-fv-or}
{\rm{properp}}\,({\rm{fv-or}}\,({\it{a\/}}, {\it{b\/}})\index{fv-or})\index{properp} $\wedge$ ({\rm{length}}\,({\rm{fv-or}}\,({\it{a\/}}, {\it{b\/}})\index{fv-or})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fv-or=v-or \\ \index{fv-or=v-or}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ {\rm{bvp}}\,({\it{b\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{length}}\,({\it{b\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{fv-or}}\,({\it{a\/}}, {\it{b\/}})\index{fv-or} $=$ {\rm{v-or}}\,({\it{a\/}}, {\it{b\/}})\index{v-or})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fv-xor} \\  
\=\+{\rm{fv-xor}}\,({\it{a\/}}, {\it{b\/}})\index{fv-xor} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{f-xor}}\,({\rm{car}}\,({\it{a\/}}), {\rm{car}}\,({\it{b\/}}))\index{f-xor}, {\rm{fv-xor}}\,({\rm{cdr}}\,({\it{a\/}}), {\rm{cdr}}\,({\it{b\/}}))\index{fv-xor})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fv-xor; name this event `fv-xor-off'.\index{fv-xor-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  properp-length-fv-xor \\ \index{properp-length-fv-xor}
{\rm{properp}}\,({\rm{fv-xor}}\,({\it{a\/}}, {\it{b\/}})\index{fv-xor})\index{properp} $\wedge$ ({\rm{length}}\,({\rm{fv-xor}}\,({\it{a\/}}, {\it{b\/}})\index{fv-xor})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fv-xor=v-xor \\ \index{fv-xor=v-xor}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ {\rm{bvp}}\,({\it{b\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{length}}\,({\it{b\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{fv-xor}}\,({\it{a\/}}, {\it{b\/}})\index{fv-xor} $=$ {\rm{v-xor}}\,({\it{a\/}}, {\it{b\/}})\index{v-xor})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fv-if} \\  
\=\+{\rm{fv-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{fv-if} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{f-if}}\,({\it{c\/}}, {\rm{car}}\,({\it{a\/}}), {\rm{car}}\,({\it{b\/}}))\index{f-if}, {\rm{fv-if}}\,({\it{c\/}}, {\rm{cdr}}\,({\it{a\/}}), {\rm{cdr}}\,({\it{b\/}}))\index{fv-if})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fv-if; name this event `fv-if-off'.\index{fv-if-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-fv-if \\ \index{length-fv-if}
{\rm{length}}\,({\rm{fv-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{fv-if})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-fv-if \\ \index{properp-fv-if}
{\rm{properp}}\,({\rm{fv-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{fv-if})\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-threefix-fv-if \\ \index{v-threefix-fv-if}
{\rm{v-threefix}}\,({\rm{fv-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{fv-if})\index{v-threefix} $=$ {\rm{fv-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{fv-if}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fv-if-when-boolp-c \\ \index{fv-if-when-boolp-c}
\=\+({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{length}}\,({\it{b\/}})\index{length}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{fv-if}}\,({\bf{t}}, {\it{a\/}}, {\it{b\/}})\index{fv-if} $=$ {\rm{v-threefix}}\,({\it{a\/}})\index{v-threefix}) \\ 
$\wedge$$\;\;\;\;$({\rm{fv-if}}\,({\bf{f}}, {\it{a\/}}, {\it{b\/}})\index{fv-if} $=$ {\rm{v-threefix}}\,({\it{b\/}})\index{v-threefix}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fv-if-when-bvp \\ \index{fv-if-when-bvp}
\=\+({\rm{boolp}}\,({\it{c\/}})\index{boolp} $\wedge$ {\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ {\rm{bvp}}\,({\it{b\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{length}}\,({\it{b\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{fv-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{fv-if} $=$ {\rm{if*}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{if*})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fv-if-rewrite \\ \index{fv-if-rewrite}
\=\+({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{length}}\,({\it{b\/}})\index{length}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{fv-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{fv-if} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{boolp}}\,({\it{c\/}})\index{boolp} \\ 
{\bf then }\=\+{\bf if }{\it{c\/}}$\;\;${\bf then }{\rm{v-threefix}}\,({\it{a\/}})\index{v-threefix} \\ 
{\bf else }{\rm{v-threefix}}\,({\it{b\/}})\index{v-threefix}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{a\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fv-if-rewrite; name this event `fv-if-rewrite-off'.\index{fv-if-rewrite-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  fv-if-v-threefix \\ \index{fv-if-v-threefix}
\=\+({\rm{fv-if}}\,({\it{c\/}}, {\rm{v-threefix}}\,({\it{a\/}})\index{v-threefix}, {\it{b\/}})\index{fv-if} $=$ {\rm{fv-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{fv-if}) \\ 
$\wedge$$\;\;\;\;$({\rm{fv-if}}\,({\it{c\/}}, {\it{a\/}}, {\rm{v-threefix}}\,({\it{b\/}})\index{v-threefix})\index{fv-if} $=$ {\rm{fv-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{fv-if})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-wire} \\  
\=\+{\rm{v-wire}}\,({\it{a\/}}, {\it{b\/}})\index{v-wire} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{ft-wire}}\,({\rm{car}}\,({\it{a\/}}), {\rm{car}}\,({\it{b\/}}))\index{ft-wire}, {\rm{v-wire}}\,({\rm{cdr}}\,({\it{a\/}}), {\rm{cdr}}\,({\it{b\/}}))\index{v-wire})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-wire; name this event `v-wire-off'.\index{v-wire-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-wire-x-x=x \\ \index{v-wire-x-x=x}
{\rm{v-wire}}\,({\it{x\/}}, {\it{x\/}})\index{v-wire} $=$ {\rm{v-fourfix}}\,({\it{x\/}})\index{v-fourfix}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-wire-make-list-z \\ \index{v-wire-make-list-z}
\=\+({\rm{length}}\,({\it{v\/}})\index{length} $=$ {\it{n\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{v-wire}}\,({\rm{make-list}}\,({\it{n\/}}, {\sc{z}}\index{z})\index{make-list}, {\it{v\/}})\index{v-wire} $=$ {\rm{v-fourfix}}\,({\it{v\/}})\index{v-fourfix}) \\ 
$\wedge$$\;\;\;\;$({\rm{v-wire}}\,({\it{v\/}}, {\rm{make-list}}\,({\it{n\/}}, {\sc{z}}\index{z})\index{make-list})\index{v-wire} $=$ {\rm{v-fourfix}}\,({\it{v\/}})\index{v-fourfix}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-length-v-wire \\ \index{properp-length-v-wire}
{\rm{properp}}\,({\rm{v-wire}}\,({\it{a\/}}, {\it{b\/}})\index{v-wire})\index{properp} $\wedge$ ({\rm{length}}\,({\rm{v-wire}}\,({\it{a\/}}, {\it{b\/}})\index{v-wire})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-wire-make-list-x \\ \index{v-wire-make-list-x}
({\it{n\/}} $=$ {\rm{length}}\,({\it{x\/}})\index{length}) $\rightarrow$ ({\rm{v-wire}}\,({\it{x\/}}, {\rm{make-list}}\,({\it{n\/}}, {\sc{x}}\index{x})\index{make-list})\index{v-wire} $=$ {\rm{make-list}}\,({\it{n\/}}, {\sc{x}}\index{x})\index{make-list})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-pullup} \\  
\=\+{\rm{v-pullup}}\,({\it{v\/}})\index{v-pullup} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{v\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{f-pullup}}\,({\rm{car}}\,({\it{v\/}}))\index{f-pullup}, {\rm{v-pullup}}\,({\rm{cdr}}\,({\it{v\/}}))\index{v-pullup})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-pullup; name this event `v-pullup-off'.\index{v-pullup-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  properp-length-v-pullup \\ \index{properp-length-v-pullup}
{\rm{properp}}\,({\rm{v-pullup}}\,({\it{v\/}})\index{v-pullup})\index{properp} $\wedge$ ({\rm{length}}\,({\rm{v-pullup}}\,({\it{v\/}})\index{v-pullup})\index{length} $=$ {\rm{length}}\,({\it{v\/}})\index{length})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-pullup-bvp \\ \index{v-pullup-bvp}
{\rm{bvp}}\,({\it{v\/}})\index{bvp} $\rightarrow$ ({\rm{v-pullup}}\,({\it{v\/}})\index{v-pullup} $=$ {\it{v\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-pullup-make-list-z \\ \index{v-pullup-make-list-z}
{\rm{v-pullup}}\,({\rm{make-list}}\,({\it{n\/}}, {\sc{z}}\index{z})\index{make-list})\index{v-pullup} $=$ {\rm{make-list}}\,({\it{n\/}}, {\bf{t}})\index{make-list}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fv-shift-right} \\  
\=\+{\rm{fv-shift-right}}\,({\it{a\/}}, {\it{si\/}})\index{fv-shift-right} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{append}}\,({\rm{v-threefix}}\,({\rm{cdr}}\,({\it{a\/}}))\index{v-threefix}, {\rm{list}}\,({\rm{threefix}}\,({\it{si\/}})\index{threefix}))$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fv-shift-right; name this event `fv-shift-right-off'.\index{fv-shift-right-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  fv-shift-right=v-shift-right \\ \index{fv-shift-right=v-shift-right}
({\rm{boolp}}\,({\it{si\/}})\index{boolp} $\wedge$ {\rm{bvp}}\,({\it{a\/}})\index{bvp}) $\rightarrow$ ({\rm{fv-shift-right}}\,({\it{a\/}}, {\it{si\/}})\index{fv-shift-right} $=$ {\rm{v-shift-right}}\,({\it{a\/}}, {\it{si\/}})\index{v-shift-right})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-length-fv-shift-right \\ \index{properp-length-fv-shift-right}
\=\+{\rm{properp}}\,({\rm{fv-shift-right}}\,({\it{a\/}}, {\it{si\/}})\index{fv-shift-right})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{fv-shift-right}}\,({\it{a\/}}, {\it{si\/}})\index{fv-shift-right})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-threefix-fv-shift-right \\ \index{v-threefix-fv-shift-right}
{\rm{v-threefix}}\,({\rm{fv-shift-right}}\,({\it{a\/}}, {\it{si\/}})\index{fv-shift-right})\index{v-threefix} $=$ {\rm{fv-shift-right}}\,({\it{a\/}}, {\it{si\/}})\index{fv-shift-right}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{vft-buf} \\  
\=\+{\rm{vft-buf}}\,({\it{c\/}}, {\it{a\/}})\index{vft-buf} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{ft-buf}}\,({\it{c\/}}, {\rm{car}}\,({\it{a\/}}))\index{ft-buf}, {\rm{vft-buf}}\,({\it{c\/}}, {\rm{cdr}}\,({\it{a\/}}))\index{vft-buf})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable vft-buf; name this event `vft-buf-off'.\index{vft-buf-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  properp-length-vft-buf \\ \index{properp-length-vft-buf}
{\rm{properp}}\,({\rm{vft-buf}}\,({\it{c\/}}, {\it{a\/}})\index{vft-buf})\index{properp} $\wedge$ ({\rm{length}}\,({\rm{vft-buf}}\,({\it{c\/}}, {\it{a\/}})\index{vft-buf})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  vft-buf-lemmas \\ \index{vft-buf-lemmas}
\=\+({\rm{vft-buf}}\,({\bf{t}}, {\it{a\/}})\index{vft-buf} $=$ {\rm{v-threefix}}\,({\it{a\/}})\index{v-threefix}) \\ 
$\wedge$$\;\;\;\;$({\rm{vft-buf}}\,({\bf{f}}, {\it{a\/}})\index{vft-buf} $=$ {\rm{make-list}}\,({\rm{length}}\,({\it{a\/}})\index{length}, {\sc{z}}\index{z})\index{make-list})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  vft-buf-rewrite \\ \index{vft-buf-rewrite}
\=\+{\rm{vft-buf}}\,({\it{c\/}}, {\it{a\/}})\index{vft-buf} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{c\/}} $=$ {\bf{t}}$\;\;${\bf then }{\rm{v-threefix}}\,({\it{a\/}})\index{v-threefix} \\ 
{\bf elseif }{\it{c\/}} $=$ {\bf{f}}$\;\;${\bf then }{\rm{make-list}}\,({\rm{length}}\,({\it{a\/}})\index{length}, {\sc{z}}\index{z})\index{make-list} \\ 
{\bf else }{\rm{make-list}}\,({\rm{length}}\,({\it{a\/}})\index{length}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable vft-buf-rewrite; name this event `vft-buf-rewrite-off'.\index{vft-buf-rewrite-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN PRIMP-DATABASE NIL
 (LIST
 '(AO2 (DELAYS ((263 737) (83 392)))
       (DRIVES 10)
       (INPUT-TYPES BOOLP BOOLP BOOLP BOOLP)
       (INPUTS A B C D)
       (LOADINGS 1 1 1 1)
       (LSI-NAME . AO2)
       (OUT-DEPENDS (A B C D))
       (OUTPUT-TYPES BOOLP)
       (OUTPUTS Z)
       (RESULTS CONS
                (F-NOR (F-AND A B) (F-AND C D))
                'NIL)
       (GATES . 2)
       (PRIMITIVES . 1)
       (TRANSISTORS . 8))
 '(AO4 (DELAYS ((260 895) (82 311)))
       (DRIVES 10)
       (INPUT-TYPES BOOLP BOOLP BOOLP BOOLP)
       (INPUTS A B C D)
       (LOADINGS 1 1 1 1)
       (LSI-NAME . AO4)
       (OUT-DEPENDS (A B C D))
       (OUTPUT-TYPES BOOLP)
       (OUTPUTS Z)
       (RESULTS CONS
                (F-NAND (F-OR A B) (F-OR C D))
                'NIL)
       (GATES . 2)
       (PRIMITIVES . 1)
       (TRANSISTORS . 8))
 '(AO6 (DELAYS ((260 745) (82 202)))
       (DRIVES 10)
       (INPUT-TYPES BOOLP BOOLP BOOLP)
       (INPUTS A B C)
       (LOADINGS 1 1 1)
       (LSI-NAME . AO6)
       (OUT-DEPENDS (A B C))
       (OUTPUT-TYPES BOOLP)
       (OUTPUTS Z)
       (RESULTS CONS
                (F-NOR (F-AND A B) C)
                'NIL)
       (GATES . 2)
       (PRIMITIVES . 1)
       (TRANSISTORS . 6))
 '(AO7 (DELAYS ((261 486) (83 293)))
       (DRIVES 10)
       (INPUT-TYPES BOOLP BOOLP BOOLP)
       (INPUTS A B C)
       (LOADINGS 1 1 1)
       (LSI-NAME . AO7)
       (OUT-DEPENDS (A B C))
       (OUTPUT-TYPES BOOLP)
       (OUTPUTS Z)
       (RESULTS CONS
                (F-NAND (F-OR A B) C)
                'NIL)
       (GATES . 2)
       (PRIMITIVES . 1)
       (TRANSISTORS . 6))
 '(B-AND (DELAYS ((144 422) (54 707)))
         (DRIVES 10)
         (INPUT-TYPES BOOLP BOOLP)
         (INPUTS A B)
         (LOADINGS 1 1)
         (LSI-NAME . AN2)
         (OUT-DEPENDS (A B))
         (OUTPUT-TYPES BOOLP)
         (OUTPUTS Z)
         (RESULTS CONS (F-AND A B) 'NIL)
         (GATES . 2)
         (PRIMITIVES . 1)
         (TRANSISTORS . 6))
 '(B-AND3 (DELAYS ((146 663) (58 809)))
          (DRIVES 10)
          (INPUT-TYPES BOOLP BOOLP BOOLP)
          (INPUTS A B C)
          (LOADINGS 1 1 1)
          (LSI-NAME . AN3)
          (OUT-DEPENDS (A B C))
          (OUTPUT-TYPES BOOLP)
          (OUTPUTS Z)
          (RESULTS CONS (F-AND3 A B C) 'NIL)
          (GATES . 2)
          (PRIMITIVES . 1)
          (TRANSISTORS . 8))
 '(B-AND4 (DELAYS ((149 934) (60 870)))
          (DRIVES 10)
          (INPUT-TYPES BOOLP BOOLP BOOLP BOOLP)
          (INPUTS A B C D)
          (LOADINGS 1 1 1 1)
          (LSI-NAME . AN4)
          (OUT-DEPENDS (A B C D))
          (OUTPUT-TYPES BOOLP)
          (OUTPUTS Z)
          (RESULTS CONS (F-AND4 A B C D) 'NIL)
          (GATES . 3)
          (PRIMITIVES . 1)
          (TRANSISTORS . 10))
 '(B-EQUV (DELAYS ((145 742) (67 973)))
          (DRIVES 10)
          (INPUT-TYPES BOOLP BOOLP)
          (INPUTS A B)
          (LOADINGS 1 2)
          (LSI-NAME . EN)
          (OUT-DEPENDS (A B))
          (OUTPUT-TYPES BOOLP)
          (OUTPUTS Z)
          (RESULTS CONS (F-EQUV A B) 'NIL)
          (GATES . 3)
          (PRIMITIVES . 1)
          (TRANSISTORS . 12))
 '(B-EQUV3 (DELAYS ((151 1806) (79 1580)))
           (DRIVES 10)
           (INPUT-TYPES BOOLP BOOLP BOOLP)
           (INPUTS A B C)
           (LOADINGS 1 3 2)
           (LSI-NAME . EN3)
           (OUT-DEPENDS (A B C))
           (OUTPUT-TYPES BOOLP)
           (OUTPUTS Z)
           (RESULTS CONS (F-EQUV3 A B C) 'NIL)
           (GATES . 7)
           (PRIMITIVES . 1)
           (TRANSISTORS . 22))
 '(B-IF (DELAYS ((70 775) (60 1040)))
        (DRIVES 10)
        (INPUT-TYPES BOOLP BOOLP BOOLP)
        (INPUTS S A B)
        (LOADINGS 2 1 1)
        (LSI-NAME MUX21H B A S)
        (OUT-DEPENDS (A B S))
        (OUTPUT-TYPES BOOLP)
        (OUTPUTS Z)
        (RESULTS CONS (F-IF S A B) 'NIL)
        (GATES . 4)
        (PRIMITIVES . 1)
        (TRANSISTORS . 12))
 '(B-NAND (DELAYS ((141 420) (82 161)))
          (DRIVES 10)
          (INPUT-TYPES BOOLP BOOLP)
          (INPUTS A B)
          (LOADINGS 1 1)
          (LSI-NAME . ND2)
          (OUT-DEPENDS (A B))
          (OUTPUT-TYPES BOOLP)
          (OUTPUTS Z)
          (RESULTS CONS (F-NAND A B) 'NIL)
          (GATES . 1)
          (PRIMITIVES . 1)
          (TRANSISTORS . 4))
 '(B-NAND3 (DELAYS ((142 537) (109 322)))
           (DRIVES 10)
           (INPUT-TYPES BOOLP BOOLP BOOLP)
           (INPUTS A B C)
           (LOADINGS 1 1 1)
           (LSI-NAME . ND3)
           (OUT-DEPENDS (A B C))
           (OUTPUT-TYPES BOOLP)
           (OUTPUTS Z)
           (RESULTS CONS (F-NAND3 A B C) 'NIL)
           (GATES . 2)
           (PRIMITIVES . 1)
           (TRANSISTORS . 6))
 '(B-NAND4 (DELAYS ((144 588) (144 418)))
           (DRIVES 10)
           (INPUT-TYPES BOOLP BOOLP BOOLP BOOLP)
           (INPUTS A B C D)
           (LOADINGS 1 1 1 1)
           (LSI-NAME . ND4)
           (OUT-DEPENDS (A B C D))
           (OUTPUT-TYPES BOOLP)
           (OUTPUTS Z)
           (RESULTS CONS (F-NAND4 A B C D) 'NIL)
           (GATES . 2)
           (PRIMITIVES . 1)
           (TRANSISTORS . 8))
 '(B-NAND5 (DELAYS ((144 1002) (59 1120)))
           (DRIVES 10)
           (INPUT-TYPES BOOLP BOOLP BOOLP BOOLP BOOLP)
           (INPUTS A B C D E)
           (LOADINGS 1 1 1 1 1)
           (LSI-NAME . ND5)
           (OUT-DEPENDS (A B C D E))
           (OUTPUT-TYPES BOOLP)
           (OUTPUTS Z)
           (RESULTS CONS
                    (F-NAND5 A B C D E)
                    'NIL)
           (GATES . 4)
           (PRIMITIVES . 1)
           (TRANSISTORS . 16))
 '(B-NAND6 (DELAYS ((144 982) (59 1090)))
           (DRIVES 10)
           (INPUT-TYPES BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP)
           (INPUTS A B C D E G)
           (LOADINGS 1 1 1 1 1 1)
           (LSI-NAME . ND6)
           (OUT-DEPENDS (A B C D E G))
           (OUTPUT-TYPES BOOLP)
           (OUTPUTS Z)
           (RESULTS CONS
                    (F-NAND6 A B C D E G)
                    'NIL)
           (GATES . 5)
           (PRIMITIVES . 1)
           (TRANSISTORS . 18))
 '(B-NAND8 (DELAYS ((144 1042) (60 1360)))
           (DRIVES 10)
           (INPUT-TYPES BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP)
           (INPUTS A B C D E G H I)
           (LOADINGS 1 1 1 1 1 1 1 1)
           (LSI-NAME . ND8)
           (OUT-DEPENDS (A B C D E G H I))
           (OUTPUT-TYPES BOOLP)
           (OUTPUTS Z)
           (RESULTS CONS
                    (F-NAND8 A B C D E G H I)
                    'NIL)
           (GATES . 6)
           (PRIMITIVES . 1)
           (TRANSISTORS . 22))
 '(B-NBUF (DELAYS ((142 447) (57 213))
                  ((143 302) (52 366)))
          (DRIVES 9 10)
          (INPUT-TYPES BOOLP)
          (INPUTS A)
          (LOADINGS 1)
          (LSI-NAME . IVDA)
          (OUT-DEPENDS (A) (A))
          (OUTPUT-TYPES BOOLP BOOLP)
          (OUTPUTS Y Z)
          (RESULTS CONS
                   (F-NOT A)
                   (CONS (F-BUF A) 'NIL))
          (GATES . 1)
          (PRIMITIVES . 1)
          (TRANSISTORS . 4))
 '(B-NOR (DELAYS ((260 460) (59 170)))
         (DRIVES 10)
         (INPUT-TYPES BOOLP BOOLP)
         (INPUTS A B)
         (LOADINGS 1 1)
         (LSI-NAME . NR2)
         (OUT-DEPENDS (A B))
         (OUTPUT-TYPES BOOLP)
         (OUTPUTS Z)
         (RESULTS CONS (F-NOR A B) 'NIL)
         (GATES . 1)
         (PRIMITIVES . 1)
         (TRANSISTORS . 4))
 '(B-NOR3 (DELAYS ((384 798) (59 224)))
          (DRIVES 10)
          (INPUT-TYPES BOOLP BOOLP BOOLP)
          (INPUTS A B C)
          (LOADINGS 1 1 1)
          (LSI-NAME . NR3)
          (OUT-DEPENDS (A B C))
          (OUTPUT-TYPES BOOLP)
          (OUTPUTS Z)
          (RESULTS CONS (F-NOR3 A B C) 'NIL)
          (GATES . 2)
          (PRIMITIVES . 1)
          (TRANSISTORS . 6))
 '(B-NOR4 (DELAYS ((510 1072) (59 225)))
          (DRIVES 10)
          (INPUT-TYPES BOOLP BOOLP BOOLP BOOLP)
          (INPUTS A B C D)
          (LOADINGS 1 1 1 1)
          (LSI-NAME . NR4)
          (OUT-DEPENDS (A B C D))
          (OUTPUT-TYPES BOOLP)
          (OUTPUTS Z)
          (RESULTS CONS (F-NOR4 A B C D) 'NIL)
          (GATES . 2)
          (PRIMITIVES . 1)
          (TRANSISTORS . 8))
 '(B-NOR5 (DELAYS ((145 1493) (55 767)))
          (DRIVES 10)
          (INPUT-TYPES BOOLP BOOLP BOOLP BOOLP BOOLP)
          (INPUTS A B C D E)
          (LOADINGS 1 1 1 1 1)
          (LSI-NAME . NR5)
          (OUT-DEPENDS (A B C D E))
          (OUTPUT-TYPES BOOLP)
          (OUTPUTS Z)
          (RESULTS CONS
                   (F-NOR5 A B C D E)
                   'NIL)
          (GATES . 4)
          (PRIMITIVES . 1)
          (TRANSISTORS . 16))
 '(B-NOR6 (DELAYS ((146 1593) (55 807)))
          (DRIVES 10)
          (INPUT-TYPES BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP)
          (INPUTS A B C D E G)
          (LOADINGS 1 1 1 1 1 1)
          (LSI-NAME . NR6)
          (OUT-DEPENDS (A B C D E G))
          (OUTPUT-TYPES BOOLP)
          (OUTPUTS Z)
          (RESULTS CONS
                   (F-NOR6 A B C D E G)
                   'NIL)
          (GATES . 5)
          (PRIMITIVES . 1)
          (TRANSISTORS . 18))
 '(B-NOR8 (DELAYS ((146 1853) (54 767)))
          (DRIVES 10)
          (INPUT-TYPES BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP)
          (INPUTS A B C D E G H I)
          (LOADINGS 1 1 1 1 1 1 1 1)
          (LSI-NAME . NR8)
          (OUT-DEPENDS (A B C D E G H I))
          (OUTPUT-TYPES BOOLP)
          (OUTPUTS Z)
          (RESULTS CONS
                   (F-NOR8 A B C D E G H I)
                   'NIL)
          (GATES . 6)
          (PRIMITIVES . 1)
          (TRANSISTORS . 22))
 '(B-NOT (DELAYS ((70 235) (57 198)))
         (DRIVES 10)
         (INPUT-TYPES BOOLP)
         (INPUTS A)
         (LOADINGS 2)
         (LSI-NAME . IVA)
         (OUT-DEPENDS (A))
         (OUTPUT-TYPES BOOLP)
         (OUTPUTS Z)
         (RESULTS CONS (F-NOT A) 'NIL)
         (GATES . 1)
         (PRIMITIVES . 1)
         (TRANSISTORS . 3))
 '(B-NOT-B4IP (DELAYS ((17 333) (12 124)))
              (DRIVES 128)
              (INPUT-TYPES BOOLP)
              (INPUTS A)
              (LOADINGS 8)
              (LSI-NAME . B4IP)
              (OUT-DEPENDS (A))
              (OUTPUT-TYPES BOOLP)
              (OUTPUTS Z)
              (RESULTS CONS (F-NOT A) 'NIL)
              (GATES . 4)
              (PRIMITIVES . 1)
              (TRANSISTORS . 12))
 '(B-NOT-IVAP (DELAYS ((38 208) (35 126)))
              (DRIVES 20)
              (INPUT-TYPES BOOLP)
              (INPUTS A)
              (LOADINGS 3)
              (LSI-NAME . IVAP)
              (OUT-DEPENDS (A))
              (OUTPUT-TYPES BOOLP)
              (OUTPUTS Z)
              (RESULTS CONS (F-NOT A) 'NIL)
              (GATES . 2)
              (PRIMITIVES . 1)
              (TRANSISTORS . 6))
 '(B-OR (DELAYS ((143 332) (58 819)))
        (DRIVES 10)
        (INPUT-TYPES BOOLP BOOLP)
        (INPUTS A B)
        (LOADINGS 1 1)
        (LSI-NAME . OR2)
        (OUT-DEPENDS (A B))
        (OUTPUT-TYPES BOOLP)
        (OUTPUTS Z)
        (RESULTS CONS (F-OR A B) 'NIL)
        (GATES . 2)
        (PRIMITIVES . 1)
        (TRANSISTORS . 6))
 '(B-OR3 (DELAYS ((144 422) (70 1185)))
         (DRIVES 10)
         (INPUT-TYPES BOOLP BOOLP BOOLP)
         (INPUTS A B C)
         (LOADINGS 1 1 1)
         (LSI-NAME . OR3)
         (OUT-DEPENDS (A B C))
         (OUTPUT-TYPES BOOLP)
         (OUTPUTS Z)
         (RESULTS CONS (F-OR3 A B C) 'NIL)
         (GATES . 2)
         (PRIMITIVES . 1)
         (TRANSISTORS . 8))
 '(B-OR4 (DELAYS ((143 352) (78 1329)))
         (DRIVES 10)
         (INPUT-TYPES BOOLP BOOLP BOOLP BOOLP)
         (INPUTS A B C D)
         (LOADINGS 1 1 1 1)
         (LSI-NAME . OR4)
         (OUT-DEPENDS (A B C D))
         (OUTPUT-TYPES BOOLP)
         (OUTPUTS Z)
         (RESULTS CONS (F-OR4 A B C D) 'NIL)
         (GATES . 3)
         (PRIMITIVES . 1)
         (TRANSISTORS . 10))
 '(B-XOR (DELAYS ((145 742) (67 973)))
         (DRIVES 10)
         (INPUT-TYPES BOOLP BOOLP)
         (INPUTS A B)
         (LOADINGS 1 2)
         (LSI-NAME . EO)
         (OUT-DEPENDS (A B))
         (OUTPUT-TYPES BOOLP)
         (OUTPUTS Z)
         (RESULTS CONS (F-XOR A B) 'NIL)
         (GATES . 3)
         (PRIMITIVES . 1)
         (TRANSISTORS . 12))
 '(B-XOR3 (DELAYS ((151 1806) (79 1580)))
          (DRIVES 10)
          (INPUT-TYPES BOOLP BOOLP BOOLP)
          (INPUTS A B C)
          (LOADINGS 1 3 2)
          (LSI-NAME . EO3)
          (OUT-DEPENDS (A B C))
          (OUTPUT-TYPES BOOLP)
          (OUTPUTS Z)
          (RESULTS CONS (F-XOR3 A B C) 'NIL)
          (GATES . 7)
          (PRIMITIVES . 1)
          (TRANSISTORS . 22))
 '(DEL2 (DELAYS ((70 2035) (38 2199)))
        (DRIVES 10)
        (INPUT-TYPES BOOLP)
        (INPUTS A)
        (LOADINGS 1)
        (LSI-NAME . DEL2)
        (OUT-DEPENDS (A))
        (OUTPUT-TYPES BOOLP)
        (OUTPUTS Z)
        (RESULTS CONS (F-BUF A) 'NIL)
        (GATES . 4)
        (PRIMITIVES . 1)
        (TRANSISTORS . 16))
 '(DEL4 (DELAYS ((73 4017) (38 4179)))
        (DRIVES 10)
        (INPUT-TYPES BOOLP)
        (INPUTS A)
        (LOADINGS 1)
        (LSI-NAME . DEL4)
        (OUT-DEPENDS (A))
        (OUTPUT-TYPES BOOLP)
        (OUTPUTS Z)
        (RESULTS CONS (F-BUF A) 'NIL)
        (GATES . 7)
        (PRIMITIVES . 1)
        (TRANSISTORS . 28))
 '(DEL10 (DELAYS ((60 10530) (49 10424)))
         (DRIVES 10)
         (INPUT-TYPES BOOLP)
         (INPUTS A)
         (LOADINGS 1)
         (LSI-NAME . DEL10)
         (OUT-DEPENDS (A))
         (OUTPUT-TYPES BOOLP)
         (OUTPUTS Z)
         (RESULTS CONS (F-BUF A) 'NIL)
         (GATES . 19)
         (PRIMITIVES . 1)
         (TRANSISTORS . 76))
 (LIST 'PROCMON
       '(DELAYS ((70 25000) (60 25000)))
       '(DRIVES 10)
       '(INPUT-TYPES PARAMETRIC PARAMETRIC PARAMETRIC PARAMETRIC)
       '(INPUTS A E S N)
       '(LOADINGS 2 2 2 1)
       '(LSI-NAME . PROCMON)
       '(OUT-DEPENDS (A E S N))
       '(OUTPUT-TYPES PARAMETRIC)
       '(OUTPUTS Z)
       (LIST 'RESULTS
             'CONS
             (LIST 'F-IF
                   'S
                   (LIST 'F-IF
                         'E
                         (LIST 'F-IF
                               'A
                               (LIST 'QUOTE F)
                               (LIST 'QUOTE F))
                         'A)
                   'N)
             ''NIL)
       '(GATES . 100)
       '(PRIMITIVES . 1)
       '(TRANSISTORS . 400))
 '(DP-RAM-16X32
   (DELAYS ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500))
           ((35 7500) (21 7500)))
   (DRIVES 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2)
   (INPUT-TYPES BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP LEVEL BOOLP
                BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                BOOLP)
   (INPUTS READ-A0 READ-A1 READ-A2 READ-A3 WRITE-B0 WRITE-B1 WRITE-B2 WRITE-B3
           WEN D0 D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D14 D15 D16 D17
           D18 D19 D20 D21 D22 D23 D24 D25 D26 D27 D28 D29 D30 D31)
   (LOADINGS 2 2 2 2 2 2 2 2 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
             1 1 1 1 1 1 1 1)
   (LSI-NAME . CMRB100A)
   (NEW-STATES DUAL-PORT-RAM-STATE '32
    '4
    (CONS READ-A0
     (CONS READ-A1
      (CONS READ-A2
       (CONS READ-A3
        (CONS WRITE-B0
         (CONS WRITE-B1
          (CONS WRITE-B2
           (CONS WRITE-B3
            (CONS WEN
             (CONS D0
              (CONS D1
               (CONS D2
                (CONS D3
                 (CONS D4
                  (CONS D5
                   (CONS D6
                    (CONS D7
                     (CONS D8
                      (CONS D9
                       (CONS D10
                        (CONS D11
                         (CONS D12
                          (CONS D13
                           (CONS D14
                            (CONS D15
                             (CONS D16
                              (CONS D17
                               (CONS D18
                                (CONS D19
                                 (CONS D20
                                  (CONS D21
                                   (CONS D22
                                    (CONS D23
                                     (CONS
                                      D24
                                      (CONS
                                       D25
                                       (CONS
                                        D26
                                        (CONS
                                         D27
                                         (CONS
                                          D28
                                          (CONS
                                           D29
                                           (CONS
                                            D30
                                            (CONS D31
                                                       'NIL)))))))))))))))))))))))))))))))))))))))))
    STATE)
   (OUTPUT-TYPES BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                 BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                 BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                 BOOLP BOOLP)
   (OUT-DEPENDS (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3)
                (READ-A0 READ-A1 READ-A2 READ-A3))
   (OUTPUTS O0 O1 O2 O3 O4 O5 O6 O7 O8 O9 O10 O11 O12 O13 O14 O15 O16 O17 O18
            O19 O20 O21 O22 O23 O24 O25 O26 O27 O28 O29 O30 O31)
   (RESULTS DUAL-PORT-RAM-VALUE '32
    '4
    (CONS READ-A0
     (CONS READ-A1
      (CONS READ-A2
       (CONS READ-A3
        (CONS WRITE-B0
         (CONS WRITE-B1
          (CONS WRITE-B2
           (CONS WRITE-B3
            (CONS WEN
             (CONS D0
              (CONS D1
               (CONS D2
                (CONS D3
                 (CONS D4
                  (CONS D5
                   (CONS D6
                    (CONS D7
                     (CONS D8
                      (CONS D9
                       (CONS D10
                        (CONS D11
                         (CONS D12
                          (CONS D13
                           (CONS D14
                            (CONS D15
                             (CONS D16
                              (CONS D17
                               (CONS D18
                                (CONS D19
                                 (CONS D20
                                  (CONS D21
                                   (CONS D22
                                    (CONS D23
                                     (CONS
                                      D24
                                      (CONS
                                       D25
                                       (CONS
                                        D26
                                        (CONS
                                         D27
                                         (CONS
                                          D28
                                          (CONS
                                           D29
                                           (CONS
                                            D30
                                            (CONS D31
                                                       'NIL)))))))))))))))))))))))))))))))))))))))))
    STATE)
   (STATE-TYPES ADDRESSED-STATE 4
                (RAM '(BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                             BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                             BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                             BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP)))
   (STATES . STATE)
   (GATES . 2368)
   (PRIMITIVES . 1)
   (TRANSISTORS . 9472))
 '(FD1 (DELAYS ((147 1024) (55 1288))
               ((145 1432) (53 1447)))
       (DRIVES 10 10)
       (INPUT-TYPES BOOLP CLK)
       (INPUTS D CP)
       (LOADINGS 1 1)
       (LSI-NAME . FD1)
       (NEW-STATES F-BUF D)
       (OUT-DEPENDS NIL NIL)
       (OUTPUT-TYPES BOOLP BOOLP)
       (OUTPUTS Q QN)
       (RESULTS CONS
                (F-BUF STATE)
                (CONS (F-NOT STATE) 'NIL))
       (STATE-TYPES . BOOLP)
       (STATES . STATE)
       (GATES . 7)
       (PRIMITIVES . 1)
       (TRANSISTORS . 26))
 '(FD1S (DELAYS ((147 1024) (55 1288))
                ((145 1432) (53 1447)))
        (DRIVES 10 10)
        (INPUT-TYPES BOOLP CLK BOOLP BOOLP)
        (INPUTS D CP TI TE)
        (LOADINGS 1 1 1 2)
        (LSI-NAME . FD1S)
        (NEW-STATES F-IF TE TI D)
        (OUT-DEPENDS NIL NIL)
        (OUTPUT-TYPES BOOLP BOOLP)
        (OUTPUTS Q QN)
        (RESULTS CONS
                 (F-BUF STATE)
                 (CONS (F-NOT STATE) 'NIL))
        (STATE-TYPES . BOOLP)
        (STATES . STATE)
        (GATES . 9)
        (PRIMITIVES . 1)
        (TRANSISTORS . 34))
 '(FD1SP (DELAYS ((68 1084) (34 1327))
                 ((65 1712) (32 1596)))
         (DRIVES 16 16)
         (INPUT-TYPES BOOLP CLK BOOLP BOOLP)
         (INPUTS D CP TI TE)
         (LOADINGS 1 1 1 2)
         (LSI-NAME . FD1SP)
         (NEW-STATES F-IF TE TI D)
         (OUT-DEPENDS NIL NIL)
         (OUTPUT-TYPES BOOLP BOOLP)
         (OUTPUTS Q QN)
         (RESULTS CONS
                  (F-BUF STATE)
                  (CONS (F-NOT STATE) 'NIL))
         (STATE-TYPES . BOOLP)
         (STATES . STATE)
         (GATES . 10)
         (PRIMITIVES . 1)
         (TRANSISTORS . 38))
 '(FD1SLP (DELAYS ((70 1085) (45 982))
                  ((67 1493) (35 1568)))
          (DRIVES 12 12)
          (INPUT-TYPES BOOLP CLK BOOLP BOOLP BOOLP)
          (INPUTS D CP LD TI TE)
          (LOADINGS 1 1 2 1 2)
          (LSI-NAME . FD1SLP)
          (NEW-STATES F-IF TE TI
                      (F-IF LD D STATE))
          (OUT-DEPENDS NIL NIL)
          (OUTPUT-TYPES BOOLP BOOLP)
          (OUTPUTS Q QN)
          (RESULTS CONS
                   (F-BUF STATE)
                   (CONS (F-NOT STATE) 'NIL))
          (STATE-TYPES . BOOLP)
          (STATES . STATE)
          (GATES . 12)
          (PRIMITIVES . 1)
          (TRANSISTORS . 40))
 '(ID (DELAYS A)
      (DRIVES A)
      (INPUT-TYPES FREE)
      (INPUTS A)
      (LOADINGS 0)
      (LSI-NAME . ID)
      (OUT-DEPENDS (A))
      (OUTPUT-TYPES (A))
      (OUTPUTS Z)
      (RESULTS CONS A 'NIL)
      (GATES . 0)
      (PRIMITIVES . 0)
      (TRANSISTORS . 0))
 '(MEM-32X32
   (DELAYS ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000))
           ((1410 20000) (820 20000)))
   (DRIVES 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
           10 10 10 10 10 10 10 10 10 10 10)
   (INPUT-TYPES BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP)
   (INPUTS RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15
           A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28 A29 A30 A31 D0
           D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D14 D15 D16 D17 D18 D19
           D20 D21 D22 D23 D24 D25 D26 D27 D28 D29 D30 D31)
   (LOADINGS 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
             1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1)
   (LSI-NAME . MEM-32X32)
   (NEW-STATES MEM-STATE
    (CONS RW-
     (CONS STROBE-
      (CONS A0
       (CONS A1
        (CONS A2
         (CONS A3
          (CONS A4
           (CONS A5
            (CONS A6
             (CONS A7
              (CONS A8
               (CONS A9
                (CONS A10
                 (CONS A11
                  (CONS A12
                   (CONS A13
                    (CONS A14
                     (CONS A15
                      (CONS A16
                       (CONS A17
                        (CONS A18
                         (CONS A19
                          (CONS A20
                           (CONS A21
                            (CONS A22
                             (CONS A23
                              (CONS A24
                               (CONS A25
                                (CONS A26
                                 (CONS A27
                                  (CONS A28
                                   (CONS A29
                                    (CONS A30
                                     (CONS
                                      A31
                                      (CONS
                                       D0
                                       (CONS
                                        D1
                                        (CONS
                                         D2
                                         (CONS
                                          D3
                                          (CONS
                                           D4
                                           (CONS
                                            D5
                                            (CONS
                                             D6
                                             (CONS
                                              D7
                                              (CONS
                                               D8
                                               (CONS
                                                D9
                                                (CONS
                                                 D10
                                                 (CONS
                                                  D11
                                                  (CONS
                                                   D12
                                                   (CONS
                                                    D13
                                                    (CONS
                                                     D14
                                                     (CONS
                                                      D15
                                                      (CONS
                                                       D16
                                                       (CONS
                                                        D17
                                                        (CONS
                                                         D18
                                                         (CONS
                                                          D19
                                                          (CONS
                                                           D20
                                                           (CONS
                                                            D21
                                                            (CONS
                                                             D22
                                                             (CONS
                                                              D23
                                                              (CONS
                                                               D24
                                                               (CONS
                                                                D25
                                                                (CONS
                                                                 D26
                                                                 (CONS
                                                                  D27
                                                                  (CONS
                                                                   D28
                                                                   (CONS
                                                                    D29
                                                                    (CONS
                                                                     D30
                                                                     (CONS D31
                                                                                                                                  'NIL))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
    STATE)
   (OUT-DEPENDS (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14
                     A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28
                     A29 A30 A31)
                (RW- STROBE- A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13
                     A14 A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27
                     A28 A29 A30 A31))
   (OUTPUT-TYPES BOOLP TRI-STATE TRI-STATE TRI-STATE TRI-STATE TRI-STATE
                 TRI-STATE TRI-STATE TRI-STATE TRI-STATE TRI-STATE TRI-STATE
                 TRI-STATE TRI-STATE TRI-STATE TRI-STATE TRI-STATE TRI-STATE
                 TRI-STATE TRI-STATE TRI-STATE TRI-STATE TRI-STATE TRI-STATE
                 TRI-STATE TRI-STATE TRI-STATE TRI-STATE TRI-STATE TRI-STATE
                 TRI-STATE TRI-STATE TRI-STATE)
   (OUTPUTS DTACK- O0 O1 O2 O3 O4 O5 O6 O7 O8 O9 O10 O11 O12 O13 O14 O15 O16
            O17 O18 O19 O20 O21 O22 O23 O24 O25 O26 O27 O28 O29 O30 O31)
   (RESULTS MEM-VALUE
    (CONS RW-
     (CONS STROBE-
      (CONS A0
       (CONS A1
        (CONS A2
         (CONS A3
          (CONS A4
           (CONS A5
            (CONS A6
             (CONS A7
              (CONS A8
               (CONS A9
                (CONS A10
                 (CONS A11
                  (CONS A12
                   (CONS A13
                    (CONS A14
                     (CONS A15
                      (CONS A16
                       (CONS A17
                        (CONS A18
                         (CONS A19
                          (CONS A20
                           (CONS A21
                            (CONS A22
                             (CONS A23
                              (CONS A24
                               (CONS A25
                                (CONS A26
                                 (CONS A27
                                  (CONS A28
                                   (CONS A29
                                    (CONS A30
                                     (CONS
                                      A31
                                      (CONS
                                       D0
                                       (CONS
                                        D1
                                        (CONS
                                         D2
                                         (CONS
                                          D3
                                          (CONS
                                           D4
                                           (CONS
                                            D5
                                            (CONS
                                             D6
                                             (CONS
                                              D7
                                              (CONS
                                               D8
                                               (CONS
                                                D9
                                                (CONS
                                                 D10
                                                 (CONS
                                                  D11
                                                  (CONS
                                                   D12
                                                   (CONS
                                                    D13
                                                    (CONS
                                                     D14
                                                     (CONS
                                                      D15
                                                      (CONS
                                                       D16
                                                       (CONS
                                                        D17
                                                        (CONS
                                                         D18
                                                         (CONS
                                                          D19
                                                          (CONS
                                                           D20
                                                           (CONS
                                                            D21
                                                            (CONS
                                                             D22
                                                             (CONS
                                                              D23
                                                              (CONS
                                                               D24
                                                               (CONS
                                                                D25
                                                                (CONS
                                                                 D26
                                                                 (CONS
                                                                  D27
                                                                  (CONS
                                                                   D28
                                                                   (CONS
                                                                    D29
                                                                    (CONS
                                                                     D30
                                                                     (CONS D31
                                                                                                                                  'NIL))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
    STATE)
   (STATE-TYPES (ADDRESSED-STATE 32
                                 (RAM '(BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                                              BOOLP BOOLP BOOLP BOOLP BOOLP
                                              BOOLP BOOLP BOOLP BOOLP BOOLP
                                              BOOLP BOOLP BOOLP BOOLP BOOLP
                                              BOOLP BOOLP BOOLP BOOLP BOOLP
                                              BOOLP BOOLP BOOLP BOOLP BOOLP
                                              BOOLP)))
                NUMBERP NUMBER-LISTP NUMBERP BOOLP BOOLP
                (BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                       BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                       BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                       BOOLP BOOLP BOOLP BOOLP)
                (BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                       BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                       BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP BOOLP
                       BOOLP BOOLP BOOLP BOOLP))
   (STATES . STATE)
   (GATES . 0)
   (PRIMITIVES . 1)
   (TRANSISTORS . 0))
 '(RAM-ENABLE-CIRCUIT (DELAYS ((68 12000) (54 12000)))
                      (DRIVES 10)
                      (INPUT-TYPES CLK BOOLP BOOLP BOOLP)
                      (INPUTS CLK TEST-REGFILE- DISABLE-REGFILE- WE)
                      (LOADINGS 1 2 2 2)
                      (LSI-NAME . RAM-ENABLE-CIRCUIT)
                      (OUT-DEPENDS (CLK TEST-REGFILE- DISABLE-REGFILE- WE))
                      (OUTPUT-TYPES LEVEL)
                      (OUTPUTS Z)
                      (RESULTS CONS
                               (F-NAND DISABLE-REGFILE- WE)
                               'NIL)
                      (GATES . 24)
                      (PRIMITIVES . 1)
                      (TRANSISTORS . 97))
 '(T-BUF (DELAYS ((146 313) (57 728)))
         (DRIVES 10)
         (INPUT-TYPES BOOLP BOOLP)
         (INPUTS E A)
         (LOADINGS 2 2)
         (LSI-NAME BTS4 A E)
         (OUT-DEPENDS (A E))
         (OUTPUT-TYPES TRI-STATE)
         (OUTPUTS Z)
         (RESULTS CONS (FT-BUF E A) 'NIL)
         (GATES . 3)
         (PRIMITIVES . 1)
         (TRANSISTORS . 12))
 '(T-WIRE (DELAYS (OR A B))
          (DRIVES (MIN A B))
          (INPUT-TYPES TRI-STATE TRI-STATE)
          (INPUTS A B)
          (LOADINGS 1 1)
          (LSI-NAME . T-WIRE)
          (OUT-DEPENDS (A B))
          (OUTPUT-TYPES TRI-STATE)
          (OUTPUTS Z)
          (RESULTS CONS (FT-WIRE A B) 'NIL)
          (GATES . 0)
          (PRIMITIVES . 0)
          (TRANSISTORS . 0))
 '(PULLUP (DELAYS A)
          (DRIVES A)
          (INPUT-TYPES TRI-STATE)
          (INPUTS A)
          (LOADINGS 1)
          (LSI-NAME . PULLUP)
          (OUT-DEPENDS (A))
          (OUTPUT-TYPES BOOLP)
          (OUTPUTS Z)
          (RESULTS CONS (F-PULLUP A) 'NIL)
          (GATES . 0)
          (PRIMITIVES . 0)
          (TRANSISTORS . 0))
 '(TTL-BIDIRECT (DELAYS (((61 PS-PF) 1633) ((41 PS-PF) 2253))
                        ((43 633) (20 638))
                        ((141 1053) (82 799)))
                (DRIVES (8 MA) 10 10)
                (INPUT-TYPES TTL-TRI-STATE BOOLP BOOLP PARAMETRIC)
                (INPUTS IO A EN PI)
                (LOADINGS (3 PF) 1 1 1)
                (LSI-NAME . BD8TRP)
                (OUT-DEPENDS (EN A)
                             (EN A IO)
                             (EN A IO PI))
                (OUTPUT-TYPES TTL-TRI-STATE BOOLP PARAMETRIC)
                (OUTPUTS IO ZI PO)
                (RESULTS CONS
                         (FT-BUF (F-NOT EN) A)
                         (CONS (F-BUF (FT-WIRE IO (FT-BUF (F-NOT EN) A)))
                               (CONS (F-NAND (FT-WIRE IO (FT-BUF (F-NOT EN) A))
                                             PI)
                                     'NIL)))
                (GATES . 0)
                (PADS . 1)
                (PRIMITIVES . 1)
                (TRANSISTORS . 0))
 '(TTL-CLK-INPUT (DELAYS ((4 1225) (4 1152))
                         ((202 1050) (117 741)))
                 (DRIVES 400 10)
                 (INPUT-TYPES TTL PARAMETRIC)
                 (INPUTS A PI)
                 (LOADINGS (3 PF) 1)
                 (LSI-NAME . DRVT8)
                 (OUT-DEPENDS (A) (A PI))
                 (OUTPUT-TYPES CLK PARAMETRIC)
                 (OUTPUTS Z PO)
                 (RESULTS CONS
                          (F-BUF A)
                          (CONS (F-NAND A PI) 'NIL))
                 (GATES . 0)
                 (PADS . 2)
                 (PRIMITIVES . 1)
                 (TRANSISTORS . 0))
 '(TTL-INPUT (DELAYS ((43 633) (20 638))
                     ((141 1053) (82 799)))
             (DRIVES 10 10)
             (INPUT-TYPES TTL PARAMETRIC)
             (INPUTS A PI)
             (LOADINGS (3 PF) 1)
             (LSI-NAME . TLCHT)
             (OUT-DEPENDS (A) (A PI))
             (OUTPUT-TYPES BOOLP PARAMETRIC)
             (OUTPUTS Z PO)
             (RESULTS CONS
                      (F-BUF A)
                      (CONS (F-NAND A PI) 'NIL))
             (GATES . 0)
             (PADS . 1)
             (PRIMITIVES . 1)
             (TRANSISTORS . 0))
 '(TTL-OUTPUT (DELAYS (((61 PS-PF) 812) ((42 PS-PF) 1155)))
              (DRIVES (8 MA))
              (INPUT-TYPES BOOLP)
              (INPUTS A)
              (LOADINGS 5)
              (LSI-NAME . B8RP)
              (OUT-DEPENDS (A))
              (OUTPUT-TYPES TTL)
              (OUTPUTS Z)
              (RESULTS CONS (F-BUF A) 'NIL)
              (GATES . 0)
              (PADS . 1)
              (PRIMITIVES . 1)
              (TRANSISTORS . 0))
 '(TTL-OUTPUT-PARAMETRIC (DELAYS (((64 PS-PF) 737) ((42 PS-PF) 1125)))
                         (DRIVES (4 MA))
                         (INPUT-TYPES PARAMETRIC)
                         (INPUTS A)
                         (LOADINGS 3)
                         (LSI-NAME . B4)
                         (OUT-DEPENDS (A))
                         (OUTPUT-TYPES TTL)
                         (OUTPUTS Z)
                         (RESULTS CONS (F-BUF A) 'NIL)
                         (GATES . 0)
                         (PADS . 1)
                         (PRIMITIVES . 1)
                         (TRANSISTORS . 0))
 '(TTL-OUTPUT-FAST (DELAYS (((36 PS-PF) 991) ((24 PS-PF) 1488)))
                   (DRIVES (8 MA))
                   (INPUT-TYPES BOOLP)
                   (INPUTS A)
                   (LOADINGS 3)
                   (LSI-NAME . B8)
                   (OUT-DEPENDS (A))
                   (OUTPUT-TYPES TTL)
                   (OUTPUTS Z)
                   (RESULTS CONS (F-BUF A) 'NIL)
                   (GATES . 0)
                   (PADS . 1)
                   (PRIMITIVES . 1)
                   (TRANSISTORS . 0))
 '(TTL-TRI-OUTPUT (DELAYS (((61 PS-PF) 1602) ((41 PS-PF) 2233)))
                  (DRIVES (8 MA))
                  (INPUT-TYPES BOOLP BOOLP)
                  (INPUTS A EN)
                  (LOADINGS 1 1)
                  (LSI-NAME . BT8RP)
                  (OUT-DEPENDS (A EN))
                  (OUTPUT-TYPES TTL-TRI-STATE)
                  (OUTPUTS Z)
                  (RESULTS CONS
                           (FT-BUF (F-NOT EN) A)
                           'NIL)
                  (GATES . 0)
                  (PADS . 1)
                  (PRIMITIVES . 1)
                  (TRANSISTORS . 0))
 '(TTL-TRI-OUTPUT-FAST (DELAYS (((36 PS-PF) 1581) ((24 PS-PF) 2198)))
                       (DRIVES (8 MA))
                       (INPUT-TYPES BOOLP BOOLP)
                       (INPUTS A EN)
                       (LOADINGS 1 1)
                       (LSI-NAME . BT8)
                       (OUT-DEPENDS (A EN))
                       (OUTPUT-TYPES TTL-TRI-STATE)
                       (OUTPUTS Z)
                       (RESULTS CONS
                                (FT-BUF (F-NOT EN) A)
                                'NIL)
                       (GATES . 0)
                       (PADS . 1)
                       (PRIMITIVES . 1)
                       (TRANSISTORS . 0))
 (LIST 'VDD
       '(DELAYS ((0 0) (0 0)))
       '(DRIVES 50)
       '(INPUT-TYPES)
       '(INPUTS)
       '(LOADINGS)
       '(LSI-NAME . VDD)
       '(OUT-DEPENDS NIL)
       '(OUTPUT-TYPES BOOLP)
       '(OUTPUTS Z)
       (LIST 'RESULTS
             'CONS
             (LIST 'QUOTE T)
             ''NIL)
       '(GATES . 0)
       '(PRIMITIVES . 1)
       '(TRANSISTORS . 0))
 (LIST 'VDD-PARAMETRIC
       '(DELAYS ((0 0) (0 0)))
       '(DRIVES 50)
       '(INPUT-TYPES)
       '(INPUTS)
       '(LOADINGS)
       '(LSI-NAME . VDD)
       '(OUT-DEPENDS NIL)
       '(OUTPUT-TYPES PARAMETRIC)
       '(OUTPUTS Z)
       (LIST 'RESULTS
             'CONS
             (LIST 'QUOTE T)
             ''NIL)
       '(GATES . 0)
       '(PRIMITIVES . 1)
       '(TRANSISTORS . 0))
 (LIST 'VSS
       '(DELAYS ((0 0) (0 0)))
       '(DRIVES 50)
       '(INPUT-TYPES)
       '(INPUTS)
       '(LOADINGS)
       '(LSI-NAME . VSS)
       '(OUT-DEPENDS NIL)
       '(OUTPUT-TYPES BOOLP)
       '(OUTPUTS Z)
       (LIST 'RESULTS
             'CONS
             (LIST 'QUOTE F)
             ''NIL)
       '(GATES . 0)
       '(PRIMITIVES . 1)
       '(TRANSISTORS . 0))))
\end{verbatim}


\begin{tabbing}{\sc Definition}:\index{lookup-module} \\  
\=\+{\rm{lookup-module}}\,({\it{name\/}}, {\it{netlist\/}})\index{lookup-module} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{netlist\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{f}} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{car}}\,({\it{netlist\/}})) $\wedge$ ({\rm{caar}}\,({\it{netlist\/}}) $=$ {\it{name\/}}) \\ 
{\bf then }{\rm{car}}\,({\it{netlist\/}}) \\ 
{\bf else }{\rm{lookup-module}}\,({\it{name\/}}, {\rm{cdr}}\,({\it{netlist\/}}))\index{lookup-module}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable lookup-module; name this event `lookup-module-off'.\index{lookup-module-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{delete-module} \\  
\=\+{\rm{delete-module}}\,({\it{name\/}}, {\it{netlist\/}})\index{delete-module} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{netlist\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{netlist\/}} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{car}}\,({\it{netlist\/}})) $\wedge$ ({\rm{caar}}\,({\it{netlist\/}}) $=$ {\it{name\/}}) \\ 
{\bf then }{\rm{cdr}}\,({\it{netlist\/}}) \\ 
{\bf else }{\rm{cons}}\,({\rm{car}}\,({\it{netlist\/}}), {\rm{delete-module}}\,({\it{name\/}}, {\rm{cdr}}\,({\it{netlist\/}}))\index{delete-module})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable delete-module; name this event `delete-module-off'.\index{delete-module-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  delete-module-lookup-module-count \\ \index{delete-module-lookup-module-cou!nt}
\=\+{\rm{lookup-module}}\,({\it{name\/}}, {\it{netlist\/}})\index{lookup-module} \\ 
$\rightarrow$$\;\;\;\;$({\rm{count}}\,({\rm{delete-module}}\,({\it{name\/}}, {\it{netlist\/}})\index{delete-module}) $<$ {\rm{count}}\,({\it{netlist\/}}))\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{pairstates} \\  
\=\+{\rm{pairstates}}\,({\it{statenames\/}}, {\it{state\/}})\index{pairstates} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{statenames\/}}) $\vee$ ({\it{statenames\/}} $=$ {\bf{nil}}) \\ 
{\bf then }{\rm{pairlist}}\,({\it{statenames\/}}, {\it{state\/}}) \\ 
{\bf else }{\rm{list}}\,({\rm{cons}}\,({\it{statenames\/}}, {\it{state\/}}))$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{collect-states} \\  
\=\+{\rm{collect-states}}\,({\it{statenames\/}}, {\it{state-bindings\/}})\index{collect-states} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{statenames\/}}) $\vee$ ({\it{statenames\/}} $=$ {\bf{nil}}) \\ 
{\bf then }{\rm{collect-value}}\,({\it{statenames\/}}, {\it{state-bindings\/}})\index{collect-value} \\ 
{\bf else }{\rm{value}}\,({\it{statenames\/}}, {\it{state-bindings\/}})\index{value}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{module-name}$\;\;$
{\rm{module-name}}\,({\it{module\/}})\index{module-name} $=$ {\rm{car}}\,({\it{module\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{module-inputs}$\;\;$
{\rm{module-inputs}}\,({\it{module\/}})\index{module-inputs} $=$ {\rm{cadr}}\,({\it{module\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{module-outputs}$\;\;$
{\rm{module-outputs}}\,({\it{module\/}})\index{module-outputs} $=$ {\rm{caddr}}\,({\it{module\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{module-occurrences}$\;\;$
{\rm{module-occurrences}}\,({\it{module\/}})\index{module-occurrences} $=$ {\rm{cadddr}}\,({\it{module\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{module-statenames}$\;\;$
{\rm{module-statenames}}\,({\it{module\/}})\index{module-statenames} $=$ {\rm{caddddr}}\,({\it{module\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{module-annotation}$\;\;$
{\rm{module-annotation}}\,({\it{module\/}})\index{module-annotation} $=$ {\rm{cadddddr}}\,({\it{module\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{occ-name}$\;\;$
{\rm{occ-name}}\,({\it{occurrence\/}})\index{occ-name} $=$ {\rm{car}}\,({\it{occurrence\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{occ-outputs}$\;\;$
{\rm{occ-outputs}}\,({\it{occurrence\/}})\index{occ-outputs} $=$ {\rm{cadr}}\,({\it{occurrence\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{occ-function}$\;\;$
{\rm{occ-function}}\,({\it{occurrence\/}})\index{occ-function} $=$ {\rm{caddr}}\,({\it{occurrence\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{occ-inputs}$\;\;$
{\rm{occ-inputs}}\,({\it{occurrence\/}})\index{occ-inputs} $=$ {\rm{cadddr}}\,({\it{occurrence\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{occ-annotation}$\;\;$
{\rm{occ-annotation}}\,({\it{occurrence\/}})\index{occ-annotation} $=$ {\rm{caddddr}}\,({\it{occurrence\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{primp}$\;\;$
{\rm{primp}}\,({\it{fn\/}})\index{primp} $=$ {\rm{lookup-module}}\,({\it{fn\/}}, {\sc{primp-database}}\index{primp-database})\index{lookup-module}
\end{tabbing}


\noindent{\sc Event}:   Enable primp; name this event `primp-off'.\index{primp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-litatom==$>$not-primp \\ \index{not-litatom==$>$not-primp}
($\neg$ {\rm{litatom}}\,({\it{fn\/}})) $\rightarrow$ ($\neg$ {\rm{primp}}\,({\it{fn\/}})\index{primp})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{primp-lookup} \\  
{\rm{primp-lookup}}\,({\it{fn\/}}, {\it{name\/}})\index{primp-lookup} $=$ {\rm{lookup-module}}\,({\it{name\/}}, {\rm{cdr}}\,({\rm{primp}}\,({\it{fn\/}})\index{primp}))\index{lookup-module}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{primp2}$\;\;$
{\rm{primp2}}\,({\it{fn\/}}, {\it{name\/}})\index{primp2} $=$ {\rm{cdr}}\,({\rm{primp-lookup}}\,({\it{fn\/}}, {\it{name\/}})\index{primp-lookup})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{dual-apply-value} \\  
\=\+{\rm{dual-apply-value}}\,({\it{fn\/}}, {\it{args\/}}, {\it{state\/}})\index{dual-apply-value} \\ 
$=$$\;\;\;\;${\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\rm{primp2}}\,({\it{fn\/}}, {\tt{'}}{\tt{results}})\index{primp2}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,({\rm{primp2}}\,({\it{fn\/}}, {\tt{'}}{\tt{inputs}})\index{primp2}, {\it{args\/}}), \\ 
{\rm{pairstates}}\,({\rm{primp2}}\,({\it{fn\/}}, {\tt{'}}{\tt{states}})\index{primp2}, {\it{state\/}})\index{pairstates})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable dual-apply-value; name this event `dual-apply-value-off'.\index{dual-apply-value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{dual-apply-state} \\  
\=\+{\rm{dual-apply-state}}\,({\it{fn\/}}, {\it{args\/}}, {\it{state\/}})\index{dual-apply-state} \\ 
$=$$\;\;\;\;${\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\rm{primp2}}\,({\it{fn\/}}, {\tt{'}}{\tt{new-states}})\index{primp2}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,({\rm{primp2}}\,({\it{fn\/}}, {\tt{'}}{\tt{inputs}})\index{primp2}, {\it{args\/}}), \\ 
{\rm{pairstates}}\,({\rm{primp2}}\,({\it{fn\/}}, {\tt{'}}{\tt{states}})\index{primp2}, {\it{state\/}})\index{pairstates})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable dual-apply-state; name this event `dual-apply-state-off'.\index{dual-apply-state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{dual-eval} \\  
\=\+{\rm{dual-eval}}\,({\it{flag\/}}, {\it{x0\/}}, {\it{x1\/}}, {\it{x2\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{flag\/}}: \\ 
{\bf case = }{\tt{0}} \\ 
{\bf then }\=\+{\bf if }{\rm{primp}}\,({\it{x0\/}})\index{primp}$\;\;${\bf then }{\rm{dual-apply-value}}\,({\it{x0\/}}, {\it{x1\/}}, {\it{x2\/}})\index{dual-apply-value} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{lookup-module}) \\ 
{\bf then }{\rm{collect-value}}\,(\=\+{\rm{module-outputs}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{lookup-module})\index{module-outputs}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\rm{pairlist}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\it{x1\/}})\-, \\ 
{\rm{pairstates}}\,(\=\+{\rm{module-statenames}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-statenames}, \\ 
{\it{x2\/}})\-\index{pairstates}, \\ 
{\rm{delete-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{delete-module})\-\index{dual-eval})\-\index{collect-value} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{1}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\rm{listp}}\,({\it{x0\/}}) \\ 
{\bf then }{\rm{dual-eval}}\,(\=\+{\tt{1}}, \\ 
{\rm{cdr}}\,({\it{x0\/}}), \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\rm{occ-outputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-outputs}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-function}, \\ 
{\rm{collect-value}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-inputs}, \\ 
{\it{x1\/}})\-\index{collect-value}, \\ 
{\rm{value}}\,(\=\+{\rm{occ-name}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-name}, \\ 
{\it{x2\/}})\-\index{value}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-, \\ 
{\it{x1\/}})\-, \\ 
{\it{x2\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
{\bf else }{\it{x1\/}}$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{2}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\rm{primp}}\,({\it{x0\/}})\index{primp}$\;\;${\bf then }{\rm{dual-apply-state}}\,({\it{x0\/}}, {\it{x1\/}}, {\it{x2\/}})\index{dual-apply-state} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{lookup-module}) \\ 
{\bf then }{\rm{collect-states}}\,(\=\+{\rm{module-statenames}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{lookup-module})\index{module-statenames}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{3}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\rm{pairlist}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\it{x1\/}})\-, \\ 
{\rm{pairstates}}\,(\=\+{\rm{module-statenames}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-statenames}, \\ 
{\it{x2\/}})\-\index{pairstates}, \\ 
{\rm{delete-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{delete-module})\-\index{dual-eval}, \\ 
{\rm{pairstates}}\,(\=\+{\rm{module-statenames}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-statenames}, \\ 
{\it{x2\/}})\-\index{pairstates}, \\ 
{\rm{delete-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{delete-module})\-\index{dual-eval})\-\index{collect-states} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{3}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\rm{listp}}\,({\it{x0\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{occ-name}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-name}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-function}, \\ 
{\rm{collect-value}}\,({\rm{occ-inputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-inputs}, {\it{x1\/}})\index{collect-value}, \\ 
{\rm{value}}\,({\rm{occ-name}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-name}, {\it{x2\/}})\index{value}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-, \\ 
{\rm{dual-eval}}\,({\tt{3}}, {\rm{cdr}}\,({\it{x0\/}}), {\it{x1\/}}, {\it{x2\/}}, {\it{netlist\/}})\index{dual-eval})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\- \\ 
{\bf otherwise }{\bf{f}}$\;${\bf  endcase}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable dual-eval; name this event `dual-eval-off'.\index{dual-eval-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  expand-top-level-dual-eval-0-calls \\ \index{expand-top-level-dual-eval-0-ca!lls}
\=\+(($\neg$ {\rm{primp}}\,({\it{fn\/}})\index{primp}) $\wedge$ {\rm{listp}}\,({\rm{lookup-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{lookup-module})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\it{fn\/}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{collect-value}}\,(\=\+{\rm{module-outputs}}\,({\rm{lookup-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{lookup-module})\index{module-outputs}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\rm{pairlist}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\it{args\/}})\-, \\ 
{\rm{pairstates}}\,(\=\+{\rm{module-statenames}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-statenames}, \\ 
{\it{state\/}})\-\index{pairstates}, \\ 
{\rm{delete-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{delete-module})\-\index{dual-eval})\-\index{collect-value})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  expand-top-level-dual-eval-2-calls \\ \index{expand-top-level-dual-eval-2-ca!lls}
\=\+(($\neg$ {\rm{primp}}\,({\it{fn\/}})\index{primp}) $\wedge$ {\rm{listp}}\,({\rm{lookup-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{lookup-module})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{2}}, {\it{fn\/}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{collect-states}}\,(\=\+{\rm{module-statenames}}\,({\rm{lookup-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{lookup-module})\index{module-statenames}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{3}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\rm{pairlist}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\it{args\/}})\-, \\ 
{\rm{pairstates}}\,(\=\+{\rm{module-statenames}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-statenames}, \\ 
{\it{state\/}})\-\index{pairstates}, \\ 
{\rm{delete-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{delete-module})\-\index{dual-eval}, \\ 
{\rm{pairstates}}\,(\=\+{\rm{module-statenames}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-statenames}, \\ 
{\it{state\/}})\-\index{pairstates}, \\ 
{\rm{delete-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{delete-module})\-\index{dual-eval})\-\index{collect-states})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  open-dual-eval-with-flag-1 \\ \index{open-dual-eval-with-flag-1}
\=\+(\=\+({\it{body\/}} $\simeq\;${{\bf{nil}}}${}$) \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{1}}, {\it{body\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\it{bindings\/}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{listp}}\,({\it{body\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{1}}, {\it{body\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{dual-eval}}\,(\=\+{\tt{1}}, \\ 
{\rm{cdr}}\,({\it{body\/}}), \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\rm{occ-outputs}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-outputs}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-function}, \\ 
{\rm{collect-value}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-inputs}, \\ 
{\it{bindings\/}})\-\index{collect-value}, \\ 
{\rm{value}}\,(\=\+{\rm{occ-name}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-name}, \\ 
{\it{state-bindings\/}})\-\index{value}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-, \\ 
{\it{bindings\/}})\-, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  open-dual-eval-with-flag-3 \\ \index{open-dual-eval-with-flag-3}
\=\+(({\it{body\/}} $\simeq\;${{\bf{nil}}}${}$) $\rightarrow$ ({\rm{dual-eval}}\,({\tt{3}}, {\it{body\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\bf{nil}})) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{listp}}\,({\it{body\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{3}}, {\it{body\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{occ-name}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-name}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-function}, \\ 
{\rm{collect-value}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-inputs}, \\ 
{\it{bindings\/}})\-\index{collect-value}, \\ 
{\rm{value}}\,(\=\+{\rm{occ-name}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-name}, \\ 
{\it{state-bindings\/}})\-\index{value}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{3}}, \\ 
{\rm{cdr}}\,({\it{body\/}}), \\ 
{\it{bindings\/}}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-dual-eval-0 \\ \index{properp-dual-eval-0}
\=\+(($\neg$ {\rm{primp}}\,({\it{fn\/}})\index{primp}) $\wedge$ {\rm{listp}}\,({\rm{lookup-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{lookup-module})) \\ 
$\rightarrow$$\;\;\;\;${\rm{properp}}\,({\rm{dual-eval}}\,({\tt{0}}, {\it{fn\/}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval})\index{properp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-dual-eval-0 \\ \index{length-dual-eval-0}
\=\+(($\neg$ {\rm{primp}}\,({\it{fn\/}})\index{primp}) $\wedge$ {\rm{listp}}\,({\rm{lookup-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{lookup-module})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{length}}\,({\rm{dual-eval}}\,({\tt{0}}, {\it{fn\/}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{module-outputs}}\,({\rm{lookup-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{lookup-module})\index{module-outputs})\index{length})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-dual-eval-2 \\ \index{properp-dual-eval-2}
\=\+(\=\+($\neg$ {\rm{primp}}\,({\it{fn\/}})\index{primp}) \\ 
$\wedge$$\;\;\;\;${\rm{listp}}\,({\rm{lookup-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{lookup-module}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{module-statenames}}\,({\rm{lookup-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{lookup-module})\index{module-statenames})\index{properp})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{properp}}\,({\rm{dual-eval}}\,({\tt{2}}, {\it{fn\/}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval})\index{properp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-dual-eval-2 \\ \index{length-dual-eval-2}
\=\+(\=\+($\neg$ {\rm{primp}}\,({\it{fn\/}})\index{primp}) \\ 
$\wedge$$\;\;\;\;${\rm{listp}}\,({\rm{lookup-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{lookup-module}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{module-statenames}}\,({\rm{lookup-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{lookup-module})\index{module-statenames})\index{properp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{length}}\,({\rm{dual-eval}}\,({\tt{2}}, {\it{fn\/}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{module-statenames}}\,({\rm{lookup-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{lookup-module})\index{module-statenames})\index{length})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{dual-eval-body-bindings} \\  
\=\+{\rm{dual-eval-body-bindings}}\,({\it{n\/}}, {\it{body\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{dual-eval-body-bindings} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\it{bindings\/}} \\ 
{\bf else }{\rm{dual-eval-body-bindings}}\,(\=\+{\it{n\/}} $-\;1$, \\ 
{\rm{cdr}}\,({\it{body\/}}), \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\rm{occ-outputs}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-outputs}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-function}, \\ 
{\rm{collect-value}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-inputs}, \\ 
{\it{bindings\/}})\-\index{collect-value}, \\ 
{\rm{value}}\,(\=\+{\rm{occ-name}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-name}, \\ 
{\it{state-bindings\/}})\-\index{value}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-, \\ 
{\it{bindings\/}})\-, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval-body-bindings}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable dual-eval-body-bindings; name this event `dual-eval-body-bindings-off'.\index{dual-eval-body-bindings-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-dual-eval-body-bindings \\ \index{open-dual-eval-body-bindings}
\=\+(\=\+({\it{n\/}} $\simeq {\tt{0}}$) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval-body-bindings}}\,({\it{n\/}}, {\it{body\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{dual-eval-body-bindings} \\ 
$=$$\;\;\;\;${\it{bindings\/}})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval-body-bindings}}\,(\=\+{\it{n\/}}, \\ 
{\it{body\/}}, \\ 
{\it{bindings\/}}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval-body-bindings} \\ 
$=$$\;\;\;\;${\rm{dual-eval-body-bindings}}\,(\=\+{\it{n\/}} $-\;1$, \\ 
{\rm{cdr}}\,({\it{body\/}}), \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\rm{occ-outputs}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-outputs}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-function}, \\ 
{\rm{collect-value}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-inputs}, \\ 
{\it{bindings\/}})\-\index{collect-value}, \\ 
{\rm{value}}\,(\=\+{\rm{occ-name}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-name}, \\ 
{\it{state-bindings\/}})\-\index{value}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-, \\ 
{\it{bindings\/}})\-, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval-body-bindings})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{simulate} \\  
\=\+{\rm{simulate}}\,({\it{fn\/}}, {\it{inputs\/}}, {\it{state\/}}, {\it{netlist\/}})\index{simulate} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{inputs\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\it{fn\/}}, {\rm{car}}\,({\it{inputs\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval}, \\ 
{\rm{dual-eval}}\,({\tt{2}}, {\it{fn\/}}, {\rm{car}}\,({\it{inputs\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval})\-, \\ 
{\rm{simulate}}\,(\=\+{\it{fn\/}}, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\rm{dual-eval}}\,({\tt{2}}, {\it{fn\/}}, {\rm{car}}\,({\it{inputs\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval}, \\ 
{\it{netlist\/}})\-\index{simulate})\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{simulate-dual-eval-2} \\  
\=\+{\rm{simulate-dual-eval-2}}\,({\it{module\/}}, {\it{inputs\/}}, {\it{state\/}}, {\it{netlist\/}}, {\it{n\/}})\index{simulate-dual-eval-2} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\it{state\/}} \\ 
{\bf else }{\rm{simulate-dual-eval-2}}\,(\=\+{\it{module\/}}, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\it{module\/}}, \\ 
{\rm{car}}\,({\it{inputs\/}}), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval}, \\ 
{\it{netlist\/}}, \\ 
{\it{n\/}} $-\;1$)\-\index{simulate-dual-eval-2}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable simulate-dual-eval-2; name this event `simulate-dual-eval-2-off'.\index{simulate-dual-eval-2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-simulate-dual-eval-2 \\ \index{open-simulate-dual-eval-2}
\=\+(({\it{n\/}} $\simeq {\tt{0}}$) $\rightarrow$ ({\rm{simulate-dual-eval-2}}\,({\it{module\/}}, {\it{inputs\/}}, {\it{state\/}}, {\it{netlist\/}}, {\it{n\/}})\index{simulate-dual-eval-2} $=$ {\it{state\/}})) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{simulate-dual-eval-2}}\,({\it{module\/}}, {\it{inputs\/}}, {\it{state\/}}, {\it{netlist\/}}, {\it{n\/}})\index{simulate-dual-eval-2} \\ 
$=$$\;\;\;\;${\rm{simulate-dual-eval-2}}\,(\=\+{\it{module\/}}, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\it{module\/}}, \\ 
{\rm{car}}\,({\it{inputs\/}}), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval}, \\ 
{\it{netlist\/}}, \\ 
{\it{n\/}} $-\;1$)\-\index{simulate-dual-eval-2})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{min} \\  
\=\+{\rm{min}}\,({\it{x\/}}, {\it{y\/}})\index{min} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{y\/}} $<$ {\it{x\/}}$\;\;${\bf then }{\it{y\/}} \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable min; name this event `min-off'.\index{min-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{insert} \\  
\=\+{\rm{insert}}\,({\it{e\/}}, {\it{x\/}})\index{insert} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{e\/}} $\in$ {\it{x\/}}$\;\;${\bf then }{\it{x\/}} \\ 
{\bf else }{\rm{cons}}\,({\it{e\/}}, {\it{x\/}})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable insert; name this event `insert-off'.\index{insert-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{set-equal}$\;\;$
{\rm{set-equal}}\,({\it{x\/}}, {\it{y\/}})\index{set-equal} $=$ ({\rm{subset}}\,({\it{x\/}}, {\it{y\/}})\index{subset} $\wedge$ {\rm{subset}}\,({\it{y\/}}, {\it{x\/}})\index{subset})
\end{tabbing}


\noindent{\sc Event}:   Enable set-equal; name this event `set-equal-off'.\index{set-equal-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{set-diff} \\  
\=\+{\rm{set-diff}}\,({\it{x\/}}, {\it{y\/}})\index{set-diff} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $\in$ {\it{y\/}}$\;\;${\bf then }{\rm{set-diff}}\,({\rm{cdr}}\,({\it{x\/}}), {\it{y\/}})\index{set-diff} \\ 
{\bf else }{\rm{cons}}\,({\rm{car}}\,({\it{x\/}}), {\rm{set-diff}}\,({\rm{cdr}}\,({\it{x\/}}), {\it{y\/}})\index{set-diff})$\;${\bf  endif}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable set-diff; name this event `set-diff-off'.\index{set-diff-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{intersection} \\  
\=\+{\rm{intersection}}\,({\it{x\/}}, {\it{y\/}})\index{intersection} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $\in$ {\it{y\/}}$\;\;${\bf then }{\rm{cons}}\,({\rm{car}}\,({\it{x\/}}), {\rm{intersection}}\,({\rm{cdr}}\,({\it{x\/}}), {\it{y\/}})\index{intersection}) \\ 
{\bf else }{\rm{intersection}}\,({\rm{cdr}}\,({\it{x\/}}), {\it{y\/}})\index{intersection}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable intersection; name this event `intersection-off'.\index{intersection-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{last-cdr} \\  
\=\+{\rm{last-cdr}}\,({\it{x\/}})\index{last-cdr} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}})$\;\;${\bf then }{\rm{last-cdr}}\,({\rm{cdr}}\,({\it{x\/}}))\index{last-cdr} \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable last-cdr; name this event `last-cdr-off'.\index{last-cdr-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{list-duplicates} \\  
\=\+{\rm{list-duplicates}}\,({\it{x\/}}, {\it{duplicates\/}})\index{list-duplicates} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }{\rm{list-duplicates}}\,(\=\+{\rm{cdr}}\,({\it{x\/}}), \\ 
\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $\in$ {\rm{cdr}}\,({\it{x\/}}) \\ 
{\bf then }{\rm{insert}}\,({\rm{car}}\,({\it{x\/}}), {\it{duplicates\/}})\index{insert} \\ 
{\bf else }{\it{duplicates\/}}$\;${\bf  endif}\-)\-\index{list-duplicates} \\ 
{\bf else }{\it{duplicates\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable list-duplicates; name this event `list-duplicates-off'.\index{list-duplicates-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{remove-duplicates} \\  
\=\+{\rm{remove-duplicates}}\,({\it{x\/}})\index{remove-duplicates} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $\in$ {\rm{cdr}}\,({\it{x\/}})$\;\;${\bf then }{\rm{remove-duplicates}}\,({\rm{cdr}}\,({\it{x\/}}))\index{remove-duplicates} \\ 
{\bf else }{\rm{cons}}\,({\rm{car}}\,({\it{x\/}}), {\rm{remove-duplicates}}\,({\rm{cdr}}\,({\it{x\/}}))\index{remove-duplicates})$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable remove-duplicates; name this event `remove-duplicates-off'.\index{remove-duplicates-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{append-list} \\  
\=\+{\rm{append-list}}\,({\it{x\/}})\index{append-list} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}})$\;\;${\bf then }{\rm{append}}\,({\rm{car}}\,({\it{x\/}}), {\rm{append-list}}\,({\rm{cdr}}\,({\it{x\/}}))\index{append-list}) \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable append-list; name this event `append-list-off'.\index{append-list-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{flatten-list}$\;\;$
{\rm{flatten-list}}\,({\it{x\/}})\index{flatten-list} $=$ {\rm{remove-duplicates}}\,({\rm{append-list}}\,({\it{x\/}})\index{append-list})\index{remove-duplicates}
\end{tabbing}


\noindent{\sc Event}:   Enable flatten-list; name this event `flatten-list-off'.\index{flatten-list-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{is-head} \\  
\=\+{\rm{is-head}}\,({\it{x\/}}, {\it{y\/}})\index{is-head} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) $\wedge$ {\rm{listp}}\,({\it{y\/}}) \\ 
{\bf then }({\rm{car}}\,({\it{x\/}}) $=$ {\rm{car}}\,({\it{y\/}})) $\wedge$ {\rm{is-head}}\,({\rm{cdr}}\,({\it{x\/}}), {\rm{cdr}}\,({\it{y\/}}))\index{is-head} \\ 
{\bf else }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable is-head; name this event `is-head-off'.\index{is-head-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{listify} \\  
\=\+{\rm{listify}}\,({\it{x\/}})\index{listify} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}})$\;\;${\bf then }{\rm{cons}}\,({\rm{list}}\,({\rm{car}}\,({\it{x\/}})), {\rm{listify}}\,({\rm{cdr}}\,({\it{x\/}}))\index{listify}) \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable listify; name this event `listify-off'.\index{listify-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{alistp} \\  
\=\+{\rm{alistp}}\,({\it{x\/}})\index{alistp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}})$\;\;${\bf then }{\rm{listp}}\,({\rm{car}}\,({\it{x\/}})) $\wedge$ {\rm{alistp}}\,({\rm{cdr}}\,({\it{x\/}}))\index{alistp} \\ 
{\bf else }{\it{x\/}} $=$ {\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable alistp; name this event `alistp-off'.\index{alistp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{boundp}$\;\;$
{\rm{boundp}}\,({\it{key\/}}, {\it{alist\/}})\index{boundp} $=$ {\rm{listp}}\,({\rm{lookup-module}}\,({\it{key\/}}, {\it{alist\/}})\index{lookup-module})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{alist-entry}$\;\;$
{\rm{alist-entry}}\,({\it{key\/}}, {\it{alist\/}})\index{alist-entry} $=$ {\rm{lookup-module}}\,({\it{key\/}}, {\it{alist\/}})\index{lookup-module}
\end{tabbing}


\noindent{\sc Event}:   Enable alist-entry; name this event `alist-entry-off'.\index{alist-entry-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{unbind}$\;\;$
{\rm{unbind}}\,({\it{key\/}}, {\it{alist\/}})\index{unbind} $=$ {\rm{delete-module}}\,({\it{key\/}}, {\it{alist\/}})\index{delete-module}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{set-value} \\  
\=\+{\rm{set-value}}\,({\it{key\/}}, {\it{value\/}}, {\it{alist\/}})\index{set-value} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{alist-entry}}\,({\it{key\/}}, {\it{alist\/}})\index{alist-entry} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{cons}}\,({\rm{cons}}\,({\it{key\/}}, {\it{value\/}}), {\it{alist\/}}) \\ 
{\bf elseif }{\it{value\/}} $=$ {\rm{cdr}}\,({\rm{alist-entry}}\,({\it{key\/}}, {\it{alist\/}})\index{alist-entry})$\;\;${\bf then }{\it{alist\/}} \\ 
{\bf else }{\rm{cons}}\,({\rm{cons}}\,({\it{key\/}}, {\it{value\/}}), {\rm{unbind}}\,({\it{key\/}}, {\it{alist\/}})\index{unbind})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable set-value; name this event `set-value-off'.\index{set-value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{union-values} \\  
\=\+{\rm{union-values}}\,({\it{keys\/}}, {\it{alist\/}})\index{union-values} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{keys\/}}) \\ 
{\bf then }{\rm{value}}\,({\rm{car}}\,({\it{keys\/}}), {\it{alist\/}})\index{value} $\cup$ {\rm{union-values}}\,({\rm{cdr}}\,({\it{keys\/}}), {\it{alist\/}})\index{union-values} \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable union-values; name this event `union-values-off'.\index{union-values-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{list-union-values} \\  
\=\+{\rm{list-union-values}}\,({\it{list-of-args\/}}, {\it{alist\/}})\index{list-union-values} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{list-of-args\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{union-values}}\,({\rm{car}}\,({\it{list-of-args\/}}), {\it{alist\/}})\index{union-values}, \\ 
{\rm{list-union-values}}\,({\rm{cdr}}\,({\it{list-of-args\/}}), {\it{alist\/}})\index{list-union-values})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable list-union-values; name this event `list-union-values-off'.\index{list-union-values-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{unbound-keys} \\  
\=\+{\rm{unbound-keys}}\,({\it{keys\/}}, {\it{alist\/}})\index{unbound-keys} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{keys\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{boundp}}\,({\rm{car}}\,({\it{keys\/}}), {\it{alist\/}})\index{boundp}$\;\;${\bf then }{\rm{unbound-keys}}\,({\rm{cdr}}\,({\it{keys\/}}), {\it{alist\/}})\index{unbound-keys} \\ 
{\bf else }{\rm{insert}}\,({\rm{car}}\,({\it{keys\/}}), {\rm{unbound-keys}}\,({\rm{cdr}}\,({\it{keys\/}}), {\it{alist\/}})\index{unbound-keys})\index{insert}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable unbound-keys; name this event `unbound-keys-off'.\index{unbound-keys-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{unbind-list} \\  
\=\+{\rm{unbind-list}}\,({\it{keys\/}}, {\it{alist\/}})\index{unbind-list} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{keys\/}})$\;\;${\bf then }{\rm{unbind}}\,({\rm{car}}\,({\it{keys\/}}), {\rm{unbind-list}}\,({\rm{cdr}}\,({\it{keys\/}}), {\it{alist\/}})\index{unbind-list})\index{unbind} \\ 
{\bf else }{\it{alist\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lookup-module-in-delete-module \\ \index{lookup-module-in-delete-module}
\=\+(({\it{k1\/}} $\not=$ {\it{k2\/}}) $\wedge$ {\rm{lookup-module}}\,({\it{k1\/}}, {\it{m\/}})\index{lookup-module}) \\ 
$\rightarrow$$\;\;\;\;${\rm{lookup-module}}\,({\it{k1\/}}, {\rm{delete-module}}\,({\it{k2\/}}, {\it{m\/}})\index{delete-module})\index{lookup-module}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lookup-module-in-unbind-list \\ \index{lookup-module-in-unbind-list}
(({\it{k\/}} $\not\in$ {\it{u\/}}) $\wedge$ {\rm{lookup-module}}\,({\it{k\/}}, {\it{m\/}})\index{lookup-module}) $\rightarrow$ {\rm{lookup-module}}\,({\it{k\/}}, {\rm{unbind-list}}\,({\it{u\/}}, {\it{m\/}})\index{unbind-list})\index{lookup-module}
\end{tabbing}


\noindent{\sc Event}:   Enable lookup-module-in-delete-module; name this event `lookup-module-in-delete-module-off'.\index{lookup-module-in-delete-module-!off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-unbind-list-count \\ \index{lessp-unbind-list-count}
\=\+(({\it{k\/}} $\not\in$ {\it{u\/}}) $\wedge$ {\rm{boundp}}\,({\it{k\/}}, {\it{m\/}})\index{boundp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{count}}\,({\rm{unbind-list}}\,({\rm{cons}}\,({\it{k\/}}, {\it{u\/}}), {\it{m\/}})\index{unbind-list}) $<$ {\rm{count}}\,({\rm{unbind-list}}\,({\it{u\/}}, {\it{m\/}})\index{unbind-list}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable boundp; name this event `boundp-off'.\index{boundp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable unbind; name this event `unbind-off'.\index{unbind-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable unbind-list; name this event `unbind-list-off'.\index{unbind-list-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lookup-module-in-unbind-list; name this event `lookup-module-in-unbind-list-off'.\index{lookup-module-in-unbind-list-of!f}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{m-states-list} \\  
\=\+{\rm{m-states-list}}\,({\it{m-states\/}})\index{m-states-list} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{m-states\/}}) $\vee$ ({\it{m-states\/}} $=$ {\bf{nil}})$\;\;${\bf then }{\it{m-states\/}} \\ 
{\bf else }{\rm{list}}\,({\it{m-states\/}})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable m-states-list; name this event `m-states-list-off'.\index{m-states-list-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{list-lessp} \\  
\=\+{\rm{list-lessp}}\,({\it{x\/}}, {\it{y\/}})\index{list-lessp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\it{y\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $<$ {\rm{car}}\,({\it{y\/}})$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\rm{car}}\,({\it{x\/}}) $=$ {\rm{car}}\,({\it{y\/}})$\;\;${\bf then }{\rm{list-lessp}}\,({\rm{cdr}}\,({\it{x\/}}), {\rm{cdr}}\,({\it{y\/}}))\index{list-lessp} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{listp}}\,({\it{y\/}})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable list-lessp; name this event `list-lessp-off'.\index{list-lessp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{token-lessp} \\  
\=\+{\rm{token-lessp}}\,({\it{x\/}}, {\it{y\/}})\index{token-lessp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{litatom}}\,({\it{x\/}}) $\wedge$ {\rm{litatom}}\,({\it{y\/}})$\;\;${\bf then }{\rm{list-lessp}}\,({\rm{unpack}}\,({\it{x\/}}), {\rm{unpack}}\,({\it{y\/}}))\index{list-lessp} \\ 
{\bf elseif }{\rm{litatom}}\,({\it{x\/}}) $\wedge$ {\rm{indexp}}\,({\it{y\/}})\index{indexp}$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\rm{indexp}}\,({\it{x\/}})\index{indexp} $\wedge$ {\rm{litatom}}\,({\it{y\/}})$\;\;${\bf then }{\bf{f}} \\ 
{\bf elseif }{\rm{indexp}}\,({\it{x\/}})\index{indexp} $\wedge$ {\rm{indexp}}\,({\it{y\/}})\index{indexp} \\ 
{\bf then }\=\+{\bf if }{\rm{i-name}}\,({\it{x\/}})\index{i-name} $=$ {\rm{i-name}}\,({\it{y\/}})\index{i-name}$\;\;${\bf then }{\rm{i-num}}\,({\it{x\/}})\index{i-num} $<$ {\rm{i-num}}\,({\it{y\/}})\index{i-num} \\ 
{\bf else }{\rm{list-lessp}}\,({\rm{unpack}}\,({\rm{i-name}}\,({\it{x\/}})\index{i-name}), {\rm{unpack}}\,({\rm{i-name}}\,({\it{y\/}})\index{i-name}))\index{list-lessp}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable token-lessp; name this event `token-lessp-off'.\index{token-lessp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{min-token-help} \\  
\=\+{\rm{min-token-help}}\,({\it{seed\/}}, {\it{list\/}})\index{min-token-help} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{list\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{token-lessp}}\,({\it{seed\/}}, {\rm{car}}\,({\it{list\/}}))\index{token-lessp} \\ 
{\bf then }{\rm{min-token-help}}\,({\it{seed\/}}, {\rm{cdr}}\,({\it{list\/}}))\index{min-token-help} \\ 
{\bf else }{\rm{min-token-help}}\,({\rm{car}}\,({\it{list\/}}), {\rm{cdr}}\,({\it{list\/}}))\index{min-token-help}$\;${\bf  endif}\- \\ 
{\bf else }{\it{seed\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable min-token-help; name this event `min-token-help-off'.\index{min-token-help-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{min-token} \\  
\=\+{\rm{min-token}}\,({\it{list\/}})\index{min-token} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{list\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{cdr}}\,({\it{list\/}}))$\;\;${\bf then }{\rm{min-token-help}}\,({\rm{car}}\,({\it{list\/}}), {\rm{cdr}}\,({\it{list\/}}))\index{min-token-help} \\ 
{\bf else }{\rm{car}}\,({\it{list\/}})$\;${\bf  endif}\- \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable min-token; name this event `min-token-off'.\index{min-token-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  min-token-help-lemma \\ \index{min-token-help-lemma}
\=\+({\rm{min-token-help}}\,({\it{seed\/}}, {\it{list\/}})\index{min-token-help} $=$ {\it{seed\/}}) \\ 
$\vee$$\;\;\;\;$({\rm{min-token-help}}\,({\it{seed\/}}, {\it{list\/}})\index{min-token-help} $\in$ {\it{list\/}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  min-token-lemma \\ \index{min-token-lemma}
{\rm{listp}}\,({\it{lst\/}}) $\rightarrow$ ({\rm{min-token}}\,({\it{lst\/}})\index{min-token} $\in$ {\it{lst\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  delete*-count \\ \index{delete*-count}
{\rm{count}}\,({\rm{delete*}}\,({\it{e\/}}, {\it{x\/}})\index{delete*}) $<$ {\rm{count}}\,({\rm{cons}}\,({\it{e\/}}, {\it{x\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  delete*-lemma \\ \index{delete*-lemma}
({\it{e\/}} $\in$ {\it{lst\/}}) $\rightarrow$ ({\rm{count}}\,({\rm{delete*}}\,({\it{e\/}}, {\it{lst\/}})\index{delete*}) $<$ {\rm{count}}\,({\it{lst\/}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{list-sort} \\  
\=\+{\rm{list-sort}}\,({\it{list\/}})\index{list-sort} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{list\/}}) \\ 
{\bf then }{\rm{cons}}\,({\rm{min-token}}\,({\it{list\/}})\index{min-token}, {\rm{list-sort}}\,({\rm{delete*}}\,({\rm{min-token}}\,({\it{list\/}})\index{min-token}, {\it{list\/}})\index{delete*})\index{list-sort}) \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable list-sort; name this event `list-sort-off'.\index{list-sort-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{list-list-sort} \\  
\=\+{\rm{list-list-sort}}\,({\it{list\/}})\index{list-list-sort} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{list\/}}) \\ 
{\bf then }{\rm{cons}}\,({\rm{list-sort}}\,({\rm{car}}\,({\it{list\/}}))\index{list-sort}, {\rm{list-list-sort}}\,({\rm{cdr}}\,({\it{list\/}}))\index{list-list-sort}) \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable list-list-sort; name this event `list-list-sort-off'.\index{list-list-sort-off}

\addvspace{18pt}


\noindent{\sc Event}:   Add the shell {\it{net-error\/}}\index{net-error}, with recognizer function symbol {\it{net-errorp\/}} and 2 accessors: {\it{error-label\/}}, with type restriction (none-of) and default value false; {\it{error-body\/}}, with type restriction (none-of) and default value true.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{report-error}$\;\;$
{\rm{report-error}}\,({\it{err\/}})\index{report-error} $=$ {\it{err\/}}
\end{tabbing}


\noindent{\sc Event}:   Enable report-error; name this event `report-error-off'.\index{report-error-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pred-error} \\  
{\rm{pred-error}}\,({\it{label\/}}, {\it{body\/}})\index{pred-error} $=$ {\rm{report-error}}\,({\rm{net-error}}\,({\it{label\/}}, {\it{body\/}})\index{net-error})\index{report-error}
\end{tabbing}


\noindent{\sc Event}:   Enable pred-error; name this event `pred-error-off'.\index{pred-error-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{error-entry} \\  
\=\+{\rm{error-entry}}\,({\it{lst\/}}, {\it{label\/}})\index{error-entry} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{lst\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{net-errorp}}\,({\rm{car}}\,({\it{lst\/}}))\index{net-errorp} \\ 
{\bf then }\=\+{\bf if }{\rm{error-label}}\,({\rm{car}}\,({\it{lst\/}}))\index{error-label} $=$ {\it{label\/}}$\;\;${\bf then }{\rm{car}}\,({\it{lst\/}}) \\ 
{\bf else }{\rm{error-entry}}\,({\rm{cdr}}\,({\it{lst\/}}), {\it{label\/}})\index{error-entry}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{error-entry}}\,({\rm{cdr}}\,({\it{lst\/}}), {\it{label\/}})\index{error-entry}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable error-entry; name this event `error-entry-off'.\index{error-entry-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{net-errors} \\  
\=\+{\rm{net-errors}}\,({\it{lst\/}})\index{net-errors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{lst\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{net-errorp}}\,({\rm{car}}\,({\it{lst\/}}))\index{net-errorp}$\;\;${\bf then }{\rm{cons}}\,({\rm{car}}\,({\it{lst\/}}), {\rm{net-errors}}\,({\rm{cdr}}\,({\it{lst\/}}))\index{net-errors}) \\ 
{\bf else }{\rm{net-errors}}\,({\rm{cdr}}\,({\it{lst\/}}))\index{net-errors}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable net-errors; name this event `net-errors-off'.\index{net-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-net-errors} \\  
\=\+{\rm{collect-net-errors}}\,({\it{lst\/}})\index{collect-net-errors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{lst\/}}) \\ 
{\bf then }{\rm{append}}\,({\rm{net-errors}}\,({\rm{car}}\,({\it{lst\/}}))\index{net-errors}, {\rm{collect-net-errors}}\,({\rm{cdr}}\,({\it{lst\/}}))\index{collect-net-errors}) \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-net-errors; name this event `collect-net-errors-off'.\index{collect-net-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{err-and} \\  
\=\+{\rm{err-and}}\,({\it{lst\/}}, {\it{label\/}})\index{err-and} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{net-errors}}\,({\it{lst\/}})\index{net-errors} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{pred-error}}\,({\it{label\/}}, {\rm{net-errors}}\,({\it{lst\/}})\index{net-errors})\index{pred-error}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable err-and; name this event `err-and-off'.\index{err-and-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{t-or-err} \\  
\=\+{\rm{t-or-err}}\,({\it{p\/}}, {\it{label\/}}, {\it{body\/}})\index{t-or-err} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{p\/}} $\wedge$ ($\neg$ {\rm{net-errorp}}\,({\it{p\/}})\index{net-errorp})$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{pred-error}}\,({\it{label\/}}, {\it{body\/}})\index{pred-error}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable t-or-err; name this event `t-or-err-off'.\index{t-or-err-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{nlistp-or-err} \\  
\=\+{\rm{nlistp-or-err}}\,({\it{x\/}}, {\it{label\/}})\index{nlistp-or-err} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{pred-error}}\,({\it{label\/}}, {\it{x\/}})\index{pred-error}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable nlistp-or-err; name this event `nlistp-or-err-off'.\index{nlistp-or-err-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{nil-or-err} \\  
\=\+{\rm{nil-or-err}}\,({\it{x\/}}, {\it{label\/}})\index{nil-or-err} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $=$ {\bf{nil}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{pred-error}}\,({\it{label\/}}, {\it{x\/}})\index{pred-error}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable nil-or-err; name this event `nil-or-err-off'.\index{nil-or-err-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{subset-or-err} \\  
\=\+{\rm{subset-or-err}}\,({\it{x\/}}, {\it{y\/}}, {\it{label\/}})\index{subset-or-err} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{set-diff}}\,({\it{x\/}}, {\it{y\/}})\index{set-diff} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{pred-error}}\,({\it{label\/}}, {\rm{set-diff}}\,({\it{x\/}}, {\it{y\/}})\index{set-diff})\index{pred-error}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable subset-or-err; name this event `subset-or-err-off'.\index{subset-or-err-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{no-duplicates-or-err} \\  
\=\+{\rm{no-duplicates-or-err}}\,({\it{x\/}}, {\it{label\/}})\index{no-duplicates-or-err} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{list-duplicates}}\,({\it{x\/}}, {\bf{nil}})\index{list-duplicates} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{pred-error}}\,({\it{label\/}}, {\rm{list-duplicates}}\,({\it{x\/}}, {\bf{nil}})\index{list-duplicates})\index{pred-error}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable no-duplicates-or-err; name this event `no-duplicates-or-err-off'.\index{no-duplicates-or-err-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{disjoint-or-err} \\  
\=\+{\rm{disjoint-or-err}}\,({\it{x\/}}, {\it{y\/}}, {\it{label\/}})\index{disjoint-or-err} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{intersection}}\,({\it{x\/}}, {\it{y\/}})\index{intersection} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{pred-error}}\,({\it{label\/}}, {\rm{intersection}}\,({\it{x\/}}, {\it{y\/}})\index{intersection})\index{pred-error}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable disjoint-or-err; name this event `disjoint-or-err-off'.\index{disjoint-or-err-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{all-bound-or-err} \\  
\=\+{\rm{all-bound-or-err}}\,({\it{keys\/}}, {\it{alist\/}}, {\it{label\/}})\index{all-bound-or-err} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{unbound-keys}}\,({\it{keys\/}}, {\it{alist\/}})\index{unbound-keys} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{pred-error}}\,({\it{label\/}}, {\rm{unbound-keys}}\,({\it{keys\/}}, {\it{alist\/}})\index{unbound-keys})\index{pred-error}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable all-bound-or-err; name this event `all-bound-or-err-off'.\index{all-bound-or-err-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{label-error} \\  
\=\+{\rm{label-error}}\,({\it{x\/}}, {\it{label\/}})\index{label-error} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{net-errorp}}\,({\it{x\/}})\index{net-errorp}$\;\;${\bf then }{\rm{pred-error}}\,({\it{label\/}}, {\it{x\/}})\index{pred-error} \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable label-error; name this event `label-error-off'.\index{label-error-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{list-collect-value} \\  
\=\+{\rm{list-collect-value}}\,({\it{list-of-args\/}}, {\it{alist\/}})\index{list-collect-value} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{list-of-args\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{flatten-list}}\,({\rm{collect-value}}\,({\rm{car}}\,({\it{list-of-args\/}}), {\it{alist\/}})\index{collect-value})\index{flatten-list}, \\ 
{\rm{list-collect-value}}\,({\rm{cdr}}\,({\it{list-of-args\/}}), {\it{alist\/}})\index{list-collect-value})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable list-collect-value; name this event `list-collect-value-off'.\index{list-collect-value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{name-simple-okp} \\  
\=\+{\rm{name-simple-okp}}\,({\it{name\/}})\index{name-simple-okp} \\ 
$=$$\;\;\;\;$({\rm{litatom}}\,({\it{name\/}}) $\vee$ ({\rm{indexp}}\,({\it{name\/}})\index{indexp} $\wedge$ {\rm{litatom}}\,({\rm{i-name}}\,({\it{name\/}})\index{i-name})))\-
\end{tabbing}


\noindent{\sc Event}:   Enable name-simple-okp; name this event `name-simple-okp-off'.\index{name-simple-okp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{name-list-simple-okp} \\  
\=\+{\rm{name-list-simple-okp}}\,({\it{name-list\/}})\index{name-list-simple-okp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{name-list\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{name-list\/}} $=$ {\bf{nil}} \\ 
{\bf else }\=\+{\rm{name-simple-okp}}\,({\rm{car}}\,({\it{name-list\/}}))\index{name-simple-okp} \\ 
$\wedge$$\;\;\;\;$({\rm{car}}\,({\it{name-list\/}}) $\not\in$ {\rm{cdr}}\,({\it{name-list\/}})) \\ 
$\wedge$$\;\;\;\;${\rm{name-list-simple-okp}}\,({\rm{cdr}}\,({\it{name-list\/}}))\index{name-list-simple-okp}\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable name-list-simple-okp; name this event `name-list-simple-okp-off'.\index{name-list-simple-okp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{occ-syntax-simple-okp} \\  
\=\+{\rm{occ-syntax-simple-okp}}\,({\it{occ\/}}, {\it{netlist\/}})\index{occ-syntax-simple-okp} \\ 
$=$$\;\;\;\;$(\=\+(\=\+({\tt{4}} $=$ {\rm{length}}\,({\it{occ\/}})\index{length}) \\ 
$\vee$$\;\;\;\;$(({\tt{5}} $=$ {\rm{length}}\,({\it{occ\/}})\index{length}) $\wedge$ {\rm{alistp}}\,({\rm{occ-annotation}}\,({\it{occ\/}})\index{occ-annotation})\index{alistp}))\- \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{occ\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;${\rm{name-simple-okp}}\,({\rm{occ-name}}\,({\it{occ\/}})\index{occ-name})\index{name-simple-okp} \\ 
$\wedge$$\;\;\;\;${\rm{name-list-simple-okp}}\,({\rm{occ-outputs}}\,({\it{occ\/}})\index{occ-outputs})\index{name-list-simple-okp} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{occ-inputs}}\,({\it{occ\/}})\index{occ-inputs})\index{properp} \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{primp}}\,({\rm{occ-function}}\,({\it{occ\/}})\index{occ-function})\index{primp} \\ 
{\bf then }\=\+(\=\+{\rm{length}}\,({\rm{primp2}}\,({\rm{occ-function}}\,({\it{occ\/}})\index{occ-function}, {\tt{'}}{\tt{inputs}})\index{primp2})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{occ-inputs}}\,({\it{occ\/}})\index{occ-inputs})\index{length})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{length}}\,({\rm{primp2}}\,({\rm{occ-function}}\,({\it{occ\/}})\index{occ-function}, {\tt{'}}{\tt{outputs}})\index{primp2})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{occ-outputs}}\,({\it{occ\/}})\index{occ-outputs})\index{length})\-\- \\ 
{\bf else }\=\+{\rm{listp}}\,({\rm{lookup-module}}\,({\rm{occ-function}}\,({\it{occ\/}})\index{occ-function}, {\it{netlist\/}})\index{lookup-module}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{length}}\,({\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\rm{occ-function}}\,({\it{occ\/}})\index{occ-function}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{occ-inputs}}\,({\it{occ\/}})\index{occ-inputs})\index{length})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{length}}\,({\rm{module-outputs}}\,({\rm{lookup-module}}\,(\=\+{\rm{occ-function}}\,({\it{occ\/}})\index{occ-function}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-outputs})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{occ-outputs}}\,({\it{occ\/}})\index{occ-outputs})\index{length})\-\-$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable occ-syntax-simple-okp; name this event `occ-syntax-simple-okp-off'.\index{occ-syntax-simple-okp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{occ-body-syntax-simple-okp} \\  
\=\+{\rm{occ-body-syntax-simple-okp}}\,(\=\+{\it{body\/}}, \\ 
{\it{signals\/}}, \\ 
{\it{non-depends\/}}, \\ 
{\it{occ-names\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{states\/}}, \\ 
{\it{netlist\/}})\-\index{occ-body-syntax-simple-okp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{body\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }\=\+({\it{body\/}} $=$ {\bf{nil}}) \\ 
$\wedge$$\;\;\;\;${\rm{subset}}\,({\it{outputs\/}}, {\it{signals\/}})\index{subset} \\ 
$\wedge$$\;\;\;\;${\rm{subset}}\,({\it{non-depends\/}}, {\it{signals\/}})\index{subset} \\ 
$\wedge$$\;\;\;\;${\rm{subset}}\,({\it{states\/}}, {\it{occ-names\/}})\index{subset} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{duplicates?}}\,({\it{signals\/}})\index{duplicates?}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{duplicates?}}\,({\it{occ-names\/}})\index{duplicates?})\- \\ 
{\bf elseif }{\rm{occ-syntax-simple-okp}}\,({\rm{car}}\,({\it{body\/}}), {\it{netlist\/}})\index{occ-syntax-simple-okp} \\ 
{\bf then }{\rm{occ-body-syntax-simple-okp}}\,(\=\+{\rm{cdr}}\,({\it{body\/}}), \\ 
{\rm{append}}\,({\rm{occ-outputs}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-outputs}, {\it{signals\/}}), \\ 
{\rm{append}}\,(\=\+{\rm{set-diff}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-inputs}, \\ 
{\it{signals\/}})\-\index{set-diff}, \\ 
{\it{non-depends\/}})\-, \\ 
{\rm{cons}}\,({\rm{occ-name}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-name}, {\it{occ-names\/}}), \\ 
{\it{outputs\/}}, \\ 
{\it{states\/}}, \\ 
{\it{netlist\/}})\-\index{occ-body-syntax-simple-okp} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable occ-body-syntax-simple-okp; name this event `occ-body-syntax-simple-okp-off'.\index{occ-body-syntax-simple-okp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{module-syntax-simple-okp} \\  
\=\+{\rm{module-syntax-simple-okp}}\,({\it{netlist\/}})\index{module-syntax-simple-okp} \\ 
$=$$\;\;\;\;$(\=\+(\=\+({\rm{length}}\,({\rm{car}}\,({\it{netlist\/}}))\index{length} $=$ {\tt{5}}) \\ 
$\vee$$\;\;\;\;$(\=\+({\rm{length}}\,({\rm{car}}\,({\it{netlist\/}}))\index{length} $=$ {\tt{6}}) \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\rm{module-annotation}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-annotation})\index{alistp})\-)\- \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{car}}\,({\it{netlist\/}}))\index{properp} \\ 
$\wedge$$\;\;\;\;${\rm{name-simple-okp}}\,({\rm{module-name}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-name})\index{name-simple-okp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{lookup-module}}\,({\rm{module-name}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-name}, {\rm{cdr}}\,({\it{netlist\/}}))\index{lookup-module}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{primp}}\,({\rm{module-name}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-name})\index{primp}) \\ 
$\wedge$$\;\;\;\;${\rm{name-list-simple-okp}}\,({\rm{module-inputs}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-inputs})\index{name-list-simple-okp} \\ 
$\wedge$$\;\;\;\;${\rm{name-list-simple-okp}}\,({\rm{module-outputs}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-outputs})\index{name-list-simple-okp} \\ 
$\wedge$$\;\;\;\;${\rm{name-list-simple-okp}}\,({\rm{m-states-list}}\,({\rm{module-statenames}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-statenames})\index{m-states-list})\index{name-list-simple-okp} \\ 
$\wedge$$\;\;\;\;${\rm{disjoint}}\,(\=\+{\rm{module-inputs}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-inputs}, \\ 
{\rm{module-outputs}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-outputs})\-\index{disjoint} \\ 
$\wedge$$\;\;\;\;${\rm{listp}}\,({\rm{module-occurrences}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-occurrences}) \\ 
$\wedge$$\;\;\;\;${\rm{occ-body-syntax-simple-okp}}\,(\=\+{\rm{module-occurrences}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-occurrences}, \\ 
{\rm{module-inputs}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-inputs}, \\ 
{\bf{nil}}, \\ 
{\bf{nil}}, \\ 
{\rm{module-outputs}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-outputs}, \\ 
{\rm{m-states-list}}\,({\rm{module-statenames}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-statenames})\index{m-states-list}, \\ 
{\rm{cdr}}\,({\it{netlist\/}}))\-\index{occ-body-syntax-simple-okp})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable module-syntax-simple-okp; name this event `module-syntax-simple-okp-off'.\index{module-syntax-simple-okp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{netlist-syntax-simple-okp} \\  
\=\+{\rm{netlist-syntax-simple-okp}}\,({\it{netlist\/}})\index{netlist-syntax-simple-okp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{netlist\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{netlist\/}} $=$ {\bf{nil}} \\ 
{\bf elseif }{\rm{module-syntax-simple-okp}}\,({\it{netlist\/}})\index{module-syntax-simple-okp} \\ 
{\bf then }{\rm{netlist-syntax-simple-okp}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{netlist-syntax-simple-okp} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable netlist-syntax-simple-okp; name this event `netlist-syntax-simple-okp-off'.\index{netlist-syntax-simple-okp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{out-depends-simple} \\  
\=\+{\rm{out-depends-simple}}\,({\it{flg\/}}, {\it{x0\/}}, {\it{x1\/}}, {\it{netlist\/}}, {\it{module-database\/}})\index{out-depends-simple} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{flg\/}}: \\ 
{\bf case = }{\tt{0}} \\ 
{\bf then }\=\+{\bf if }{\rm{primp}}\,({\it{x0\/}})\index{primp} \\ 
{\bf then }{\rm{list-collect-value}}\,(\=\+{\rm{primp2}}\,({\it{x0\/}}, {\tt{'}}{\tt{out-depends}})\index{primp2}, \\ 
{\rm{pairlist}}\,({\rm{primp2}}\,({\it{x0\/}}, {\tt{'}}{\tt{inputs}})\index{primp2}, {\it{x1\/}}))\-\index{list-collect-value} \\ 
{\bf elseif }{\rm{lookup-module}}\,(\=\+{\tt{'}}{\tt{out-depends}}, \\ 
{\rm{cdr}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{module-database\/}})\index{lookup-module}))\-\index{lookup-module} \\ 
{\bf then }{\rm{list-collect-value}}\,(\=\+{\rm{cdr}}\,({\rm{lookup-module}}\,(\=\+{\tt{'}}{\tt{out-depends}}, \\ 
{\rm{cdr}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{module-database\/}})\-\index{lookup-module}))\-\index{lookup-module}), \\ 
{\rm{pairlist}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\it{x1\/}})\-)\-\index{list-collect-value} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{lookup-module}) \\ 
{\bf then }\=\+{\bf if }\=\+{\rm{out-depends-simple}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\rm{pairlist}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\it{x1\/}})\-, \\ 
{\rm{delete-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{delete-module}, \\ 
{\it{module-database\/}})\-\index{out-depends-simple} \\ 
$\wedge$$\;\;\;\;${\rm{subset}}\,(\=\+{\rm{module-outputs}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{lookup-module})\index{module-outputs}, \\ 
{\rm{strip-cars}}\,({\rm{out-depends-simple}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\rm{pairlist}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\it{x1\/}})\-, \\ 
{\rm{delete-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\it{module-database\/}})\-\index{out-depends-simple}))\-\index{subset}\- \\ 
{\bf then }{\rm{collect-value}}\,(\=\+{\rm{module-outputs}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{lookup-module})\index{module-outputs}, \\ 
{\rm{out-depends-simple}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\rm{pairlist}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\it{x1\/}})\-, \\ 
{\rm{delete-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\it{module-database\/}})\-\index{out-depends-simple})\-\index{collect-value} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{1}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\it{x0\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{x1\/}} \\ 
{\bf elseif }\=\+{\rm{subset}}\,(\=\+{\rm{flatten-list}}\,({\rm{out-depends-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-function}, \\ 
{\rm{listify}}\,({\rm{occ-inputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-inputs})\index{listify}, \\ 
{\it{netlist\/}}, \\ 
{\it{module-database\/}})\-\index{out-depends-simple})\index{flatten-list}, \\ 
{\rm{strip-cars}}\,({\it{x1\/}}))\-\index{subset} \\ 
$\wedge$$\;\;\;\;${\rm{out-depends-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-function}, \\ 
{\rm{listify}}\,({\rm{occ-inputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-inputs})\index{listify}, \\ 
{\it{netlist\/}}, \\ 
{\it{module-database\/}})\-\index{out-depends-simple}\- \\ 
{\bf then }{\rm{out-depends-simple}}\,(\=\+{\tt{1}}, \\ 
{\rm{cdr}}\,({\it{x0\/}}), \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\rm{occ-outputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-outputs}, \\ 
{\rm{list-collect-value}}\,(\=\+{\rm{out-depends-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-function}, \\ 
{\rm{listify}}\,({\rm{occ-inputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-inputs})\index{listify}, \\ 
{\it{netlist\/}}, \\ 
{\it{module-database\/}})\-\index{out-depends-simple}, \\ 
{\it{x1\/}})\-\index{list-collect-value})\-, \\ 
{\it{x1\/}})\-, \\ 
{\it{netlist\/}}, \\ 
{\it{module-database\/}})\-\index{out-depends-simple} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf otherwise }{\bf{f}}$\;${\bf  endcase}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable out-depends-simple; name this event `out-depends-simple-off'.\index{out-depends-simple-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{simple-dependency-table} \\  
\=\+{\rm{simple-dependency-table}}\,({\it{netlist\/}})\index{simple-dependency-table} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{netlist\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf elseif }{\rm{simple-dependency-table}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{simple-dependency-table} \\ 
{\bf then }\=\+{\bf if }{\rm{out-depends-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{module-name}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-name}, \\ 
{\rm{listify}}\,({\rm{module-inputs}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-inputs})\index{listify}, \\ 
{\it{netlist\/}}, \\ 
{\rm{simple-dependency-table}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{simple-dependency-table})\-\index{out-depends-simple} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{module-name}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-name}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{out-depends}}, \\ 
{\rm{out-depends-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{module-name}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-name}, \\ 
{\rm{listify}}\,({\rm{module-inputs}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-inputs})\index{listify}, \\ 
{\it{netlist\/}}, \\ 
{\rm{simple-dependency-table}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{simple-dependency-table})\-\index{out-depends-simple})\-)\-, \\ 
{\rm{simple-dependency-table}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{simple-dependency-table})\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable simple-dependency-table; name this event `simple-dependency-table-off'.\index{simple-dependency-table-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{output-dependencies-simple} \\  
\=\+{\rm{output-dependencies-simple}}\,({\it{module-name\/}}, {\it{args\/}}, {\it{netlist\/}})\index{output-dependencies-simple} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+(\=\+{\rm{primp}}\,({\it{module-name\/}})\index{primp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{args\/}})\index{length} $=$ {\rm{length}}\,({\rm{primp2}}\,({\it{module-name\/}}, {\tt{'}}{\tt{inputs}})\index{primp2})\index{length}))\- \\ 
$\vee$$\;\;\;\;$(\=\+{\rm{lookup-module}}\,({\it{module-name\/}}, {\it{netlist\/}})\index{lookup-module} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{length}}\,({\it{args\/}})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{module-name\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs})\index{length})\-)\-\- \\ 
{\bf then }{\rm{list-list-sort}}\,({\rm{out-depends-simple}}\,(\=\+{\tt{0}}, \\ 
{\it{module-name\/}}, \\ 
{\it{args\/}}, \\ 
{\it{netlist\/}}, \\ 
{\rm{simple-dependency-table}}\,({\it{netlist\/}})\index{simple-dependency-table})\-\index{out-depends-simple})\index{list-list-sort} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable output-dependencies-simple; name this event `output-dependencies-simple-off'.\index{output-dependencies-simple-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{type-value-simple} \\  
\=\+{\rm{type-value-simple}}\,({\it{n\/}}, {\it{alist\/}}, {\it{default\/}})\index{type-value-simple} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{lookup-module}}\,({\it{n\/}}, {\it{alist\/}})\index{lookup-module} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }\=\+{\bf if }{\it{default\/}}$\;\;${\bf then }{\tt{'}}{\tt{free}} \\ 
{\bf else }{\rm{list}}\,({\it{n\/}})$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{cdr}}\,({\rm{lookup-module}}\,({\it{n\/}}, {\it{alist\/}})\index{lookup-module}) $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }{\rm{cdr}}\,({\rm{lookup-module}}\,({\it{n\/}}, {\it{alist\/}})\index{lookup-module}) \\ 
{\bf elseif }{\rm{cadr}}\,({\rm{lookup-module}}\,({\it{n\/}}, {\it{alist\/}})\index{lookup-module}) $=$ {\it{n\/}} \\ 
{\bf then }\=\+{\bf if }{\it{default\/}}$\;\;${\bf then }{\tt{'}}{\tt{free}} \\ 
{\bf else }{\rm{cdr}}\,({\rm{lookup-module}}\,({\it{n\/}}, {\it{alist\/}})\index{lookup-module})$\;${\bf  endif}\- \\ 
{\bf else }{\rm{type-value-simple}}\,(\=\+{\rm{cadr}}\,({\rm{lookup-module}}\,({\it{n\/}}, {\it{alist\/}})\index{lookup-module}), \\ 
{\rm{delete-module}}\,({\it{n\/}}, {\it{alist\/}})\index{delete-module}, \\ 
{\it{default\/}})\-\index{type-value-simple}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable type-value-simple; name this event `type-value-simple-off'.\index{type-value-simple-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-types} \\  
\=\+{\rm{collect-types}}\,({\it{names\/}}, {\it{alist\/}}, {\it{default\/}})\index{collect-types} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{names\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{type-value-simple}}\,({\rm{car}}\,({\it{names\/}}), {\it{alist\/}}, {\it{default\/}})\index{type-value-simple}, \\ 
{\rm{collect-types}}\,({\rm{cdr}}\,({\it{names\/}}), {\it{alist\/}}, {\it{default\/}})\index{collect-types})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-types; name this event `collect-types-off'.\index{collect-types-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{add-new-type} \\  
\=\+{\rm{add-new-type}}\,({\it{new-type-entry\/}}, {\it{known-types\/}})\index{add-new-type} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{cdr}}\,({\it{new-type-entry\/}}) $=$ {\tt{'}}{\tt{free}}$\;\;${\bf then }{\it{known-types\/}} \\ 
{\bf elseif }{\rm{lookup-module}}\,({\rm{car}}\,({\it{new-type-entry\/}}), {\it{known-types\/}})\index{lookup-module} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }{\rm{cons}}\,({\it{new-type-entry\/}}, {\it{known-types\/}}) \\ 
{\bf elseif }\=\+{\rm{cdr}}\,({\it{new-type-entry\/}}) \\ 
$=$$\;\;\;\;${\rm{cdr}}\,({\rm{lookup-module}}\,({\rm{car}}\,({\it{new-type-entry\/}}), {\it{known-types\/}})\index{lookup-module})\- \\ 
{\bf then }{\it{known-types\/}} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{cdr}}\,({\it{new-type-entry\/}})) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{cadr}}\,({\it{new-type-entry\/}}), \\ 
{\rm{cdr}}\,({\rm{lookup-module}}\,({\rm{car}}\,({\it{new-type-entry\/}}), {\it{known-types\/}})\index{lookup-module}))\-, \\ 
{\it{known-types\/}})\- \\ 
{\bf elseif }{\rm{listp}}\,({\rm{cdr}}\,({\rm{lookup-module}}\,({\rm{car}}\,({\it{new-type-entry\/}}), {\it{known-types\/}})\index{lookup-module})) \\ 
{\bf then }\=\+{\bf if }{\rm{add-new-type}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{cadr}}\,({\rm{lookup-module}}\,(\=\+{\rm{car}}\,({\it{new-type-entry\/}}), \\ 
{\it{known-types\/}})\-\index{lookup-module}), \\ 
{\rm{cdr}}\,({\it{new-type-entry\/}}))\-, \\ 
{\rm{delete-module}}\,({\rm{car}}\,({\it{new-type-entry\/}}), {\it{known-types\/}})\index{delete-module})\-\index{add-new-type} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\it{new-type-entry\/}}, \\ 
{\rm{add-new-type}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{cadr}}\,({\rm{lookup-module}}\,(\=\+{\rm{car}}\,({\it{new-type-entry\/}}), \\ 
{\it{known-types\/}})\-\index{lookup-module}), \\ 
{\rm{cdr}}\,({\it{new-type-entry\/}}))\-, \\ 
{\rm{delete-module}}\,(\=\+{\rm{car}}\,({\it{new-type-entry\/}}), \\ 
{\it{known-types\/}})\-\index{delete-module})\-\index{add-new-type})\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable add-new-type; name this event `add-new-type-off'.\index{add-new-type-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{update-known-types} \\  
\=\+{\rm{update-known-types}}\,({\it{new-types\/}}, {\it{known-types\/}})\index{update-known-types} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{new-types\/}} $\simeq\;${{\bf{nil}}}${}$) $\vee$ {\rm{falsep}}\,({\it{known-types\/}})$\;\;${\bf then }{\it{known-types\/}} \\ 
{\bf else }{\rm{update-known-types}}\,(\=\+{\rm{cdr}}\,({\it{new-types\/}}), \\ 
{\rm{add-new-type}}\,({\rm{car}}\,({\it{new-types\/}}), {\it{known-types\/}})\index{add-new-type})\-\index{update-known-types}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable update-known-types; name this event `update-known-types-off'.\index{update-known-types-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fix-dependent-types} \\  
\=\+{\rm{fix-dependent-types}}\,({\it{types\/}}, {\it{alist\/}})\index{fix-dependent-types} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{types\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{car}}\,({\it{types\/}})) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{value}}\,({\rm{caar}}\,({\it{types\/}}), {\it{alist\/}})\index{value}, \\ 
{\rm{fix-dependent-types}}\,({\rm{cdr}}\,({\it{types\/}}), {\it{alist\/}})\index{fix-dependent-types})\- \\ 
{\bf else }{\rm{cons}}\,({\rm{car}}\,({\it{types\/}}), {\rm{fix-dependent-types}}\,({\rm{cdr}}\,({\it{types\/}}), {\it{alist\/}})\index{fix-dependent-types})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fix-dependent-types; name this event `fix-dependent-types-off'.\index{fix-dependent-types-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{io-types-simple} \\  
\=\+{\rm{io-types-simple}}\,({\it{flg\/}}, {\it{x0\/}}, {\it{x1\/}}, {\it{netlist\/}}, {\it{type-table\/}})\index{io-types-simple} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{flg\/}}: \\ 
{\bf case = }{\tt{0}} \\ 
{\bf then }\=\+{\bf if }{\rm{primp}}\,({\it{x0\/}})\index{primp} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{primp2}}\,({\it{x0\/}}, {\tt{'}}{\tt{input-types}})\index{primp2}, \\ 
{\rm{fix-dependent-types}}\,(\=\+{\rm{primp2}}\,({\it{x0\/}}, {\tt{'}}{\tt{output-types}})\index{primp2}, \\ 
{\rm{pairlist}}\,({\rm{primp2}}\,({\it{x0\/}}, {\tt{'}}{\tt{inputs}})\index{primp2}, {\it{x1\/}}))\-\index{fix-dependent-types})\- \\ 
{\bf elseif }\=\+{\rm{lookup-module}}\,(\=\+{\tt{'}}{\tt{input-types}}, \\ 
{\rm{cdr}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{type-table\/}})\index{lookup-module}))\-\index{lookup-module} \\ 
$\wedge$$\;\;\;\;${\rm{lookup-module}}\,(\=\+{\tt{'}}{\tt{output-types}}, \\ 
{\rm{cdr}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{type-table\/}})\index{lookup-module}))\-\index{lookup-module}\- \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{cdr}}\,({\rm{lookup-module}}\,(\=\+{\tt{'}}{\tt{input-types}}, \\ 
{\rm{cdr}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{type-table\/}})\index{lookup-module}))\-\index{lookup-module}), \\ 
{\rm{fix-dependent-types}}\,(\=\+{\rm{cdr}}\,({\rm{lookup-module}}\,(\=\+{\tt{'}}{\tt{output-types}}, \\ 
{\rm{cdr}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{type-table\/}})\-\index{lookup-module}))\-\index{lookup-module}), \\ 
{\rm{pairlist}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\it{x1\/}})\-)\-\index{fix-dependent-types})\- \\ 
{\bf elseif }{\rm{listp}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{lookup-module}) \\ 
{\bf then }\=\+{\bf if }{\rm{io-types-simple}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\bf{nil}}, \\ 
{\rm{delete-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{delete-module}, \\ 
{\it{type-table\/}})\-\index{io-types-simple} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{collect-types}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\rm{io-types-simple}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\bf{nil}}, \\ 
{\rm{delete-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\it{type-table\/}})\-\index{io-types-simple}, \\ 
{\bf{t}})\-\index{collect-types}, \\ 
{\rm{fix-dependent-types}}\,(\=\+{\rm{collect-types}}\,(\=\+{\rm{module-outputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-outputs}, \\ 
{\rm{io-types-simple}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\bf{nil}}, \\ 
{\rm{delete-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\it{type-table\/}})\-\index{io-types-simple}, \\ 
{\bf{f}})\-\index{collect-types}, \\ 
{\rm{pairlist}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\it{x1\/}})\-)\-\index{fix-dependent-types})\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{1}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\it{x0\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{x1\/}} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{io-types-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-function}, \\ 
{\rm{collect-types}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-inputs}, \\ 
{\it{x1\/}}, \\ 
{\bf{f}})\-\index{collect-types}, \\ 
{\it{netlist\/}}, \\ 
{\it{type-table\/}})\-\index{io-types-simple}) \\ 
{\bf then }\=\+{\bf if }{\rm{update-known-types}}\,(\=\+{\rm{pairlist}}\,(\=\+{\rm{occ-outputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-outputs}, \\ 
{\rm{cdr}}\,({\rm{io-types-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-function}, \\ 
{\rm{collect-types}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-inputs}, \\ 
{\it{x1\/}}, \\ 
{\bf{f}})\-\index{collect-types}, \\ 
{\it{netlist\/}}, \\ 
{\it{type-table\/}})\-\index{io-types-simple}))\-, \\ 
{\rm{update-known-types}}\,(\=\+{\rm{pairlist}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-inputs}, \\ 
{\rm{car}}\,({\rm{io-types-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-function}, \\ 
{\rm{collect-types}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-inputs}, \\ 
{\it{x1\/}}, \\ 
{\bf{f}})\-\index{collect-types}, \\ 
{\it{netlist\/}}, \\ 
{\it{type-table\/}})\-\index{io-types-simple}))\-, \\ 
{\it{x1\/}})\-\index{update-known-types})\-\index{update-known-types} \\ 
{\bf then }{\rm{io-types-simple}}\,(\=\+{\tt{1}}, \\ 
{\rm{cdr}}\,({\it{x0\/}}), \\ 
{\rm{update-known-types}}\,(\=\+{\rm{pairlist}}\,(\=\+{\rm{occ-outputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-outputs}, \\ 
{\rm{cdr}}\,({\rm{io-types-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-function}, \\ 
{\rm{collect-types}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-inputs}, \\ 
{\it{x1\/}}, \\ 
{\bf{f}})\-\index{collect-types}, \\ 
{\it{netlist\/}}, \\ 
{\it{type-table\/}})\-\index{io-types-simple}))\-, \\ 
{\rm{update-known-types}}\,(\=\+{\rm{pairlist}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-inputs}, \\ 
{\rm{car}}\,({\rm{io-types-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-function}, \\ 
{\rm{collect-types}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-inputs}, \\ 
{\it{x1\/}}, \\ 
{\bf{f}})\-\index{collect-types}, \\ 
{\it{netlist\/}}, \\ 
{\it{type-table\/}})\-\index{io-types-simple}))\-, \\ 
{\it{x1\/}})\-\index{update-known-types})\-\index{update-known-types}, \\ 
{\it{netlist\/}}, \\ 
{\it{type-table\/}})\-\index{io-types-simple} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf otherwise }{\bf{f}}$\;${\bf  endcase}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable io-types-simple; name this event `io-types-simple-off'.\index{io-types-simple-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{netlist-type-table-simple} \\  
\=\+{\rm{netlist-type-table-simple}}\,({\it{netlist\/}})\index{netlist-type-table-simple} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{netlist\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf elseif }{\rm{netlist-type-table-simple}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{netlist-type-table-simple} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{io-types-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{module-name}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-name}, \\ 
{\rm{listify}}\,({\rm{module-inputs}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-inputs})\index{listify}, \\ 
{\it{netlist\/}}, \\ 
{\rm{netlist-type-table-simple}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{netlist-type-table-simple})\-\index{io-types-simple}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{module-name}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-name}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{input-types}}, \\ 
{\rm{car}}\,({\rm{io-types-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{module-name}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-name}, \\ 
{\rm{listify}}\,({\rm{module-inputs}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-inputs})\index{listify}, \\ 
{\it{netlist\/}}, \\ 
{\rm{netlist-type-table-simple}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{netlist-type-table-simple})\-\index{io-types-simple}))\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{output-types}}, \\ 
{\rm{cdr}}\,({\rm{io-types-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{module-name}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-name}, \\ 
{\rm{listify}}\,({\rm{module-inputs}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-inputs})\index{listify}, \\ 
{\it{netlist\/}}, \\ 
{\rm{netlist-type-table-simple}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{netlist-type-table-simple})\-\index{io-types-simple}))\-)\-, \\ 
{\rm{netlist-type-table-simple}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{netlist-type-table-simple})\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable netlist-type-table-simple; name this event `netlist-type-table-simple-off'.\index{netlist-type-table-simple-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{types-acceptablep} \\  
\=\+{\rm{types-acceptablep}}\,({\it{flg\/}}, {\it{x0\/}}, {\it{netlist\/}}, {\it{acceptable-types\/}}, {\it{checked-modules\/}})\index{types-acceptablep} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{flg\/}}: \\ 
{\bf case = }{\tt{0}} \\ 
{\bf then }\=\+{\bf if }{\rm{primp}}\,({\it{x0\/}})\index{primp} \\ 
{\bf then }\=\+{\rm{subset}}\,({\rm{primp2}}\,({\it{x0\/}}, {\tt{'}}{\tt{input-types}})\index{primp2}, {\it{acceptable-types\/}})\index{subset} \\ 
$\wedge$$\;\;\;\;${\rm{subset}}\,(\=\+{\rm{fix-dependent-types}}\,(\=\+{\rm{primp2}}\,(\=\+{\it{x0\/}}, \\ 
{\tt{'}}{\tt{output-types}})\-\index{primp2}, \\ 
{\rm{pairlist}}\,(\=\+{\rm{primp2}}\,(\=\+{\it{x0\/}}, \\ 
{\tt{'}}{\tt{inputs}})\-\index{primp2}, \\ 
{\rm{primp2}}\,(\=\+{\it{x0\/}}, \\ 
{\tt{'}}{\tt{input-types}})\-\index{primp2})\-)\-\index{fix-dependent-types}, \\ 
{\it{acceptable-types\/}})\-\index{subset}\- \\ 
{\bf elseif }{\it{x0\/}} $\in$ {\it{checked-modules\/}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{lookup-module}) \\ 
{\bf then }{\rm{types-acceptablep}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\rm{delete-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{delete-module}, \\ 
{\it{acceptable-types\/}}, \\ 
{\it{checked-modules\/}})\-\index{types-acceptablep} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{1}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\it{x0\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\rm{types-acceptablep}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-function}, \\ 
{\it{netlist\/}}, \\ 
{\it{acceptable-types\/}}, \\ 
{\it{checked-modules\/}})\-\index{types-acceptablep} \\ 
{\bf then }{\rm{types-acceptablep}}\,(\=\+{\tt{1}}, \\ 
{\rm{cdr}}\,({\it{x0\/}}), \\ 
{\it{netlist\/}}, \\ 
{\it{acceptable-types\/}}, \\ 
{\it{checked-modules\/}})\-\index{types-acceptablep} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf otherwise }{\bf{f}}$\;${\bf  endcase}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable types-acceptablep; name this event `types-acceptablep-off'.\index{types-acceptablep-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{netlist-types-acceptable-list} \\  
\=\+{\rm{netlist-types-acceptable-list}}\,({\it{netlist\/}})\index{netlist-types-acceptable-list} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{netlist\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf elseif }{\rm{netlist-types-acceptable-list}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{netlist-types-acceptable-list} \\ 
{\bf then }\=\+{\bf if }{\rm{types-acceptablep}}\,(\=\+{\tt{0}}, \\ 
{\rm{module-name}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-name}, \\ 
{\it{netlist\/}}, \\ 
{\tt{'}}{\tt{(}}{\tt{boolp}}{\tt{ }}{\tt{clk}}{\tt{ }}{\tt{level}}{\tt{ }}{\tt{clk-10}}{\tt{ }}{\tt{free}}{\tt{)}}, \\ 
{\rm{netlist-types-acceptable-list}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{netlist-types-acceptable-list})\-\index{types-acceptablep} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{module-name}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-name}, \\ 
{\rm{netlist-types-acceptable-list}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{netlist-types-acceptable-list})\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable netlist-types-acceptable-list; name this event `netlist-types-acceptable-list-off'.\index{netlist-types-acceptable-list-o!ff}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{netlist-type-check-simple-okp} \\  
\=\+{\rm{netlist-type-check-simple-okp}}\,({\it{netlist\/}})\index{netlist-type-check-simple-okp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{netlist-types-acceptable-list}}\,({\it{netlist\/}})\index{netlist-types-acceptable-list} \\ 
{\bf then }{\rm{netlist-type-table-simple}}\,({\it{netlist\/}})\index{netlist-type-table-simple} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable netlist-type-check-simple-okp; name this event `netlist-type-check-simple-okp-off'.\index{netlist-type-check-simple-okp-o!ff}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{arg-types-match-simplep} \\  
\=\+{\rm{arg-types-match-simplep}}\,({\it{actuals\/}}, {\it{formals\/}})\index{arg-types-match-simplep} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{actuals\/}} $\simeq\;${{\bf{nil}}}${}$) $\vee$ ({\it{formals\/}} $\simeq\;${{\bf{nil}}}${}$)$\;\;${\bf then }{\it{actuals\/}} $=$ {\it{formals\/}} \\ 
{\bf else }\=\+(\=\+({\rm{car}}\,({\it{actuals\/}}) $=$ {\rm{car}}\,({\it{formals\/}})) \\ 
$\vee$$\;\;\;\;$({\rm{car}}\,({\it{formals\/}}) $=$ {\tt{'}}{\tt{free}}))\- \\ 
$\wedge$$\;\;\;\;${\rm{arg-types-match-simplep}}\,({\rm{cdr}}\,({\it{actuals\/}}), {\rm{cdr}}\,({\it{formals\/}}))\index{arg-types-match-simplep}\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable arg-types-match-simplep; name this event `arg-types-match-simplep-off'.\index{arg-types-match-simplep-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{arg-types-simple-okp} \\  
\=\+{\rm{arg-types-simple-okp}}\,({\it{fn\/}}, {\it{arg-types\/}}, {\it{netlist\/}})\index{arg-types-simple-okp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }$\neg$ {\rm{subset}}\,({\it{arg-types\/}}, {\tt{'}}{\tt{(}}{\tt{boolp}}{\tt{ }}{\tt{clk}}{\tt{ }}{\tt{level}}{\tt{ }}{\tt{clk-10}}{\tt{)}})\index{subset}$\;\;${\bf then }{\bf{f}} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{io-types-simple}}\,(\=\+{\tt{0}}, \\ 
{\it{fn\/}}, \\ 
{\it{arg-types\/}}, \\ 
{\it{netlist\/}}, \\ 
{\rm{netlist-type-table-simple}}\,({\it{netlist\/}})\index{netlist-type-table-simple})\-\index{io-types-simple}) \\ 
{\bf then }{\rm{arg-types-match-simplep}}\,(\=\+{\it{arg-types\/}}, \\ 
{\rm{car}}\,({\rm{io-types-simple}}\,(\=\+{\tt{0}}, \\ 
{\it{fn\/}}, \\ 
{\it{arg-types\/}}, \\ 
{\it{netlist\/}}, \\ 
{\rm{netlist-type-table-simple}}\,({\it{netlist\/}})\index{netlist-type-table-simple})\-\index{io-types-simple}))\-\index{arg-types-match-simplep} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable arg-types-simple-okp; name this event `arg-types-simple-okp-off'.\index{arg-types-simple-okp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{make-ram-state} \\  
\=\+{\rm{make-ram-state}}\,({\it{structure\/}}, {\it{width\/}}, {\it{bit-value\/}})\index{make-ram-state} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{structure\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{ram}}\,({\rm{make-list}}\,({\it{width\/}}, {\it{bit-value\/}})\index{make-list})\index{ram} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{make-ram-state}}\,({\rm{car}}\,({\it{structure\/}}), {\it{width\/}}, {\it{bit-value\/}})\index{make-ram-state}, \\ 
{\rm{make-ram-state}}\,({\rm{cdr}}\,({\it{structure\/}}), {\it{width\/}}, {\it{bit-value\/}})\index{make-ram-state})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable make-ram-state; name this event `make-ram-state-off'.\index{make-ram-state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{state-type-requirement-simple} \\  
\=\+{\rm{state-type-requirement-simple}}\,({\it{flg\/}}, {\it{x0\/}}, {\it{x1\/}}, {\it{netlist\/}}, {\it{type-table\/}})\index{state-type-requirement-simple} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{flg\/}}: \\ 
{\bf case = }{\tt{0}} \\ 
{\bf then }\=\+{\bf if }{\rm{primp}}\,({\it{x0\/}})\index{primp} \\ 
{\bf then }\=\+{\bf if }{\rm{lookup-module}}\,({\tt{'}}{\tt{state-types}}, {\rm{cdr}}\,({\rm{primp}}\,({\it{x0\/}})\index{primp}))\index{lookup-module} \\ 
{\bf then }{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\rm{cdr}}\,({\rm{lookup-module}}\,(\=\+{\tt{'}}{\tt{state-types}}, \\ 
{\rm{cdr}}\,({\rm{primp}}\,({\it{x0\/}})\index{primp}))\-\index{lookup-module}), \\ 
{\bf{nil}})\- \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{lookup-module}}\,({\it{x0\/}}, {\it{type-table\/}})\index{lookup-module} \\ 
{\bf then }\=\+{\bf if }{\rm{lookup-module}}\,(\=\+{\tt{'}}{\tt{state-types}}, \\ 
{\rm{cdr}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{type-table\/}})\index{lookup-module}))\-\index{lookup-module} \\ 
{\bf then }{\rm{cdr}}\,({\rm{lookup-module}}\,(\=\+{\tt{'}}{\tt{state-types}}, \\ 
{\rm{cdr}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{type-table\/}})\index{lookup-module}))\-\index{lookup-module}) \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{listp}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{lookup-module}) \\ 
{\bf then }\=\+{\bf if }{\rm{set-equal}}\,(\=\+{\rm{m-states-list}}\,({\rm{module-statenames}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-statenames})\index{m-states-list}, \\ 
{\rm{strip-cars}}\,({\rm{state-type-requirement-simple}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\bf{nil}}, \\ 
{\rm{delete-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\it{type-table\/}})\-\index{state-type-requirement-simple}))\-\index{set-equal} \\ 
{\bf then }\=\+{\bf if }\=\+{\rm{module-statenames}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{lookup-module})\index{module-statenames} \\ 
$=$$\;\;\;\;${\bf{nil}}\-$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{collect-states}}\,(\=\+{\rm{module-statenames}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-statenames}, \\ 
{\rm{state-type-requirement-simple}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\bf{nil}}, \\ 
{\rm{delete-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\it{type-table\/}})\-\index{state-type-requirement-simple})\-\index{collect-states}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{1}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\it{x0\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{x1\/}} \\ 
{\bf elseif }{\rm{truep}}\,({\rm{state-type-requirement-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-function}, \\ 
{\bf{nil}}, \\ 
{\it{netlist\/}}, \\ 
{\it{type-table\/}})\-\index{state-type-requirement-simple}) \\ 
{\bf then }{\rm{state-type-requirement-simple}}\,(\=\+{\tt{1}}, \\ 
{\rm{cdr}}\,({\it{x0\/}}), \\ 
{\it{x1\/}}, \\ 
{\it{netlist\/}}, \\ 
{\it{type-table\/}})\-\index{state-type-requirement-simple} \\ 
{\bf elseif }{\rm{state-type-requirement-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-function}, \\ 
{\bf{nil}}, \\ 
{\it{netlist\/}}, \\ 
{\it{type-table\/}})\-\index{state-type-requirement-simple} \\ 
{\bf then }{\rm{state-type-requirement-simple}}\,(\=\+{\tt{1}}, \\ 
{\rm{cdr}}\,({\it{x0\/}}), \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{occ-name}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-name}, \\ 
{\rm{state-type-requirement-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-function}, \\ 
{\bf{nil}}, \\ 
{\it{netlist\/}}, \\ 
{\it{type-table\/}})\-\index{state-type-requirement-simple})\-, \\ 
{\it{x1\/}})\-, \\ 
{\it{netlist\/}}, \\ 
{\it{type-table\/}})\-\index{state-type-requirement-simple} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf otherwise }{\bf{f}}$\;${\bf  endcase}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable state-type-requirement-simple; name this event `state-type-requirement-simple-off'.\index{state-type-requirement-simple-o!ff}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{netlist-state-types-simple} \\  
\=\+{\rm{netlist-state-types-simple}}\,({\it{netlist\/}})\index{netlist-state-types-simple} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{netlist\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf elseif }{\rm{netlist-state-types-simple}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{netlist-state-types-simple} \\ 
{\bf then }\=\+{\bf if }{\rm{truep}}\,({\rm{state-type-requirement-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{module-name}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-name}, \\ 
{\bf{nil}}, \\ 
{\it{netlist\/}}, \\ 
{\rm{netlist-state-types-simple}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{netlist-state-types-simple})\-\index{state-type-requirement-simple}) \\ 
{\bf then }{\rm{netlist-state-types-simple}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{netlist-state-types-simple} \\ 
{\bf elseif }{\rm{state-type-requirement-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{module-name}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-name}, \\ 
{\bf{nil}}, \\ 
{\it{netlist\/}}, \\ 
{\rm{netlist-state-types-simple}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{netlist-state-types-simple})\-\index{state-type-requirement-simple} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{module-name}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-name}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{state-types}}, \\ 
{\rm{state-type-requirement-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{module-name}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-name}, \\ 
{\bf{nil}}, \\ 
{\it{netlist\/}}, \\ 
{\rm{netlist-state-types-simple}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{netlist-state-types-simple})\-\index{state-type-requirement-simple})\-)\-, \\ 
{\rm{netlist-state-types-simple}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{netlist-state-types-simple})\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable netlist-state-types-simple; name this event `netlist-state-types-simple-off'.\index{netlist-state-types-simple-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{state-simple-okp} \\  
\=\+{\rm{state-simple-okp}}\,({\it{state\/}}, {\it{type\/}})\index{state-simple-okp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{truep}}\,({\it{type\/}})$\;\;${\bf then }{\it{state\/}} $=$ {\bf{nil}} \\ 
{\bf elseif }{\it{type\/}} $=$ {\tt{'}}{\tt{boolp}}$\;\;${\bf then }{\rm{boolp}}\,({\it{state\/}})\index{boolp} \\ 
{\bf elseif }{\rm{ramp}}\,({\it{type\/}})\index{ramp} \\ 
{\bf then }\=\+{\rm{ramp}}\,({\it{state\/}})\index{ramp} \\ 
$\wedge$$\;\;\;\;${\rm{state-simple-okp}}\,({\rm{ram-guts}}\,({\it{state\/}})\index{ram-guts}, {\rm{ram-guts}}\,({\it{type\/}})\index{ram-guts})\index{state-simple-okp}\- \\ 
{\bf elseif }{\rm{romp}}\,({\it{type\/}})\index{romp} \\ 
{\bf then }\=\+{\rm{romp}}\,({\it{state\/}})\index{romp} \\ 
$\wedge$$\;\;\;\;${\rm{state-simple-okp}}\,({\rm{rom-guts}}\,({\it{state\/}})\index{rom-guts}, {\rm{rom-guts}}\,({\it{type\/}})\index{rom-guts})\index{state-simple-okp}\- \\ 
{\bf elseif }{\rm{stubp}}\,({\it{type\/}})\index{stubp} \\ 
{\bf then }\=\+{\rm{stubp}}\,({\it{state\/}})\index{stubp} \\ 
$\wedge$$\;\;\;\;${\rm{state-simple-okp}}\,({\rm{stub-guts}}\,({\it{state\/}})\index{stub-guts}, {\rm{stub-guts}}\,({\it{type\/}})\index{stub-guts})\index{state-simple-okp}\- \\ 
{\bf elseif }{\rm{listp}}\,({\it{type\/}}) \\ 
{\bf then }\=\+{\rm{listp}}\,({\it{state\/}}) \\ 
$\wedge$$\;\;\;\;${\rm{state-simple-okp}}\,({\rm{car}}\,({\it{state\/}}), {\rm{car}}\,({\it{type\/}}))\index{state-simple-okp} \\ 
$\wedge$$\;\;\;\;${\rm{state-simple-okp}}\,({\rm{cdr}}\,({\it{state\/}}), {\rm{cdr}}\,({\it{type\/}}))\index{state-simple-okp}\- \\ 
{\bf elseif }{\it{type\/}} $=$ {\bf{nil}}$\;\;${\bf then }{\it{state\/}} $=$ {\bf{nil}} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable state-simple-okp; name this event `state-simple-okp-off'.\index{state-simple-okp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{apply-state-simple-okp} \\  
\=\+{\rm{apply-state-simple-okp}}\,({\it{fn\/}}, {\it{state\/}}, {\it{netlist\/}})\index{apply-state-simple-okp} \\ 
$=$$\;\;\;\;${\rm{state-simple-okp}}\,(\=\+{\it{state\/}}, \\ 
{\rm{state-type-requirement-simple}}\,(\=\+{\tt{0}}, \\ 
{\it{fn\/}}, \\ 
{\bf{nil}}, \\ 
{\it{netlist\/}}, \\ 
{\rm{netlist-state-types-simple}}\,({\it{netlist\/}})\index{netlist-state-types-simple})\-\index{state-type-requirement-simple})\-\index{state-simple-okp}\-
\end{tabbing}


\noindent{\sc Event}:   Enable apply-state-simple-okp; name this event `apply-state-simple-okp-off'.\index{apply-state-simple-okp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fix-dependent-lds} \\  
\=\+{\rm{fix-dependent-lds}}\,({\it{lds\/}}, {\it{alist\/}})\index{fix-dependent-lds} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{lds\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{lds\/}} \\ 
{\bf else }{\rm{cons}}\,(\=\+\=\+{\bf if }{\rm{litatom}}\,({\rm{car}}\,({\it{lds\/}})) $\vee$ {\rm{indexp}}\,({\rm{car}}\,({\it{lds\/}}))\index{indexp} \\ 
{\bf then }{\rm{value}}\,({\rm{car}}\,({\it{lds\/}}), {\it{alist\/}})\index{value} \\ 
{\bf elseif }{\rm{car}}\,({\it{lds\/}}) $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{car}}\,({\it{lds\/}}) \\ 
{\bf else }{\rm{fix-dependent-lds}}\,({\rm{car}}\,({\it{lds\/}}), {\it{alist\/}})\index{fix-dependent-lds}$\;${\bf  endif}\-, \\ 
{\rm{fix-dependent-lds}}\,({\rm{cdr}}\,({\it{lds\/}}), {\it{alist\/}})\index{fix-dependent-lds})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fix-dependent-lds; name this event `fix-dependent-lds-off'.\index{fix-dependent-lds-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{parent-synonym-simple} \\  
\=\+{\rm{parent-synonym-simple}}\,({\it{name\/}}, {\it{slist\/}})\index{parent-synonym-simple} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\rm{lookup-module}}\,({\it{name\/}}, {\it{slist\/}})\index{lookup-module}) \\ 
{\bf then }\=\+{\bf if }\=\+{\rm{litatom}}\,({\rm{cdr}}\,({\rm{lookup-module}}\,({\it{name\/}}, {\it{slist\/}})\index{lookup-module})) \\ 
$\vee$$\;\;\;\;${\rm{indexp}}\,({\rm{cdr}}\,({\rm{lookup-module}}\,({\it{name\/}}, {\it{slist\/}})\index{lookup-module}))\index{indexp}\- \\ 
{\bf then }{\rm{parent-synonym-simple}}\,(\=\+{\rm{cdr}}\,({\rm{lookup-module}}\,({\it{name\/}}, {\it{slist\/}})\index{lookup-module}), \\ 
{\rm{delete-module}}\,({\it{name\/}}, {\it{slist\/}})\index{delete-module})\-\index{parent-synonym-simple} \\ 
{\bf else }{\it{name\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{name\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable parent-synonym-simple; name this event `parent-synonym-simple-off'.\index{parent-synonym-simple-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{add-loading-simple} \\  
\=\+{\rm{add-loading-simple}}\,({\it{name\/}}, {\it{loading\/}}, {\it{ld-list\/}})\index{add-loading-simple} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{lookup-module}}\,({\it{name\/}}, {\it{ld-list\/}})\index{lookup-module} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\it{name\/}}, \\ 
\=\+{\bf if }{\rm{listp}}\,({\it{loading\/}})$\;\;${\bf then }{\it{loading\/}} \\ 
{\bf else }{\rm{list}}\,({\it{loading\/}})$\;${\bf  endif}\-)\-, \\ 
{\it{ld-list\/}})\- \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\it{name\/}}, \\ 
\=\+{\bf if }{\rm{listp}}\,({\it{loading\/}}) \\ 
{\bf then }{\rm{append}}\,(\=\+{\it{loading\/}}, \\ 
{\rm{cdr}}\,({\rm{lookup-module}}\,({\it{name\/}}, {\it{ld-list\/}})\index{lookup-module}))\- \\ 
{\bf else }{\rm{cons}}\,(\=\+{\it{loading\/}}, \\ 
{\rm{cdr}}\,({\rm{lookup-module}}\,({\it{name\/}}, {\it{ld-list\/}})\index{lookup-module}))\-$\;${\bf  endif}\-)\-, \\ 
{\rm{delete-module}}\,({\it{name\/}}, {\it{ld-list\/}})\index{delete-module})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable add-loading-simple; name this event `add-loading-simple-off'.\index{add-loading-simple-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{add-loading-simples} \\  
\=\+{\rm{add-loading-simples}}\,({\it{names\/}}, {\it{loadings\/}}, {\it{ld-list\/}})\index{add-loading-simples} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{names\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{ld-list\/}} \\ 
{\bf else }{\rm{add-loading-simples}}\,(\=\+{\rm{cdr}}\,({\it{names\/}}), \\ 
{\rm{cdr}}\,({\it{loadings\/}}), \\ 
{\rm{add-loading-simple}}\,(\=\+{\rm{car}}\,({\it{names\/}}), \\ 
{\rm{car}}\,({\it{loadings\/}}), \\ 
{\it{ld-list\/}})\-\index{add-loading-simple})\-\index{add-loading-simples}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable add-loading-simples; name this event `add-loading-simples-off'.\index{add-loading-simples-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{sum-numbers} \\  
\=\+{\rm{sum-numbers}}\,({\it{lst\/}})\index{sum-numbers} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{lst\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf elseif }{\rm{car}}\,({\it{lst\/}}) $\in\;${\bf{N}}${}$$\;\;${\bf then }{\rm{car}}\,({\it{lst\/}}) $+$ {\rm{sum-numbers}}\,({\rm{cdr}}\,({\it{lst\/}}))\index{sum-numbers} \\ 
{\bf else }{\rm{sum-numbers}}\,({\rm{cdr}}\,({\it{lst\/}}))\index{sum-numbers}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable sum-numbers; name this event `sum-numbers-off'.\index{sum-numbers-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{extract-names-simple} \\  
\=\+{\rm{extract-names-simple}}\,({\it{lst\/}})\index{extract-names-simple} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{lst\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf elseif }\=\+({\rm{litatom}}\,({\rm{car}}\,({\it{lst\/}})) $\vee$ {\rm{indexp}}\,({\rm{car}}\,({\it{lst\/}}))\index{indexp}) \\ 
$\wedge$$\;\;\;\;$({\rm{car}}\,({\it{lst\/}}) $\not\in$ {\rm{cdr}}\,({\it{lst\/}}))\- \\ 
{\bf then }{\rm{cons}}\,({\rm{car}}\,({\it{lst\/}}), {\rm{extract-names-simple}}\,({\rm{cdr}}\,({\it{lst\/}}))\index{extract-names-simple}) \\ 
{\bf else }{\rm{extract-names-simple}}\,({\rm{cdr}}\,({\it{lst\/}}))\index{extract-names-simple}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable extract-names-simple; name this event `extract-names-simple-off'.\index{extract-names-simple-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{sum-loading} \\  
\=\+{\rm{sum-loading}}\,({\it{ld\/}})\index{sum-loading} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{car}}\,({\it{ld\/}}), \\ 
\=\+{\bf if }{\rm{extract-names-simple}}\,({\rm{cdr}}\,({\it{ld\/}}))\index{extract-names-simple} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }{\rm{list}}\,({\rm{sum-numbers}}\,({\rm{cdr}}\,({\it{ld\/}}))\index{sum-numbers}) \\ 
{\bf elseif }{\rm{sum-numbers}}\,({\rm{cdr}}\,({\it{ld\/}}))\index{sum-numbers} $\simeq {\tt{0}}$ \\ 
{\bf then }{\rm{extract-names-simple}}\,({\rm{cdr}}\,({\it{ld\/}}))\index{extract-names-simple} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{sum-numbers}}\,({\rm{cdr}}\,({\it{ld\/}}))\index{sum-numbers}, \\ 
{\rm{extract-names-simple}}\,({\rm{cdr}}\,({\it{ld\/}}))\index{extract-names-simple})\-$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable sum-loading; name this event `sum-loading-off'.\index{sum-loading-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{sum-loadings} \\  
\=\+{\rm{sum-loadings}}\,({\it{lds\/}})\index{sum-loadings} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{lds\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{sum-loading}}\,({\rm{car}}\,({\it{lds\/}}))\index{sum-loading}, {\rm{sum-loadings}}\,({\rm{cdr}}\,({\it{lds\/}}))\index{sum-loadings})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable sum-loadings; name this event `sum-loadings-off'.\index{sum-loadings-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fix-loadings} \\  
\=\+{\rm{fix-loadings}}\,({\it{slist\/}}, {\it{lds\/}})\index{fix-loadings} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{slist\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{sum-loadings}}\,({\it{lds\/}})\index{sum-loadings} \\ 
{\bf elseif }{\rm{litatom}}\,({\rm{cdar}}\,({\it{slist\/}})) $\vee$ {\rm{indexp}}\,({\rm{cdar}}\,({\it{slist\/}}))\index{indexp} \\ 
{\bf then }{\rm{fix-loadings}}\,(\=\+{\rm{cdr}}\,({\it{slist\/}}), \\ 
{\rm{add-loading-simple}}\,(\=\+{\rm{cdar}}\,({\it{slist\/}}), \\ 
{\rm{value}}\,({\rm{caar}}\,({\it{slist\/}}), {\it{lds\/}})\index{value}, \\ 
{\rm{delete-module}}\,({\rm{caar}}\,({\it{slist\/}}), {\it{lds\/}})\index{delete-module})\-\index{add-loading-simple})\-\index{fix-loadings} \\ 
{\bf else }{\rm{fix-loadings}}\,({\rm{cdr}}\,({\it{slist\/}}), {\it{lds\/}})\index{fix-loadings}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fix-loadings; name this event `fix-loadings-off'.\index{fix-loadings-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fix-drives} \\  
\=\+{\rm{fix-drives}}\,({\it{drs\/}}, {\it{slist\/}})\index{fix-drives} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{drs\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf elseif }{\rm{litatom}}\,({\rm{cdar}}\,({\it{drs\/}})) $\vee$ {\rm{indexp}}\,({\rm{cdar}}\,({\it{drs\/}}))\index{indexp} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{cons}}\,({\rm{caar}}\,({\it{drs\/}}), {\rm{parent-synonym-simple}}\,({\rm{cdar}}\,({\it{drs\/}}), {\it{slist\/}})\index{parent-synonym-simple}), \\ 
{\rm{fix-drives}}\,({\rm{cdr}}\,({\it{drs\/}}), {\it{slist\/}})\index{fix-drives})\- \\ 
{\bf else }{\rm{cons}}\,({\rm{car}}\,({\it{drs\/}}), {\rm{fix-drives}}\,({\rm{cdr}}\,({\it{drs\/}}), {\it{slist\/}})\index{fix-drives})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fix-drives; name this event `fix-drives-off'.\index{fix-drives-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{net-drives} \\  
\=\+{\rm{net-drives}}\,({\it{drs\/}}, {\it{lds\/}})\index{net-drives} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{drs\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf elseif }{\rm{cdar}}\,({\it{drs\/}}) $\in\;${\bf{N}}${}$ \\ 
{\bf then }\=\+{\bf if }{\rm{cdar}}\,({\it{drs\/}}) $<$ {\rm{sum-numbers}}\,({\rm{value}}\,({\rm{caar}}\,({\it{drs\/}}), {\it{lds\/}})\index{value})\index{sum-numbers}$\;\;${\bf then }{\bf{f}} \\ 
{\bf elseif }{\rm{net-drives}}\,({\rm{cdr}}\,({\it{drs\/}}), {\it{lds\/}})\index{net-drives} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{caar}}\,({\it{drs\/}}), \\ 
{\rm{cdar}}\,({\it{drs\/}}) $-$ {\rm{sum-numbers}}\,({\rm{value}}\,({\rm{caar}}\,({\it{drs\/}}), {\it{lds\/}})\index{value})\index{sum-numbers})\-, \\ 
{\rm{net-drives}}\,({\rm{cdr}}\,({\it{drs\/}}), {\it{lds\/}})\index{net-drives})\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{net-drives}}\,({\rm{cdr}}\,({\it{drs\/}}), {\it{lds\/}})\index{net-drives} \\ 
{\bf then }{\rm{cons}}\,({\rm{car}}\,({\it{drs\/}}), {\rm{net-drives}}\,({\rm{cdr}}\,({\it{drs\/}}), {\it{lds\/}})\index{net-drives}) \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable net-drives; name this event `net-drives-off'.\index{net-drives-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{external-loading} \\  
\=\+{\rm{external-loading}}\,({\it{ld-lst\/}}, {\it{external-names\/}})\index{external-loading} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{ld-lst\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{ld-lst\/}} \\ 
{\bf elseif }\=\+({\rm{litatom}}\,({\rm{car}}\,({\it{ld-lst\/}})) $\vee$ {\rm{indexp}}\,({\rm{car}}\,({\it{ld-lst\/}}))\index{indexp}) \\ 
$\wedge$$\;\;\;\;$({\rm{car}}\,({\it{ld-lst\/}}) $\not\in$ {\it{external-names\/}})\- \\ 
{\bf then }{\rm{external-loading}}\,({\rm{cdr}}\,({\it{ld-lst\/}}), {\it{external-names\/}})\index{external-loading} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{car}}\,({\it{ld-lst\/}}), \\ 
{\rm{external-loading}}\,({\rm{cdr}}\,({\it{ld-lst\/}}), {\it{external-names\/}})\index{external-loading})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable external-loading; name this event `external-loading-off'.\index{external-loading-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-loadings-simple} \\  
\=\+{\rm{collect-loadings-simple}}\,({\it{names\/}}, {\it{loadings\/}}, {\it{external-names\/}})\index{collect-loadings-simple} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{names\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf elseif }{\rm{lookup-module}}\,({\rm{car}}\,({\it{names\/}}), {\it{loadings\/}})\index{lookup-module} \\ 
{\bf then }{\rm{cons}}\,(\=\+\=\+{\bf if }{\rm{external-loading}}\,(\=\+{\rm{value}}\,({\rm{car}}\,({\it{names\/}}), {\it{loadings\/}})\index{value}, \\ 
{\it{external-names\/}})\-\index{external-loading} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf elseif }{\rm{cdr}}\,({\rm{external-loading}}\,(\=\+{\rm{value}}\,({\rm{car}}\,({\it{names\/}}), {\it{loadings\/}})\index{value}, \\ 
{\it{external-names\/}})\-\index{external-loading}) $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }{\rm{car}}\,({\rm{external-loading}}\,(\=\+{\rm{value}}\,({\rm{car}}\,({\it{names\/}}), {\it{loadings\/}})\index{value}, \\ 
{\it{external-names\/}})\-\index{external-loading}) \\ 
{\bf else }{\rm{external-loading}}\,(\=\+{\rm{value}}\,({\rm{car}}\,({\it{names\/}}), {\it{loadings\/}})\index{value}, \\ 
{\it{external-names\/}})\-\index{external-loading}$\;${\bf  endif}\-, \\ 
{\rm{collect-loadings-simple}}\,({\rm{cdr}}\,({\it{names\/}}), {\it{loadings\/}}, {\it{external-names\/}})\index{collect-loadings-simple})\- \\ 
{\bf else }{\rm{cons}}\,(\=\+{\tt{0}}, \\ 
{\rm{collect-loadings-simple}}\,(\=\+{\rm{cdr}}\,({\it{names\/}}), \\ 
{\it{loadings\/}}, \\ 
{\it{external-names\/}})\-\index{collect-loadings-simple})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-loadings-simple; name this event `collect-loadings-simple-off'.\index{collect-loadings-simple-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-drives-simple} \\  
\=\+{\rm{collect-drives-simple}}\,({\it{names\/}}, {\it{drives\/}}, {\it{external-names\/}})\index{collect-drives-simple} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{names\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf elseif }\=\+($\neg$ (\=\+{\rm{litatom}}\,({\rm{value}}\,({\rm{car}}\,({\it{names\/}}), {\it{drives\/}})\index{value}) \\ 
$\vee$$\;\;\;\;${\rm{indexp}}\,({\rm{value}}\,({\rm{car}}\,({\it{names\/}}), {\it{drives\/}})\index{value})\index{indexp})\-) \\ 
$\vee$$\;\;\;\;$({\rm{value}}\,({\rm{car}}\,({\it{names\/}}), {\it{drives\/}})\index{value} $\in$ {\it{external-names\/}})\- \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{value}}\,({\rm{car}}\,({\it{names\/}}), {\it{drives\/}})\index{value}, \\ 
{\rm{collect-drives-simple}}\,({\rm{cdr}}\,({\it{names\/}}), {\it{drives\/}}, {\it{external-names\/}})\index{collect-drives-simple})\- \\ 
{\bf elseif }\=\+{\rm{parent-synonym-simple}}\,({\rm{value}}\,({\rm{car}}\,({\it{names\/}}), {\it{drives\/}})\index{value}, {\it{drives\/}})\index{parent-synonym-simple} \\ 
$=$$\;\;\;\;${\rm{value}}\,({\rm{car}}\,({\it{names\/}}), {\it{drives\/}})\index{value}\- \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{value}}\,({\rm{value}}\,({\rm{car}}\,({\it{names\/}}), {\it{drives\/}})\index{value}, {\it{drives\/}})\index{value}, \\ 
{\rm{collect-drives-simple}}\,(\=\+{\rm{cdr}}\,({\it{names\/}}), \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{value}}\,({\rm{car}}\,({\it{names\/}}), {\it{drives\/}})\index{value}, \\ 
{\rm{car}}\,({\it{names\/}}))\-, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{car}}\,({\it{names\/}}), \\ 
{\rm{value}}\,(\=\+{\rm{value}}\,(\=\+{\rm{car}}\,({\it{names\/}}), \\ 
{\it{drives\/}})\-\index{value}, \\ 
{\it{drives\/}})\-\index{value})\-, \\ 
{\rm{delete-module}}\,(\=\+{\rm{car}}\,({\it{names\/}}), \\ 
{\rm{delete-module}}\,(\=\+{\rm{value}}\,(\=\+{\rm{car}}\,({\it{names\/}}), \\ 
{\it{drives\/}})\-\index{value}, \\ 
{\it{drives\/}})\-\index{delete-module})\-\index{delete-module})\-)\-, \\ 
{\it{external-names\/}})\-\index{collect-drives-simple})\- \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{parent-synonym-simple}}\,({\rm{value}}\,({\rm{car}}\,({\it{names\/}}), {\it{drives\/}})\index{value}, {\it{drives\/}})\index{parent-synonym-simple}, \\ 
{\rm{collect-drives-simple}}\,(\=\+{\rm{cdr}}\,({\it{names\/}}), \\ 
{\it{drives\/}}, \\ 
{\it{external-names\/}})\-\index{collect-drives-simple})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-drives-simple; name this event `collect-drives-simple-off'.\index{collect-drives-simple-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{loadings-and-drives-simple} \\  
\=\+{\rm{loadings-and-drives-simple}}\,({\it{flg\/}}, {\it{x0\/}}, {\it{x1\/}}, {\it{x2\/}}, {\it{netlist\/}}, {\it{lds-table\/}})\index{loadings-and-drives-simple} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{flg\/}}: \\ 
{\bf case = }{\tt{0}} \\ 
{\bf then }\=\+{\bf if }{\rm{primp}}\,({\it{x0\/}})\index{primp} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{fix-dependent-lds}}\,(\=\+{\rm{primp2}}\,({\it{x0\/}}, {\tt{'}}{\tt{loadings}})\index{primp2}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\rm{primp2}}\,({\it{x0\/}}, {\tt{'}}{\tt{inputs}})\index{primp2}, \\ 
{\it{x1\/}})\-, \\ 
{\rm{pairlist}}\,(\=\+{\rm{primp2}}\,(\=\+{\it{x0\/}}, \\ 
{\tt{'}}{\tt{outputs}})\-\index{primp2}, \\ 
{\it{x2\/}})\-)\-)\-\index{fix-dependent-lds}, \\ 
{\rm{fix-dependent-lds}}\,(\=\+{\rm{primp2}}\,({\it{x0\/}}, {\tt{'}}{\tt{drives}})\index{primp2}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\rm{primp2}}\,({\it{x0\/}}, {\tt{'}}{\tt{inputs}})\index{primp2}, \\ 
{\it{x1\/}})\-, \\ 
{\rm{pairlist}}\,(\=\+{\rm{primp2}}\,(\=\+{\it{x0\/}}, \\ 
{\tt{'}}{\tt{outputs}})\-\index{primp2}, \\ 
{\it{x2\/}})\-)\-)\-\index{fix-dependent-lds})\- \\ 
{\bf elseif }\=\+{\rm{lookup-module}}\,(\=\+{\tt{'}}{\tt{loadings}}, \\ 
{\rm{cdr}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{lds-table\/}})\index{lookup-module}))\-\index{lookup-module} \\ 
$\wedge$$\;\;\;\;${\rm{lookup-module}}\,(\=\+{\tt{'}}{\tt{drives}}, \\ 
{\rm{cdr}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{lds-table\/}})\index{lookup-module}))\-\index{lookup-module}\- \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{fix-dependent-lds}}\,(\=\+{\rm{cdr}}\,({\rm{lookup-module}}\,(\=\+{\tt{'}}{\tt{loadings}}, \\ 
{\rm{cdr}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{lds-table\/}})\-\index{lookup-module}))\-\index{lookup-module}), \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\it{x1\/}})\-, \\ 
{\rm{pairlist}}\,(\=\+{\rm{module-outputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-outputs}, \\ 
{\it{x2\/}})\-)\-)\-\index{fix-dependent-lds}, \\ 
{\rm{fix-dependent-lds}}\,(\=\+{\rm{cdr}}\,({\rm{lookup-module}}\,(\=\+{\tt{'}}{\tt{drives}}, \\ 
{\rm{cdr}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{lds-table\/}})\-\index{lookup-module}))\-\index{lookup-module}), \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\it{x1\/}})\-, \\ 
{\rm{pairlist}}\,(\=\+{\rm{module-outputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-outputs}, \\ 
{\it{x2\/}})\-)\-)\-\index{fix-dependent-lds})\- \\ 
{\bf elseif }{\rm{listp}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{lookup-module}) \\ 
{\bf then }\=\+{\bf if }{\rm{loadings-and-drives-simple}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\bf{nil}}, \\ 
{\bf{nil}}, \\ 
{\rm{delete-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{delete-module}, \\ 
{\it{lds-table\/}})\-\index{loadings-and-drives-simple} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{fix-dependent-lds}}\,(\=\+{\rm{collect-loadings-simple}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\rm{car}}\,({\rm{loadings-and-drives-simple}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\bf{nil}}, \\ 
{\bf{nil}}, \\ 
{\rm{delete-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\it{lds-table\/}})\-\index{loadings-and-drives-simple}), \\ 
{\rm{module-outputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-outputs})\-\index{collect-loadings-simple}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\it{x1\/}})\-, \\ 
{\rm{pairlist}}\,(\=\+{\rm{module-outputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-outputs}, \\ 
{\it{x2\/}})\-)\-)\-\index{fix-dependent-lds}, \\ 
{\rm{fix-dependent-lds}}\,(\=\+{\rm{collect-drives-simple}}\,(\=\+{\rm{module-outputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-outputs}, \\ 
{\rm{cdr}}\,({\rm{loadings-and-drives-simple}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\bf{nil}}, \\ 
{\bf{nil}}, \\ 
{\rm{delete-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\it{lds-table\/}})\-\index{loadings-and-drives-simple}), \\ 
{\rm{append}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\rm{module-outputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-outputs})\-)\-\index{collect-drives-simple}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\it{x1\/}})\-, \\ 
{\rm{pairlist}}\,(\=\+{\rm{module-outputs}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-outputs}, \\ 
{\it{x2\/}})\-)\-)\-\index{fix-dependent-lds})\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{1}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\it{x0\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }\=\+{\bf if }\=\+{\rm{fix-loadings}}\,({\rm{fix-drives}}\,({\it{x2\/}}, {\it{x2\/}})\index{fix-drives}, {\it{x1\/}})\index{fix-loadings} \\ 
$\wedge$$\;\;\;\;${\rm{net-drives}}\,(\=\+{\rm{fix-drives}}\,({\it{x2\/}}, {\it{x2\/}})\index{fix-drives}, \\ 
{\rm{fix-loadings}}\,({\rm{fix-drives}}\,({\it{x2\/}}, {\it{x2\/}})\index{fix-drives}, {\it{x1\/}})\index{fix-loadings})\-\index{net-drives}\- \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{fix-loadings}}\,({\rm{fix-drives}}\,({\it{x2\/}}, {\it{x2\/}})\index{fix-drives}, {\it{x1\/}})\index{fix-loadings}, \\ 
{\rm{net-drives}}\,(\=\+{\rm{fix-drives}}\,({\it{x2\/}}, {\it{x2\/}})\index{fix-drives}, \\ 
{\rm{fix-loadings}}\,({\rm{fix-drives}}\,({\it{x2\/}}, {\it{x2\/}})\index{fix-drives}, {\it{x1\/}})\index{fix-loadings})\-\index{net-drives})\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{loadings-and-drives-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-function}, \\ 
{\rm{occ-inputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-inputs}, \\ 
{\rm{occ-outputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-outputs}, \\ 
{\it{netlist\/}}, \\ 
{\it{lds-table\/}})\-\index{loadings-and-drives-simple} \\ 
{\bf then }{\rm{loadings-and-drives-simple}}\,(\=\+{\tt{1}}, \\ 
{\rm{cdr}}\,({\it{x0\/}}), \\ 
{\rm{add-loading-simples}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-inputs}, \\ 
{\rm{car}}\,({\rm{loadings-and-drives-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-function}, \\ 
{\rm{occ-inputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-inputs}, \\ 
{\rm{occ-outputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-outputs}, \\ 
{\it{netlist\/}}, \\ 
{\it{lds-table\/}})\-\index{loadings-and-drives-simple}), \\ 
{\it{x1\/}})\-\index{add-loading-simples}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\rm{occ-outputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-outputs}, \\ 
{\rm{cdr}}\,({\rm{loadings-and-drives-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-function}, \\ 
{\rm{occ-inputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-inputs}, \\ 
{\rm{occ-outputs}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-outputs}, \\ 
{\it{netlist\/}}, \\ 
{\it{lds-table\/}})\-\index{loadings-and-drives-simple}))\-, \\ 
{\it{x2\/}})\-, \\ 
{\it{netlist\/}}, \\ 
{\it{lds-table\/}})\-\index{loadings-and-drives-simple} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf otherwise }{\bf{f}}$\;${\bf  endcase}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable loadings-and-drives-simple; name this event `loadings-and-drives-simple-off'.\index{loadings-and-drives-simple-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{netlist-loadings-and-drives-simp!le} \\  
\=\+{\rm{netlist-loadings-and-drives-simple}}\,({\it{netlist\/}})\index{netlist-loadings-and-drives-simp!le} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{netlist\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf elseif }{\rm{netlist-loadings-and-drives-simple}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{netlist-loadings-and-drives-simp!le} \\ 
{\bf then }\=\+{\bf if }{\rm{loadings-and-drives-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{module-name}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-name}, \\ 
{\rm{module-inputs}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-inputs}, \\ 
{\rm{module-outputs}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-outputs}, \\ 
{\it{netlist\/}}, \\ 
{\rm{netlist-loadings-and-drives-simple}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{netlist-loadings-and-drives-simp!le})\-\index{loadings-and-drives-simple} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{module-name}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-name}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{loadings}}, \\ 
{\rm{car}}\,({\rm{loadings-and-drives-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{module-name}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-name}, \\ 
{\rm{module-inputs}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-inputs}, \\ 
{\rm{module-outputs}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-outputs}, \\ 
{\it{netlist\/}}, \\ 
{\rm{netlist-loadings-and-drives-simple}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{netlist-loadings-and-drives-simp!le})\-\index{loadings-and-drives-simple}))\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{drives}}, \\ 
{\rm{cdr}}\,({\rm{loadings-and-drives-simple}}\,(\=\+{\tt{0}}, \\ 
{\rm{module-name}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-name}, \\ 
{\rm{module-inputs}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-inputs}, \\ 
{\rm{module-outputs}}\,({\rm{car}}\,({\it{netlist\/}}))\index{module-outputs}, \\ 
{\it{netlist\/}}, \\ 
{\rm{netlist-loadings-and-drives-simple}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{netlist-loadings-and-drives-simp!le})\-\index{loadings-and-drives-simple}))\-)\-, \\ 
{\rm{netlist-loadings-and-drives-simple}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{netlist-loadings-and-drives-simp!le})\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable netlist-loadings-and-drives-simple; name this event `netlist-loadings-and-drives-simple-off'.\index{netlist-loadings-and-drives-simp!le-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{top-level-predicate-simple} \\  
\=\+{\rm{top-level-predicate-simple}}\,({\it{netlist\/}})\index{top-level-predicate-simple} \\ 
$=$$\;\;\;\;$\=\+{\bf if }$\neg$ {\rm{netlist-syntax-simple-okp}}\,({\it{netlist\/}})\index{netlist-syntax-simple-okp} \\ 
{\bf then }{\tt{'}}{\tt{netlist-syntax-simple-okp-error}} \\ 
{\bf elseif }$\neg$ {\rm{simple-dependency-table}}\,({\it{netlist\/}})\index{simple-dependency-table} \\ 
{\bf then }{\tt{'}}{\tt{dependency-table-simple-error}} \\ 
{\bf elseif }$\neg$ {\rm{netlist-type-check-simple-okp}}\,({\it{netlist\/}})\index{netlist-type-check-simple-okp} \\ 
{\bf then }{\tt{'}}{\tt{netlist-type-check-simple-okp-error}} \\ 
{\bf elseif }$\neg$ {\rm{netlist-state-types-simple}}\,({\it{netlist\/}})\index{netlist-state-types-simple} \\ 
{\bf then }{\tt{'}}{\tt{netlist-state-types-simple-error}} \\ 
{\bf elseif }$\neg$ {\rm{netlist-loadings-and-drives-simple}}\,({\it{netlist\/}})\index{netlist-loadings-and-drives-simp!le} \\ 
{\bf then }{\tt{'}}{\tt{netlist-loadings-and-drives-simple-error}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{name-okp} \\  
\=\+{\rm{name-okp}}\,({\it{name\/}})\index{name-okp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{litatom}}\,({\it{name\/}})$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{indexp}}\,({\it{name\/}})\index{indexp} $\wedge$ {\rm{litatom}}\,({\rm{i-name}}\,({\it{name\/}})\index{i-name})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable name-okp; name this event `name-okp-off'.\index{name-okp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{bad-names} \\  
\=\+{\rm{bad-names}}\,({\it{name-list\/}})\index{bad-names} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{name-list\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{name-okp}}\,({\rm{car}}\,({\it{name-list\/}}))\index{name-okp}$\;\;${\bf then }{\rm{bad-names}}\,({\rm{cdr}}\,({\it{name-list\/}}))\index{bad-names} \\ 
{\bf else }{\rm{insert}}\,({\rm{car}}\,({\it{name-list\/}}), {\rm{bad-names}}\,({\rm{cdr}}\,({\it{name-list\/}}))\index{bad-names})\index{insert}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable bad-names; name this event `bad-names-off'.\index{bad-names-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{name-list-errors} \\  
\=\+{\rm{name-list-errors}}\,({\it{name-list\/}}, {\it{duplicates-ok?\/}})\index{name-list-errors} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{nlistp-or-err}}\,({\rm{bad-names}}\,({\it{name-list\/}})\index{bad-names}, {\tt{'}}{\tt{bad-names}})\index{nlistp-or-err}, \\ 
\=\+{\bf if }{\it{duplicates-ok?\/}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{no-duplicates-or-err}}\,({\it{name-list\/}}, {\tt{'}}{\tt{duplicates}})\index{no-duplicates-or-err}$\;${\bf  endif}\-, \\ 
{\rm{nil-or-err}}\,({\rm{last-cdr}}\,({\it{name-list\/}})\index{last-cdr}, {\tt{'}}{\tt{not-proper-list}})\index{nil-or-err})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable name-list-errors; name this event `name-list-errors-off'.\index{name-list-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{name-list-ok} \\  
\=\+{\rm{name-list-ok}}\,({\it{name-list\/}}, {\it{label\/}}, {\it{duplicates-ok?\/}})\index{name-list-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,({\rm{name-list-errors}}\,({\it{name-list\/}}, {\it{duplicates-ok?\/}})\index{name-list-errors}, {\it{label\/}})\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable name-list-ok; name this event `name-list-ok-off'.\index{name-list-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{occ-arg-length-error} \\  
\=\+{\rm{occ-arg-length-error}}\,({\it{fn\/}}, {\it{expected-args\/}}, {\it{actual-args\/}}, {\it{label\/}})\index{occ-arg-length-error} \\ 
$=$$\;\;\;\;${\rm{t-or-err}}\,(\=\+{\rm{length}}\,({\it{expected-args\/}})\index{length} $=$ {\rm{length}}\,({\it{actual-args\/}})\index{length}, \\ 
{\it{label\/}}, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{occ-function}}, \\ 
{\it{fn\/}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{expected}}, {\rm{length}}\,({\it{expected-args\/}})\index{length}), \\ 
{\rm{list}}\,({\tt{'}}{\tt{got}}, {\rm{length}}\,({\it{actual-args\/}})\index{length}))\-)\-\index{t-or-err}\-
\end{tabbing}


\noindent{\sc Event}:   Enable occ-arg-length-error; name this event `occ-arg-length-error-off'.\index{occ-arg-length-error-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{occ-form-ok} \\  
\=\+{\rm{occ-form-ok}}\,({\it{occ\/}}, {\it{o-length\/}})\index{occ-form-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+{\rm{list}}\,(\=\+{\rm{t-or-err}}\,(\=\+({\tt{4}} $=$ {\it{o-length\/}}) $\vee$ ({\tt{5}} $=$ {\it{o-length\/}}), \\ 
{\tt{'}}{\tt{bad-occurrence-length}}, \\ 
{\it{o-length\/}})\-\index{t-or-err}, \\ 
{\rm{nil-or-err}}\,({\rm{last-cdr}}\,({\it{occ\/}})\index{last-cdr}, {\tt{'}}{\tt{not-proper-list}})\index{nil-or-err})\-, \\ 
{\tt{'}}{\tt{occurrence-form}})\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable occ-form-ok; name this event `occ-form-ok-off'.\index{occ-form-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{occ-name-ok} \\  
\=\+{\rm{occ-name-ok}}\,({\it{o-name\/}}, {\it{o-length\/}})\index{occ-name-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\bf if }{\it{o-length\/}} $<$ {\tt{1}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf then }{\rm{label-error}}\,(\=\+{\rm{t-or-err}}\,({\rm{name-okp}}\,({\it{o-name\/}})\index{name-okp}, {\tt{'}}{\tt{bad-name}}, {\it{o-name\/}})\index{t-or-err}, \\ 
{\tt{'}}{\tt{occurrence-name}})\-\index{label-error} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable occ-name-ok; name this event `occ-name-ok-off'.\index{occ-name-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{occ-outputs-ok} \\  
\=\+{\rm{occ-outputs-ok}}\,({\it{o-outs\/}}, {\it{o-length\/}})\index{occ-outputs-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\bf if }{\it{o-length\/}} $<$ {\tt{2}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf then }{\rm{name-list-ok}}\,({\it{o-outs\/}}, {\tt{'}}{\tt{occurrence-outputs}}, {\bf{f}})\index{name-list-ok} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable occ-outputs-ok; name this event `occ-outputs-ok-off'.\index{occ-outputs-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{occ-inputs-ok} \\  
\=\+{\rm{occ-inputs-ok}}\,({\it{o-ins\/}}, {\it{o-length\/}})\index{occ-inputs-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\bf if }{\it{o-length\/}} $<$ {\tt{4}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-$\;\;${\bf then }{\rm{name-list-ok}}\,({\it{o-ins\/}}, {\tt{'}}{\tt{occurrence-inputs}}, {\bf{t}})\index{name-list-ok} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable occ-inputs-ok; name this event `occ-inputs-ok-off'.\index{occ-inputs-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{occ-function-ok} \\  
\=\+{\rm{occ-function-ok}}\,({\it{o-fn\/}}, {\it{o-ins\/}}, {\it{o-outs\/}}, {\it{o-length\/}}, {\it{netlist\/}})\index{occ-function-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{o-length\/}} $<$ {\tt{3}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\rm{primp}}\,({\it{o-fn\/}})\index{primp} \\ 
{\bf then }{\rm{err-and}}\,(\=\+{\rm{list}}\,(\=\+\=\+{\bf if }\=\+{\bf if }{\it{o-length\/}} $<$ {\tt{4}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf then }{\rm{occ-arg-length-error}}\,(\=\+{\it{o-fn\/}}, \\ 
{\rm{primp2}}\,({\it{o-fn\/}}, {\tt{'}}{\tt{inputs}})\index{primp2}, \\ 
{\it{o-ins\/}}, \\ 
{\tt{'}}{\tt{wrong-number-of-inputs}})\-\index{occ-arg-length-error} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-, \\ 
{\rm{occ-arg-length-error}}\,(\=\+{\it{o-fn\/}}, \\ 
{\rm{primp2}}\,({\it{o-fn\/}}, {\tt{'}}{\tt{outputs}})\index{primp2}, \\ 
{\it{o-outs\/}}, \\ 
{\tt{'}}{\tt{wrong-number-of-outputs}})\-\index{occ-arg-length-error})\-, \\ 
{\tt{'}}{\tt{occurrence-function}})\-\index{err-and} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{lookup-module}}\,({\it{o-fn\/}}, {\it{netlist\/}})\index{lookup-module}) \\ 
{\bf then }{\rm{err-and}}\,(\=\+{\rm{list}}\,(\=\+\=\+{\bf if }\=\+{\bf if }{\it{o-length\/}} $<$ {\tt{4}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf then }{\rm{occ-arg-length-error}}\,(\=\+{\it{o-fn\/}}, \\ 
{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{o-fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\it{o-ins\/}}, \\ 
{\tt{'}}{\tt{wrong-number-of-inputs}})\-\index{occ-arg-length-error} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-, \\ 
{\rm{occ-arg-length-error}}\,(\=\+{\it{o-fn\/}}, \\ 
{\rm{module-outputs}}\,({\rm{lookup-module}}\,(\=\+{\it{o-fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-outputs}, \\ 
{\it{o-outs\/}}, \\ 
{\tt{'}}{\tt{wrong-number-of-outputs}})\-\index{occ-arg-length-error})\-, \\ 
{\tt{'}}{\tt{occurrence-function}})\-\index{err-and} \\ 
{\bf else }{\rm{pred-error}}\,({\tt{'}}{\tt{unknown-occurrence-function}}, {\it{o-fn\/}})\index{pred-error}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable occ-function-ok; name this event `occ-function-ok-off'.\index{occ-function-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{occ-annotation-ok} \\  
\=\+{\rm{occ-annotation-ok}}\,({\it{o-anno\/}}, {\it{o-length\/}})\index{occ-annotation-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{o-length\/}} $=$ {\tt{5}} \\ 
{\bf then }{\rm{label-error}}\,(\=\+{\rm{t-or-err}}\,({\rm{alistp}}\,({\it{o-anno\/}})\index{alistp}, {\tt{'}}{\tt{not-alist}}, {\it{o-anno\/}})\index{t-or-err}, \\ 
{\tt{'}}{\tt{occurrence-annotation}})\-\index{label-error} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable occ-annotation-ok; name this event `occ-annotation-ok-off'.\index{occ-annotation-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{occ-syntax-errors} \\  
\=\+{\rm{occ-syntax-errors}}\,({\it{occ\/}}, {\it{netlist\/}})\index{occ-syntax-errors} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{occ-form-ok}}\,({\it{occ\/}}, {\rm{length}}\,({\it{occ\/}})\index{length})\index{occ-form-ok}, \\ 
{\rm{occ-name-ok}}\,({\rm{occ-name}}\,({\it{occ\/}})\index{occ-name}, {\rm{length}}\,({\it{occ\/}})\index{length})\index{occ-name-ok}, \\ 
{\rm{occ-outputs-ok}}\,({\rm{occ-outputs}}\,({\it{occ\/}})\index{occ-outputs}, {\rm{length}}\,({\it{occ\/}})\index{length})\index{occ-outputs-ok}, \\ 
{\rm{occ-inputs-ok}}\,({\rm{occ-inputs}}\,({\it{occ\/}})\index{occ-inputs}, {\rm{length}}\,({\it{occ\/}})\index{length})\index{occ-inputs-ok}, \\ 
{\rm{occ-function-ok}}\,(\=\+{\rm{occ-function}}\,({\it{occ\/}})\index{occ-function}, \\ 
{\rm{occ-inputs}}\,({\it{occ\/}})\index{occ-inputs}, \\ 
{\rm{occ-outputs}}\,({\it{occ\/}})\index{occ-outputs}, \\ 
{\rm{length}}\,({\it{occ\/}})\index{length}, \\ 
{\it{netlist\/}})\-\index{occ-function-ok}, \\ 
{\rm{occ-annotation-ok}}\,({\rm{occ-annotation}}\,({\it{occ\/}})\index{occ-annotation}, {\rm{length}}\,({\it{occ\/}})\index{length})\index{occ-annotation-ok})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable occ-syntax-errors; name this event `occ-syntax-errors-off'.\index{occ-syntax-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{occ-syntax-ok} \\  
\=\+{\rm{occ-syntax-ok}}\,({\it{occ\/}}, {\it{netlist\/}})\index{occ-syntax-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+{\rm{occ-syntax-errors}}\,({\it{occ\/}}, {\it{netlist\/}})\index{occ-syntax-errors}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{occurrence}}, {\rm{occ-name}}\,({\it{occ\/}})\index{occ-name}))\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable occ-syntax-ok; name this event `occ-syntax-ok-off'.\index{occ-syntax-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{initial-occ-syntax-data} \\  
\=\+{\rm{initial-occ-syntax-data}}\,({\it{m-ins\/}}, {\it{m-outs\/}})\index{initial-occ-syntax-data} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{cons}}\,({\tt{'}}{\tt{signals}}, {\it{m-ins\/}}), \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,({\tt{'}}{\tt{pending-io}}, {\rm{intersection}}\,({\it{m-ins\/}}, {\it{m-outs\/}})\index{intersection}), \\ 
{\tt{'}}{\tt{(}}{\tt{(}}{\tt{non-depends}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{occ-names}}{\tt{)}}{\tt{)}})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable initial-occ-syntax-data; name this event `initial-occ-syntax-data-off'.\index{initial-occ-syntax-data-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{update-occ-syntax-data} \\  
\=\+{\rm{update-occ-syntax-data}}\,({\it{occ\/}}, {\it{occ-data\/}})\index{update-occ-syntax-data} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{signals}}, \\ 
{\rm{append}}\,(\=\+\=\+{\bf if }{\rm{listp}}\,({\rm{value}}\,({\tt{'}}{\tt{pending-io}}, {\it{occ-data\/}})\index{value}) \\ 
{\bf then }{\rm{set-diff}}\,(\=\+{\rm{occ-outputs}}\,({\it{occ\/}})\index{occ-outputs}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{pending-io}}, {\it{occ-data\/}})\index{value})\-\index{set-diff} \\ 
{\bf else }{\rm{occ-outputs}}\,({\it{occ\/}})\index{occ-outputs}$\;${\bf  endif}\-, \\ 
{\rm{value}}\,({\tt{'}}{\tt{signals}}, {\it{occ-data\/}})\index{value})\-)\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{pending-io}}, \\ 
{\rm{set-diff}}\,({\rm{value}}\,({\tt{'}}{\tt{pending-io}}, {\it{occ-data\/}})\index{value}, {\rm{occ-outputs}}\,({\it{occ\/}})\index{occ-outputs})\index{set-diff})\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{non-depends}}, \\ 
{\rm{append}}\,(\=\+{\rm{set-diff}}\,({\rm{occ-inputs}}\,({\it{occ\/}})\index{occ-inputs}, {\rm{value}}\,({\tt{'}}{\tt{signals}}, {\it{occ-data\/}})\index{value})\index{set-diff}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{non-depends}}, {\it{occ-data\/}})\index{value})\-)\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{occ-names}}, \\ 
{\rm{cons}}\,({\rm{occ-name}}\,({\it{occ\/}})\index{occ-name}, {\rm{value}}\,({\tt{'}}{\tt{occ-names}}, {\it{occ-data\/}})\index{value}))\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable update-occ-syntax-data; name this event `update-occ-syntax-data-off'.\index{update-occ-syntax-data-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{composite-occ-body-syntax-error!s} \\  
\=\+{\rm{composite-occ-body-syntax-errors}}\,({\it{body\/}}, {\it{occ-data\/}}, {\it{outputs\/}}, {\it{states\/}})\index{composite-occ-body-syntax-error!s} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{nil-or-err}}\,({\it{body\/}}, {\tt{'}}{\tt{not-proper-list}})\index{nil-or-err}, \\ 
{\rm{nlistp-or-err}}\,(\=\+{\rm{value}}\,({\tt{'}}{\tt{pending-io}}, {\it{occ-data\/}})\index{value}, \\ 
{\tt{'}}{\tt{io-signals-not-in-outputs}})\-\index{nlistp-or-err}, \\ 
{\rm{subset-or-err}}\,(\=\+{\it{outputs\/}}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{signals}}, {\it{occ-data\/}})\index{value}, \\ 
{\tt{'}}{\tt{outputs-not-in-signals}})\-\index{subset-or-err}, \\ 
{\rm{subset-or-err}}\,(\=\+{\rm{value}}\,({\tt{'}}{\tt{non-depends}}, {\it{occ-data\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{signals}}, {\it{occ-data\/}})\index{value}, \\ 
{\tt{'}}{\tt{non-depends-not-in-signals}})\-\index{subset-or-err}, \\ 
{\rm{subset-or-err}}\,(\=\+{\it{states\/}}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{occ-names}}, {\it{occ-data\/}})\index{value}, \\ 
{\tt{'}}{\tt{states-not-in-occ-names}})\-\index{subset-or-err}, \\ 
{\rm{no-duplicates-or-err}}\,(\=\+{\rm{value}}\,({\tt{'}}{\tt{signals}}, {\it{occ-data\/}})\index{value}, \\ 
{\tt{'}}{\tt{duplicates-in-signals}})\-\index{no-duplicates-or-err}, \\ 
{\rm{no-duplicates-or-err}}\,(\=\+{\rm{value}}\,({\tt{'}}{\tt{occ-names}}, {\it{occ-data\/}})\index{value}, \\ 
{\tt{'}}{\tt{duplicates-in-occ-names}})\-\index{no-duplicates-or-err})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable composite-occ-body-syntax-errors; name this event `composite-occ-body-syntax-errors-off'.\index{composite-occ-body-syntax-error!s-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{occ-body-syntax-errors} \\  
\=\+{\rm{occ-body-syntax-errors}}\,({\it{body\/}}, {\it{occ-data\/}}, {\it{outputs\/}}, {\it{states\/}}, {\it{netlist\/}})\index{occ-body-syntax-errors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{body\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }{\rm{composite-occ-body-syntax-errors}}\,({\it{body\/}}, {\it{occ-data\/}}, {\it{outputs\/}}, {\it{states\/}})\index{composite-occ-body-syntax-error!s} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{occ-syntax-ok}}\,({\rm{car}}\,({\it{body\/}}), {\it{netlist\/}})\index{occ-syntax-ok}, \\ 
{\rm{occ-body-syntax-errors}}\,(\=\+{\rm{cdr}}\,({\it{body\/}}), \\ 
{\rm{update-occ-syntax-data}}\,(\=\+{\rm{car}}\,({\it{body\/}}), \\ 
{\it{occ-data\/}})\-\index{update-occ-syntax-data}, \\ 
{\it{outputs\/}}, \\ 
{\it{states\/}}, \\ 
{\it{netlist\/}})\-\index{occ-body-syntax-errors})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable occ-body-syntax-errors; name this event `occ-body-syntax-errors-off'.\index{occ-body-syntax-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{module-form-ok} \\  
\=\+{\rm{module-form-ok}}\,({\it{module\/}}, {\it{m-length\/}})\index{module-form-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+{\rm{list}}\,(\=\+{\rm{t-or-err}}\,(\=\+({\it{m-length\/}} $=$ {\tt{5}}) $\vee$ ({\it{m-length\/}} $=$ {\tt{6}}), \\ 
{\tt{'}}{\tt{bad-module-length}}, \\ 
{\it{m-length\/}})\-\index{t-or-err}, \\ 
{\rm{nil-or-err}}\,({\rm{last-cdr}}\,({\it{module\/}})\index{last-cdr}, {\tt{'}}{\tt{not-proper-list}})\index{nil-or-err})\-, \\ 
{\tt{'}}{\tt{module-form}})\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable module-form-ok; name this event `module-form-ok-off'.\index{module-form-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{module-name-ok} \\  
\=\+{\rm{module-name-ok}}\,({\it{m-name\/}}, {\it{m-length\/}}, {\it{netlist\/}})\index{module-name-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\bf if }{\it{m-length\/}} $<$ {\tt{1}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf then }{\rm{err-and}}\,(\=\+{\rm{list}}\,(\=\+{\rm{t-or-err}}\,({\rm{name-okp}}\,({\it{m-name\/}})\index{name-okp}, {\tt{'}}{\tt{bad-name}}, {\it{m-name\/}})\index{t-or-err}, \\ 
{\rm{t-or-err}}\,(\=\+$\neg$ {\rm{lookup-module}}\,({\it{m-name\/}}, {\it{netlist\/}})\index{lookup-module}, \\ 
{\tt{'}}{\tt{duplicate-module-defns}}, \\ 
{\it{m-name\/}})\-\index{t-or-err}, \\ 
{\rm{t-or-err}}\,(\=\+$\neg$ {\rm{primp}}\,({\it{m-name\/}})\index{primp}, \\ 
{\tt{'}}{\tt{module-name-same-as-primitive}}, \\ 
{\it{m-name\/}})\-\index{t-or-err})\-, \\ 
{\tt{'}}{\tt{module-name}})\-\index{err-and} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable module-name-ok; name this event `module-name-ok-off'.\index{module-name-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{module-inputs-ok} \\  
\=\+{\rm{module-inputs-ok}}\,({\it{m-ins\/}}, {\it{m-length\/}})\index{module-inputs-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\bf if }{\it{m-length\/}} $<$ {\tt{2}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-$\;\;${\bf then }{\rm{name-list-ok}}\,({\it{m-ins\/}}, {\tt{'}}{\tt{module-inputs}}, {\bf{f}})\index{name-list-ok} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable module-inputs-ok; name this event `module-inputs-ok-off'.\index{module-inputs-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{module-outputs-ok} \\  
\=\+{\rm{module-outputs-ok}}\,({\it{m-outs\/}}, {\it{m-length\/}})\index{module-outputs-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\bf if }{\it{m-length\/}} $<$ {\tt{3}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-$\;\;${\bf then }{\rm{name-list-ok}}\,({\it{m-outs\/}}, {\tt{'}}{\tt{module-outputs}}, {\bf{f}})\index{name-list-ok} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable module-outputs-ok; name this event `module-outputs-ok-off'.\index{module-outputs-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{states-list-or-nil} \\  
\=\+{\rm{states-list-or-nil}}\,({\it{m-states\/}}, {\it{m-length\/}})\index{states-list-or-nil} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\bf if }{\it{m-length\/}} $<$ {\tt{5}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-$\;\;${\bf then }{\rm{m-states-list}}\,({\it{m-states\/}})\index{m-states-list} \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable states-list-or-nil; name this event `states-list-or-nil-off'.\index{states-list-or-nil-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{module-occurrences-ok} \\  
\=\+{\rm{module-occurrences-ok}}\,({\it{m-occs\/}}, {\it{m-ins\/}}, {\it{m-outs\/}}, {\it{m-states\/}}, {\it{m-length\/}}, {\it{netlist\/}})\index{module-occurrences-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\bf if }{\it{m-length\/}} $<$ {\tt{4}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf then }{\rm{err-and}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{t-or-err}}\,({\rm{listp}}\,({\it{m-occs\/}}), {\tt{'}}{\tt{no-occurrences}}, {\it{m-occs\/}})\index{t-or-err}, \\ 
{\rm{occ-body-syntax-errors}}\,(\=\+{\it{m-occs\/}}, \\ 
{\rm{initial-occ-syntax-data}}\,(\=\+{\it{m-ins\/}}, \\ 
{\it{m-outs\/}})\-\index{initial-occ-syntax-data}, \\ 
{\it{m-outs\/}}, \\ 
{\rm{states-list-or-nil}}\,(\=\+{\it{m-states\/}}, \\ 
{\it{m-length\/}})\-\index{states-list-or-nil}, \\ 
{\it{netlist\/}})\-\index{occ-body-syntax-errors})\-, \\ 
{\tt{'}}{\tt{module-occurrences}})\-\index{err-and} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable module-occurrences-ok; name this event `module-occurrences-ok-off'.\index{module-occurrences-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{module-statenames-ok} \\  
\=\+{\rm{module-statenames-ok}}\,({\it{m-states\/}}, {\it{m-length\/}})\index{module-statenames-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\bf if }{\it{m-length\/}} $<$ {\tt{5}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf then }{\rm{err-and}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{t-or-err}}\,(\=\+\=\+{\bf if }{\rm{listp}}\,({\it{m-states\/}}) \\ 
{\bf then }{\rm{listp}}\,({\rm{cdr}}\,({\it{m-states\/}})) \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-, \\ 
{\tt{'}}{\tt{list-of-length-1-not-allowed}}, \\ 
{\it{m-states\/}})\-\index{t-or-err}, \\ 
{\rm{name-list-errors}}\,({\rm{m-states-list}}\,({\it{m-states\/}})\index{m-states-list}, {\bf{f}})\index{name-list-errors})\-, \\ 
{\tt{'}}{\tt{module-statenames}})\-\index{err-and} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable module-statenames-ok; name this event `module-statenames-ok-off'.\index{module-statenames-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{module-annotation-ok} \\  
\=\+{\rm{module-annotation-ok}}\,({\it{m-anno\/}}, {\it{m-length\/}})\index{module-annotation-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{m-length\/}} $=$ {\tt{6}} \\ 
{\bf then }{\rm{label-error}}\,(\=\+{\rm{t-or-err}}\,({\rm{alistp}}\,({\it{m-anno\/}})\index{alistp}, {\tt{'}}{\tt{not-alist}}, {\it{m-anno\/}})\index{t-or-err}, \\ 
{\tt{'}}{\tt{module-annotation}})\-\index{label-error} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable module-annotation-ok; name this event `module-annotation-ok-off'.\index{module-annotation-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{module-syntax-errors} \\  
\=\+{\rm{module-syntax-errors}}\,({\it{module\/}}, {\it{netlist\/}})\index{module-syntax-errors} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{module-form-ok}}\,({\it{module\/}}, {\rm{length}}\,({\it{module\/}})\index{length})\index{module-form-ok}, \\ 
{\rm{module-name-ok}}\,({\rm{module-name}}\,({\it{module\/}})\index{module-name}, {\rm{length}}\,({\it{module\/}})\index{length}, {\it{netlist\/}})\index{module-name-ok}, \\ 
{\rm{module-inputs-ok}}\,({\rm{module-inputs}}\,({\it{module\/}})\index{module-inputs}, {\rm{length}}\,({\it{module\/}})\index{length})\index{module-inputs-ok}, \\ 
{\rm{module-outputs-ok}}\,({\rm{module-outputs}}\,({\it{module\/}})\index{module-outputs}, {\rm{length}}\,({\it{module\/}})\index{length})\index{module-outputs-ok}, \\ 
{\rm{module-occurrences-ok}}\,(\=\+{\rm{module-occurrences}}\,({\it{module\/}})\index{module-occurrences}, \\ 
{\rm{module-inputs}}\,({\it{module\/}})\index{module-inputs}, \\ 
{\rm{module-outputs}}\,({\it{module\/}})\index{module-outputs}, \\ 
{\rm{module-statenames}}\,({\it{module\/}})\index{module-statenames}, \\ 
{\rm{length}}\,({\it{module\/}})\index{length}, \\ 
{\it{netlist\/}})\-\index{module-occurrences-ok}, \\ 
{\rm{module-statenames-ok}}\,({\rm{module-statenames}}\,({\it{module\/}})\index{module-statenames}, {\rm{length}}\,({\it{module\/}})\index{length})\index{module-statenames-ok}, \\ 
{\rm{module-annotation-ok}}\,({\rm{module-annotation}}\,({\it{module\/}})\index{module-annotation}, {\rm{length}}\,({\it{module\/}})\index{length})\index{module-annotation-ok})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable module-syntax-errors; name this event `module-syntax-errors-off'.\index{module-syntax-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{module-syntax-ok} \\  
\=\+{\rm{module-syntax-ok}}\,({\it{module\/}}, {\it{netlist\/}})\index{module-syntax-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+{\rm{module-syntax-errors}}\,({\it{module\/}}, {\it{netlist\/}})\index{module-syntax-errors}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{module}}, {\rm{module-name}}\,({\it{module\/}})\index{module-name}))\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable module-syntax-ok; name this event `module-syntax-ok-off'.\index{module-syntax-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{netlist-syntax-errors} \\  
\=\+{\rm{netlist-syntax-errors}}\,({\it{netlist\/}})\index{netlist-syntax-errors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{netlist\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{module-syntax-ok}}\,({\rm{car}}\,({\it{netlist\/}}), {\rm{cdr}}\,({\it{netlist\/}}))\index{module-syntax-ok}, \\ 
{\rm{netlist-syntax-errors}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{netlist-syntax-errors})\- \\ 
{\bf else }{\rm{list}}\,({\rm{nil-or-err}}\,({\it{netlist\/}}, {\tt{'}}{\tt{not-proper-list}})\index{nil-or-err})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable netlist-syntax-errors; name this event `netlist-syntax-errors-off'.\index{netlist-syntax-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{netlist-syntax-ok} \\  
\=\+{\rm{netlist-syntax-ok}}\,({\it{netlist\/}})\index{netlist-syntax-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,({\rm{netlist-syntax-errors}}\,({\it{netlist\/}})\index{netlist-syntax-errors}, {\tt{'}}{\tt{netlist-syntax-errors}})\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable netlist-syntax-ok; name this event `netlist-syntax-ok-off'.\index{netlist-syntax-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{letterp} \\  
{\rm{letterp}}\,({\it{char\/}})\index{letterp} $=$ ({\it{char\/}} $\in$ {\rm{unpack}}\,({\tt{'}}{\tt{abcdefghijklmnopqrstuvwxyz}}))
\end{tabbing}


\noindent{\sc Event}:   Enable letterp; name this event `letterp-off'.\index{letterp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{digitp} \\  
{\rm{digitp}}\,({\it{char\/}})\index{digitp} $=$ ({\it{char\/}} $\in$ {\rm{cdr}}\,({\rm{unpack}}\,({\tt{'}}{\tt{a0123456789}})))
\end{tabbing}


\noindent{\sc Event}:   Enable digitp; name this event `digitp-off'.\index{digitp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{bad-lsi-name-chars} \\  
\=\+{\rm{bad-lsi-name-chars}}\,({\it{char-list\/}}, {\it{special-characters\/}})\index{bad-lsi-name-chars} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{char-list\/}}) \\ 
{\bf then }\=\+{\bf if }\=\+{\rm{letterp}}\,({\rm{car}}\,({\it{char-list\/}}))\index{letterp} \\ 
$\vee$$\;\;\;\;${\rm{digitp}}\,({\rm{car}}\,({\it{char-list\/}}))\index{digitp} \\ 
$\vee$$\;\;\;\;$({\rm{car}}\,({\it{char-list\/}}) $\in$ {\it{special-characters\/}})\- \\ 
{\bf then }{\rm{bad-lsi-name-chars}}\,({\rm{cdr}}\,({\it{char-list\/}}), {\it{special-characters\/}})\index{bad-lsi-name-chars} \\ 
{\bf else }{\rm{insert}}\,(\=\+{\rm{car}}\,({\it{char-list\/}}), \\ 
{\rm{bad-lsi-name-chars}}\,(\=\+{\rm{cdr}}\,({\it{char-list\/}}), \\ 
{\it{special-characters\/}})\-\index{bad-lsi-name-chars})\-\index{insert}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable bad-lsi-name-chars; name this event `bad-lsi-name-chars-off'.\index{bad-lsi-name-chars-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{lsi-keywords} \\  
\=\+{\sc{lsi-keywords}}\index{lsi-keywords} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{action}}{\tt{ }}{\tt{angle}}{\tt{ }}{\tt{annotations}}{\tt{ }}{\tt{bloat}}{\tt{ }}{\tt{block}}{\tt{ }}{\tt{bus}}{\tt{ }}{\tt{cell}}{\tt{ }}{\tt{celstat}} \\ 
{\tt{chksum}}{\tt{ }}{\tt{clk\_line}}{\tt{ }}{\tt{direction}}{\tt{ }}{\tt{dummy}}{\tt{ }}{\tt{end}}{\tt{ }}{\tt{flip}}{\tt{ }}{\tt{function}} \\ 
{\tt{hm\_bidi}}{\tt{ }}{\tt{hm\_input}}{\tt{ }}{\tt{hm\_output}}{\tt{ }}{\tt{library}}{\tt{ }}{\tt{name}}{\tt{ }}{\tt{nc}}{\tt{ }}{\tt{net}}{\tt{ }}{\tt{pin}} \\ 
{\tt{powercells}}{\tt{ }}{\tt{priority}}{\tt{ }}{\tt{psecured}}{\tt{ }}{\tt{region}}{\tt{ }}{\tt{scale}}{\tt{ }}{\tt{technology}} \\ 
{\tt{tsecured}}{\tt{ }}{\tt{via}}{\tt{ }}{\tt{wire}}{\tt{)}}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable lsi-keywords; name this event `lsi-keywords-off'.\index{lsi-keywords-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*lsi-keywords; name this event `g*1*lsi-keywords-off'.\index{g*1*lsi-keywords-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{lsi-name-ok} \\  
\=\+{\rm{lsi-name-ok}}\,({\it{name\/}}, {\it{token-size\/}})\index{lsi-name-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{name\/}} $\in$ {\sc{lsi-keywords}}\index{lsi-keywords} \\ 
{\bf then }{\rm{pred-error}}\,({\tt{'}}{\tt{lsi-name-is-keyword}}, {\it{name\/}})\index{pred-error} \\ 
{\bf elseif }{\rm{litatom}}\,({\it{name\/}}) \\ 
{\bf then }{\rm{err-and}}\,(\=\+{\rm{list}}\,(\=\+{\rm{t-or-err}}\,(\=\+\=\+{\bf if }{\it{token-size\/}} $<$ {\rm{length}}\,({\rm{unpack}}\,({\it{name\/}}))\index{length} \\ 
{\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-, \\ 
{\tt{'}}{\tt{name-too-long}}, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{name-length}}, \\ 
{\rm{length}}\,({\rm{unpack}}\,({\it{name\/}}))\index{length})\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{max-allowed-length}}, \\ 
{\it{token-size\/}})\-)\-)\-\index{t-or-err}, \\ 
{\rm{t-or-err}}\,(\=\+{\rm{letterp}}\,({\rm{car}}\,({\rm{unpack}}\,({\it{name\/}})))\index{letterp}, \\ 
{\tt{'}}{\tt{name-begins-with-nonletter}}, \\ 
{\rm{car}}\,({\rm{unpack}}\,({\it{name\/}})))\-\index{t-or-err}, \\ 
{\rm{nlistp-or-err}}\,(\=\+{\rm{bad-lsi-name-chars}}\,(\=\+{\rm{cdr}}\,({\rm{unpack}}\,({\it{name\/}})), \\ 
{\rm{cdr}}\,({\rm{unpack}}\,({\tt{'}}{\tt{a-\_}})))\-\index{bad-lsi-name-chars}, \\ 
{\tt{'}}{\tt{illegal-chars-in-name}})\-\index{nlistp-or-err}, \\ 
{\rm{t-or-err}}\,(\=\+{\rm{last-cdr}}\,({\rm{unpack}}\,({\it{name\/}}))\index{last-cdr} $=$ {\tt{0}}, \\ 
{\tt{'}}{\tt{not-standard-litatom}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{last-cdr}}, {\rm{last-cdr}}\,({\rm{unpack}}\,({\it{name\/}}))\index{last-cdr}))\-\index{t-or-err})\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{bad-lsi-name}}, {\it{name\/}}))\-\index{err-and} \\ 
{\bf else }{\rm{pred-error}}\,({\tt{'}}{\tt{lsi-name-not-litatom}}, {\it{name\/}})\index{pred-error}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable lsi-name-ok; name this event `lsi-name-ok-off'.\index{lsi-name-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{lsi-bad-names} \\  
\=\+{\rm{lsi-bad-names}}\,({\it{name-list\/}}, {\it{token-size\/}})\index{lsi-bad-names} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{name-list\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{lsi-name-ok}}\,({\rm{car}}\,({\it{name-list\/}}), {\it{token-size\/}})\index{lsi-name-ok}, \\ 
{\rm{lsi-bad-names}}\,({\rm{cdr}}\,({\it{name-list\/}}), {\it{token-size\/}})\index{lsi-bad-names})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable lsi-bad-names; name this event `lsi-bad-names-off'.\index{lsi-bad-names-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{lsi-name-list-errors} \\  
\=\+{\rm{lsi-name-list-errors}}\,({\it{name-list\/}}, {\it{token-size\/}}, {\it{duplicates-ok?\/}})\index{lsi-name-list-errors} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{err-and}}\,({\rm{lsi-bad-names}}\,({\it{name-list\/}}, {\it{token-size\/}})\index{lsi-bad-names}, {\tt{'}}{\tt{bad-lsi-names}})\index{err-and}, \\ 
\=\+{\bf if }{\it{duplicates-ok?\/}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{no-duplicates-or-err}}\,({\it{name-list\/}}, {\tt{'}}{\tt{duplicates}})\index{no-duplicates-or-err}$\;${\bf  endif}\-, \\ 
{\rm{nil-or-err}}\,({\rm{last-cdr}}\,({\it{name-list\/}})\index{last-cdr}, {\tt{'}}{\tt{not-proper-list}})\index{nil-or-err})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable lsi-name-list-errors; name this event `lsi-name-list-errors-off'.\index{lsi-name-list-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{lsi-name-list-ok} \\  
\=\+{\rm{lsi-name-list-ok}}\,({\it{name-list\/}}, {\it{token-size\/}}, {\it{label\/}}, {\it{duplicates-ok?\/}})\index{lsi-name-list-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+{\rm{lsi-name-list-errors}}\,({\it{name-list\/}}, {\it{token-size\/}}, {\it{duplicates-ok?\/}})\index{lsi-name-list-errors}, \\ 
{\it{label\/}})\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable lsi-name-list-ok; name this event `lsi-name-list-ok-off'.\index{lsi-name-list-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{lsi-function-name} \\  
\=\+{\rm{lsi-function-name}}\,({\it{fname\/}})\index{lsi-function-name} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{primp}}\,({\it{fname\/}})\index{primp} $\wedge$ {\rm{primp-lookup}}\,({\it{fname\/}}, {\tt{'}}{\tt{lsi-name}})\index{primp-lookup} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{primp2}}\,({\it{fname\/}}, {\tt{'}}{\tt{lsi-name}})\index{primp2}) \\ 
{\bf then }{\rm{car}}\,({\rm{primp2}}\,({\it{fname\/}}, {\tt{'}}{\tt{lsi-name}})\index{primp2}) \\ 
{\bf else }{\rm{primp2}}\,({\it{fname\/}}, {\tt{'}}{\tt{lsi-name}})\index{primp2}$\;${\bf  endif}\- \\ 
{\bf else }{\it{fname\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable lsi-function-name; name this event `lsi-function-name-off'.\index{lsi-function-name-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{name-length}$\;\;$
{\rm{name-length}}\,({\it{name\/}})\index{name-length} $=$ {\rm{length}}\,({\rm{unpack}}\,({\it{name\/}}))\index{length}
\end{tabbing}


\noindent{\sc Event}:   Enable name-length; name this event `name-length-off'.\index{name-length-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{hierarchical-name-max} \\  
\=\+{\rm{hierarchical-name-max}}\,({\it{n1\/}}, {\it{n2\/}})\index{hierarchical-name-max} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{n1\/}} $\simeq\;${{\bf{nil}}}${}$) $\wedge$ ({\it{n2\/}} $\simeq\;${{\bf{nil}}}${}$)$\;\;${\bf then }{\tt{0}} \\ 
{\bf elseif }{\it{n1\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{n2\/}} \\ 
{\bf elseif }{\it{n2\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{n1\/}} \\ 
{\bf elseif }{\rm{car}}\,({\it{n1\/}}) $<$ {\rm{car}}\,({\it{n2\/}})$\;\;${\bf then }{\it{n2\/}} \\ 
{\bf else }{\it{n1\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable hierarchical-name-max; name this event `hierarchical-name-max-off'.\index{hierarchical-name-max-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{max-hierarchical-length-and-name} \\  
\=\+{\rm{max-hierarchical-length-and-name}}\,({\it{names\/}})\index{max-hierarchical-length-and-name} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{names\/}}) \\ 
{\bf then }{\rm{hierarchical-name-max}}\,(\=\+{\rm{list}}\,(\=\+$1\;+$ {\rm{name-length}}\,({\rm{car}}\,({\it{names\/}}))\index{name-length}, \\ 
{\rm{car}}\,({\it{names\/}}))\-, \\ 
{\rm{max-hierarchical-length-and-name}}\,({\rm{cdr}}\,({\it{names\/}}))\index{max-hierarchical-length-and-name})\-\index{hierarchical-name-max} \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable max-hierarchical-length-and-name; name this event `max-hierarchical-length-and-name-off'.\index{max-hierarchical-length-and-name!-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{max-occ-hierarchical-name} \\  
\=\+{\rm{max-occ-hierarchical-name}}\,({\it{occ\/}}, {\it{hierarchical-table\/}}, {\it{hierarchical-size\/}})\index{max-occ-hierarchical-name} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,(\=\+{\bf if }{\rm{primp}}\,({\rm{occ-function}}\,({\it{occ\/}})\index{occ-function})\index{primp} \\ 
{\bf then }{\rm{max-hierarchical-length-and-name}}\,({\rm{append}}\,(\=\+{\rm{occ-inputs}}\,({\it{occ\/}})\index{occ-inputs}, \\ 
{\rm{occ-outputs}}\,({\it{occ\/}})\index{occ-outputs})\-)\index{max-hierarchical-length-and-name} \\ 
{\bf else }{\rm{value}}\,({\rm{occ-function}}\,({\it{occ\/}})\index{occ-function}, {\it{hierarchical-table\/}})\index{value}$\;${\bf  endif}\-) \\ 
{\bf then }\=\+{\bf if }\=\+{\bf if }{\it{hierarchical-size\/}} $<$ (\=\+($1\;+$ {\rm{name-length}}\,({\rm{occ-name}}\,({\it{occ\/}})\index{occ-name})\index{name-length}) \\ 
$+$$\;\;\;\;${\rm{car}}\,(\=\+{\bf if }{\rm{primp}}\,({\rm{occ-function}}\,({\it{occ\/}})\index{occ-function})\index{primp} \\ 
{\bf then }{\rm{max-hierarchical-length-and-name}}\,({\rm{append}}\,(\=\+{\rm{occ-inputs}}\,({\it{occ\/}})\index{occ-inputs}, \\ 
{\rm{occ-outputs}}\,({\it{occ\/}})\index{occ-outputs})\-)\index{max-hierarchical-length-and-name} \\ 
{\bf else }{\rm{value}}\,(\=\+{\rm{occ-function}}\,({\it{occ\/}})\index{occ-function}, \\ 
{\it{hierarchical-table\/}})\-\index{value}$\;${\bf  endif}\-))\- \\ 
{\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf then }{\rm{cons}}\,(\=\+\=\+($1\;+$ {\rm{name-length}}\,({\rm{occ-name}}\,({\it{occ\/}})\index{occ-name})\index{name-length}) \\ 
$+$$\;\;\;\;${\rm{car}}\,(\=\+{\bf if }{\rm{primp}}\,({\rm{occ-function}}\,({\it{occ\/}})\index{occ-function})\index{primp} \\ 
{\bf then }{\rm{max-hierarchical-length-and-name}}\,({\rm{append}}\,(\=\+{\rm{occ-inputs}}\,({\it{occ\/}})\index{occ-inputs}, \\ 
{\rm{occ-outputs}}\,({\it{occ\/}})\index{occ-outputs})\-)\index{max-hierarchical-length-and-name} \\ 
{\bf else }{\rm{value}}\,(\=\+{\rm{occ-function}}\,({\it{occ\/}})\index{occ-function}, \\ 
{\it{hierarchical-table\/}})\-\index{value}$\;${\bf  endif}\-)\-, \\ 
{\rm{cons}}\,(\=\+{\rm{occ-name}}\,({\it{occ\/}})\index{occ-name}, \\ 
{\rm{cdr}}\,(\=\+{\bf if }{\rm{primp}}\,({\rm{occ-function}}\,({\it{occ\/}})\index{occ-function})\index{primp} \\ 
{\bf then }{\rm{max-hierarchical-length-and-name}}\,({\rm{append}}\,(\=\+{\rm{occ-inputs}}\,({\it{occ\/}})\index{occ-inputs}, \\ 
{\rm{occ-outputs}}\,({\it{occ\/}})\index{occ-outputs})\-)\index{max-hierarchical-length-and-name} \\ 
{\bf else }{\rm{value}}\,(\=\+{\rm{occ-function}}\,({\it{occ\/}})\index{occ-function}, \\ 
{\it{hierarchical-table\/}})\-\index{value}$\;${\bf  endif}\-))\-)\- \\ 
{\bf else }{\rm{pred-error}}\,(\=\+{\tt{'}}{\tt{hierarchical-name-too-long}}, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{name-length}}, \\ 
\=\+($1\;+$ {\rm{name-length}}\,({\rm{occ-name}}\,({\it{occ\/}})\index{occ-name})\index{name-length}) \\ 
$+$$\;\;\;\;${\rm{car}}\,(\=\+{\bf if }{\rm{primp}}\,({\rm{occ-function}}\,({\it{occ\/}})\index{occ-function})\index{primp} \\ 
{\bf then }{\rm{max-hierarchical-length-and-name}}\,({\rm{append}}\,(\=\+{\rm{occ-inputs}}\,({\it{occ\/}})\index{occ-inputs}, \\ 
{\rm{occ-outputs}}\,({\it{occ\/}})\index{occ-outputs})\-)\index{max-hierarchical-length-and-name} \\ 
{\bf else }{\rm{value}}\,(\=\+{\rm{occ-function}}\,({\it{occ\/}})\index{occ-function}, \\ 
{\it{hierarchical-table\/}})\-\index{value}$\;${\bf  endif}\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{max-allowed-length}}, \\ 
{\it{hierarchical-size\/}})\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{name}}, \\ 
{\rm{cons}}\,(\=\+{\rm{occ-name}}\,({\it{occ\/}})\index{occ-name}, \\ 
{\rm{cdr}}\,(\=\+{\bf if }{\rm{primp}}\,({\rm{occ-function}}\,({\it{occ\/}})\index{occ-function})\index{primp} \\ 
{\bf then }{\rm{max-hierarchical-length-and-name}}\,({\rm{append}}\,(\=\+{\rm{occ-inputs}}\,({\it{occ\/}})\index{occ-inputs}, \\ 
{\rm{occ-outputs}}\,({\it{occ\/}})\index{occ-outputs})\-)\index{max-hierarchical-length-and-name} \\ 
{\bf else }{\rm{value}}\,(\=\+{\rm{occ-function}}\,({\it{occ\/}})\index{occ-function}, \\ 
{\it{hierarchical-table\/}})\-\index{value}$\;${\bf  endif}\-))\-)\-)\-)\-\index{pred-error}$\;${\bf  endif}\- \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable max-occ-hierarchical-name; name this event `max-occ-hierarchical-name-off'.\index{max-occ-hierarchical-name-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{lsi-occ-name-ok} \\  
\=\+{\rm{lsi-occ-name-ok}}\,({\it{o-name\/}}, {\it{o-length\/}}, {\it{o-outs\/}}, {\it{occ-data\/}}, {\it{token-size\/}})\index{lsi-occ-name-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\bf if }{\it{o-length\/}} $<$ {\tt{1}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf then }{\rm{err-and}}\,(\=\+{\rm{list}}\,(\=\+{\rm{lsi-name-ok}}\,({\it{o-name\/}}, {\it{token-size\/}})\index{lsi-name-ok}, \\ 
{\rm{t-or-err}}\,(\=\+{\it{o-name\/}} $\not\in$ {\rm{value}}\,({\tt{'}}{\tt{signals}}, {\it{occ-data\/}})\index{value}, \\ 
{\tt{'}}{\tt{occ-name-is-signal}}, \\ 
{\it{o-name\/}})\-\index{t-or-err}, \\ 
{\rm{t-or-err}}\,(\=\+\=\+({\rm{cdr}}\,({\it{o-outs\/}}) $=$ {\bf{nil}}) \\ 
$\vee$$\;\;\;\;$({\it{o-name\/}} $\not\in$ {\it{o-outs\/}})\-, \\ 
{\tt{'}}{\tt{occ-name-is-same-as-output-name}}, \\ 
{\it{o-name\/}})\-\index{t-or-err})\-, \\ 
{\tt{'}}{\tt{occurrence-name}})\-\index{err-and} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable lsi-occ-name-ok; name this event `lsi-occ-name-ok-off'.\index{lsi-occ-name-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{lsi-occ-outputs-ok} \\  
\=\+{\rm{lsi-occ-outputs-ok}}\,({\it{o-outs\/}}, {\it{o-length\/}}, {\it{occ-data\/}}, {\it{token-size\/}})\index{lsi-occ-outputs-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\bf if }{\it{o-length\/}} $<$ {\tt{2}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf then }{\rm{err-and}}\,(\=\+{\rm{list}}\,(\=\+{\rm{lsi-name-list-ok}}\,(\=\+{\it{o-outs\/}}, \\ 
{\it{token-size\/}}, \\ 
{\tt{'}}{\tt{occ-outputs}}, \\ 
{\bf{f}})\-\index{lsi-name-list-ok}, \\ 
{\rm{disjoint-or-err}}\,(\=\+{\it{o-outs\/}}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{occ-names}}, {\it{occ-data\/}})\index{value}, \\ 
{\tt{'}}{\tt{occ-outputs-in-occ-names}})\-\index{disjoint-or-err})\-, \\ 
{\tt{'}}{\tt{occurrence-outputs}})\-\index{err-and} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable lsi-occ-outputs-ok; name this event `lsi-occ-outputs-ok-off'.\index{lsi-occ-outputs-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{lsi-occ-inputs-ok} \\  
\=\+{\rm{lsi-occ-inputs-ok}}\,({\it{o-ins\/}}, {\it{o-length\/}}, {\it{token-size\/}})\index{lsi-occ-inputs-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\bf if }{\it{o-length\/}} $<$ {\tt{4}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf then }{\rm{lsi-name-list-ok}}\,({\it{o-ins\/}}, {\it{token-size\/}}, {\tt{'}}{\tt{occurrence-inputs}}, {\bf{t}})\index{lsi-name-list-ok} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable lsi-occ-inputs-ok; name this event `lsi-occ-inputs-ok-off'.\index{lsi-occ-inputs-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{lsi-occ-syntax-ok} \\  
\=\+{\rm{lsi-occ-syntax-ok}}\,({\it{occ\/}}, {\it{hierarchical-name-error\/}}, {\it{occ-data\/}}, {\it{netlist\/}}, {\it{token-size\/}})\index{lsi-occ-syntax-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+{\rm{list}}\,(\=\+{\rm{occ-form-ok}}\,({\it{occ\/}}, {\rm{length}}\,({\it{occ\/}})\index{length})\index{occ-form-ok}, \\ 
{\rm{lsi-occ-name-ok}}\,(\=\+{\rm{occ-name}}\,({\it{occ\/}})\index{occ-name}, \\ 
{\rm{length}}\,({\it{occ\/}})\index{length}, \\ 
{\rm{occ-outputs}}\,({\it{occ\/}})\index{occ-outputs}, \\ 
{\it{occ-data\/}}, \\ 
{\it{token-size\/}})\-\index{lsi-occ-name-ok}, \\ 
{\rm{lsi-occ-outputs-ok}}\,(\=\+{\rm{occ-outputs}}\,({\it{occ\/}})\index{occ-outputs}, \\ 
{\rm{length}}\,({\it{occ\/}})\index{length}, \\ 
{\it{occ-data\/}}, \\ 
{\it{token-size\/}})\-\index{lsi-occ-outputs-ok}, \\ 
{\rm{lsi-occ-inputs-ok}}\,({\rm{occ-inputs}}\,({\it{occ\/}})\index{occ-inputs}, {\rm{length}}\,({\it{occ\/}})\index{length}, {\it{token-size\/}})\index{lsi-occ-inputs-ok}, \\ 
{\rm{occ-function-ok}}\,(\=\+{\rm{occ-function}}\,({\it{occ\/}})\index{occ-function}, \\ 
{\rm{occ-inputs}}\,({\it{occ\/}})\index{occ-inputs}, \\ 
{\rm{occ-outputs}}\,({\it{occ\/}})\index{occ-outputs}, \\ 
{\rm{length}}\,({\it{occ\/}})\index{length}, \\ 
{\it{netlist\/}})\-\index{occ-function-ok}, \\ 
{\rm{occ-annotation-ok}}\,({\rm{occ-annotation}}\,({\it{occ\/}})\index{occ-annotation}, {\rm{length}}\,({\it{occ\/}})\index{length})\index{occ-annotation-ok}, \\ 
{\it{hierarchical-name-error\/}})\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{occurrence}}, {\rm{occ-name}}\,({\it{occ\/}})\index{occ-name}))\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable lsi-occ-syntax-ok; name this event `lsi-occ-syntax-ok-off'.\index{lsi-occ-syntax-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{initial-lsi-occ-syntax-data} \\  
\=\+{\rm{initial-lsi-occ-syntax-data}}\,({\it{m-ins\/}}, {\it{m-outs\/}})\index{initial-lsi-occ-syntax-data} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{occ-fns}}{\tt{)}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{hierarchical-name}}{\tt{ .\ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{initial-occ-syntax-data}}\,({\it{m-ins\/}}, {\it{m-outs\/}})\index{initial-occ-syntax-data})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable initial-lsi-occ-syntax-data; name this event `initial-lsi-occ-syntax-data-off'.\index{initial-lsi-occ-syntax-data-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{update-lsi-occ-syntax-data} \\  
\=\+{\rm{update-lsi-occ-syntax-data}}\,({\it{occ\/}}, {\it{o-hname\/}}, {\it{occ-data\/}})\index{update-lsi-occ-syntax-data} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{occ-fns}}, \\ 
{\rm{cons}}\,(\=\+{\rm{lsi-function-name}}\,({\rm{occ-function}}\,({\it{occ\/}})\index{occ-function})\index{lsi-function-name}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{occ-fns}}, {\it{occ-data\/}})\index{value})\-)\-, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{hierarchical-name}}, \\ 
{\rm{hierarchical-name-max}}\,(\=\+{\rm{value}}\,(\=\+{\tt{'}}{\tt{hierarchical-name}}, \\ 
{\it{occ-data\/}})\-\index{value}, \\ 
{\it{o-hname\/}})\-\index{hierarchical-name-max})\-, \\ 
{\rm{update-occ-syntax-data}}\,({\it{occ\/}}, {\it{occ-data\/}})\index{update-occ-syntax-data})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable update-lsi-occ-syntax-data; name this event `update-lsi-occ-syntax-data-off'.\index{update-lsi-occ-syntax-data-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{lsi-occ-body-syntax-check} \\  
\=\+{\rm{lsi-occ-body-syntax-check}}\,(\=\+{\it{body\/}}, \\ 
{\it{occ-data\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{states\/}}, \\ 
{\it{netlist\/}}, \\ 
{\it{token-size\/}}, \\ 
{\it{hierarchical-table\/}}, \\ 
{\it{hierarchical-size\/}})\-\index{lsi-occ-body-syntax-check} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{body\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }{\rm{append}}\,(\=\+{\rm{composite-occ-body-syntax-errors}}\,(\=\+{\it{body\/}}, \\ 
{\it{occ-data\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{states\/}})\-\index{composite-occ-body-syntax-error!s}, \\ 
{\rm{list}}\,(\=\+{\rm{alist-entry}}\,({\tt{'}}{\tt{hierarchical-name}}, {\it{occ-data\/}})\index{alist-entry}, \\ 
{\rm{disjoint-or-err}}\,(\=\+{\rm{value}}\,({\tt{'}}{\tt{signals}}, {\it{occ-data\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{occ-fns}}, {\it{occ-data\/}})\index{value}, \\ 
{\tt{'}}{\tt{signal-occ-fn-overlap}})\-\index{disjoint-or-err}, \\ 
{\rm{disjoint-or-err}}\,(\=\+{\rm{value}}\,({\tt{'}}{\tt{occ-names}}, {\it{occ-data\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{occ-fns}}, {\it{occ-data\/}})\index{value}, \\ 
{\tt{'}}{\tt{occ-name-occ-fn-overlap}})\-\index{disjoint-or-err})\-)\- \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{lsi-occ-syntax-ok}}\,(\=\+{\rm{car}}\,({\it{body\/}}), \\ 
{\rm{max-occ-hierarchical-name}}\,(\=\+{\rm{car}}\,({\it{body\/}}), \\ 
{\it{hierarchical-table\/}}, \\ 
{\it{hierarchical-size\/}})\-\index{max-occ-hierarchical-name}, \\ 
{\it{occ-data\/}}, \\ 
{\it{netlist\/}}, \\ 
{\it{token-size\/}})\-\index{lsi-occ-syntax-ok}, \\ 
{\rm{lsi-occ-body-syntax-check}}\,(\=\+{\rm{cdr}}\,({\it{body\/}}), \\ 
{\rm{update-lsi-occ-syntax-data}}\,(\=\+{\rm{car}}\,({\it{body\/}}), \\ 
{\rm{max-occ-hierarchical-name}}\,(\=\+{\rm{car}}\,({\it{body\/}}), \\ 
{\it{hierarchical-table\/}}, \\ 
{\it{hierarchical-size\/}})\-\index{max-occ-hierarchical-name}, \\ 
{\it{occ-data\/}})\-\index{update-lsi-occ-syntax-data}, \\ 
{\it{outputs\/}}, \\ 
{\it{states\/}}, \\ 
{\it{netlist\/}}, \\ 
{\it{token-size\/}}, \\ 
{\it{hierarchical-table\/}}, \\ 
{\it{hierarchical-size\/}})\-\index{lsi-occ-body-syntax-check})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable lsi-occ-body-syntax-check; name this event `lsi-occ-body-syntax-check-off'.\index{lsi-occ-body-syntax-check-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{lsi-module-name-ok} \\  
\=\+{\rm{lsi-module-name-ok}}\,({\it{m-name\/}}, {\it{m-length\/}}, {\it{token-size\/}}, {\it{netlist\/}})\index{lsi-module-name-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\bf if }{\it{m-length\/}} $<$ {\tt{1}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf then }{\rm{err-and}}\,(\=\+{\rm{list}}\,(\=\+{\rm{lsi-name-ok}}\,({\it{m-name\/}}, {\it{token-size\/}})\index{lsi-name-ok}, \\ 
{\rm{t-or-err}}\,(\=\+$\neg$ {\rm{lookup-module}}\,({\it{m-name\/}}, {\it{netlist\/}})\index{lookup-module}, \\ 
{\tt{'}}{\tt{duplicate-module-defns}}, \\ 
{\it{m-name\/}})\-\index{t-or-err}, \\ 
{\rm{t-or-err}}\,(\=\+$\neg$ {\rm{primp}}\,({\it{m-name\/}})\index{primp}, \\ 
{\tt{'}}{\tt{module-name-same-as-primitive}}, \\ 
{\it{m-name\/}})\-\index{t-or-err})\-, \\ 
{\tt{'}}{\tt{module-name}})\-\index{err-and} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable lsi-module-name-ok; name this event `lsi-module-name-ok-off'.\index{lsi-module-name-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{lsi-module-inputs-ok} \\  
\=\+{\rm{lsi-module-inputs-ok}}\,({\it{m-ins\/}}, {\it{m-length\/}}, {\it{token-size\/}})\index{lsi-module-inputs-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\bf if }{\it{m-length\/}} $<$ {\tt{2}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf then }{\rm{lsi-name-list-ok}}\,({\it{m-ins\/}}, {\it{token-size\/}}, {\tt{'}}{\tt{module-inputs}}, {\bf{f}})\index{lsi-name-list-ok} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable lsi-module-inputs-ok; name this event `lsi-module-inputs-ok-off'.\index{lsi-module-inputs-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{lsi-module-outputs-ok} \\  
\=\+{\rm{lsi-module-outputs-ok}}\,({\it{m-outs\/}}, {\it{m-length\/}}, {\it{token-size\/}})\index{lsi-module-outputs-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\bf if }{\it{m-length\/}} $<$ {\tt{3}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf then }{\rm{lsi-name-list-ok}}\,({\it{m-outs\/}}, {\it{token-size\/}}, {\tt{'}}{\tt{module-outputs}}, {\bf{f}})\index{lsi-name-list-ok} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable lsi-module-outputs-ok; name this event `lsi-module-outputs-ok-off'.\index{lsi-module-outputs-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{lsi-module-occurrences-check} \\  
\=\+{\rm{lsi-module-occurrences-check}}\,(\=\+{\it{m-occs\/}}, \\ 
{\it{m-ins\/}}, \\ 
{\it{m-outs\/}}, \\ 
{\it{m-states\/}}, \\ 
{\it{m-length\/}}, \\ 
{\it{netlist\/}}, \\ 
{\it{token-size\/}}, \\ 
{\it{hierarchical-table\/}}, \\ 
{\it{hierarchical-size\/}})\-\index{lsi-module-occurrences-check} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\bf if }{\it{m-length\/}} $<$ {\tt{4}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{t-or-err}}\,({\rm{listp}}\,({\it{m-occs\/}}), {\tt{'}}{\tt{no-occurrences}}, {\it{m-occs\/}})\index{t-or-err}, \\ 
{\rm{lsi-occ-body-syntax-check}}\,(\=\+{\it{m-occs\/}}, \\ 
{\rm{initial-lsi-occ-syntax-data}}\,(\=\+{\it{m-ins\/}}, \\ 
{\it{m-outs\/}})\-\index{initial-lsi-occ-syntax-data}, \\ 
{\it{m-outs\/}}, \\ 
{\rm{states-list-or-nil}}\,(\=\+{\it{m-states\/}}, \\ 
{\it{m-length\/}})\-\index{states-list-or-nil}, \\ 
{\it{netlist\/}}, \\ 
{\it{token-size\/}}, \\ 
{\it{hierarchical-table\/}}, \\ 
{\it{hierarchical-size\/}})\-\index{lsi-occ-body-syntax-check})\- \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable lsi-module-occurrences-check; name this event `lsi-module-occurrences-check-off'.\index{lsi-module-occurrences-check-of!f}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{lsi-module-syntax-check} \\  
\=\+{\rm{lsi-module-syntax-check}}\,(\=\+{\it{module\/}}, \\ 
{\it{netlist\/}}, \\ 
{\it{token-size\/}}, \\ 
{\it{hierarchical-table\/}}, \\ 
{\it{hierarchical-size\/}})\-\index{lsi-module-syntax-check} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{module-name}}\,({\it{module\/}})\index{module-name}, \\ 
{\rm{value}}\,(\=\+{\tt{'}}{\tt{hierarchical-name}}, \\ 
{\rm{lsi-module-occurrences-check}}\,(\=\+{\rm{module-occurrences}}\,({\it{module\/}})\index{module-occurrences}, \\ 
{\rm{module-inputs}}\,({\it{module\/}})\index{module-inputs}, \\ 
{\rm{module-outputs}}\,({\it{module\/}})\index{module-outputs}, \\ 
{\rm{module-statenames}}\,({\it{module\/}})\index{module-statenames}, \\ 
{\rm{length}}\,({\it{module\/}})\index{length}, \\ 
{\it{netlist\/}}, \\ 
{\it{token-size\/}}, \\ 
{\it{hierarchical-table\/}}, \\ 
{\it{hierarchical-size\/}})\-\index{lsi-module-occurrences-check})\-\index{value})\-, \\ 
{\rm{err-and}}\,(\=\+{\rm{list}}\,(\=\+{\rm{module-form-ok}}\,({\it{module\/}}, {\rm{length}}\,({\it{module\/}})\index{length})\index{module-form-ok}, \\ 
{\rm{lsi-module-name-ok}}\,(\=\+{\rm{module-name}}\,({\it{module\/}})\index{module-name}, \\ 
{\rm{length}}\,({\it{module\/}})\index{length}, \\ 
{\it{token-size\/}}, \\ 
{\it{netlist\/}})\-\index{lsi-module-name-ok}, \\ 
{\rm{lsi-module-inputs-ok}}\,(\=\+{\rm{module-inputs}}\,({\it{module\/}})\index{module-inputs}, \\ 
{\rm{length}}\,({\it{module\/}})\index{length}, \\ 
{\it{token-size\/}})\-\index{lsi-module-inputs-ok}, \\ 
{\rm{lsi-module-outputs-ok}}\,(\=\+{\rm{module-outputs}}\,({\it{module\/}})\index{module-outputs}, \\ 
{\rm{length}}\,({\it{module\/}})\index{length}, \\ 
{\it{token-size\/}})\-\index{lsi-module-outputs-ok}, \\ 
{\rm{err-and}}\,(\=\+{\rm{lsi-module-occurrences-check}}\,(\=\+{\rm{module-occurrences}}\,({\it{module\/}})\index{module-occurrences}, \\ 
{\rm{module-inputs}}\,({\it{module\/}})\index{module-inputs}, \\ 
{\rm{module-outputs}}\,({\it{module\/}})\index{module-outputs}, \\ 
{\rm{module-statenames}}\,({\it{module\/}})\index{module-statenames}, \\ 
{\rm{length}}\,({\it{module\/}})\index{length}, \\ 
{\it{netlist\/}}, \\ 
{\it{token-size\/}}, \\ 
{\it{hierarchical-table\/}}, \\ 
{\it{hierarchical-size\/}})\-\index{lsi-module-occurrences-check}, \\ 
{\tt{'}}{\tt{module-occurrences}})\-\index{err-and}, \\ 
{\rm{module-statenames-ok}}\,(\=\+{\rm{module-statenames}}\,({\it{module\/}})\index{module-statenames}, \\ 
{\rm{length}}\,({\it{module\/}})\index{length})\-\index{module-statenames-ok}, \\ 
{\rm{module-annotation-ok}}\,(\=\+{\rm{module-annotation}}\,({\it{module\/}})\index{module-annotation}, \\ 
{\rm{length}}\,({\it{module\/}})\index{length})\-\index{module-annotation-ok})\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{module}}, {\rm{module-name}}\,({\it{module\/}})\index{module-name}))\-\index{err-and})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable lsi-module-syntax-check; name this event `lsi-module-syntax-check-off'.\index{lsi-module-syntax-check-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{lsi-netlist-syntax-check} \\  
\=\+{\rm{lsi-netlist-syntax-check}}\,({\it{netlist\/}}, {\it{token-size\/}}, {\it{hierarchical-size\/}})\index{lsi-netlist-syntax-check} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{netlist\/}}) \\ 
{\bf then }{\rm{append}}\,(\=\+{\rm{lsi-module-syntax-check}}\,(\=\+{\rm{car}}\,({\it{netlist\/}}), \\ 
{\rm{cdr}}\,({\it{netlist\/}}), \\ 
{\it{token-size\/}}, \\ 
{\rm{lsi-netlist-syntax-check}}\,(\=\+{\rm{cdr}}\,({\it{netlist\/}}), \\ 
{\it{token-size\/}}, \\ 
{\it{hierarchical-size\/}})\-\index{lsi-netlist-syntax-check}, \\ 
{\it{hierarchical-size\/}})\-\index{lsi-module-syntax-check}, \\ 
{\rm{lsi-netlist-syntax-check}}\,(\=\+{\rm{cdr}}\,({\it{netlist\/}}), \\ 
{\it{token-size\/}}, \\ 
{\it{hierarchical-size\/}})\-\index{lsi-netlist-syntax-check})\- \\ 
{\bf else }{\rm{list}}\,({\rm{nil-or-err}}\,({\it{netlist\/}}, {\tt{'}}{\tt{not-proper-list}})\index{nil-or-err})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable lsi-netlist-syntax-check; name this event `lsi-netlist-syntax-check-off'.\index{lsi-netlist-syntax-check-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{lsi-netlist-syntax-ok} \\  
\=\+{\rm{lsi-netlist-syntax-ok}}\,({\it{netlist\/}}, {\it{token-size\/}}, {\it{hierarchical-size\/}})\index{lsi-netlist-syntax-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+{\rm{lsi-netlist-syntax-check}}\,({\it{netlist\/}}, {\it{token-size\/}}, {\it{hierarchical-size\/}})\index{lsi-netlist-syntax-check}, \\ 
{\tt{'}}{\tt{lsi-netlist-syntax-errors}})\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable lsi-netlist-syntax-ok; name this event `lsi-netlist-syntax-ok-off'.\index{lsi-netlist-syntax-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{primitive-properties} \\  
\=\+{\sc{primitive-properties}}\index{primitive-properties} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{delays}}{\tt{ }}{\tt{drives}}{\tt{ }}{\tt{input-types}}{\tt{ }}{\tt{inputs}}{\tt{ }}{\tt{loadings}}{\tt{ }}{\tt{lsi-name}} \\ 
{\tt{new-states}}{\tt{ }}{\tt{out-depends}}{\tt{ }}{\tt{output-types}}{\tt{ }}{\tt{outputs}}{\tt{ }}{\tt{results}} \\ 
{\tt{state-types}}{\tt{ }}{\tt{states}}{\tt{ }}{\tt{gates}}{\tt{ }}{\tt{pads}}{\tt{ }}{\tt{primitives}}{\tt{ }}{\tt{transistors}}{\tt{)}}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable primitive-properties; name this event `primitive-properties-off'.\index{primitive-properties-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*primitive-properties; name this event `g*1*primitive-properties-off'.\index{g*1*primitive-properties-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{all-module-props} \\  
\=\+{\sc{all-module-props}}\index{all-module-props} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{delays}}{\tt{ }}{\tt{drives}}{\tt{ }}{\tt{input-types}}{\tt{ }}{\tt{inputs}}{\tt{ }}{\tt{loadings}}{\tt{ }}{\tt{out-depends}} \\ 
{\tt{output-types}}{\tt{ }}{\tt{outputs}}{\tt{ }}{\tt{state-types}}{\tt{ }}{\tt{states}}{\tt{ }}{\tt{gates}}{\tt{ }}{\tt{pads}} \\ 
{\tt{primitives}}{\tt{ }}{\tt{transistors}}{\tt{)}}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable all-module-props; name this event `all-module-props-off'.\index{all-module-props-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*all-module-props; name this event `g*1*all-module-props-off'.\index{g*1*all-module-props-off}

\addvspace{18pt}


\noindent{\sc Event}:   Add the shell {\it{unknown\/}}\index{unknown}, with recognizer function symbol {\it{unknownp\/}} and no accessors.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{value-or-unknown} \\  
\=\+{\rm{value-or-unknown}}\,({\it{key\/}}, {\it{alist\/}})\index{value-or-unknown} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{boundp}}\,({\it{key\/}}, {\it{alist\/}})\index{boundp}$\;\;${\bf then }{\rm{value}}\,({\it{key\/}}, {\it{alist\/}})\index{value} \\ 
{\bf else }{\sc{unknown}}\index{unknown}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable value-or-unknown; name this event `value-or-unknown-off'.\index{value-or-unknown-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-value-or-unknown} \\  
\=\+{\rm{collect-value-or-unknown}}\,({\it{keys\/}}, {\it{alist\/}})\index{collect-value-or-unknown} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{keys\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{value-or-unknown}}\,({\rm{car}}\,({\it{keys\/}}), {\it{alist\/}})\index{value-or-unknown}, \\ 
{\rm{collect-value-or-unknown}}\,({\rm{cdr}}\,({\it{keys\/}}), {\it{alist\/}})\index{collect-value-or-unknown})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-value-or-unknown; name this event `collect-value-or-unknown-off'.\index{collect-value-or-unknown-off}

\addvspace{18pt}


\noindent{\sc Event}:   Add the shell {\it{io-out\/}}\index{io-out}, with recognizer function symbol {\it{io-outp\/}} and 1 accessor: {\it{io-out-signal\/}}, with type restriction (none-of) and default value false.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{mark-io-out} \\  
\=\+{\rm{mark-io-out}}\,({\it{name\/}}, {\it{io-outs\/}})\index{mark-io-out} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{name\/}} $\in$ {\it{io-outs\/}}$\;\;${\bf then }{\rm{io-out}}\,({\it{name\/}})\index{io-out} \\ 
{\bf else }{\it{name\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable mark-io-out; name this event `mark-io-out-off'.\index{mark-io-out-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{mark-io-outs-0} \\  
\=\+{\rm{mark-io-outs-0}}\,({\it{names\/}}, {\it{io-outs\/}})\index{mark-io-outs-0} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{names\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{mark-io-out}}\,({\rm{car}}\,({\it{names\/}}), {\it{io-outs\/}})\index{mark-io-out}, \\ 
{\rm{mark-io-outs-0}}\,({\rm{cdr}}\,({\it{names\/}}), {\it{io-outs\/}})\index{mark-io-outs-0})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable mark-io-outs-0; name this event `mark-io-outs-0-off'.\index{mark-io-outs-0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{mark-io-outs} \\  
\=\+{\rm{mark-io-outs}}\,({\it{names\/}}, {\it{io-outs\/}})\index{mark-io-outs} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{disjoint}}\,({\it{io-outs\/}}, {\it{names\/}})\index{disjoint}$\;\;${\bf then }{\it{names\/}} \\ 
{\bf else }{\rm{mark-io-outs-0}}\,({\it{names\/}}, {\it{io-outs\/}})\index{mark-io-outs-0}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable mark-io-outs; name this event `mark-io-outs-off'.\index{mark-io-outs-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{unmark-io-out} \\  
\=\+{\rm{unmark-io-out}}\,({\it{name\/}})\index{unmark-io-out} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{io-outp}}\,({\it{name\/}})\index{io-outp}$\;\;${\bf then }{\rm{io-out-signal}}\,({\it{name\/}})\index{io-out-signal} \\ 
{\bf else }{\it{name\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable unmark-io-out; name this event `unmark-io-out-off'.\index{unmark-io-out-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{unmark-io-outs} \\  
\=\+{\rm{unmark-io-outs}}\,({\it{names\/}})\index{unmark-io-outs} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{names\/}}) \\ 
{\bf then }\=\+{\bf if }\=\+({\rm{unmark-io-out}}\,({\rm{car}}\,({\it{names\/}}))\index{unmark-io-out} $=$ {\rm{car}}\,({\it{names\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{unmark-io-outs}}\,({\rm{cdr}}\,({\it{names\/}}))\index{unmark-io-outs} $=$ {\rm{cdr}}\,({\it{names\/}}))\-$\;\;${\bf then }{\it{names\/}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{unmark-io-out}}\,({\rm{car}}\,({\it{names\/}}))\index{unmark-io-out}, \\ 
{\rm{unmark-io-outs}}\,({\rm{cdr}}\,({\it{names\/}}))\index{unmark-io-outs})\-$\;${\bf  endif}\- \\ 
{\bf else }{\it{names\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable unmark-io-outs; name this event `unmark-io-outs-off'.\index{unmark-io-outs-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{value2} \\  
\=\+{\rm{value2}}\,({\it{s\/}}, {\it{in-map\/}}, {\it{out-map\/}})\index{value2} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{boundp}}\,({\it{s\/}}, {\it{in-map\/}})\index{boundp}$\;\;${\bf then }{\rm{value}}\,({\it{s\/}}, {\it{in-map\/}})\index{value} \\ 
{\bf else }{\rm{value}}\,({\rm{unmark-io-out}}\,({\it{s\/}})\index{unmark-io-out}, {\it{out-map\/}})\index{value}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable value2; name this event `value2-off'.\index{value2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-value2} \\  
\=\+{\rm{collect-value2}}\,({\it{lst\/}}, {\it{in-map\/}}, {\it{out-map\/}})\index{collect-value2} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{lst\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{value2}}\,({\rm{car}}\,({\it{lst\/}}), {\it{in-map\/}}, {\it{out-map\/}})\index{value2}, \\ 
{\rm{collect-value2}}\,({\rm{cdr}}\,({\it{lst\/}}), {\it{in-map\/}}, {\it{out-map\/}})\index{collect-value2})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-value2; name this event `collect-value2-off'.\index{collect-value2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{signal-namep} \\  
{\rm{signal-namep}}\,({\it{x\/}})\index{signal-namep} $=$ ({\rm{litatom}}\,({\it{x\/}}) $\vee$ {\rm{indexp}}\,({\it{x\/}})\index{indexp} $\vee$ {\rm{io-outp}}\,({\it{x\/}})\index{io-outp})
\end{tabbing}


\noindent{\sc Event}:   Enable signal-namep; name this event `signal-namep-off'.\index{signal-namep-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{parent-synonym0} \\  
\=\+{\rm{parent-synonym0}}\,({\it{name\/}}, {\it{slist\/}}, {\it{used-names\/}})\index{parent-synonym0} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{name\/}} $\in$ {\it{used-names\/}}$\;\;${\bf then }{\it{name\/}} \\ 
{\bf elseif }{\rm{boundp}}\,({\it{name\/}}, {\it{slist\/}})\index{boundp} \\ 
{\bf then }\=\+{\bf if }{\rm{signal-namep}}\,({\rm{value}}\,({\it{name\/}}, {\it{slist\/}})\index{value})\index{signal-namep} \\ 
{\bf then }{\rm{parent-synonym0}}\,(\=\+{\rm{value}}\,({\it{name\/}}, {\it{slist\/}})\index{value}, \\ 
{\it{slist\/}}, \\ 
{\rm{cons}}\,({\it{name\/}}, {\it{used-names\/}}))\-\index{parent-synonym0} \\ 
{\bf else }{\it{name\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{name\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable parent-synonym0; name this event `parent-synonym0-off'.\index{parent-synonym0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{parent-synonym} \\  
{\rm{parent-synonym}}\,({\it{name\/}}, {\it{slist\/}})\index{parent-synonym} $=$ {\rm{parent-synonym0}}\,({\it{name\/}}, {\it{slist\/}}, {\bf{nil}})\index{parent-synonym0}
\end{tabbing}


\noindent{\sc Event}:   Enable parent-synonym; name this event `parent-synonym-off'.\index{parent-synonym-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{parent-synonyms-list} \\  
\=\+{\rm{parent-synonyms-list}}\,({\it{lst\/}}, {\it{slist\/}})\index{parent-synonyms-list} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{lst\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{parent-synonym}}\,({\rm{car}}\,({\it{lst\/}}), {\it{slist\/}})\index{parent-synonym}, \\ 
{\rm{parent-synonyms-list}}\,({\rm{cdr}}\,({\it{lst\/}}), {\it{slist\/}})\index{parent-synonyms-list})\- \\ 
{\bf else }{\it{lst\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable parent-synonyms-list; name this event `parent-synonyms-list-off'.\index{parent-synonyms-list-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{extract-names} \\  
\=\+{\rm{extract-names}}\,({\it{lst\/}})\index{extract-names} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{lst\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf elseif }{\rm{signal-namep}}\,({\rm{car}}\,({\it{lst\/}}))\index{signal-namep} \\ 
{\bf then }{\rm{insert}}\,({\rm{car}}\,({\it{lst\/}}), {\rm{extract-names}}\,({\rm{cdr}}\,({\it{lst\/}}))\index{extract-names})\index{insert} \\ 
{\bf else }{\rm{extract-names}}\,({\rm{cdr}}\,({\it{lst\/}}))\index{extract-names}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable extract-names; name this event `extract-names-off'.\index{extract-names-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{externalize-parents} \\  
\=\+{\rm{externalize-parents}}\,({\it{names\/}}, {\it{alist\/}}, {\it{inputs\/}}, {\it{outputs\/}})\index{externalize-parents} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{names\/}}) \\ 
{\bf then }{\rm{externalize-parents}}\,(\=\+{\rm{cdr}}\,({\it{names\/}}), \\ 
\=\+{\bf if }\=\+(\=\+{\rm{parent-synonym}}\,({\rm{car}}\,({\it{names\/}}), {\it{alist\/}})\index{parent-synonym} \\ 
$\in$$\;\;\;\;${\it{inputs\/}})\- \\ 
$\vee$$\;\;\;\;$(\=\+{\rm{parent-synonym}}\,({\rm{car}}\,({\it{names\/}}), {\it{alist\/}})\index{parent-synonym} \\ 
$\in$$\;\;\;\;${\it{outputs\/}})\-\-$\;\;${\bf then }{\it{alist\/}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{parent-synonym}}\,(\=\+{\rm{car}}\,({\it{names\/}}), \\ 
{\it{alist\/}})\-\index{parent-synonym}, \\ 
{\rm{car}}\,({\it{names\/}}))\-, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{car}}\,({\it{names\/}}), \\ 
{\rm{value-or-unknown}}\,(\=\+{\rm{parent-synonym}}\,(\=\+{\rm{car}}\,({\it{names\/}}), \\ 
{\it{alist\/}})\-\index{parent-synonym}, \\ 
{\it{alist\/}})\-\index{value-or-unknown})\-, \\ 
{\rm{unbind}}\,(\=\+{\rm{car}}\,({\it{names\/}}), \\ 
{\rm{unbind}}\,(\=\+{\rm{parent-synonym}}\,(\=\+{\rm{car}}\,({\it{names\/}}), \\ 
{\it{alist\/}})\-\index{parent-synonym}, \\ 
{\it{alist\/}})\-\index{unbind})\-\index{unbind})\-)\-$\;${\bf  endif}\-, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}})\-\index{externalize-parents} \\ 
{\bf else }{\it{alist\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable externalize-parents; name this event `externalize-parents-off'.\index{externalize-parents-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{subtype} \\  
\=\+{\rm{subtype}}\,({\it{x\/}}, {\it{y\/}})\index{subtype} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{y\/}} $=$ {\tt{'}}{\tt{free}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\it{x\/}} $=$ {\tt{'}}{\tt{boolp}} \\ 
{\bf then }{\it{y\/}} $\in$ {\tt{'}}{\tt{(}}{\tt{boolp}}{\tt{ }}{\tt{tri-state}}{\tt{ }}{\tt{ttl-tri-state}}{\tt{ }}{\tt{ttl}}{\tt{)}} \\ 
{\bf elseif }{\it{x\/}} $=$ {\tt{'}}{\tt{ttl-tri-state}} \\ 
{\bf then }{\it{y\/}} $\in$ {\tt{'}}{\tt{(}}{\tt{tri-state}}{\tt{ }}{\tt{ttl-tri-state}}{\tt{)}} \\ 
{\bf else }{\it{x\/}} $=$ {\it{y\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable subtype; name this event `subtype-off'.\index{subtype-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{types-compatiblep} \\  
\=\+{\rm{types-compatiblep}}\,({\it{t1\/}}, {\it{t2\/}})\index{types-compatiblep} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{t1\/}} $=$ {\it{t2\/}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }({\it{t1\/}} $=$ {\tt{'}}{\tt{free}}) $\vee$ ({\it{t2\/}} $=$ {\tt{'}}{\tt{free}})$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\it{t1\/}} $=$ {\tt{'}}{\tt{tri-state}}$\;\;${\bf then }{\it{t2\/}} $=$ {\tt{'}}{\tt{ttl-tri-state}} \\ 
{\bf elseif }{\it{t2\/}} $=$ {\tt{'}}{\tt{tri-state}}$\;\;${\bf then }{\it{t1\/}} $=$ {\tt{'}}{\tt{ttl-tri-state}} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable types-compatiblep; name this event `types-compatiblep-off'.\index{types-compatiblep-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tri-state-typep} \\  
{\rm{tri-state-typep}}\,({\it{type\/}})\index{tri-state-typep} $=$ ({\it{type\/}} $\in$ {\tt{'}}{\tt{(}}{\tt{tri-state}}{\tt{ }}{\tt{ttl-tri-state}}{\tt{)}})
\end{tabbing}


\noindent{\sc Event}:   Enable tri-state-typep; name this event `tri-state-typep-off'.\index{tri-state-typep-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{type-value0} \\  
\=\+{\rm{type-value0}}\,({\it{n\/}}, {\it{alist\/}}, {\it{free\/}}, {\it{used-names\/}})\index{type-value0} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{n\/}} $\in$ {\it{used-names\/}}) $\vee$ ($\neg$ {\rm{boundp}}\,({\it{n\/}}, {\it{alist\/}})\index{boundp}) \\ 
{\bf then }\=\+{\bf if }{\it{free\/}}$\;\;${\bf then }{\tt{'}}{\tt{free}} \\ 
{\bf else }{\rm{list}}\,({\it{n\/}})$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{listp}}\,({\rm{value}}\,({\it{n\/}}, {\it{alist\/}})\index{value}) \\ 
{\bf then }{\rm{type-value0}}\,({\rm{car}}\,({\rm{value}}\,({\it{n\/}}, {\it{alist\/}})\index{value}), {\it{alist\/}}, {\it{free\/}}, {\rm{cons}}\,({\it{n\/}}, {\it{used-names\/}}))\index{type-value0} \\ 
{\bf else }{\rm{value}}\,({\it{n\/}}, {\it{alist\/}})\index{value}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable type-value0; name this event `type-value0-off'.\index{type-value0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{type-value} \\  
{\rm{type-value}}\,({\it{n\/}}, {\it{alist\/}}, {\it{free\/}})\index{type-value} $=$ {\rm{type-value0}}\,({\it{n\/}}, {\it{alist\/}}, {\it{free\/}}, {\bf{nil}})\index{type-value0}
\end{tabbing}


\noindent{\sc Event}:   Enable type-value; name this event `type-value-off'.\index{type-value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{input-type} \\  
{\rm{input-type}}\,({\it{name\/}}, {\it{alist\/}})\index{input-type} $=$ {\rm{type-value}}\,({\rm{unmark-io-out}}\,({\it{name\/}})\index{unmark-io-out}, {\it{alist\/}}, {\bf{t}})\index{type-value}
\end{tabbing}


\noindent{\sc Event}:   Enable input-type; name this event `input-type-off'.\index{input-type-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{output-type} \\  
\=\+{\rm{output-type}}\,({\it{name\/}}, {\it{out-map\/}}, {\it{in-map\/}})\index{output-type} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\rm{type-value}}\,({\it{name\/}}, {\it{out-map\/}}, {\bf{f}})\index{type-value}) \\ 
{\bf then }{\rm{type-value}}\,({\rm{car}}\,({\rm{type-value}}\,({\it{name\/}}, {\it{out-map\/}}, {\bf{f}})\index{type-value}), {\it{in-map\/}}, {\bf{f}})\index{type-value} \\ 
{\bf else }{\rm{type-value}}\,({\it{name\/}}, {\it{out-map\/}}, {\bf{f}})\index{type-value}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable output-type; name this event `output-type-off'.\index{output-type-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{initial-occ-in-types}$\;\;$
{\sc{initial-occ-in-types}}\index{initial-occ-in-types} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{initial-occ-out-types}$\;\;$
{\sc{initial-occ-out-types}}\index{initial-occ-out-types} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{add-in-type} \\  
\=\+{\rm{add-in-type}}\,({\it{name\/}}, {\it{type\/}}, {\it{type-map\/}})\index{add-in-type} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{type\/}} $=$ {\tt{'}}{\tt{free}}$\;\;${\bf then }{\it{type-map\/}} \\ 
{\bf elseif }{\rm{boundp}}\,({\rm{unmark-io-out}}\,({\it{name\/}})\index{unmark-io-out}, {\it{type-map\/}})\index{boundp} \\ 
{\bf then }\=\+{\bf if }\=\+{\rm{unknownp}}\,({\rm{value}}\,({\rm{unmark-io-out}}\,({\it{name\/}})\index{unmark-io-out}, {\it{type-map\/}})\index{value})\index{unknownp} \\ 
$\vee$$\;\;\;\;${\rm{subtype}}\,({\rm{value}}\,({\rm{unmark-io-out}}\,({\it{name\/}})\index{unmark-io-out}, {\it{type-map\/}})\index{value}, {\it{type\/}})\index{subtype}\- \\ 
{\bf then }{\it{type-map\/}} \\ 
{\bf elseif }\=\+{\rm{unknownp}}\,({\it{type\/}})\index{unknownp} \\ 
$\vee$$\;\;\;\;${\rm{subtype}}\,({\it{type\/}}, {\rm{value}}\,({\rm{unmark-io-out}}\,({\it{name\/}})\index{unmark-io-out}, {\it{type-map\/}})\index{value})\index{subtype}\- \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{cons}}\,({\rm{unmark-io-out}}\,({\it{name\/}})\index{unmark-io-out}, {\it{type\/}}), \\ 
{\rm{unbind}}\,({\rm{unmark-io-out}}\,({\it{name\/}})\index{unmark-io-out}, {\it{type-map\/}})\index{unbind})\- \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{pred-error}}\,(\=\+{\rm{list}}\,({\tt{'}}{\tt{signal}}, {\rm{unmark-io-out}}\,({\it{name\/}})\index{unmark-io-out}), \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{old-type}}, \\ 
{\rm{value}}\,(\=\+{\rm{unmark-io-out}}\,({\it{name\/}})\index{unmark-io-out}, \\ 
{\it{type-map\/}})\-\index{value})\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{new-type}}, {\it{type\/}}))\-)\-\index{pred-error}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,({\rm{unmark-io-out}}\,({\it{name\/}})\index{unmark-io-out}, {\sc{unknown}}\index{unknown}), \\ 
{\rm{unbind}}\,({\rm{unmark-io-out}}\,({\it{name\/}})\index{unmark-io-out}, {\it{type-map\/}})\index{unbind})\-)\-$\;${\bf  endif}\- \\ 
{\bf else }{\rm{cons}}\,({\rm{cons}}\,({\rm{unmark-io-out}}\,({\it{name\/}})\index{unmark-io-out}, {\it{type\/}}), {\it{type-map\/}})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable add-in-type; name this event `add-in-type-off'.\index{add-in-type-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{add-in-types} \\  
\=\+{\rm{add-in-types}}\,({\it{inputs\/}}, {\it{types\/}}, {\it{type-map\/}})\index{add-in-types} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{inputs\/}}) \\ 
{\bf then }{\rm{add-in-types}}\,(\=\+{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\rm{cdr}}\,({\it{types\/}}), \\ 
{\rm{add-in-type}}\,({\rm{car}}\,({\it{inputs\/}}), {\rm{car}}\,({\it{types\/}}), {\it{type-map\/}})\index{add-in-type})\-\index{add-in-types} \\ 
{\bf else }{\it{type-map\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable add-in-types; name this event `add-in-types-off'.\index{add-in-types-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{update-in-types} \\  
\=\+{\rm{update-in-types}}\,({\it{in-types\/}}, {\it{o-ins\/}}, {\it{o-fn-props\/}})\index{update-in-types} \\ 
$=$$\;\;\;\;${\rm{add-in-types}}\,({\it{o-ins\/}}, {\rm{value}}\,({\tt{'}}{\tt{input-types}}, {\it{o-fn-props\/}})\index{value}, {\it{in-types\/}})\index{add-in-types}\-
\end{tabbing}


\noindent{\sc Event}:   Enable update-in-types; name this event `update-in-types-off'.\index{update-in-types-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{add-out-type} \\  
\=\+{\rm{add-out-type}}\,({\it{name\/}}, {\it{type\/}}, {\it{arg-map\/}}, {\it{type-map\/}})\index{add-out-type} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\it{name\/}}, \\ 
\=\+{\bf if }{\rm{listp}}\,({\it{type\/}})$\;\;${\bf then }{\rm{collect-value}}\,({\it{type\/}}, {\it{arg-map\/}})\index{collect-value} \\ 
{\bf else }{\it{type\/}}$\;${\bf  endif}\-)\-, \\ 
{\it{type-map\/}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable add-out-type; name this event `add-out-type-off'.\index{add-out-type-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{add-out-types} \\  
\=\+{\rm{add-out-types}}\,({\it{outputs\/}}, {\it{types\/}}, {\it{arg-map\/}}, {\it{type-map\/}})\index{add-out-types} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{outputs\/}}) \\ 
{\bf then }{\rm{add-out-types}}\,(\=\+{\rm{cdr}}\,({\it{outputs\/}}), \\ 
{\rm{cdr}}\,({\it{types\/}}), \\ 
{\it{arg-map\/}}, \\ 
{\rm{add-out-type}}\,(\=\+{\rm{car}}\,({\it{outputs\/}}), \\ 
{\rm{car}}\,({\it{types\/}}), \\ 
{\it{arg-map\/}}, \\ 
{\it{type-map\/}})\-\index{add-out-type})\-\index{add-out-types} \\ 
{\bf else }{\it{type-map\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable add-out-types; name this event `add-out-types-off'.\index{add-out-types-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{update-out-types} \\  
\=\+{\rm{update-out-types}}\,({\it{out-types\/}}, {\it{o-outs\/}}, {\it{o-fn-props\/}}, {\it{in-map\/}})\index{update-out-types} \\ 
$=$$\;\;\;\;${\rm{add-out-types}}\,(\=\+{\it{o-outs\/}}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{output-types}}, {\it{o-fn-props\/}})\index{value}, \\ 
{\it{in-map\/}}, \\ 
{\it{out-types\/}})\-\index{add-out-types}\-
\end{tabbing}


\noindent{\sc Event}:   Enable update-out-types; name this event `update-out-types-off'.\index{update-out-types-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{io-type-error} \\  
\=\+{\rm{io-type-error}}\,({\it{name\/}}, {\it{in-type\/}}, {\it{out-type\/}})\index{io-type-error} \\ 
$=$$\;\;\;\;${\rm{pred-error}}\,(\=\+{\rm{list}}\,(\=\+\=\+{\bf if }{\rm{io-outp}}\,({\it{name\/}})\index{io-outp}$\;\;${\bf then }{\tt{'}}{\tt{io-signal}} \\ 
{\bf else }{\tt{'}}{\tt{signal}}$\;${\bf  endif}\-, \\ 
{\rm{unmark-io-out}}\,({\it{name\/}})\index{unmark-io-out})\-, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,({\tt{'}}{\tt{input-type}}, {\it{in-type\/}}), \\ 
{\rm{list}}\,({\tt{'}}{\tt{output-type}}, {\it{out-type\/}}))\-)\-\index{pred-error}\-
\end{tabbing}


\noindent{\sc Event}:   Enable io-type-error; name this event `io-type-error-off'.\index{io-type-error-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{io-types-compatible} \\  
\=\+{\rm{io-types-compatible}}\,({\it{name\/}}, {\it{in-type\/}}, {\it{out-type\/}}, {\it{t-wire-ins\/}})\index{io-types-compatible} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{unknownp}}\,({\it{in-type\/}})\index{unknownp}$\;\;${\bf then }{\rm{unknownp}}\,({\it{out-type\/}})\index{unknownp} \\ 
{\bf elseif }{\rm{unknownp}}\,({\it{out-type\/}})\index{unknownp}$\;\;${\bf then }{\rm{unknownp}}\,({\it{in-type\/}})\index{unknownp} \\ 
{\bf elseif }{\rm{io-outp}}\,({\it{name\/}})\index{io-outp} \\ 
{\bf then }\=\+{\bf if }{\rm{tri-state-typep}}\,({\it{out-type\/}})\index{tri-state-typep} $\wedge$ {\rm{subtype}}\,({\it{out-type\/}}, {\it{in-type\/}})\index{subtype} \\ 
{\bf then }{\bf{t}} \\ 
{\bf else }{\rm{io-type-error}}\,({\it{name\/}}, {\it{in-type\/}}, {\it{out-type\/}})\index{io-type-error}$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{name\/}} $\in$ {\it{t-wire-ins\/}} \\ 
{\bf then }\=\+{\bf if }\=\+{\rm{tri-state-typep}}\,({\it{in-type\/}})\index{tri-state-typep} \\ 
$\wedge$$\;\;\;\;${\rm{types-compatiblep}}\,({\it{in-type\/}}, {\it{out-type\/}})\index{types-compatiblep}\-$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{io-type-error}}\,({\it{name\/}}, {\it{in-type\/}}, {\it{out-type\/}})\index{io-type-error}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{subtype}}\,({\it{out-type\/}}, {\it{in-type\/}})\index{subtype}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{io-type-error}}\,({\it{name\/}}, {\it{in-type\/}}, {\it{out-type\/}})\index{io-type-error}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable io-types-compatible; name this event `io-types-compatible-off'.\index{io-types-compatible-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ok-in-type} \\  
\=\+{\rm{ok-in-type}}\,({\it{ok\/}}, {\it{name\/}}, {\it{out-type\/}}, {\it{in-map\/}})\index{ok-in-type} \\ 
$=$$\;\;\;\;$\=\+{\bf if }($\neg$ {\it{ok\/}}) $\vee$ {\rm{net-errorp}}\,({\it{ok\/}})\index{net-errorp} \\ 
{\bf then }{\rm{set-value}}\,({\rm{unmark-io-out}}\,({\it{name\/}})\index{unmark-io-out}, {\sc{unknown}}\index{unknown}, {\it{in-map\/}})\index{set-value} \\ 
{\bf elseif }{\rm{io-outp}}\,({\it{name\/}})\index{io-outp} \\ 
{\bf then }{\rm{set-value}}\,({\rm{unmark-io-out}}\,({\it{name\/}})\index{unmark-io-out}, {\it{out-type\/}}, {\it{in-map\/}})\index{set-value} \\ 
{\bf else }{\it{in-map\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ok-in-type; name this event `ok-in-type-off'.\index{ok-in-type-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ok-out-type} \\  
\=\+{\rm{ok-out-type}}\,({\it{ok\/}}, {\it{name\/}}, {\it{out-map\/}})\index{ok-out-type} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{net-errorp}}\,({\it{ok\/}})\index{net-errorp}$\;\;${\bf then }{\rm{cons}}\,({\it{ok\/}}, {\rm{set-value}}\,({\it{name\/}}, {\sc{unknown}}\index{unknown}, {\it{out-map\/}})\index{set-value}) \\ 
{\bf elseif }{\it{ok\/}}$\;\;${\bf then }{\it{out-map\/}} \\ 
{\bf else }{\rm{set-value}}\,({\it{name\/}}, {\sc{unknown}}\index{unknown}, {\it{out-map\/}})\index{set-value}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ok-out-type; name this event `ok-out-type-off'.\index{ok-out-type-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{transfer-in-type} \\  
\=\+{\rm{transfer-in-type}}\,({\it{name\/}}, {\it{out-type\/}}, {\it{in-map\/}})\index{transfer-in-type} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{out-type\/}}) \\ 
{\bf then }{\rm{add-in-type}}\,({\rm{car}}\,({\it{out-type\/}}), {\rm{input-type}}\,({\it{name\/}}, {\it{in-map\/}})\index{input-type}, {\it{in-map\/}})\index{add-in-type} \\ 
{\bf else }{\it{in-map\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable transfer-in-type; name this event `transfer-in-type-off'.\index{transfer-in-type-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{compose-type} \\  
\=\+{\rm{compose-type}}\,({\it{name\/}}, {\it{type\/}}, {\it{maps\/}}, {\it{t-wire-ins\/}})\index{compose-type} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{ok-in-type}}\,(\=\+{\rm{io-types-compatible}}\,(\=\+{\it{name\/}}, \\ 
{\rm{input-type}}\,({\it{name\/}}, {\rm{car}}\,({\it{maps\/}}))\index{input-type}, \\ 
\=\+{\bf if }{\rm{listp}}\,(\=\+{\bf if }{\rm{listp}}\,({\it{type\/}}) \\ 
{\bf then }{\rm{output-type}}\,(\=\+{\rm{car}}\,({\it{type\/}}), \\ 
{\rm{cdr}}\,({\it{maps\/}}), \\ 
{\rm{car}}\,({\it{maps\/}}))\-\index{output-type} \\ 
{\bf else }{\it{type\/}}$\;${\bf  endif}\-) \\ 
{\bf then }{\tt{'}}{\tt{free}} \\ 
{\bf elseif }{\rm{listp}}\,({\it{type\/}}) \\ 
{\bf then }{\rm{output-type}}\,(\=\+{\rm{car}}\,({\it{type\/}}), \\ 
{\rm{cdr}}\,({\it{maps\/}}), \\ 
{\rm{car}}\,({\it{maps\/}}))\-\index{output-type} \\ 
{\bf else }{\it{type\/}}$\;${\bf  endif}\-, \\ 
{\it{t-wire-ins\/}})\-\index{io-types-compatible}, \\ 
{\it{name\/}}, \\ 
\=\+{\bf if }{\rm{listp}}\,({\it{type\/}}) \\ 
{\bf then }{\rm{output-type}}\,({\rm{car}}\,({\it{type\/}}), {\rm{cdr}}\,({\it{maps\/}}), {\rm{car}}\,({\it{maps\/}}))\index{output-type} \\ 
{\bf else }{\it{type\/}}$\;${\bf  endif}\-, \\ 
{\rm{car}}\,({\it{maps\/}}))\-\index{ok-in-type}, \\ 
{\rm{ok-out-type}}\,(\=\+{\rm{io-types-compatible}}\,(\=\+{\it{name\/}}, \\ 
{\rm{input-type}}\,({\it{name\/}}, {\rm{car}}\,({\it{maps\/}}))\index{input-type}, \\ 
\=\+{\bf if }{\rm{listp}}\,(\=\+{\bf if }{\rm{listp}}\,({\it{type\/}}) \\ 
{\bf then }{\rm{output-type}}\,(\=\+{\rm{car}}\,({\it{type\/}}), \\ 
{\rm{cdr}}\,({\it{maps\/}}), \\ 
{\rm{car}}\,({\it{maps\/}}))\-\index{output-type} \\ 
{\bf else }{\it{type\/}}$\;${\bf  endif}\-) \\ 
{\bf then }{\tt{'}}{\tt{free}} \\ 
{\bf elseif }{\rm{listp}}\,({\it{type\/}}) \\ 
{\bf then }{\rm{output-type}}\,(\=\+{\rm{car}}\,({\it{type\/}}), \\ 
{\rm{cdr}}\,({\it{maps\/}}), \\ 
{\rm{car}}\,({\it{maps\/}}))\-\index{output-type} \\ 
{\bf else }{\it{type\/}}$\;${\bf  endif}\-, \\ 
{\it{t-wire-ins\/}})\-\index{io-types-compatible}, \\ 
{\it{name\/}}, \\ 
{\rm{cdr}}\,({\it{maps\/}}))\-\index{ok-out-type})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable compose-type; name this event `compose-type-off'.\index{compose-type-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{composed-type-maps} \\  
\=\+{\rm{composed-type-maps}}\,({\it{out-types\/}}, {\it{in-map\/}}, {\it{out-map\/}}, {\it{t-wire-ins\/}})\index{composed-type-maps} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{out-types\/}}) \\ 
{\bf then }{\rm{compose-type}}\,(\=\+{\rm{caar}}\,({\it{out-types\/}}), \\ 
{\rm{cdar}}\,({\it{out-types\/}}), \\ 
{\rm{composed-type-maps}}\,(\=\+{\rm{cdr}}\,({\it{out-types\/}}), \\ 
{\rm{transfer-in-type}}\,(\=\+{\rm{caar}}\,({\it{out-types\/}}), \\ 
{\rm{cdar}}\,({\it{out-types\/}}), \\ 
{\it{in-map\/}})\-\index{transfer-in-type}, \\ 
{\it{out-map\/}}, \\ 
{\it{t-wire-ins\/}})\-\index{composed-type-maps}, \\ 
{\it{t-wire-ins\/}})\-\index{compose-type} \\ 
{\bf else }{\rm{cons}}\,({\it{in-map\/}}, {\it{out-map\/}})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable composed-type-maps; name this event `composed-type-maps-off'.\index{composed-type-maps-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{compose-io-types} \\  
\=\+{\rm{compose-io-types}}\,({\it{in-map\/}}, {\it{out-map\/}}, {\it{t-wire-ins\/}})\index{compose-io-types} \\ 
$=$$\;\;\;\;${\rm{composed-type-maps}}\,({\it{out-map\/}}, {\it{in-map\/}}, {\it{out-map\/}}, {\it{t-wire-ins\/}})\index{composed-type-maps}\-
\end{tabbing}


\noindent{\sc Event}:   Enable compose-io-types; name this event `compose-io-types-off'.\index{compose-io-types-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-in-types} \\  
\=\+{\rm{collect-in-types}}\,({\it{names\/}}, {\it{alist\/}})\index{collect-in-types} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{names\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{type-value}}\,({\rm{car}}\,({\it{names\/}}), {\it{alist\/}}, {\bf{t}})\index{type-value}, \\ 
{\rm{collect-in-types}}\,({\rm{cdr}}\,({\it{names\/}}), {\it{alist\/}})\index{collect-in-types})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-in-types; name this event `collect-in-types-off'.\index{collect-in-types-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-out-type} \\  
\=\+{\rm{collect-out-type}}\,({\it{name\/}}, {\it{out-map\/}}, {\it{inputs\/}}, {\it{in-map\/}})\index{collect-out-type} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\rm{listp}}\,({\rm{output-type}}\,({\it{name\/}}, {\it{out-map\/}}, {\it{in-map\/}})\index{output-type}) \\ 
$\wedge$$\;\;\;\;$({\rm{car}}\,({\rm{output-type}}\,({\it{name\/}}, {\it{out-map\/}}, {\it{in-map\/}})\index{output-type}) $\not\in$ {\it{inputs\/}})\- \\ 
{\bf then }{\sc{unknown}}\index{unknown} \\ 
{\bf else }{\rm{output-type}}\,({\it{name\/}}, {\it{out-map\/}}, {\it{in-map\/}})\index{output-type}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-out-type; name this event `collect-out-type-off'.\index{collect-out-type-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-out-types} \\  
\=\+{\rm{collect-out-types}}\,({\it{outputs\/}}, {\it{out-map\/}}, {\it{inputs\/}}, {\it{in-map\/}})\index{collect-out-types} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{outputs\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{collect-out-type}}\,({\rm{car}}\,({\it{outputs\/}}), {\it{out-map\/}}, {\it{inputs\/}}, {\it{in-map\/}})\index{collect-out-type}, \\ 
{\rm{collect-out-types}}\,({\rm{cdr}}\,({\it{outputs\/}}), {\it{out-map\/}}, {\it{inputs\/}}, {\it{in-map\/}})\index{collect-out-types})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-out-types; name this event `collect-out-types-off'.\index{collect-out-types-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{in-types-error} \\  
{\rm{in-types-error}}\,({\it{in-map\/}})\index{in-types-error} $=$ {\rm{err-and}}\,({\it{in-map\/}}, {\tt{'}}{\tt{input-type-conflicts}})\index{err-and}
\end{tabbing}


\noindent{\sc Event}:   Enable in-types-error; name this event `in-types-error-off'.\index{in-types-error-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{out-types-error} \\  
{\rm{out-types-error}}\,({\it{out-map\/}})\index{out-types-error} $=$ {\rm{err-and}}\,({\it{out-map\/}}, {\tt{'}}{\tt{io-type-conflicts}})\index{err-and}
\end{tabbing}


\noindent{\sc Event}:   Enable out-types-error; name this event `out-types-error-off'.\index{out-types-error-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{map} \\  
\=\+{\rm{map}}\,({\it{dr\/}})\index{map} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\rm{length}}\,({\it{dr\/}})\index{length}: \\ 
{\bf case = }{\tt{2}} \\ 
{\bf then }({\rm{car}}\,({\it{dr\/}}) $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{cadr}}\,({\it{dr\/}}) $=$ {\tt{'}}{\tt{ma}}) $\wedge$ ({\rm{cddr}}\,({\it{dr\/}}) $=$ {\bf{nil}}) \\ 
{\bf case = }{\tt{3}} \\ 
{\bf $\;\;$then }\=\+({\rm{car}}\,({\it{dr\/}}) $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\rm{cadr}}\,({\it{dr\/}}))\index{length} $=$ {\tt{2}}) \\ 
$\wedge$$\;\;\;\;$({\rm{caadr}}\,({\it{dr\/}}) $=$ {\tt{'}}{\tt{point}}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadadr}}\,({\it{dr\/}}) $\in\;${\bf{N}}${}$))\- \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\it{dr\/}}) $=$ {\tt{'}}{\tt{ma}}) \\ 
$\wedge$$\;\;\;\;$({\rm{cdddr}}\,({\it{dr\/}}) $=$ {\bf{nil}})\- \\ 
{\bf otherwise }{\bf{f}}$\;${\bf  endcase}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable map; name this event `map-off'.\index{map-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pfp} \\  
\=\+{\rm{pfp}}\,({\it{ld\/}})\index{pfp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{ld\/}})\index{length} $=$ {\tt{2}} \\ 
{\bf then }({\rm{car}}\,({\it{ld\/}}) $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{cadr}}\,({\it{ld\/}}) $=$ {\tt{'}}{\tt{pf}}) $\wedge$ ({\rm{cddr}}\,({\it{ld\/}}) $=$ {\bf{nil}}) \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable pfp; name this event `pfp-off'.\index{pfp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ma-to-pf} \\  
{\rm{ma-to-pf}}\,({\it{x\/}})\index{ma-to-pf} $=$ {\rm{cons}}\,(({\rm{car}}\,({\it{x\/}}) $*$ {\tt{10}}) $+$ {\rm{cadadr}}\,({\it{x\/}}), {\tt{'}}{\tt{(}}{\tt{pf}}{\tt{)}})
\end{tabbing}


\noindent{\sc Event}:   Enable ma-to-pf; name this event `ma-to-pf-off'.\index{ma-to-pf-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pf-to-ma} \\  
\=\+{\rm{pf-to-ma}}\,({\it{x\/}})\index{pf-to-ma} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\rm{car}}\,({\it{x\/}}) ${}${\bf{mod}}${}$ {\tt{10}}) $\simeq {\tt{0}}$$\;\;${\bf then }{\rm{cons}}\,({\rm{car}}\,({\it{x\/}}) $\div$ {\tt{10}}, {\tt{'}}{\tt{(}}{\tt{ma}}{\tt{)}}) \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{car}}\,({\it{x\/}}) $\div$ {\tt{10}}, \\ 
{\rm{cons}}\,({\rm{list}}\,({\tt{'}}{\tt{point}}, {\rm{car}}\,({\it{x\/}}) ${}${\bf{mod}}${}$ {\tt{10}}), {\tt{'}}{\tt{(}}{\tt{ma}}{\tt{)}}))\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable pf-to-ma; name this event `pf-to-ma-off'.\index{pf-to-ma-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{std-load-to-pf}$\;\;$
{\rm{std-load-to-pf}}\,({\it{x\/}})\index{std-load-to-pf} $=$ {\rm{cons}}\,({\it{x\/}} $*$ {\tt{10}}, {\tt{'}}{\tt{(}}{\tt{pf}}{\tt{)}})
\end{tabbing}


\noindent{\sc Event}:   Enable std-load-to-pf; name this event `std-load-to-pf-off'.\index{std-load-to-pf-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pf-to-std-load} \\  
\=\+{\rm{pf-to-std-load}}\,({\it{x\/}})\index{pf-to-std-load} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\rm{car}}\,({\it{x\/}}) ${}${\bf{mod}}${}$ {\tt{10}}) $<$ {\tt{5}}$\;\;${\bf then }{\rm{car}}\,({\it{x\/}}) $\div$ {\tt{10}} \\ 
{\bf else }({\rm{car}}\,({\it{x\/}}) $\div$ {\tt{10}}) $+$ {\tt{1}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable pf-to-std-load; name this event `pf-to-std-load-off'.\index{pf-to-std-load-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ma-to-std-drive}$\;\;$
{\rm{ma-to-std-drive}}\,({\it{x\/}})\index{ma-to-std-drive} $=$ {\rm{car}}\,({\it{x\/}})
\end{tabbing}


\noindent{\sc Event}:   Enable ma-to-std-drive; name this event `ma-to-std-drive-off'.\index{ma-to-std-drive-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{std-drive-to-ma}$\;\;$
{\rm{std-drive-to-ma}}\,({\it{x\/}})\index{std-drive-to-ma} $=$ {\rm{cons}}\,({\it{x\/}}, {\tt{'}}{\tt{(}}{\tt{ma}}{\tt{)}})
\end{tabbing}


\noindent{\sc Event}:   Enable std-drive-to-ma; name this event `std-drive-to-ma-off'.\index{std-drive-to-ma-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{zero-loadingp} \\  
\=\+{\rm{zero-loadingp}}\,({\it{a\/}})\index{zero-loadingp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{pfp}}\,({\it{a\/}})\index{pfp}$\;\;${\bf then }{\rm{car}}\,({\it{a\/}}) $\simeq {\tt{0}}$ \\ 
{\bf else }{\it{a\/}} $\simeq {\tt{0}}$$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable zero-loadingp; name this event `zero-loadingp-off'.\index{zero-loadingp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pf-plus}$\;\;$
{\rm{pf-plus}}\,({\it{a\/}}, {\it{b\/}})\index{pf-plus} $=$ {\rm{cons}}\,({\rm{car}}\,({\it{a\/}}) $+$ {\rm{car}}\,({\it{b\/}}), {\tt{'}}{\tt{(}}{\tt{pf}}{\tt{)}})
\end{tabbing}


\noindent{\sc Event}:   Enable pf-plus; name this event `pf-plus-off'.\index{pf-plus-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pf-difference} \\  
{\rm{pf-difference}}\,({\it{a\/}}, {\it{b\/}})\index{pf-difference} $=$ {\rm{cons}}\,({\rm{car}}\,({\it{a\/}}) $-$ {\rm{car}}\,({\it{b\/}}), {\tt{'}}{\tt{(}}{\tt{pf}}{\tt{)}})
\end{tabbing}


\noindent{\sc Event}:   Enable pf-difference; name this event `pf-difference-off'.\index{pf-difference-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pf-lessp}$\;\;$
{\rm{pf-lessp}}\,({\it{a\/}}, {\it{b\/}})\index{pf-lessp} $=$ ({\rm{car}}\,({\it{a\/}}) $<$ {\rm{car}}\,({\it{b\/}}))
\end{tabbing}


\noindent{\sc Event}:   Enable pf-lessp; name this event `pf-lessp-off'.\index{pf-lessp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ma-lessp} \\  
\=\+{\rm{ma-lessp}}\,({\it{a\/}}, {\it{b\/}})\index{ma-lessp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{car}}\,({\it{a\/}}) $<$ {\rm{car}}\,({\it{b\/}})$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\rm{car}}\,({\it{a\/}}) $=$ {\rm{car}}\,({\it{b\/}})$\;\;${\bf then }{\rm{cadadr}}\,({\it{a\/}}) $<$ {\rm{cadadr}}\,({\it{b\/}}) \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ma-lessp; name this event `ma-lessp-off'.\index{ma-lessp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{loading-plus} \\  
\=\+{\rm{loading-plus}}\,({\it{x\/}}, {\it{y\/}})\index{loading-plus} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\in\;${\bf{N}}${}$ \\ 
{\bf then }\=\+{\bf if }{\it{y\/}} $\in\;${\bf{N}}${}$$\;\;${\bf then }{\it{x\/}} $+$ {\it{y\/}} \\ 
{\bf elseif }{\rm{pfp}}\,({\it{y\/}})\index{pfp}$\;\;${\bf then }{\rm{pf-plus}}\,({\rm{std-load-to-pf}}\,({\it{x\/}})\index{std-load-to-pf}, {\it{y\/}})\index{pf-plus} \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{pfp}}\,({\it{x\/}})\index{pfp} \\ 
{\bf then }\=\+{\bf if }{\rm{pfp}}\,({\it{y\/}})\index{pfp}$\;\;${\bf then }{\rm{pf-plus}}\,({\it{x\/}}, {\it{y\/}})\index{pf-plus} \\ 
{\bf elseif }{\it{y\/}} $\in\;${\bf{N}}${}$$\;\;${\bf then }{\rm{pf-plus}}\,({\it{x\/}}, {\rm{std-load-to-pf}}\,({\it{y\/}})\index{std-load-to-pf})\index{pf-plus} \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\- \\ 
{\bf elseif }({\it{y\/}} $\in\;${\bf{N}}${}$) $\vee$ {\rm{pfp}}\,({\it{y\/}})\index{pfp}$\;\;${\bf then }{\it{y\/}} \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable loading-plus; name this event `loading-plus-off'.\index{loading-plus-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{initial-occ-loadings}$\;\;$
{\sc{initial-occ-loadings}}\index{initial-occ-loadings} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{initial-occ-drives}$\;\;$
{\sc{initial-occ-drives}}\index{initial-occ-drives} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{add-loading} \\  
\=\+{\rm{add-loading}}\,({\it{name\/}}, {\it{loading\/}}, {\it{load-map\/}})\index{add-loading} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{zero-loadingp}}\,({\it{loading\/}})\index{zero-loadingp}$\;\;${\bf then }{\it{load-map\/}} \\ 
{\bf elseif }{\rm{boundp}}\,({\it{name\/}}, {\it{load-map\/}})\index{boundp} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{cons}}\,({\it{name\/}}, {\rm{loading-plus}}\,({\it{loading\/}}, {\rm{value}}\,({\it{name\/}}, {\it{load-map\/}})\index{value})\index{loading-plus}), \\ 
{\rm{unbind}}\,({\it{name\/}}, {\it{load-map\/}})\index{unbind})\- \\ 
{\bf else }{\rm{cons}}\,({\rm{cons}}\,({\it{name\/}}, {\it{loading\/}}), {\it{load-map\/}})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable add-loading; name this event `add-loading-off'.\index{add-loading-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{add-loadings} \\  
\=\+{\rm{add-loadings}}\,({\it{names\/}}, {\it{loadings\/}}, {\it{load-map\/}})\index{add-loadings} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{names\/}}) \\ 
{\bf then }{\rm{add-loadings}}\,(\=\+{\rm{cdr}}\,({\it{names\/}}), \\ 
{\rm{cdr}}\,({\it{loadings\/}}), \\ 
{\rm{add-loading}}\,({\rm{car}}\,({\it{names\/}}), {\rm{car}}\,({\it{loadings\/}}), {\it{load-map\/}})\index{add-loading})\-\index{add-loadings} \\ 
{\bf else }{\it{load-map\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable add-loadings; name this event `add-loadings-off'.\index{add-loadings-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{update-loadings} \\  
\=\+{\rm{update-loadings}}\,({\it{loadings\/}}, {\it{o-ins\/}}, {\it{o-fn-props\/}})\index{update-loadings} \\ 
$=$$\;\;\;\;${\rm{add-loadings}}\,({\it{o-ins\/}}, {\rm{value}}\,({\tt{'}}{\tt{loadings}}, {\it{o-fn-props\/}})\index{value}, {\it{loadings\/}})\index{add-loadings}\-
\end{tabbing}


\noindent{\sc Event}:   Enable update-loadings; name this event `update-loadings-off'.\index{update-loadings-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{local-drive} \\  
\=\+{\rm{local-drive}}\,({\it{drive\/}}, {\it{listp\/}}, {\it{in-map\/}}, {\it{out-map\/}}, {\it{drive-map\/}})\index{local-drive} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{listp\/}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\it{drive\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{local-drive}}\,({\rm{car}}\,({\it{drive\/}}), {\bf{f}}, {\it{in-map\/}}, {\it{out-map\/}}, {\it{drive-map\/}})\index{local-drive}, \\ 
{\rm{local-drive}}\,({\rm{cdr}}\,({\it{drive\/}}), {\bf{t}}, {\it{in-map\/}}, {\it{out-map\/}}, {\it{drive-map\/}})\index{local-drive})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{signal-namep}}\,({\it{drive\/}})\index{signal-namep} \\ 
{\bf then }{\rm{parent-synonym}}\,({\rm{value2}}\,({\it{drive\/}}, {\it{in-map\/}}, {\it{out-map\/}})\index{value2}, {\it{drive-map\/}})\index{parent-synonym} \\ 
{\bf elseif }{\rm{listp}}\,({\it{drive\/}}) $\wedge$ ({\rm{car}}\,({\it{drive\/}}) $=$ {\tt{'}}{\tt{min}}) \\ 
{\bf then }{\rm{cons}}\,({\tt{'}}{\tt{min}}, {\rm{local-drive}}\,({\rm{cdr}}\,({\it{drive\/}}), {\bf{t}}, {\it{in-map\/}}, {\it{out-map\/}}, {\it{drive-map\/}})\index{local-drive}) \\ 
{\bf else }{\it{drive\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable local-drive; name this event `local-drive-off'.\index{local-drive-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{add-drives} \\  
\=\+{\rm{add-drives}}\,({\it{outputs\/}}, {\it{drives\/}}, {\it{in-map\/}}, {\it{out-map\/}}, {\it{drive-map\/}})\index{add-drives} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{outputs\/}}) \\ 
{\bf then }{\rm{add-drives}}\,(\=\+{\rm{cdr}}\,({\it{outputs\/}}), \\ 
{\rm{cdr}}\,({\it{drives\/}}), \\ 
{\it{in-map\/}}, \\ 
{\it{out-map\/}}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{car}}\,({\it{outputs\/}}), \\ 
{\rm{local-drive}}\,(\=\+{\rm{car}}\,({\it{drives\/}}), \\ 
{\bf{f}}, \\ 
{\it{in-map\/}}, \\ 
{\it{out-map\/}}, \\ 
{\it{drive-map\/}})\-\index{local-drive})\-, \\ 
{\it{drive-map\/}})\-)\-\index{add-drives} \\ 
{\bf else }{\it{drive-map\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable add-drives; name this event `add-drives-off'.\index{add-drives-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{update-drives} \\  
\=\+{\rm{update-drives}}\,({\it{drives\/}}, {\it{o-outs\/}}, {\it{o-fn-props\/}}, {\it{in-map\/}}, {\it{out-map\/}})\index{update-drives} \\ 
$=$$\;\;\;\;${\rm{add-drives}}\,({\it{o-outs\/}}, {\rm{value}}\,({\tt{'}}{\tt{drives}}, {\it{o-fn-props\/}})\index{value}, {\it{in-map\/}}, {\it{out-map\/}}, {\it{drives\/}})\index{add-drives}\-
\end{tabbing}


\noindent{\sc Event}:   Enable update-drives; name this event `update-drives-off'.\index{update-drives-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{transfer-loading} \\  
\=\+{\rm{transfer-loading}}\,({\it{drive\/}}, {\it{listp\/}}, {\it{load\/}}, {\it{loadings\/}})\index{transfer-loading} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{listp\/}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\it{drive\/}}) \\ 
{\bf then }{\rm{transfer-loading}}\,(\=\+{\rm{cdr}}\,({\it{drive\/}}), \\ 
{\bf{t}}, \\ 
{\it{load\/}}, \\ 
{\rm{transfer-loading}}\,(\=\+{\rm{car}}\,({\it{drive\/}}), \\ 
{\bf{f}}, \\ 
{\it{load\/}}, \\ 
{\it{loadings\/}})\-\index{transfer-loading})\-\index{transfer-loading} \\ 
{\bf else }{\it{loadings\/}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{signal-namep}}\,({\it{drive\/}})\index{signal-namep}$\;\;${\bf then }{\rm{add-loading}}\,({\it{drive\/}}, {\it{load\/}}, {\it{loadings\/}})\index{add-loading} \\ 
{\bf elseif }{\rm{listp}}\,({\it{drive\/}}) $\wedge$ ({\rm{car}}\,({\it{drive\/}}) $=$ {\tt{'}}{\tt{min}}) \\ 
{\bf then }{\rm{transfer-loading}}\,({\rm{cdr}}\,({\it{drive\/}}), {\bf{t}}, {\it{load\/}}, {\it{loadings\/}})\index{transfer-loading} \\ 
{\bf else }{\it{loadings\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable transfer-loading; name this event `transfer-loading-off'.\index{transfer-loading-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{transfer-loadings} \\  
\=\+{\rm{transfer-loadings}}\,({\it{loadings\/}}, {\it{drives\/}})\index{transfer-loadings} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{drives\/}}) \\ 
{\bf then }{\rm{transfer-loadings}}\,(\=\+{\rm{transfer-loading}}\,(\=\+{\rm{cdar}}\,({\it{drives\/}}), \\ 
{\bf{f}}, \\ 
{\rm{value}}\,({\rm{caar}}\,({\it{drives\/}}), {\it{loadings\/}})\index{value}, \\ 
{\it{loadings\/}})\-\index{transfer-loading}, \\ 
{\rm{cdr}}\,({\it{drives\/}}))\-\index{transfer-loadings} \\ 
{\bf else }{\it{loadings\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable transfer-loadings; name this event `transfer-loadings-off'.\index{transfer-loadings-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{literal-net-drive} \\  
\=\+{\rm{literal-net-drive}}\,({\it{drive\/}}, {\it{load\/}}, {\it{label\/}})\index{literal-net-drive} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{drive\/}} $\in\;${\bf{N}}${}$ \\ 
{\bf then }\=\+{\bf if }{\it{drive\/}} $<$ \=\+{\bf if }{\it{load\/}} $\in\;${\bf{N}}${}$$\;\;${\bf then }{\it{load\/}} \\ 
{\bf elseif }{\rm{pfp}}\,({\it{load\/}})\index{pfp}$\;\;${\bf then }{\rm{pf-to-std-load}}\,({\it{load\/}})\index{pf-to-std-load} \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\- \\ 
{\bf then }{\rm{pred-error}}\,(\=\+{\it{label\/}}, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,({\tt{'}}{\tt{drive}}, {\it{drive\/}}), \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{loading}}, \\ 
{\rm{cons}}\,(\=\+{\it{load\/}}, \\ 
\=\+{\bf if }{\it{load\/}} $=$ \=\+{\bf if }{\it{load\/}} $\in\;${\bf{N}}${}$$\;\;${\bf then }{\it{load\/}} \\ 
{\bf elseif }{\rm{pfp}}\,({\it{load\/}})\index{pfp} \\ 
{\bf then }{\rm{pf-to-std-load}}\,({\it{load\/}})\index{pf-to-std-load} \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\- \\ 
{\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{list}}\,(\=\+{\bf if }{\it{load\/}} $\in\;${\bf{N}}${}$ \\ 
{\bf then }{\it{load\/}} \\ 
{\bf elseif }{\rm{pfp}}\,({\it{load\/}})\index{pfp} \\ 
{\bf then }{\rm{pf-to-std-load}}\,({\it{load\/}})\index{pf-to-std-load} \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-)$\;${\bf  endif}\-)\-)\-)\-)\-\index{pred-error} \\ 
{\bf else }{\it{drive\/}} $-$ \=\+{\bf if }{\it{load\/}} $\in\;${\bf{N}}${}$$\;\;${\bf then }{\it{load\/}} \\ 
{\bf elseif }{\rm{pfp}}\,({\it{load\/}})\index{pfp}$\;\;${\bf then }{\rm{pf-to-std-load}}\,({\it{load\/}})\index{pf-to-std-load} \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{map}}\,({\it{drive\/}})\index{map} \\ 
{\bf then }\=\+{\bf if }{\rm{pf-lessp}}\,(\=\+{\rm{ma-to-pf}}\,({\it{drive\/}})\index{ma-to-pf}, \\ 
\=\+{\bf if }{\rm{pfp}}\,({\it{load\/}})\index{pfp}$\;\;${\bf then }{\it{load\/}} \\ 
{\bf elseif }{\it{load\/}} $\in\;${\bf{N}}${}$$\;\;${\bf then }{\rm{std-load-to-pf}}\,({\it{load\/}})\index{std-load-to-pf} \\ 
{\bf else }{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{pf}}{\tt{)}}$\;${\bf  endif}\-)\-\index{pf-lessp} \\ 
{\bf then }{\rm{pred-error}}\,(\=\+{\it{label\/}}, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,({\tt{'}}{\tt{drive}}, {\it{drive\/}}, {\rm{ma-to-pf}}\,({\it{drive\/}})\index{ma-to-pf}), \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{loading}}, \\ 
{\rm{cons}}\,(\=\+{\it{load\/}}, \\ 
\=\+{\bf if }{\it{load\/}} $=$ \=\+{\bf if }{\rm{pfp}}\,({\it{load\/}})\index{pfp} \\ 
{\bf then }{\it{load\/}} \\ 
{\bf elseif }{\it{load\/}} $\in\;${\bf{N}}${}$ \\ 
{\bf then }{\rm{std-load-to-pf}}\,({\it{load\/}})\index{std-load-to-pf} \\ 
{\bf else }{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{pf}}{\tt{)}}$\;${\bf  endif}\- \\ 
{\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{list}}\,(\=\+{\bf if }{\rm{pfp}}\,({\it{load\/}})\index{pfp} \\ 
{\bf then }{\it{load\/}} \\ 
{\bf elseif }{\it{load\/}} $\in\;${\bf{N}}${}$ \\ 
{\bf then }{\rm{std-load-to-pf}}\,({\it{load\/}})\index{std-load-to-pf} \\ 
{\bf else }{\tt{'}}{\tt{(}}\=\+{\tt{0}} \\ 
{\tt{pf}}{\tt{)}}\-$\;${\bf  endif}\-)$\;${\bf  endif}\-)\-)\-)\-)\-\index{pred-error} \\ 
{\bf else }{\rm{pf-to-ma}}\,({\rm{pf-difference}}\,(\=\+{\rm{ma-to-pf}}\,({\it{drive\/}})\index{ma-to-pf}, \\ 
\=\+{\bf if }{\rm{pfp}}\,({\it{load\/}})\index{pfp}$\;\;${\bf then }{\it{load\/}} \\ 
{\bf elseif }{\it{load\/}} $\in\;${\bf{N}}${}$ \\ 
{\bf then }{\rm{std-load-to-pf}}\,({\it{load\/}})\index{std-load-to-pf} \\ 
{\bf else }{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{pf}}{\tt{)}}$\;${\bf  endif}\-)\-\index{pf-difference})\index{pf-to-ma}$\;${\bf  endif}\- \\ 
{\bf else }{\sc{unknown}}\index{unknown}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable literal-net-drive; name this event `literal-net-drive-off'.\index{literal-net-drive-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{net-min-args} \\  
\=\+{\rm{net-min-args}}\,({\it{a\/}}, {\it{load\/}}, {\it{listp\/}})\index{net-min-args} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{listp\/}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\it{a\/}}) \\ 
{\bf then }\=\+{\rm{net-min-args}}\,({\rm{car}}\,({\it{a\/}}), {\it{load\/}}, {\bf{f}})\index{net-min-args} \\ 
$\cup$$\;\;\;\;${\rm{net-min-args}}\,({\rm{cdr}}\,({\it{a\/}}), {\it{load\/}}, {\bf{t}})\index{net-min-args}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\- \\ 
{\bf elseif }({\it{a\/}} $\in\;${\bf{N}}${}$) $\vee$ {\rm{map}}\,({\it{a\/}})\index{map} \\ 
{\bf then }{\rm{list}}\,({\rm{literal-net-drive}}\,({\it{a\/}}, {\it{load\/}}, {\tt{'}}{\tt{min-arg}})\index{literal-net-drive}) \\ 
{\bf elseif }{\rm{listp}}\,({\it{a\/}}) $\wedge$ ({\rm{car}}\,({\it{a\/}}) $=$ {\tt{'}}{\tt{min}}) \\ 
{\bf then }{\rm{net-min-args}}\,({\rm{cdr}}\,({\it{a\/}}), {\it{load\/}}, {\bf{t}})\index{net-min-args} \\ 
{\bf else }{\rm{list}}\,({\it{a\/}})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable net-min-args; name this event `net-min-args-off'.\index{net-min-args-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{add-net-min-drive} \\  
\=\+{\rm{add-net-min-drive}}\,({\it{name\/}}, {\it{args\/}}, {\it{load\/}}, {\it{drive-map\/}})\index{add-net-min-drive} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{net-errorp}}\,({\rm{err-and}}\,({\rm{net-min-args}}\,({\it{args\/}}, {\it{load\/}}, {\bf{t}})\index{net-min-args}, {\rm{list}}\,({\tt{'}}{\tt{signal}}, {\it{name\/}}))\index{err-and})\index{net-errorp} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{extract-names}}\,({\rm{net-min-args}}\,({\it{args\/}}, {\it{load\/}}, {\bf{t}})\index{net-min-args})\index{extract-names}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{err-and}}\,(\=\+{\rm{net-min-args}}\,({\it{args\/}}, {\it{load\/}}, {\bf{t}})\index{net-min-args}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{signal}}, {\it{name\/}}))\-\index{err-and}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\it{name\/}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{min}}, \\ 
{\rm{cons}}\,(\=\+{\sc{unknown}}\index{unknown}, \\ 
{\rm{extract-names}}\,({\rm{net-min-args}}\,(\=\+{\it{args\/}}, \\ 
{\it{load\/}}, \\ 
{\bf{t}})\-\index{net-min-args})\index{extract-names})\-)\-)\-, \\ 
{\it{drive-map\/}})\-)\- \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{err-and}}\,(\=\+{\rm{net-min-args}}\,({\it{args\/}}, {\it{load\/}}, {\bf{t}})\index{net-min-args}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{signal}}, {\it{name\/}}))\-\index{err-and}, \\ 
{\it{drive-map\/}})\-$\;${\bf  endif}\- \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{cons}}\,({\it{name\/}}, {\rm{cons}}\,({\tt{'}}{\tt{min}}, {\rm{net-min-args}}\,({\it{args\/}}, {\it{load\/}}, {\bf{t}})\index{net-min-args})), \\ 
{\it{drive-map\/}})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable add-net-min-drive; name this event `add-net-min-drive-off'.\index{add-net-min-drive-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{add-net-drive} \\  
\=\+{\rm{add-net-drive}}\,({\it{drive\/}}, {\it{loadings\/}}, {\it{drive-map\/}})\index{add-net-drive} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{drive\/}}) \\ 
{\bf then }\=\+{\bf if }({\rm{cdr}}\,({\it{drive\/}}) $\in\;${\bf{N}}${}$) $\vee$ {\rm{map}}\,({\rm{cdr}}\,({\it{drive\/}}))\index{map} \\ 
{\bf then }{\rm{cons}}\,(\=\+\=\+{\bf if }{\rm{net-errorp}}\,({\rm{literal-net-drive}}\,(\=\+{\rm{cdr}}\,({\it{drive\/}}), \\ 
{\rm{value}}\,(\=\+{\rm{car}}\,({\it{drive\/}}), \\ 
{\it{loadings\/}})\-\index{value}, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{signal}}, \\ 
{\rm{car}}\,({\it{drive\/}}))\-)\-\index{literal-net-drive})\index{net-errorp} \\ 
{\bf then }{\rm{literal-net-drive}}\,(\=\+{\rm{cdr}}\,({\it{drive\/}}), \\ 
{\rm{value}}\,({\rm{car}}\,({\it{drive\/}}), {\it{loadings\/}})\index{value}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{signal}}, {\rm{car}}\,({\it{drive\/}})))\-\index{literal-net-drive} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{car}}\,({\it{drive\/}}), \\ 
{\rm{literal-net-drive}}\,(\=\+{\rm{cdr}}\,({\it{drive\/}}), \\ 
{\rm{value}}\,(\=\+{\rm{car}}\,({\it{drive\/}}), \\ 
{\it{loadings\/}})\-\index{value}, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{signal}}, \\ 
{\rm{car}}\,({\it{drive\/}}))\-)\-\index{literal-net-drive})\-$\;${\bf  endif}\-, \\ 
{\it{drive-map\/}})\- \\ 
{\bf elseif }{\rm{cadr}}\,({\it{drive\/}}) $=$ {\tt{'}}{\tt{min}} \\ 
{\bf then }{\rm{add-net-min-drive}}\,(\=\+{\rm{car}}\,({\it{drive\/}}), \\ 
{\rm{cddr}}\,({\it{drive\/}}), \\ 
{\rm{value}}\,({\rm{car}}\,({\it{drive\/}}), {\it{loadings\/}})\index{value}, \\ 
{\it{drive-map\/}})\-\index{add-net-min-drive} \\ 
{\bf else }{\rm{cons}}\,({\it{drive\/}}, {\it{drive-map\/}})$\;${\bf  endif}\- \\ 
{\bf else }{\rm{cons}}\,({\it{drive\/}}, {\it{drive-map\/}})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable add-net-drive; name this event `add-net-drive-off'.\index{add-net-drive-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{net-drives-simple} \\  
\=\+{\rm{net-drives-simple}}\,({\it{drs\/}}, {\it{lds\/}})\index{net-drives-simple} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{drs\/}}) \\ 
{\bf then }{\rm{add-net-drive}}\,({\rm{car}}\,({\it{drs\/}}), {\it{lds\/}}, {\rm{net-drives-simple}}\,({\rm{cdr}}\,({\it{drs\/}}), {\it{lds\/}})\index{net-drives-simple})\index{add-net-drive} \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable net-drives-simple; name this event `net-drives-simple-off'.\index{net-drives-simple-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{type-loading} \\  
\=\+{\rm{type-loading}}\,({\it{load\/}}, {\it{type\/}})\index{type-loading} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{type\/}} $\in$ {\tt{'}}{\tt{(}}{\tt{boolp}}{\tt{ }}{\tt{clk}}{\tt{ }}{\tt{level}}{\tt{ }}{\tt{parametric}}{\tt{ }}{\tt{tri-state}}{\tt{)}} \\ 
{\bf then }\=\+{\bf if }{\rm{pfp}}\,({\it{load\/}})\index{pfp}$\;\;${\bf then }{\rm{pf-to-std-load}}\,({\it{load\/}})\index{pf-to-std-load} \\ 
{\bf else }{\it{load\/}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{type\/}} $\in$ {\tt{'}}{\tt{(}}{\tt{ttl}}{\tt{ }}{\tt{ttl-tri-state}}{\tt{)}} \\ 
{\bf then }\=\+{\bf if }{\it{load\/}} $\in\;${\bf{N}}${}$$\;\;${\bf then }{\rm{std-load-to-pf}}\,({\it{load\/}})\index{std-load-to-pf} \\ 
{\bf else }{\it{load\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{load\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable type-loading; name this event `type-loading-off'.\index{type-loading-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-loadings} \\  
\=\+{\rm{collect-loadings}}\,({\it{names\/}}, {\it{types\/}}, {\it{loadings\/}})\index{collect-loadings} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{names\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{type-loading}}\,({\rm{value}}\,({\rm{car}}\,({\it{names\/}}), {\it{loadings\/}})\index{value}, {\rm{car}}\,({\it{types\/}}))\index{type-loading}, \\ 
{\rm{collect-loadings}}\,({\rm{cdr}}\,({\it{names\/}}), {\rm{cdr}}\,({\it{types\/}}), {\it{loadings\/}})\index{collect-loadings})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-loadings; name this event `collect-loadings-off'.\index{collect-loadings-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{loadings-error} \\  
{\rm{loadings-error}}\,({\it{loadings\/}})\index{loadings-error} $=$ {\rm{err-and}}\,({\it{loadings\/}}, {\tt{'}}{\tt{bad-loadings}})\index{err-and}
\end{tabbing}


\noindent{\sc Event}:   Enable loadings-error; name this event `loadings-error-off'.\index{loadings-error-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-min-args} \\  
\=\+{\rm{collect-min-args}}\,({\it{a\/}}, {\it{listp\/}}, {\it{drives\/}}, {\it{used-names\/}}, {\it{inputs\/}}, {\it{outputs\/}})\index{collect-min-args} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{listp\/}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\it{a\/}}) \\ 
{\bf then }\=\+{\rm{collect-min-args}}\,({\rm{car}}\,({\it{a\/}}), {\bf{f}}, {\it{drives\/}}, {\it{used-names\/}}, {\it{inputs\/}}, {\it{outputs\/}})\index{collect-min-args} \\ 
$\cup$$\;\;\;\;${\rm{collect-min-args}}\,(\=\+{\rm{cdr}}\,({\it{a\/}}), \\ 
{\bf{t}}, \\ 
{\it{drives\/}}, \\ 
{\it{used-names\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}})\-\index{collect-min-args}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{signal-namep}}\,({\it{a\/}})\index{signal-namep} \\ 
{\bf then }\=\+{\bf if }{\it{a\/}} $\in$ {\it{inputs\/}}$\;\;${\bf then }{\rm{list}}\,({\it{a\/}}) \\ 
{\bf elseif }\=\+($\neg$ (({\it{a\/}} $\in$ {\it{outputs\/}}) $\vee$ ({\it{a\/}} $\in$ {\it{used-names\/}}))) \\ 
$\wedge$$\;\;\;\;${\rm{boundp}}\,({\it{a\/}}, {\it{drives\/}})\index{boundp}\- \\ 
{\bf then }{\rm{collect-min-args}}\,(\=\+{\rm{value}}\,({\it{a\/}}, {\it{drives\/}})\index{value}, \\ 
{\bf{f}}, \\ 
{\it{drives\/}}, \\ 
{\rm{cons}}\,({\it{a\/}}, {\it{used-names\/}}), \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}})\-\index{collect-min-args} \\ 
{\bf else }{\rm{list}}\,({\sc{unknown}}\index{unknown})$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{listp}}\,({\it{a\/}}) $\wedge$ ({\rm{car}}\,({\it{a\/}}) $=$ {\tt{'}}{\tt{min}}) \\ 
{\bf then }{\rm{collect-min-args}}\,({\rm{cdr}}\,({\it{a\/}}), {\bf{t}}, {\it{drives\/}}, {\it{used-names\/}}, {\it{inputs\/}}, {\it{outputs\/}})\index{collect-min-args} \\ 
{\bf elseif }({\it{a\/}} $\in\;${\bf{N}}${}$) $\vee$ {\rm{map}}\,({\it{a\/}})\index{map}$\;\;${\bf then }{\rm{list}}\,({\it{a\/}}) \\ 
{\bf else }{\rm{list}}\,({\sc{unknown}}\index{unknown})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-min-args; name this event `collect-min-args-off'.\index{collect-min-args-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{numeric-drives} \\  
\=\+{\rm{numeric-drives}}\,({\it{drs\/}})\index{numeric-drives} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{drs\/}}) \\ 
{\bf then }\=\+{\bf if }({\rm{car}}\,({\it{drs\/}}) $\in\;${\bf{N}}${}$) $\vee$ {\rm{map}}\,({\rm{car}}\,({\it{drs\/}}))\index{map} \\ 
{\bf then }{\rm{cons}}\,({\rm{car}}\,({\it{drs\/}}), {\rm{numeric-drives}}\,({\rm{cdr}}\,({\it{drs\/}}))\index{numeric-drives}) \\ 
{\bf else }{\rm{numeric-drives}}\,({\rm{cdr}}\,({\it{drs\/}}))\index{numeric-drives}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable numeric-drives; name this event `numeric-drives-off'.\index{numeric-drives-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{type-drive} \\  
\=\+{\rm{type-drive}}\,({\it{drive\/}}, {\it{type\/}})\index{type-drive} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{type\/}} $\in$ {\tt{'}}{\tt{(}}{\tt{boolp}}{\tt{ }}{\tt{clk}}{\tt{ }}{\tt{level}}{\tt{ }}{\tt{parametric}}{\tt{ }}{\tt{tri-state}}{\tt{)}} \\ 
{\bf then }\=\+{\bf if }{\rm{map}}\,({\it{drive\/}})\index{map}$\;\;${\bf then }{\rm{ma-to-std-drive}}\,({\it{drive\/}})\index{ma-to-std-drive} \\ 
{\bf else }{\it{drive\/}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{type\/}} $\in$ {\tt{'}}{\tt{(}}{\tt{ttl}}{\tt{ }}{\tt{ttl-tri-state}}{\tt{)}} \\ 
{\bf then }\=\+{\bf if }{\it{drive\/}} $\in\;${\bf{N}}${}$$\;\;${\bf then }{\rm{std-drive-to-ma}}\,({\it{drive\/}})\index{std-drive-to-ma} \\ 
{\bf else }{\it{drive\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{drive\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable type-drive; name this event `type-drive-off'.\index{type-drive-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{drive-lessp} \\  
\=\+{\rm{drive-lessp}}\,({\it{x\/}}, {\it{y\/}})\index{drive-lessp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{x\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{y\/}} $\in\;${\bf{N}}${}$)$\;\;${\bf then }{\it{x\/}} $<$ {\it{y\/}} \\ 
{\bf elseif }{\rm{map}}\,({\it{x\/}})\index{map} $\wedge$ {\rm{map}}\,({\it{y\/}})\index{map}$\;\;${\bf then }{\rm{ma-lessp}}\,({\it{x\/}}, {\it{y\/}})\index{ma-lessp} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable drive-lessp; name this event `drive-lessp-off'.\index{drive-lessp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{drive-min} \\  
\=\+{\rm{drive-min}}\,({\it{lst\/}}, {\it{type\/}})\index{drive-min} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{lst\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\sc{unknown}}\index{unknown} \\ 
{\bf elseif }{\rm{cdr}}\,({\it{lst\/}}) $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{type-drive}}\,({\rm{car}}\,({\it{lst\/}}), {\it{type\/}})\index{type-drive} \\ 
{\bf elseif }{\rm{drive-lessp}}\,({\rm{type-drive}}\,({\rm{car}}\,({\it{lst\/}}), {\it{type\/}})\index{type-drive}, {\rm{drive-min}}\,({\rm{cdr}}\,({\it{lst\/}}), {\it{type\/}})\index{drive-min})\index{drive-lessp} \\ 
{\bf then }{\rm{type-drive}}\,({\rm{car}}\,({\it{lst\/}}), {\it{type\/}})\index{type-drive} \\ 
{\bf else }{\rm{drive-min}}\,({\rm{cdr}}\,({\it{lst\/}}), {\it{type\/}})\index{drive-min}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable drive-min; name this event `drive-min-off'.\index{drive-min-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{make-drive-min} \\  
\=\+{\rm{make-drive-min}}\,({\it{args\/}}, {\it{type\/}}, {\it{drives\/}}, {\it{inputs\/}}, {\it{outputs\/}})\index{make-drive-min} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{extract-names}}\,({\rm{collect-min-args}}\,({\it{args\/}}, {\bf{t}}, {\it{drives\/}}, {\bf{nil}}, {\it{inputs\/}}, {\it{outputs\/}})\index{collect-min-args})\index{extract-names} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }{\rm{drive-min}}\,(\=\+{\rm{numeric-drives}}\,({\rm{collect-min-args}}\,(\=\+{\it{args\/}}, \\ 
{\bf{t}}, \\ 
{\it{drives\/}}, \\ 
{\bf{nil}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}})\-\index{collect-min-args})\index{numeric-drives}, \\ 
{\it{type\/}})\-\index{drive-min} \\ 
{\bf elseif }{\rm{numeric-drives}}\,({\rm{collect-min-args}}\,(\=\+{\it{args\/}}, \\ 
{\bf{t}}, \\ 
{\it{drives\/}}, \\ 
{\bf{nil}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}})\-\index{collect-min-args})\index{numeric-drives} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{cdr}}\,({\rm{extract-names}}\,({\rm{collect-min-args}}\,(\=\+{\it{args\/}}, \\ 
{\bf{t}}, \\ 
{\it{drives\/}}, \\ 
{\bf{nil}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}})\-\index{collect-min-args})\index{extract-names})) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\tt{'}}{\tt{min}}, \\ 
{\rm{extract-names}}\,({\rm{collect-min-args}}\,(\=\+{\it{args\/}}, \\ 
{\bf{t}}, \\ 
{\it{drives\/}}, \\ 
{\bf{nil}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}})\-\index{collect-min-args})\index{extract-names})\- \\ 
{\bf else }{\rm{cons}}\,(\=\+{\tt{'}}{\tt{min}}, \\ 
{\rm{cons}}\,(\=\+{\sc{unknown}}\index{unknown}, \\ 
{\rm{extract-names}}\,({\rm{collect-min-args}}\,(\=\+{\it{args\/}}, \\ 
{\bf{t}}, \\ 
{\it{drives\/}}, \\ 
{\bf{nil}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}})\-\index{collect-min-args})\index{extract-names})\-)\-$\;${\bf  endif}\- \\ 
{\bf else }{\rm{cons}}\,(\=\+{\tt{'}}{\tt{min}}, \\ 
{\rm{cons}}\,(\=\+{\rm{drive-min}}\,(\=\+{\rm{numeric-drives}}\,({\rm{collect-min-args}}\,(\=\+{\it{args\/}}, \\ 
{\bf{t}}, \\ 
{\it{drives\/}}, \\ 
{\bf{nil}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}})\-\index{collect-min-args})\index{numeric-drives}, \\ 
{\it{type\/}})\-\index{drive-min}, \\ 
{\rm{extract-names}}\,({\rm{collect-min-args}}\,(\=\+{\it{args\/}}, \\ 
{\bf{t}}, \\ 
{\it{drives\/}}, \\ 
{\bf{nil}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}})\-\index{collect-min-args})\index{extract-names})\-)\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable make-drive-min; name this event `make-drive-min-off'.\index{make-drive-min-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-drives-0} \\  
\=\+{\rm{collect-drives-0}}\,({\it{names\/}}, {\it{output-types\/}}, {\it{drives\/}}, {\it{inputs\/}}, {\it{outputs\/}})\index{collect-drives-0} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{names\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+\=\+{\bf if }\=\+({\rm{value-or-unknown}}\,({\rm{car}}\,({\it{names\/}}), {\it{drives\/}})\index{value-or-unknown} $\in\;${\bf{N}}${}$) \\ 
$\vee$$\;\;\;\;${\rm{map}}\,({\rm{value-or-unknown}}\,({\rm{car}}\,({\it{names\/}}), {\it{drives\/}})\index{value-or-unknown})\index{map}\- \\ 
{\bf then }{\rm{type-drive}}\,(\=\+{\rm{value-or-unknown}}\,({\rm{car}}\,({\it{names\/}}), {\it{drives\/}})\index{value-or-unknown}, \\ 
{\rm{car}}\,({\it{output-types\/}}))\-\index{type-drive} \\ 
{\bf elseif }{\rm{signal-namep}}\,({\rm{value-or-unknown}}\,({\rm{car}}\,({\it{names\/}}), {\it{drives\/}})\index{value-or-unknown})\index{signal-namep} \\ 
{\bf then }{\rm{parent-synonym}}\,(\=\+{\rm{value-or-unknown}}\,({\rm{car}}\,({\it{names\/}}), {\it{drives\/}})\index{value-or-unknown}, \\ 
{\it{drives\/}})\-\index{parent-synonym} \\ 
{\bf elseif }\=\+{\rm{listp}}\,({\rm{value-or-unknown}}\,({\rm{car}}\,({\it{names\/}}), {\it{drives\/}})\index{value-or-unknown}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{car}}\,({\rm{value-or-unknown}}\,({\rm{car}}\,({\it{names\/}}), {\it{drives\/}})\index{value-or-unknown}) \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{min}})\-\- \\ 
{\bf then }{\rm{make-drive-min}}\,(\=\+{\rm{cdr}}\,({\rm{value-or-unknown}}\,({\rm{car}}\,({\it{names\/}}), {\it{drives\/}})\index{value-or-unknown}), \\ 
{\rm{car}}\,({\it{output-types\/}}), \\ 
{\it{drives\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}})\-\index{make-drive-min} \\ 
{\bf else }{\sc{unknown}}\index{unknown}$\;${\bf  endif}\-, \\ 
{\rm{collect-drives-0}}\,(\=\+{\rm{cdr}}\,({\it{names\/}}), \\ 
{\rm{cdr}}\,({\it{output-types\/}}), \\ 
{\it{drives\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}})\-\index{collect-drives-0})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-drives-0; name this event `collect-drives-0-off'.\index{collect-drives-0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-drives} \\  
\=\+{\rm{collect-drives}}\,({\it{outputs\/}}, {\it{output-types\/}}, {\it{drives\/}}, {\it{inputs\/}})\index{collect-drives} \\ 
$=$$\;\;\;\;${\rm{collect-drives-0}}\,(\=\+{\it{outputs\/}}, \\ 
{\it{output-types\/}}, \\ 
{\rm{externalize-parents}}\,({\it{outputs\/}}, {\it{drives\/}}, {\it{inputs\/}}, {\it{outputs\/}})\index{externalize-parents}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}})\-\index{collect-drives-0}\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-drives; name this event `collect-drives-off'.\index{collect-drives-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{drives-error} \\  
{\rm{drives-error}}\,({\it{drives\/}})\index{drives-error} $=$ {\rm{err-and}}\,({\it{drives\/}}, {\tt{'}}{\tt{bad-drives}})\index{err-and}
\end{tabbing}


\noindent{\sc Event}:   Enable drives-error; name this event `drives-error-off'.\index{drives-error-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ps-pfp} \\  
\=\+{\rm{ps-pfp}}\,({\it{x\/}})\index{ps-pfp} \\ 
$=$$\;\;\;\;$(\=\+{\rm{properp}}\,({\it{x\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{x\/}})\index{length} $=$ {\tt{2}}) \\ 
$\wedge$$\;\;\;\;$({\rm{car}}\,({\it{x\/}}) $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$({\rm{cadr}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{ps-pf}}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ps-pfp; name this event `ps-pfp-off'.\index{ps-pfp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{delay-lh} \\  
\=\+{\rm{delay-lh}}\,({\it{d\/}})\index{delay-lh} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{d\/}}) $\wedge$ ({\rm{car}}\,({\it{d\/}}) $\not=$ {\tt{'}}{\tt{or}})$\;\;${\bf then }{\rm{car}}\,({\it{d\/}}) \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable delay-lh; name this event `delay-lh-off'.\index{delay-lh-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{delay-hl} \\  
\=\+{\rm{delay-hl}}\,({\it{d\/}})\index{delay-hl} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{d\/}}) $\wedge$ ({\rm{car}}\,({\it{d\/}}) $\not=$ {\tt{'}}{\tt{or}})$\;\;${\bf then }{\rm{cadr}}\,({\it{d\/}}) \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable delay-hl; name this event `delay-hl-off'.\index{delay-hl-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{delay-slope-lh} \\  
\=\+{\rm{delay-slope-lh}}\,({\it{d\/}})\index{delay-slope-lh} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{d\/}}) $\wedge$ ({\rm{car}}\,({\it{d\/}}) $\not=$ {\tt{'}}{\tt{or}})$\;\;${\bf then }{\rm{caar}}\,({\it{d\/}}) \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable delay-slope-lh; name this event `delay-slope-lh-off'.\index{delay-slope-lh-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{delay-slope-hl} \\  
\=\+{\rm{delay-slope-hl}}\,({\it{d\/}})\index{delay-slope-hl} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{d\/}}) $\wedge$ ({\rm{car}}\,({\it{d\/}}) $\not=$ {\tt{'}}{\tt{or}})$\;\;${\bf then }{\rm{caadr}}\,({\it{d\/}}) \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable delay-slope-hl; name this event `delay-slope-hl-off'.\index{delay-slope-hl-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{delay-intercept-lh} \\  
\=\+{\rm{delay-intercept-lh}}\,({\it{d\/}})\index{delay-intercept-lh} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{d\/}}) $\wedge$ ({\rm{car}}\,({\it{d\/}}) $\not=$ {\tt{'}}{\tt{or}})$\;\;${\bf then }{\rm{cadar}}\,({\it{d\/}}) \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable delay-intercept-lh; name this event `delay-intercept-lh-off'.\index{delay-intercept-lh-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{delay-intercept-hl} \\  
\=\+{\rm{delay-intercept-hl}}\,({\it{d\/}})\index{delay-intercept-hl} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{d\/}}) $\wedge$ ({\rm{car}}\,({\it{d\/}}) $\not=$ {\tt{'}}{\tt{or}})$\;\;${\bf then }{\rm{cadadr}}\,({\it{d\/}}) \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable delay-intercept-hl; name this event `delay-intercept-hl-off'.\index{delay-intercept-hl-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{delay-dependencies} \\  
\=\+{\rm{delay-dependencies}}\,({\it{d\/}})\index{delay-dependencies} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{d\/}}) $\wedge$ ({\rm{car}}\,({\it{d\/}}) $\not=$ {\tt{'}}{\tt{or}})$\;\;${\bf then }{\rm{cddr}}\,({\it{d\/}}) \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable delay-dependencies; name this event `delay-dependencies-off'.\index{delay-dependencies-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{make-delay-0}$\;\;$
{\rm{make-delay-0}}\,({\it{lh\/}}, {\it{hl\/}}, {\it{deps\/}})\index{make-delay-0} $=$ {\rm{cons}}\,({\it{lh\/}}, {\rm{cons}}\,({\it{hl\/}}, {\it{deps\/}}))
\end{tabbing}


\noindent{\sc Event}:   Enable make-delay-0; name this event `make-delay-0-off'.\index{make-delay-0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{make-delay} \\  
\=\+{\rm{make-delay}}\,({\it{s-lh\/}}, {\it{i-lh\/}}, {\it{s-hl\/}}, {\it{i-hl\/}}, {\it{deps\/}})\index{make-delay} \\ 
$=$$\;\;\;\;${\rm{make-delay-0}}\,({\rm{list}}\,({\it{s-lh\/}}, {\it{i-lh\/}}), {\rm{list}}\,({\it{s-hl\/}}, {\it{i-hl\/}}), {\it{deps\/}})\index{make-delay-0}\-
\end{tabbing}


\noindent{\sc Event}:   Enable make-delay; name this event `make-delay-off'.\index{make-delay-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{determined-delayp} \\  
\=\+{\rm{determined-delayp}}\,({\it{d\/}})\index{determined-delayp} \\ 
$=$$\;\;\;\;$({\rm{listp}}\,({\it{d\/}}) $\wedge$ ({\rm{car}}\,({\it{d\/}}) $\not=$ {\tt{'}}{\tt{or}}) $\wedge$ ({\rm{delay-dependencies}}\,({\it{d\/}})\index{delay-dependencies} $\simeq\;${{\bf{nil}}}${}$))\-
\end{tabbing}


\noindent{\sc Event}:   Enable determined-delayp; name this event `determined-delayp-off'.\index{determined-delayp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{make-range} \\  
\=\+{\rm{make-range}}\,({\it{lo\/}}, {\it{hi\/}}, {\it{deps\/}})\index{make-range} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{lo\/}} $=$ {\it{hi\/}}) $\wedge$ ({\it{deps\/}} $\simeq\;${{\bf{nil}}}${}$)$\;\;${\bf then }{\it{lo\/}} \\ 
{\bf else }{\rm{cons}}\,({\tt{'}}{\tt{range}}, {\rm{cons}}\,({\it{lo\/}}, {\rm{cons}}\,({\it{hi\/}}, {\it{deps\/}})))$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable make-range; name this event `make-range-off'.\index{make-range-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{rangep} \\  
\=\+{\rm{rangep}}\,({\it{x\/}})\index{rangep} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}})$\;\;${\bf then }{\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{range}} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable rangep; name this event `rangep-off'.\index{rangep-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{range-min} \\  
\=\+{\rm{range-min}}\,({\it{x\/}})\index{range-min} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{rangep}}\,({\it{x\/}})\index{rangep}$\;\;${\bf then }{\rm{cadr}}\,({\it{x\/}}) \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable range-min; name this event `range-min-off'.\index{range-min-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{range-max} \\  
\=\+{\rm{range-max}}\,({\it{x\/}})\index{range-max} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{rangep}}\,({\it{x\/}})\index{rangep}$\;\;${\bf then }{\rm{caddr}}\,({\it{x\/}}) \\ 
{\bf else }{\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable range-max; name this event `range-max-off'.\index{range-max-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{range-dependencies} \\  
\=\+{\rm{range-dependencies}}\,({\it{x\/}})\index{range-dependencies} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{rangep}}\,({\it{x\/}})\index{rangep}$\;\;${\bf then }{\rm{cdddr}}\,({\it{x\/}}) \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable range-dependencies; name this event `range-dependencies-off'.\index{range-dependencies-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{determined-rangep} \\  
\=\+{\rm{determined-rangep}}\,({\it{x\/}})\index{determined-rangep} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{rangep}}\,({\it{x\/}})\index{rangep}$\;\;${\bf then }{\rm{range-dependencies}}\,({\it{x\/}})\index{range-dependencies} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf else }{\it{x\/}} $\in\;${\bf{N}}${}$$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable determined-rangep; name this event `determined-rangep-off'.\index{determined-rangep-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{per-std-load-delay-slope} \\  
\=\+{\rm{per-std-load-delay-slope}}\,({\it{slope\/}})\index{per-std-load-delay-slope} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{ps-pfp}}\,({\it{slope\/}})\index{ps-pfp}$\;\;${\bf then }{\rm{car}}\,({\it{slope\/}}) $*$ {\tt{10}} \\ 
{\bf else }{\it{slope\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable per-std-load-delay-slope; name this event `per-std-load-delay-slope-off'.\index{per-std-load-delay-slope-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{per-pf-delay-slope} \\  
\=\+{\rm{per-pf-delay-slope}}\,({\it{slope\/}})\index{per-pf-delay-slope} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{slope\/}} $\in\;${\bf{N}}${}$ \\ 
{\bf then }{\rm{cons}}\,(\=\+\=\+{\bf if }({\it{slope\/}} ${}${\bf{mod}}${}$ {\tt{10}}) $<$ {\tt{5}}$\;\;${\bf then }{\it{slope\/}} $\div$ {\tt{10}} \\ 
{\bf else }$1\;+$ ({\it{slope\/}} $\div$ {\tt{10}})$\;${\bf  endif}\-, \\ 
{\tt{'}}{\tt{(}}{\tt{ps-pf}}{\tt{)}})\- \\ 
{\bf else }{\it{slope\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable per-pf-delay-slope; name this event `per-pf-delay-slope-off'.\index{per-pf-delay-slope-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{range-plus} \\  
\=\+{\rm{range-plus}}\,({\it{i1\/}}, {\it{i2\/}}, {\it{deps\/}})\index{range-plus} \\ 
$=$$\;\;\;\;${\rm{make-range}}\,(\=\+{\rm{range-min}}\,({\it{i1\/}})\index{range-min} $+$ {\rm{range-min}}\,({\it{i2\/}})\index{range-min}, \\ 
{\rm{range-max}}\,({\it{i1\/}})\index{range-max} $+$ {\rm{range-max}}\,({\it{i2\/}})\index{range-max}, \\ 
{\it{deps\/}})\-\index{make-range}\-
\end{tabbing}


\noindent{\sc Event}:   Enable range-plus; name this event `range-plus-off'.\index{range-plus-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{slope-times-load} \\  
\=\+{\rm{slope-times-load}}\,({\it{slope\/}}, {\it{load\/}})\index{slope-times-load} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{slope\/}} $\in\;${\bf{N}}${}$ \\ 
{\bf then }\=\+{\bf if }{\it{load\/}} $\in\;${\bf{N}}${}$$\;\;${\bf then }{\it{slope\/}} $*$ {\it{load\/}} \\ 
{\bf elseif }{\rm{pfp}}\,({\it{load\/}})\index{pfp}$\;\;${\bf then }{\it{slope\/}} $*$ {\rm{pf-to-std-load}}\,({\it{load\/}})\index{pf-to-std-load} \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{ps-pfp}}\,({\it{slope\/}})\index{ps-pfp} \\ 
{\bf then }\=\+{\bf if }{\rm{pfp}}\,({\it{load\/}})\index{pfp}$\;\;${\bf then }{\rm{car}}\,({\it{slope\/}}) $*$ {\rm{car}}\,({\it{load\/}}) \\ 
{\bf elseif }{\it{load\/}} $\in\;${\bf{N}}${}$$\;\;${\bf then }{\rm{car}}\,({\it{slope\/}}) $*$ {\rm{car}}\,({\rm{std-load-to-pf}}\,({\it{load\/}})\index{std-load-to-pf}) \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\- \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable slope-times-load; name this event `slope-times-load-off'.\index{slope-times-load-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{initial-occ-delays}$\;\;$
{\sc{initial-occ-delays}}\index{initial-occ-delays} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  local-delay-count-help-0 \\ \index{local-delay-count-help-0}
{\rm{listp}}\,({\it{x\/}}) $\rightarrow$ ({\rm{count}}\,({\it{x\/}}) $=$ ($1\;+$ ({\rm{count}}\,({\rm{car}}\,({\it{x\/}})) $+$ {\rm{count}}\,({\rm{cdr}}\,({\it{x\/}})))))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  local-delay-count-help \\ \index{local-delay-count-help}
{\rm{listp}}\,({\it{x\/}}) $\rightarrow$ (({\rm{count}}\,({\it{x\/}}) $=$ {\tt{0}}) $=$ {\bf{f}})
\end{tabbing}


\noindent{\sc Event}:   Enable local-delay-count-help-0; name this event `local-delay-count-help-0-off'.\index{local-delay-count-help-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Disable range-dependencies; name this event `range-dependencies-on'.\index{range-dependencies-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable delay-dependencies; name this event `delay-dependencies-on'.\index{delay-dependencies-on}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{local-delay} \\  
\=\+{\rm{local-delay}}\,({\it{delay\/}}, {\it{out-depends\/}}, {\it{listp\/}}, {\it{in-map\/}}, {\it{out-map\/}}, {\it{delay-map\/}})\index{local-delay} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{listp\/}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\it{delay\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{local-delay}}\,(\=\+{\rm{car}}\,({\it{delay\/}}), \\ 
{\it{out-depends\/}}, \\ 
{\bf{f}}, \\ 
{\it{in-map\/}}, \\ 
{\it{out-map\/}}, \\ 
{\it{delay-map\/}})\-\index{local-delay}, \\ 
{\rm{local-delay}}\,(\=\+{\rm{cdr}}\,({\it{delay\/}}), \\ 
{\it{out-depends\/}}, \\ 
{\bf{t}}, \\ 
{\it{in-map\/}}, \\ 
{\it{out-map\/}}, \\ 
{\it{delay-map\/}})\-\index{local-delay})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{signal-namep}}\,({\it{delay\/}})\index{signal-namep} \\ 
{\bf then }{\rm{parent-synonym}}\,({\rm{value2}}\,({\it{delay\/}}, {\it{in-map\/}}, {\it{out-map\/}})\index{value2}, {\it{delay-map\/}})\index{parent-synonym} \\ 
{\bf elseif }{\it{delay\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{delay\/}} \\ 
{\bf elseif }{\rm{car}}\,({\it{delay\/}}) $=$ {\tt{'}}{\tt{or}} \\ 
{\bf then }{\rm{cons}}\,({\tt{'}}{\tt{or}}, {\rm{local-delay}}\,({\rm{cdr}}\,({\it{delay\/}}), {\bf{f}}, {\bf{t}}, {\it{in-map\/}}, {\it{out-map\/}}, {\it{delay-map\/}})\index{local-delay}) \\ 
{\bf elseif }{\rm{rangep}}\,({\it{delay\/}})\index{rangep} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{range-dependencies}}\,({\it{delay\/}})\index{range-dependencies}) \\ 
{\bf then }{\rm{make-range}}\,(\=\+{\rm{range-min}}\,({\it{delay\/}})\index{range-min}, \\ 
{\rm{range-max}}\,({\it{delay\/}})\index{range-max}, \\ 
{\rm{local-delay}}\,(\=\+{\rm{range-dependencies}}\,({\it{delay\/}})\index{range-dependencies}, \\ 
{\bf{f}}, \\ 
{\bf{t}}, \\ 
{\it{in-map\/}}, \\ 
{\it{out-map\/}}, \\ 
{\it{delay-map\/}})\-\index{local-delay})\-\index{make-range} \\ 
{\bf else }{\it{delay\/}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{listp}}\,(\=\+{\bf if }{\rm{listp}}\,({\rm{delay-dependencies}}\,({\it{delay\/}})\index{delay-dependencies}) \\ 
{\bf then }{\rm{delay-dependencies}}\,({\it{delay\/}})\index{delay-dependencies} \\ 
{\bf else }{\it{out-depends\/}}$\;${\bf  endif}\-) \\ 
{\bf then }{\rm{make-delay-0}}\,(\=\+{\rm{delay-lh}}\,({\it{delay\/}})\index{delay-lh}, \\ 
{\rm{delay-hl}}\,({\it{delay\/}})\index{delay-hl}, \\ 
{\rm{local-delay}}\,(\=\+\=\+{\bf if }{\rm{listp}}\,({\rm{delay-dependencies}}\,({\it{delay\/}})\index{delay-dependencies}) \\ 
{\bf then }{\rm{delay-dependencies}}\,({\it{delay\/}})\index{delay-dependencies} \\ 
{\bf else }{\it{out-depends\/}}$\;${\bf  endif}\-, \\ 
{\bf{f}}, \\ 
{\bf{t}}, \\ 
{\it{in-map\/}}, \\ 
{\it{out-map\/}}, \\ 
{\it{delay-map\/}})\-\index{local-delay})\-\index{make-delay-0} \\ 
{\bf else }{\it{delay\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable local-delay-count-help; name this event `local-delay-count-help-off'.\index{local-delay-count-help-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable range-dependencies; name this event `range-dependencies-off1'.\index{range-dependencies-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable delay-dependencies; name this event `delay-dependencies-off1'.\index{delay-dependencies-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable local-delay; name this event `local-delay-off'.\index{local-delay-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{add-delays} \\  
\=\+{\rm{add-delays}}\,({\it{outputs\/}}, {\it{delays\/}}, {\it{out-depends\/}}, {\it{in-map\/}}, {\it{out-map\/}}, {\it{delay-map\/}})\index{add-delays} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{outputs\/}}) \\ 
{\bf then }{\rm{add-delays}}\,(\=\+{\rm{cdr}}\,({\it{outputs\/}}), \\ 
{\rm{cdr}}\,({\it{delays\/}}), \\ 
{\rm{cdr}}\,({\it{out-depends\/}}), \\ 
{\it{in-map\/}}, \\ 
{\it{out-map\/}}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{car}}\,({\it{outputs\/}}), \\ 
{\rm{local-delay}}\,(\=\+{\rm{car}}\,({\it{delays\/}}), \\ 
{\rm{car}}\,({\it{out-depends\/}}), \\ 
{\bf{f}}, \\ 
{\it{in-map\/}}, \\ 
{\it{out-map\/}}, \\ 
{\it{delay-map\/}})\-\index{local-delay})\-, \\ 
{\it{delay-map\/}})\-)\-\index{add-delays} \\ 
{\bf else }{\it{delay-map\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable add-delays; name this event `add-delays-off'.\index{add-delays-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{update-delays} \\  
\=\+{\rm{update-delays}}\,({\it{delays\/}}, {\it{o-outs\/}}, {\it{o-fn-props\/}}, {\it{in-map\/}}, {\it{out-map\/}})\index{update-delays} \\ 
$=$$\;\;\;\;${\rm{add-delays}}\,(\=\+{\it{o-outs\/}}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{delays}}, {\it{o-fn-props\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{out-depends}}, {\it{o-fn-props\/}})\index{value}, \\ 
{\it{in-map\/}}, \\ 
{\it{out-map\/}}, \\ 
{\it{delays\/}})\-\index{add-delays}\-
\end{tabbing}


\noindent{\sc Event}:   Enable update-delays; name this event `update-delays-off'.\index{update-delays-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{add-load-delay} \\  
\=\+{\rm{add-load-delay}}\,({\it{delay\/}}, {\it{load\/}})\index{add-load-delay} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{zero-loadingp}}\,({\it{load\/}})\index{zero-loadingp}$\;\;${\bf then }{\it{delay\/}} \\ 
{\bf else }{\rm{make-delay}}\,(\=\+{\rm{delay-slope-lh}}\,({\it{delay\/}})\index{delay-slope-lh}, \\ 
{\rm{range-plus}}\,(\=\+{\rm{delay-intercept-lh}}\,({\it{delay\/}})\index{delay-intercept-lh}, \\ 
{\rm{slope-times-load}}\,(\=\+{\rm{delay-slope-lh}}\,({\it{delay\/}})\index{delay-slope-lh}, \\ 
{\it{load\/}})\-\index{slope-times-load}, \\ 
{\bf{nil}})\-\index{range-plus}, \\ 
{\rm{delay-slope-hl}}\,({\it{delay\/}})\index{delay-slope-hl}, \\ 
{\rm{range-plus}}\,(\=\+{\rm{delay-intercept-hl}}\,({\it{delay\/}})\index{delay-intercept-hl}, \\ 
{\rm{slope-times-load}}\,(\=\+{\rm{delay-slope-hl}}\,({\it{delay\/}})\index{delay-slope-hl}, \\ 
{\it{load\/}})\-\index{slope-times-load}, \\ 
{\bf{nil}})\-\index{range-plus}, \\ 
{\rm{delay-dependencies}}\,({\it{delay\/}})\index{delay-dependencies})\-\index{make-delay}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable add-load-delay; name this event `add-load-delay-off'.\index{add-load-delay-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{loaded-delay} \\  
\=\+{\rm{loaded-delay}}\,({\it{delay\/}}, {\it{load\/}}, {\it{listp\/}})\index{loaded-delay} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{listp\/}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\it{delay\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{loaded-delay}}\,({\rm{car}}\,({\it{delay\/}}), {\it{load\/}}, {\bf{f}})\index{loaded-delay}, \\ 
{\rm{loaded-delay}}\,({\rm{cdr}}\,({\it{delay\/}}), {\it{load\/}}, {\bf{t}})\index{loaded-delay})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{delay\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{delay\/}} \\ 
{\bf elseif }{\rm{car}}\,({\it{delay\/}}) $=$ {\tt{'}}{\tt{or}} \\ 
{\bf then }{\rm{cons}}\,({\tt{'}}{\tt{or}}, {\rm{loaded-delay}}\,({\rm{cdr}}\,({\it{delay\/}}), {\it{load\/}}, {\bf{t}})\index{loaded-delay}) \\ 
{\bf else }{\rm{add-load-delay}}\,({\it{delay\/}}, {\it{load\/}})\index{add-load-delay}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable loaded-delay; name this event `loaded-delay-off'.\index{loaded-delay-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{loaded-delays} \\  
\=\+{\rm{loaded-delays}}\,({\it{delays\/}}, {\it{loadings\/}})\index{loaded-delays} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{delays\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{delays\/}}) $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }{\rm{cons}}\,({\rm{car}}\,({\it{delays\/}}), {\rm{loaded-delays}}\,({\rm{cdr}}\,({\it{delays\/}}), {\it{loadings\/}})\index{loaded-delays}) \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{caar}}\,({\it{delays\/}}), \\ 
{\rm{loaded-delay}}\,(\=\+{\rm{cdar}}\,({\it{delays\/}}), \\ 
{\rm{value}}\,({\rm{caar}}\,({\it{delays\/}}), {\it{loadings\/}})\index{value}, \\ 
{\bf{f}})\-\index{loaded-delay})\-, \\ 
{\rm{loaded-delays}}\,({\rm{cdr}}\,({\it{delays\/}}), {\it{loadings\/}})\index{loaded-delays})\-$\;${\bf  endif}\- \\ 
{\bf else }{\it{delays\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable loaded-delays; name this event `loaded-delays-off'.\index{loaded-delays-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{merge-input-delays} \\  
\=\+{\rm{merge-input-delays}}\,({\it{r1\/}}, {\it{r2\/}}, {\it{or-args?\/}})\index{merge-input-delays} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{rangep}}\,({\it{r1\/}})\index{rangep} $\vee$ ({\it{r1\/}} $\in\;${\bf{N}}${}$) \\ 
{\bf then }\=\+{\bf if }{\rm{rangep}}\,({\it{r2\/}})\index{rangep} $\vee$ ({\it{r2\/}} $\in\;${\bf{N}}${}$) \\ 
{\bf then }{\rm{make-range}}\,(\=\+\=\+{\bf if }{\it{or-args?\/}} \\ 
{\bf then }{\rm{min}}\,({\rm{range-min}}\,({\it{r1\/}})\index{range-min}, {\rm{range-min}}\,({\it{r2\/}})\index{range-min})\index{min} \\ 
{\bf else }{\rm{max}}\,({\rm{range-min}}\,({\it{r1\/}})\index{range-min}, {\rm{range-min}}\,({\it{r2\/}})\index{range-min})$\;${\bf  endif}\-, \\ 
{\rm{max}}\,({\rm{range-max}}\,({\it{r1\/}})\index{range-max}, {\rm{range-max}}\,({\it{r2\/}})\index{range-max}), \\ 
\=\+{\rm{range-dependencies}}\,({\it{r1\/}})\index{range-dependencies} \\ 
$\cup$$\;\;\;\;${\rm{range-dependencies}}\,({\it{r2\/}})\index{range-dependencies}\-)\-\index{make-range} \\ 
{\bf else }{\rm{make-range}}\,(\=\+{\rm{range-min}}\,({\it{r1\/}})\index{range-min}, \\ 
{\rm{range-max}}\,({\it{r1\/}})\index{range-max}, \\ 
{\rm{insert}}\,({\it{r2\/}}, {\rm{range-dependencies}}\,({\it{r1\/}})\index{range-dependencies})\index{insert})\-\index{make-range}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{rangep}}\,({\it{r2\/}})\index{rangep} $\vee$ ({\it{r2\/}} $\in\;${\bf{N}}${}$) \\ 
{\bf then }{\rm{make-range}}\,(\=\+{\rm{range-min}}\,({\it{r2\/}})\index{range-min}, \\ 
{\rm{range-max}}\,({\it{r2\/}})\index{range-max}, \\ 
{\rm{insert}}\,({\it{r1\/}}, {\rm{range-dependencies}}\,({\it{r2\/}})\index{range-dependencies})\index{insert})\-\index{make-range} \\ 
{\bf else }{\rm{make-range}}\,({\tt{0}}, {\tt{0}}, {\rm{insert}}\,({\it{r1\/}}, {\rm{list}}\,({\it{r2\/}}))\index{insert})\index{make-range}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable merge-input-delays; name this event `merge-input-delays-off'.\index{merge-input-delays-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{mergeable-input-delay-p} \\  
\=\+{\rm{mergeable-input-delay-p}}\,({\it{d\/}}, {\it{approxp\/}})\index{mergeable-input-delay-p} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{approxp\/}}$\;\;${\bf then }{\rm{rangep}}\,({\it{d\/}})\index{rangep} $\vee$ ({\it{d\/}} $\in\;${\bf{N}}${}$) $\vee$ {\rm{signal-namep}}\,({\it{d\/}})\index{signal-namep} \\ 
{\bf else }{\rm{determined-rangep}}\,({\it{d\/}})\index{determined-rangep}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable mergeable-input-delay-p; name this event `mergeable-input-delay-p-off'.\index{mergeable-input-delay-p-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{insert-input-delay} \\  
\=\+{\rm{insert-input-delay}}\,({\it{d\/}}, {\it{dlist\/}}, {\it{or-args?\/}}, {\it{approxp\/}})\index{insert-input-delay} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{unknownp}}\,({\it{d\/}})\index{unknownp}$\;\;${\bf then }{\it{dlist\/}} \\ 
{\bf elseif }{\it{dlist\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }\=\+{\bf if }{\it{or-args?\/}} $\wedge$ ({\rm{car}}\,({\it{d\/}}) $=$ {\tt{'}}{\tt{or}})$\;\;${\bf then }{\rm{cdr}}\,({\it{d\/}}) \\ 
{\bf else }{\rm{list}}\,({\it{d\/}})$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{or-args?\/}} $\wedge$ {\rm{listp}}\,({\it{d\/}}) $\wedge$ ({\rm{car}}\,({\it{d\/}}) $=$ {\tt{'}}{\tt{or}}) \\ 
{\bf then }{\rm{insert-input-delay}}\,(\=\+{\rm{cadr}}\,({\it{d\/}}), \\ 
{\rm{insert}}\,({\rm{car}}\,({\it{dlist\/}}), {\rm{cddr}}\,({\it{d\/}}) $\cup$ {\rm{cdr}}\,({\it{dlist\/}}))\index{insert}, \\ 
{\it{or-args?\/}}, \\ 
{\it{approxp\/}})\-\index{insert-input-delay} \\ 
{\bf elseif }{\rm{mergeable-input-delay-p}}\,({\it{d\/}}, {\it{approxp\/}} $\wedge$ ($\neg$ {\it{or-args?\/}}))\index{mergeable-input-delay-p} \\ 
{\bf then }\=\+{\bf if }{\rm{mergeable-input-delay-p}}\,({\rm{car}}\,({\it{dlist\/}}), {\it{approxp\/}} $\wedge$ ($\neg$ {\it{or-args?\/}}))\index{mergeable-input-delay-p} \\ 
{\bf then }{\rm{cons}}\,({\rm{merge-input-delays}}\,({\it{d\/}}, {\rm{car}}\,({\it{dlist\/}}), {\it{or-args?\/}})\index{merge-input-delays}, {\rm{cdr}}\,({\it{dlist\/}})) \\ 
{\bf else }{\rm{cons}}\,({\it{d\/}}, {\it{dlist\/}})$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{mergeable-input-delay-p}}\,({\rm{car}}\,({\it{dlist\/}}), {\it{approxp\/}} $\wedge$ ($\neg$ {\it{or-args?\/}}))\index{mergeable-input-delay-p} \\ 
{\bf then }{\rm{cons}}\,({\rm{car}}\,({\it{dlist\/}}), {\rm{insert}}\,({\it{d\/}}, {\rm{cdr}}\,({\it{dlist\/}}))\index{insert}) \\ 
{\bf else }{\rm{insert}}\,({\it{d\/}}, {\it{dlist\/}})\index{insert}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable insert-input-delay; name this event `insert-input-delay-off'.\index{insert-input-delay-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{literal-delay-to-range} \\  
\=\+{\rm{literal-delay-to-range}}\,({\it{d\/}})\index{literal-delay-to-range} \\ 
$=$$\;\;\;\;${\rm{make-range}}\,(\=\+{\rm{min}}\,(\=\+{\rm{range-min}}\,({\rm{delay-intercept-lh}}\,({\it{d\/}})\index{delay-intercept-lh})\index{range-min}, \\ 
{\rm{range-min}}\,({\rm{delay-intercept-hl}}\,({\it{d\/}})\index{delay-intercept-hl})\index{range-min})\-\index{min}, \\ 
{\rm{max}}\,(\=\+{\rm{range-max}}\,({\rm{delay-intercept-lh}}\,({\it{d\/}})\index{delay-intercept-lh})\index{range-max}, \\ 
{\rm{range-max}}\,({\rm{delay-intercept-hl}}\,({\it{d\/}})\index{delay-intercept-hl})\index{range-max})\-, \\ 
{\rm{delay-dependencies}}\,({\it{d\/}})\index{delay-dependencies})\-\index{make-range}\-
\end{tabbing}


\noindent{\sc Event}:   Enable literal-delay-to-range; name this event `literal-delay-to-range-off'.\index{literal-delay-to-range-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{or-delay-args-to-ranges} \\  
\=\+{\rm{or-delay-args-to-ranges}}\,({\it{args\/}}, {\it{result\/}})\index{or-delay-args-to-ranges} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{args\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{args\/}}) $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }{\rm{insert-input-delay}}\,(\=\+{\rm{car}}\,({\it{args\/}}), \\ 
{\rm{or-delay-args-to-ranges}}\,({\rm{cdr}}\,({\it{args\/}}), {\it{result\/}})\index{or-delay-args-to-ranges}, \\ 
{\bf{t}}, \\ 
{\bf{f}})\-\index{insert-input-delay} \\ 
{\bf elseif }{\rm{caar}}\,({\it{args\/}}) $=$ {\tt{'}}{\tt{or}} \\ 
{\bf then }{\rm{or-delay-args-to-ranges}}\,(\=\+{\rm{cdar}}\,({\it{args\/}}), \\ 
{\rm{or-delay-args-to-ranges}}\,(\=\+{\rm{cdr}}\,({\it{args\/}}), \\ 
{\it{result\/}})\-\index{or-delay-args-to-ranges})\-\index{or-delay-args-to-ranges} \\ 
{\bf else }{\rm{insert-input-delay}}\,(\=\+{\rm{literal-delay-to-range}}\,({\rm{car}}\,({\it{args\/}}))\index{literal-delay-to-range}, \\ 
{\rm{or-delay-args-to-ranges}}\,(\=\+{\rm{cdr}}\,({\it{args\/}}), \\ 
{\it{result\/}})\-\index{or-delay-args-to-ranges}, \\ 
{\bf{t}}, \\ 
{\bf{f}})\-\index{insert-input-delay}$\;${\bf  endif}\- \\ 
{\bf else }{\it{result\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable or-delay-args-to-ranges; name this event `or-delay-args-to-ranges-off'.\index{or-delay-args-to-ranges-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{make-delay-or} \\  
\=\+{\rm{make-delay-or}}\,({\it{args\/}})\index{make-delay-or} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{args\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\sc{unknown}}\index{unknown} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{cdr}}\,({\it{args\/}}))$\;\;${\bf then }{\rm{cons}}\,({\tt{'}}{\tt{or}}, {\it{args\/}}) \\ 
{\bf elseif }{\rm{signal-namep}}\,({\rm{car}}\,({\it{args\/}}))\index{signal-namep}$\;\;${\bf then }{\rm{cons}}\,({\tt{'}}{\tt{or}}, {\rm{cons}}\,({\sc{unknown}}\index{unknown}, {\it{args\/}})) \\ 
{\bf else }{\rm{car}}\,({\it{args\/}})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable make-delay-or; name this event `make-delay-or-off'.\index{make-delay-or-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{delay-to-range} \\  
\=\+{\rm{delay-to-range}}\,({\it{d\/}})\index{delay-to-range} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{d\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{d\/}} \\ 
{\bf elseif }{\rm{car}}\,({\it{d\/}}) $=$ {\tt{'}}{\tt{or}} \\ 
{\bf then }{\rm{make-delay-or}}\,({\rm{or-delay-args-to-ranges}}\,({\rm{cdr}}\,({\it{d\/}}), {\bf{nil}})\index{or-delay-args-to-ranges})\index{make-delay-or} \\ 
{\bf else }{\rm{literal-delay-to-range}}\,({\it{d\/}})\index{literal-delay-to-range}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable delay-to-range; name this event `delay-to-range-off'.\index{delay-to-range-off}

\addvspace{18pt}


\noindent{\sc Event}:   Disable range-dependencies; name this event `range-dependencies-on1'.\index{range-dependencies-on1}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{addable-input-delay} \\  
\=\+{\rm{addable-input-delay}}\,({\it{in-delays\/}}, {\it{approxp\/}})\index{addable-input-delay} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{in-delays\/}}) $\wedge$ ({\rm{cdr}}\,({\it{in-delays\/}}) $\simeq\;${{\bf{nil}}}${}$) \\ 
{\bf then }\=\+{\bf if }\=\+{\bf if }{\it{approxp\/}} \\ 
{\bf then }{\rm{rangep}}\,({\rm{car}}\,({\it{in-delays\/}}))\index{rangep} $\vee$ ({\rm{car}}\,({\it{in-delays\/}}) $\in\;${\bf{N}}${}$) \\ 
{\bf else }{\rm{determined-rangep}}\,({\rm{car}}\,({\it{in-delays\/}}))\index{determined-rangep}$\;${\bf  endif}\- \\ 
{\bf then }{\rm{car}}\,({\it{in-delays\/}}) \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable addable-input-delay; name this event `addable-input-delay-off'.\index{addable-input-delay-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{input-delay0} \\  
\=\+{\rm{input-delay0}}\,({\it{dep\/}}, {\it{delays\/}}, {\it{inputs\/}}, {\it{outputs\/}}, {\it{or-args?\/}}, {\it{list?\/}}, {\it{used-names\/}}, {\it{approxp\/}})\index{input-delay0} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{list?\/}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\it{dep\/}}) \\ 
{\bf then }{\rm{insert-input-delay}}\,(\=\+{\rm{input-delay0}}\,(\=\+{\rm{car}}\,({\it{dep\/}}), \\ 
{\it{delays\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{or-args?\/}}, \\ 
{\bf{f}}, \\ 
{\it{used-names\/}}, \\ 
{\it{approxp\/}})\-\index{input-delay0}, \\ 
{\rm{input-delay0}}\,(\=\+{\rm{cdr}}\,({\it{dep\/}}), \\ 
{\it{delays\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{or-args?\/}}, \\ 
{\bf{t}}, \\ 
{\it{used-names\/}}, \\ 
{\it{approxp\/}})\-\index{input-delay0}, \\ 
{\it{or-args?\/}}, \\ 
{\it{approxp\/}})\-\index{insert-input-delay} \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{dep\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }\=\+{\bf if }{\it{dep\/}} $\in\;${\bf{N}}${}$$\;\;${\bf then }{\it{dep\/}} \\ 
{\bf elseif }{\it{dep\/}} $\in$ {\it{inputs\/}}$\;\;${\bf then }{\it{dep\/}} \\ 
{\bf elseif }{\it{dep\/}} $\in$ {\it{used-names\/}}$\;\;${\bf then }{\sc{unknown}}\index{unknown} \\ 
{\bf elseif }{\it{dep\/}} $\in$ {\it{outputs\/}} \\ 
{\bf then }\=\+{\bf if }{\it{or-args?\/}}$\;\;${\bf then }{\sc{unknown}}\index{unknown} \\ 
{\bf else }{\rm{parent-synonym}}\,({\it{dep\/}}, {\it{delays\/}})\index{parent-synonym}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{boundp}}\,({\it{dep\/}}, {\it{delays\/}})\index{boundp} \\ 
{\bf then }{\rm{input-delay0}}\,(\=\+{\rm{delay-to-range}}\,({\rm{value}}\,({\it{dep\/}}, {\it{delays\/}})\index{value})\index{delay-to-range}, \\ 
{\it{delays\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{or-args?\/}}, \\ 
{\bf{f}}, \\ 
{\rm{cons}}\,({\it{dep\/}}, {\it{used-names\/}}), \\ 
{\it{approxp\/}})\-\index{input-delay0} \\ 
{\bf else }{\sc{unknown}}\index{unknown}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{car}}\,({\it{dep\/}}) $=$ {\tt{'}}{\tt{or}} \\ 
{\bf then }{\rm{make-delay-or}}\,({\rm{input-delay0}}\,(\=\+{\rm{cdr}}\,({\it{dep\/}}), \\ 
{\it{delays\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{used-names\/}}, \\ 
{\it{approxp\/}})\-\index{input-delay0})\index{make-delay-or} \\ 
{\bf elseif }{\rm{rangep}}\,({\it{dep\/}})\index{rangep} \\ 
{\bf then }\=\+{\bf if }{\rm{addable-input-delay}}\,(\=\+{\rm{input-delay0}}\,(\=\+{\rm{range-dependencies}}\,({\it{dep\/}})\index{range-dependencies}, \\ 
{\it{delays\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\bf{f}}, \\ 
{\bf{t}}, \\ 
{\it{used-names\/}}, \\ 
{\it{approxp\/}})\-\index{input-delay0}, \\ 
{\it{approxp\/}})\-\index{addable-input-delay} \\ 
{\bf then }{\rm{range-plus}}\,(\=\+{\it{dep\/}}, \\ 
{\rm{addable-input-delay}}\,(\=\+{\rm{input-delay0}}\,(\=\+{\rm{range-dependencies}}\,({\it{dep\/}})\index{range-dependencies}, \\ 
{\it{delays\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\bf{f}}, \\ 
{\bf{t}}, \\ 
{\it{used-names\/}}, \\ 
{\it{approxp\/}})\-\index{input-delay0}, \\ 
{\it{approxp\/}})\-\index{addable-input-delay}, \\ 
{\rm{range-dependencies}}\,({\rm{addable-input-delay}}\,(\=\+{\rm{input-delay0}}\,(\=\+{\rm{range-dependencies}}\,({\it{dep\/}})\index{range-dependencies}, \\ 
{\it{delays\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\bf{f}}, \\ 
{\bf{t}}, \\ 
{\it{used-names\/}}, \\ 
{\it{approxp\/}})\-\index{input-delay0}, \\ 
{\it{approxp\/}})\-\index{addable-input-delay})\index{range-dependencies})\-\index{range-plus} \\ 
{\bf else }{\rm{make-range}}\,(\=\+{\rm{range-min}}\,({\it{dep\/}})\index{range-min}, \\ 
{\rm{range-max}}\,({\it{dep\/}})\index{range-max}, \\ 
{\rm{input-delay0}}\,(\=\+{\rm{range-dependencies}}\,({\it{dep\/}})\index{range-dependencies}, \\ 
{\it{delays\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\bf{f}}, \\ 
{\bf{t}}, \\ 
{\it{used-names\/}}, \\ 
{\it{approxp\/}})\-\index{input-delay0})\-\index{make-range}$\;${\bf  endif}\- \\ 
{\bf else }{\sc{unknown}}\index{unknown}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable range-dependencies; name this event `range-dependencies-off2'.\index{range-dependencies-off2}

\addvspace{18pt}


\noindent{\sc Event}:   Enable input-delay0; name this event `input-delay0-off'.\index{input-delay0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{input-delay} \\  
\=\+{\rm{input-delay}}\,({\it{dep\/}}, {\it{delays\/}}, {\it{inputs\/}}, {\it{outputs\/}}, {\it{or-args?\/}}, {\it{list?\/}}, {\it{used-names\/}}, {\it{approxp\/}})\index{input-delay} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\rm{listp}}\,({\rm{input-delay0}}\,(\=\+{\it{dep\/}}, \\ 
{\it{delays\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{or-args?\/}}, \\ 
{\it{list?\/}}, \\ 
{\it{used-names\/}}, \\ 
{\it{approxp\/}})\-\index{input-delay0}) \\ 
$\wedge$$\;\;\;\;${\rm{rangep}}\,({\rm{car}}\,({\rm{input-delay0}}\,(\=\+{\it{dep\/}}, \\ 
{\it{delays\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{or-args?\/}}, \\ 
{\it{list?\/}}, \\ 
{\it{used-names\/}}, \\ 
{\it{approxp\/}})\-\index{input-delay0}))\index{rangep}\- \\ 
{\bf then }\=\+{\bf if }\=\+(\=\+{\rm{range-min}}\,({\rm{car}}\,({\rm{input-delay0}}\,(\=\+{\it{dep\/}}, \\ 
{\it{delays\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{or-args?\/}}, \\ 
{\it{list?\/}}, \\ 
{\it{used-names\/}}, \\ 
{\it{approxp\/}})\-\index{input-delay0}))\index{range-min} \\ 
$=$$\;\;\;\;${\tt{0}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{range-max}}\,({\rm{car}}\,({\rm{input-delay0}}\,(\=\+{\it{dep\/}}, \\ 
{\it{delays\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{or-args?\/}}, \\ 
{\it{list?\/}}, \\ 
{\it{used-names\/}}, \\ 
{\it{approxp\/}})\-\index{input-delay0}))\index{range-max} \\ 
$=$$\;\;\;\;${\tt{0}})\-\- \\ 
{\bf then }\=\+{\rm{range-dependencies}}\,({\rm{car}}\,({\rm{input-delay0}}\,(\=\+{\it{dep\/}}, \\ 
{\it{delays\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{or-args?\/}}, \\ 
{\it{list?\/}}, \\ 
{\it{used-names\/}}, \\ 
{\it{approxp\/}})\-\index{input-delay0}))\index{range-dependencies} \\ 
$\cup$$\;\;\;\;${\rm{cdr}}\,({\rm{input-delay0}}\,(\=\+{\it{dep\/}}, \\ 
{\it{delays\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{or-args?\/}}, \\ 
{\it{list?\/}}, \\ 
{\it{used-names\/}}, \\ 
{\it{approxp\/}})\-\index{input-delay0})\- \\ 
{\bf else }{\rm{input-delay0}}\,(\=\+{\it{dep\/}}, \\ 
{\it{delays\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{or-args?\/}}, \\ 
{\it{list?\/}}, \\ 
{\it{used-names\/}}, \\ 
{\it{approxp\/}})\-\index{input-delay0}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{input-delay0}}\,(\=\+{\it{dep\/}}, \\ 
{\it{delays\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{or-args?\/}}, \\ 
{\it{list?\/}}, \\ 
{\it{used-names\/}}, \\ 
{\it{approxp\/}})\-\index{input-delay0}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable input-delay; name this event `input-delay-off'.\index{input-delay-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{type-delay-slope} \\  
\=\+{\rm{type-delay-slope}}\,({\it{slope\/}}, {\it{type\/}})\index{type-delay-slope} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{type\/}} $\in$ {\tt{'}}{\tt{(}}{\tt{boolp}}{\tt{ }}{\tt{clk}}{\tt{ }}{\tt{level}}{\tt{ }}{\tt{parametric}}{\tt{ }}{\tt{tri-state}}{\tt{)}} \\ 
{\bf then }{\rm{per-std-load-delay-slope}}\,({\it{slope\/}})\index{per-std-load-delay-slope} \\ 
{\bf elseif }{\it{type\/}} $\in$ {\tt{'}}{\tt{(}}{\tt{ttl}}{\tt{ }}{\tt{ttl-tri-state}}{\tt{)}} \\ 
{\bf then }{\rm{per-pf-delay-slope}}\,({\it{slope\/}})\index{per-pf-delay-slope} \\ 
{\bf else }{\it{slope\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable type-delay-slope; name this event `type-delay-slope-off'.\index{type-delay-slope-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{make-output-delay} \\  
\=\+{\rm{make-output-delay}}\,({\it{delay\/}}, {\it{type\/}}, {\it{input-delay-list\/}}, {\it{approxp\/}})\index{make-output-delay} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{addable-input-delay}}\,({\it{input-delay-list\/}}, {\it{approxp\/}})\index{addable-input-delay} \\ 
{\bf then }{\rm{make-delay}}\,(\=\+{\rm{type-delay-slope}}\,({\rm{delay-slope-lh}}\,({\it{delay\/}})\index{delay-slope-lh}, {\it{type\/}})\index{type-delay-slope}, \\ 
{\rm{range-plus}}\,(\=\+{\rm{delay-intercept-lh}}\,({\it{delay\/}})\index{delay-intercept-lh}, \\ 
{\rm{addable-input-delay}}\,(\=\+{\it{input-delay-list\/}}, \\ 
{\it{approxp\/}})\-\index{addable-input-delay}, \\ 
{\bf{nil}})\-\index{range-plus}, \\ 
{\rm{type-delay-slope}}\,({\rm{delay-slope-hl}}\,({\it{delay\/}})\index{delay-slope-hl}, {\it{type\/}})\index{type-delay-slope}, \\ 
{\rm{range-plus}}\,(\=\+{\rm{delay-intercept-hl}}\,({\it{delay\/}})\index{delay-intercept-hl}, \\ 
{\rm{addable-input-delay}}\,(\=\+{\it{input-delay-list\/}}, \\ 
{\it{approxp\/}})\-\index{addable-input-delay}, \\ 
{\bf{nil}})\-\index{range-plus}, \\ 
{\rm{range-dependencies}}\,({\rm{addable-input-delay}}\,(\=\+{\it{input-delay-list\/}}, \\ 
{\it{approxp\/}})\-\index{addable-input-delay})\index{range-dependencies})\-\index{make-delay} \\ 
{\bf else }{\rm{make-delay}}\,(\=\+{\rm{type-delay-slope}}\,({\rm{delay-slope-lh}}\,({\it{delay\/}})\index{delay-slope-lh}, {\it{type\/}})\index{type-delay-slope}, \\ 
{\rm{delay-intercept-lh}}\,({\it{delay\/}})\index{delay-intercept-lh}, \\ 
{\rm{type-delay-slope}}\,({\rm{delay-slope-hl}}\,({\it{delay\/}})\index{delay-slope-hl}, {\it{type\/}})\index{type-delay-slope}, \\ 
{\rm{delay-intercept-hl}}\,({\it{delay\/}})\index{delay-intercept-hl}, \\ 
{\it{input-delay-list\/}})\-\index{make-delay}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable make-output-delay; name this event `make-output-delay-off'.\index{make-output-delay-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{or-delay-args} \\  
\=\+{\rm{or-delay-args}}\,({\it{a\/}}, {\it{listp\/}}, {\it{type\/}}, {\it{delays\/}}, {\it{used-names\/}}, {\it{inputs\/}}, {\it{outputs\/}}, {\it{approxp\/}})\index{or-delay-args} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{listp\/}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\it{a\/}}) \\ 
{\bf then }\=\+{\rm{or-delay-args}}\,(\=\+{\rm{car}}\,({\it{a\/}}), \\ 
{\bf{f}}, \\ 
{\it{type\/}}, \\ 
{\it{delays\/}}, \\ 
{\it{used-names\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{approxp\/}})\-\index{or-delay-args} \\ 
$\cup$$\;\;\;\;${\rm{or-delay-args}}\,(\=\+{\rm{cdr}}\,({\it{a\/}}), \\ 
{\bf{t}}, \\ 
{\it{type\/}}, \\ 
{\it{delays\/}}, \\ 
{\it{used-names\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{approxp\/}})\-\index{or-delay-args}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{signal-namep}}\,({\it{a\/}})\index{signal-namep} \\ 
{\bf then }\=\+{\bf if }{\it{a\/}} $\in$ {\it{inputs\/}}$\;\;${\bf then }{\rm{list}}\,({\it{a\/}}) \\ 
{\bf elseif }\=\+($\neg$ (({\it{a\/}} $\in$ {\it{outputs\/}}) $\vee$ ({\it{a\/}} $\in$ {\it{used-names\/}}))) \\ 
$\wedge$$\;\;\;\;${\rm{boundp}}\,({\it{a\/}}, {\it{delays\/}})\index{boundp}\- \\ 
{\bf then }{\rm{or-delay-args}}\,(\=\+{\rm{value}}\,({\it{a\/}}, {\it{delays\/}})\index{value}, \\ 
{\bf{f}}, \\ 
{\it{type\/}}, \\ 
{\it{delays\/}}, \\ 
{\rm{cons}}\,({\it{a\/}}, {\it{used-names\/}}), \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{approxp\/}})\-\index{or-delay-args} \\ 
{\bf else }{\rm{list}}\,({\sc{unknown}}\index{unknown})$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{a\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{list}}\,({\sc{unknown}}\index{unknown}) \\ 
{\bf elseif }{\rm{car}}\,({\it{a\/}}) $=$ {\tt{'}}{\tt{or}} \\ 
{\bf then }{\rm{or-delay-args}}\,(\=\+{\rm{cdr}}\,({\it{a\/}}), \\ 
{\bf{t}}, \\ 
{\it{type\/}}, \\ 
{\it{delays\/}}, \\ 
{\it{used-names\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{approxp\/}})\-\index{or-delay-args} \\ 
{\bf else }{\rm{list}}\,({\rm{make-output-delay}}\,(\=\+{\it{a\/}}, \\ 
{\it{type\/}}, \\ 
{\rm{input-delay}}\,(\=\+{\rm{delay-dependencies}}\,({\it{a\/}})\index{delay-dependencies}, \\ 
{\it{delays\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\bf{f}}, \\ 
{\bf{t}}, \\ 
{\it{used-names\/}}, \\ 
{\it{approxp\/}})\-\index{input-delay}, \\ 
{\it{approxp\/}})\-\index{make-output-delay})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable or-delay-args; name this event `or-delay-args-off'.\index{or-delay-args-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{output-delay} \\  
\=\+{\rm{output-delay}}\,({\it{name\/}}, {\it{type\/}}, {\it{delays\/}}, {\it{inputs\/}}, {\it{outputs\/}}, {\it{approxp\/}})\index{output-delay} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{signal-namep}}\,({\rm{value-or-unknown}}\,({\it{name\/}}, {\it{delays\/}})\index{value-or-unknown})\index{signal-namep} \\ 
{\bf then }{\rm{parent-synonym}}\,({\rm{value-or-unknown}}\,({\it{name\/}}, {\it{delays\/}})\index{value-or-unknown}, {\it{delays\/}})\index{parent-synonym} \\ 
{\bf elseif }{\rm{value-or-unknown}}\,({\it{name\/}}, {\it{delays\/}})\index{value-or-unknown} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\sc{unknown}}\index{unknown} \\ 
{\bf elseif }{\rm{car}}\,({\rm{value-or-unknown}}\,({\it{name\/}}, {\it{delays\/}})\index{value-or-unknown}) $=$ {\tt{'}}{\tt{or}} \\ 
{\bf then }{\rm{make-delay-or}}\,({\rm{or-delay-args}}\,(\=\+{\rm{cdr}}\,({\rm{value-or-unknown}}\,({\it{name\/}}, {\it{delays\/}})\index{value-or-unknown}), \\ 
{\bf{t}}, \\ 
{\it{type\/}}, \\ 
{\it{delays\/}}, \\ 
{\rm{list}}\,({\it{name\/}}), \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{approxp\/}})\-\index{or-delay-args})\index{make-delay-or} \\ 
{\bf else }{\rm{make-output-delay}}\,(\=\+{\rm{value-or-unknown}}\,({\it{name\/}}, {\it{delays\/}})\index{value-or-unknown}, \\ 
{\it{type\/}}, \\ 
{\rm{input-delay}}\,(\=\+{\rm{delay-dependencies}}\,({\rm{value-or-unknown}}\,(\=\+{\it{name\/}}, \\ 
{\it{delays\/}})\-\index{value-or-unknown})\index{delay-dependencies}, \\ 
{\it{delays\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\bf{f}}, \\ 
{\bf{t}}, \\ 
{\rm{list}}\,({\it{name\/}}), \\ 
{\it{approxp\/}})\-\index{input-delay}, \\ 
{\it{approxp\/}})\-\index{make-output-delay}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable output-delay; name this event `output-delay-off'.\index{output-delay-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-delays-0} \\  
\=\+{\rm{collect-delays-0}}\,({\it{names\/}}, {\it{types\/}}, {\it{delays\/}}, {\it{inputs\/}}, {\it{outputs\/}}, {\it{approxp\/}})\index{collect-delays-0} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{names\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{output-delay}}\,(\=\+{\rm{car}}\,({\it{names\/}}), \\ 
{\rm{car}}\,({\it{types\/}}), \\ 
{\it{delays\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{approxp\/}})\-\index{output-delay}, \\ 
{\rm{collect-delays-0}}\,(\=\+{\rm{cdr}}\,({\it{names\/}}), \\ 
{\rm{cdr}}\,({\it{types\/}}), \\ 
{\it{delays\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{approxp\/}})\-\index{collect-delays-0})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-delays-0; name this event `collect-delays-0-off'.\index{collect-delays-0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-delays} \\  
\=\+{\rm{collect-delays}}\,({\it{outputs\/}}, {\it{output-types\/}}, {\it{delays\/}}, {\it{inputs\/}}, {\it{approxp\/}})\index{collect-delays} \\ 
$=$$\;\;\;\;${\rm{collect-delays-0}}\,(\=\+{\it{outputs\/}}, \\ 
{\it{output-types\/}}, \\ 
{\rm{externalize-parents}}\,({\it{outputs\/}}, {\it{delays\/}}, {\it{inputs\/}}, {\it{outputs\/}})\index{externalize-parents}, \\ 
{\it{inputs\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{approxp\/}})\-\index{collect-delays-0}\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-delays; name this event `collect-delays-off'.\index{collect-delays-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{delays-error} \\  
{\rm{delays-error}}\,({\it{delays\/}})\index{delays-error} $=$ {\rm{err-and}}\,({\it{delays\/}}, {\tt{'}}{\tt{bad-delays}})\index{err-and}
\end{tabbing}


\noindent{\sc Event}:   Enable delays-error; name this event `delays-error-off'.\index{delays-error-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{initial-occ-out-depends} \\  
\=\+{\rm{initial-occ-out-depends}}\,({\it{m-ins\/}}, {\it{m-outs\/}})\index{initial-occ-out-depends} \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\it{m-outs\/}}, {\rm{pairlist}}\,({\it{m-ins\/}}, {\rm{listify}}\,({\it{m-ins\/}})\index{listify}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable initial-occ-out-depends; name this event `initial-occ-out-depends-off'.\index{initial-occ-out-depends-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{add-out-depends} \\  
\=\+{\rm{add-out-depends}}\,({\it{outputs\/}}, {\it{out-depends\/}}, {\it{arg-map\/}}, {\it{deps-map\/}})\index{add-out-depends} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{outputs\/}}) \\ 
{\bf then }{\rm{add-out-depends}}\,(\=\+{\rm{cdr}}\,({\it{outputs\/}}), \\ 
{\rm{cdr}}\,({\it{out-depends\/}}), \\ 
{\it{arg-map\/}}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{car}}\,({\it{outputs\/}}), \\ 
{\rm{union-values}}\,(\=\+{\rm{collect-value}}\,(\=\+{\rm{car}}\,({\it{out-depends\/}}), \\ 
{\it{arg-map\/}})\-\index{collect-value}, \\ 
{\it{deps-map\/}})\-\index{union-values})\-, \\ 
{\rm{cons}}\,(\=\+{\rm{all-bound-or-err}}\,(\=\+{\rm{collect-value}}\,(\=\+{\rm{car}}\,({\it{out-depends\/}}), \\ 
{\it{arg-map\/}})\-\index{collect-value}, \\ 
{\it{deps-map\/}}, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{output}}, \\ 
{\rm{car}}\,({\it{outputs\/}}))\-)\-\index{all-bound-or-err}, \\ 
{\it{deps-map\/}})\-)\-)\-\index{add-out-depends} \\ 
{\bf else }{\it{deps-map\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable add-out-depends; name this event `add-out-depends-off'.\index{add-out-depends-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{update-out-depends} \\  
\=\+{\rm{update-out-depends}}\,({\it{out-depends\/}}, {\it{o-outs\/}}, {\it{o-fn-props\/}}, {\it{o-ins\/}}, {\it{arg-map\/}})\index{update-out-depends} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\it{o-ins\/}} $\cup$ {\rm{car}}\,({\it{out-depends\/}}), \\ 
{\rm{add-out-depends}}\,(\=\+{\it{o-outs\/}}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{out-depends}}, {\it{o-fn-props\/}})\index{value}, \\ 
{\it{arg-map\/}}, \\ 
{\rm{cdr}}\,({\it{out-depends\/}}))\-\index{add-out-depends})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable update-out-depends; name this event `update-out-depends-off'.\index{update-out-depends-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-out-depends} \\  
\=\+{\rm{collect-out-depends}}\,({\it{outputs\/}}, {\it{dependencies\/}})\index{collect-out-depends} \\ 
$=$$\;\;\;\;${\rm{collect-value}}\,({\it{outputs\/}}, {\rm{cdr}}\,({\it{dependencies\/}}))\index{collect-value}\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-out-depends; name this event `collect-out-depends-off'.\index{collect-out-depends-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-out-depends-errors} \\  
\=\+{\rm{collect-out-depends-errors}}\,({\it{deps-map\/}}, {\it{used-signals\/}})\index{collect-out-depends-errors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{deps-map\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{net-errorp}}\,({\rm{car}}\,({\it{deps-map\/}}))\index{net-errorp} \\ 
{\bf then }\=\+{\bf if }{\rm{cadr}}\,({\rm{error-label}}\,({\rm{car}}\,({\it{deps-map\/}}))\index{error-label}) $\in$ {\it{used-signals\/}} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{car}}\,({\it{deps-map\/}}), \\ 
{\rm{collect-out-depends-errors}}\,(\=\+{\rm{cdr}}\,({\it{deps-map\/}}), \\ 
{\it{used-signals\/}})\-\index{collect-out-depends-errors})\- \\ 
{\bf else }{\rm{collect-out-depends-errors}}\,(\=\+{\rm{cdr}}\,({\it{deps-map\/}}), \\ 
{\it{used-signals\/}})\-\index{collect-out-depends-errors}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{collect-out-depends-errors}}\,({\rm{cdr}}\,({\it{deps-map\/}}), {\it{used-signals\/}})\index{collect-out-depends-errors}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-out-depends-errors; name this event `collect-out-depends-errors-off'.\index{collect-out-depends-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{out-depends-error} \\  
\=\+{\rm{out-depends-error}}\,({\it{dependencies\/}})\index{out-depends-error} \\ 
$=$$\;\;\;\;${\rm{nlistp-or-err}}\,(\=\+{\rm{collect-out-depends-errors}}\,(\=\+{\rm{cdr}}\,({\it{dependencies\/}}), \\ 
{\rm{car}}\,({\it{dependencies\/}}))\-\index{collect-out-depends-errors}, \\ 
{\tt{'}}{\tt{unbound-output-dependencies}})\-\index{nlistp-or-err}\-
\end{tabbing}


\noindent{\sc Event}:   Enable out-depends-error; name this event `out-depends-error-off'.\index{out-depends-error-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{initial-occ-state-types}$\;\;$
{\sc{initial-occ-state-types}}\index{initial-occ-state-types} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{update-state-types} \\  
\=\+{\rm{update-state-types}}\,({\it{state-types\/}}, {\it{o-name\/}}, {\it{o-fn-props\/}})\index{update-state-types} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{boundp}}\,({\tt{'}}{\tt{state-types}}, {\it{o-fn-props\/}})\index{boundp} \\ 
{\bf then }{\rm{cons}}\,({\rm{cons}}\,({\it{o-name\/}}, {\rm{value}}\,({\tt{'}}{\tt{state-types}}, {\it{o-fn-props\/}})\index{value}), {\it{state-types\/}}) \\ 
{\bf else }{\it{state-types\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable update-state-types; name this event `update-state-types-off'.\index{update-state-types-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-state-types} \\  
\=\+{\rm{collect-state-types}}\,({\it{states\/}}, {\it{state-types\/}})\index{collect-state-types} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{states\/}}) $\vee$ ({\it{states\/}} $=$ {\bf{nil}}) \\ 
{\bf then }{\rm{collect-value-or-unknown}}\,({\it{states\/}}, {\it{state-types\/}})\index{collect-value-or-unknown} \\ 
{\bf else }{\rm{value-or-unknown}}\,({\it{states\/}}, {\it{state-types\/}})\index{value-or-unknown}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-state-types; name this event `collect-state-types-off'.\index{collect-state-types-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{state-types-error} \\  
\=\+{\rm{state-types-error}}\,({\it{state-types\/}}, {\it{states\/}})\index{state-types-error} \\ 
$=$$\;\;\;\;${\rm{t-or-err}}\,(\=\+{\rm{set-equal}}\,({\rm{strip-cars}}\,({\it{state-types\/}}), {\rm{m-states-list}}\,({\it{states\/}})\index{m-states-list})\index{set-equal}, \\ 
{\tt{'}}{\tt{bad-state-types}}, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,({\tt{'}}{\tt{module-states}}, {\it{states\/}}), \\ 
{\rm{list}}\,({\tt{'}}{\tt{computed-states}}, {\rm{strip-cars}}\,({\it{state-types\/}})))\-)\-\index{t-or-err}\-
\end{tabbing}


\noindent{\sc Event}:   Enable state-types-error; name this event `state-types-error-off'.\index{state-types-error-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{initial-occ-tri-state-data} \\  
\=\+{\rm{initial-occ-tri-state-data}}\,({\it{m-outs\/}})\index{initial-occ-tri-state-data} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{cons}}\,({\tt{'}}{\tt{free-signals}}, {\it{m-outs\/}}), \\ 
{\tt{'}}{\tt{(}}{\tt{(}}{\tt{t-wire-ins}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{synonyms}}{\tt{)}}{\tt{)}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable initial-occ-tri-state-data; name this event `initial-occ-tri-state-data-off'.\index{initial-occ-tri-state-data-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{function-t-wire-ins} \\  
\=\+{\rm{function-t-wire-ins}}\,({\it{fn\/}}, {\it{data\/}})\index{function-t-wire-ins} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{boundp}}\,({\tt{'}}{\tt{tri-state-data}}, {\it{data\/}})\index{boundp} \\ 
{\bf then }{\rm{value}}\,({\tt{'}}{\tt{t-wire-ins}}, {\rm{value}}\,({\tt{'}}{\tt{tri-state-data}}, {\it{data\/}})\index{value})\index{value} \\ 
{\bf elseif }{\it{fn\/}} $=$ {\tt{'}}{\tt{t-wire}}$\;\;${\bf then }{\rm{value}}\,({\tt{'}}{\tt{inputs}}, {\it{data\/}})\index{value} \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable function-t-wire-ins; name this event `function-t-wire-ins-off'.\index{function-t-wire-ins-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{function-synonyms} \\  
\=\+{\rm{function-synonyms}}\,({\it{fn\/}}, {\it{data\/}})\index{function-synonyms} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{boundp}}\,({\tt{'}}{\tt{tri-state-data}}, {\it{data\/}})\index{boundp} \\ 
{\bf then }{\rm{value}}\,({\tt{'}}{\tt{synonyms}}, {\rm{value}}\,({\tt{'}}{\tt{tri-state-data}}, {\it{data\/}})\index{value})\index{value} \\ 
{\bf elseif }{\it{fn\/}} $=$ {\tt{'}}{\tt{id}} \\ 
{\bf then }{\rm{pairlist}}\,({\rm{value}}\,({\tt{'}}{\tt{outputs}}, {\it{data\/}})\index{value}, {\rm{value}}\,({\tt{'}}{\tt{inputs}}, {\it{data\/}})\index{value}) \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable function-synonyms; name this event `function-synonyms-off'.\index{function-synonyms-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{add-synonyms} \\  
\=\+{\rm{add-synonyms}}\,({\it{f-synonyms\/}}, {\it{in-map\/}}, {\it{out-map\/}}, {\it{slist\/}})\index{add-synonyms} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{f-synonyms\/}}) \\ 
{\bf then }{\rm{add-synonyms}}\,(\=\+{\rm{cdr}}\,({\it{f-synonyms\/}}), \\ 
{\it{in-map\/}}, \\ 
{\it{out-map\/}}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{value}}\,({\rm{caar}}\,({\it{f-synonyms\/}}), {\it{out-map\/}})\index{value}, \\ 
{\rm{value2}}\,({\rm{cdar}}\,({\it{f-synonyms\/}}), {\it{in-map\/}}, {\it{out-map\/}})\index{value2})\-, \\ 
{\it{slist\/}})\-)\-\index{add-synonyms} \\ 
{\bf else }{\it{slist\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable add-synonyms; name this event `add-synonyms-off'.\index{add-synonyms-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{update-tri-state-data} \\  
\=\+{\rm{update-tri-state-data}}\,({\it{data\/}}, {\it{o-ins\/}}, {\it{o-fn\/}}, {\it{o-fn-data\/}}, {\it{in-map\/}}, {\it{out-map\/}})\index{update-tri-state-data} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{free-signals}}, \\ 
\=\+\=\+{\bf if }{\rm{listp}}\,({\rm{collect-value2}}\,(\=\+{\rm{function-t-wire-ins}}\,({\it{o-fn\/}}, {\it{o-fn-data\/}})\index{function-t-wire-ins}, \\ 
{\it{in-map\/}}, \\ 
{\it{out-map\/}})\-\index{collect-value2}) \\ 
{\bf then }{\rm{set-diff}}\,(\=\+{\it{o-ins\/}}, \\ 
{\rm{collect-value2}}\,(\=\+{\rm{function-t-wire-ins}}\,(\=\+{\it{o-fn\/}}, \\ 
{\it{o-fn-data\/}})\-\index{function-t-wire-ins}, \\ 
{\it{in-map\/}}, \\ 
{\it{out-map\/}})\-\index{collect-value2})\-\index{set-diff} \\ 
{\bf elseif }{\it{o-fn\/}} $=$ {\tt{'}}{\tt{id}}$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\it{o-ins\/}}$\;${\bf  endif}\- \\ 
$\cup$$\;\;\;\;${\rm{value}}\,({\tt{'}}{\tt{free-signals}}, {\it{data\/}})\index{value}\-)\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{t-wire-ins}}, \\ 
{\rm{append}}\,(\=\+{\rm{collect-value2}}\,(\=\+{\rm{function-t-wire-ins}}\,({\it{o-fn\/}}, {\it{o-fn-data\/}})\index{function-t-wire-ins}, \\ 
{\it{in-map\/}}, \\ 
{\it{out-map\/}})\-\index{collect-value2}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{t-wire-ins}}, {\it{data\/}})\index{value})\-)\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{synonyms}}, \\ 
{\rm{add-synonyms}}\,(\=\+{\rm{function-synonyms}}\,({\it{o-fn\/}}, {\it{o-fn-data\/}})\index{function-synonyms}, \\ 
{\it{in-map\/}}, \\ 
{\it{out-map\/}}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{synonyms}}, {\it{data\/}})\index{value})\-\index{add-synonyms})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable update-tri-state-data; name this event `update-tri-state-data-off'.\index{update-tri-state-data-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{io-signal-renames} \\  
\=\+{\rm{io-signal-renames}}\,({\it{synonyms\/}}, {\it{io-signals\/}}, {\it{slist\/}})\index{io-signal-renames} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{synonyms\/}}) \\ 
{\bf then }\=\+{\bf if }\=\+(\=\+{\rm{io-outp}}\,({\rm{caar}}\,({\it{synonyms\/}}))\index{io-outp} \\ 
$\vee$$\;\;\;\;${\rm{io-outp}}\,({\rm{parent-synonym}}\,({\rm{cdar}}\,({\it{synonyms\/}}), {\it{slist\/}})\index{parent-synonym})\index{io-outp} \\ 
$\vee$$\;\;\;\;$({\rm{parent-synonym}}\,({\rm{cdar}}\,({\it{synonyms\/}}), {\it{slist\/}})\index{parent-synonym} $\in$ {\it{io-signals\/}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{caar}}\,({\it{synonyms\/}}) \\ 
$\not=$$\;\;\;\;${\rm{parent-synonym}}\,({\rm{cdar}}\,({\it{synonyms\/}}), {\it{slist\/}})\index{parent-synonym})\-\- \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{caar}}\,({\it{synonyms\/}}), \\ 
{\rm{parent-synonym}}\,({\rm{cdar}}\,({\it{synonyms\/}}), {\it{slist\/}})\index{parent-synonym})\-, \\ 
{\rm{io-signal-renames}}\,({\rm{cdr}}\,({\it{synonyms\/}}), {\it{io-signals\/}}, {\it{slist\/}})\index{io-signal-renames})\- \\ 
{\bf else }{\rm{io-signal-renames}}\,({\rm{cdr}}\,({\it{synonyms\/}}), {\it{io-signals\/}}, {\it{slist\/}})\index{io-signal-renames}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable io-signal-renames; name this event `io-signal-renames-off'.\index{io-signal-renames-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{io-rename-error} \\  
\=\+{\rm{io-rename-error}}\,({\it{synonyms\/}}, {\it{io-signals\/}})\index{io-rename-error} \\ 
$=$$\;\;\;\;${\rm{nlistp-or-err}}\,(\=\+{\rm{io-signal-renames}}\,({\it{synonyms\/}}, {\it{io-signals\/}}, {\it{synonyms\/}})\index{io-signal-renames}, \\ 
{\tt{'}}{\tt{renamed-io-signals}})\-\index{nlistp-or-err}\-
\end{tabbing}


\noindent{\sc Event}:   Enable io-rename-error; name this event `io-rename-error-off'.\index{io-rename-error-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{t-wire-error} \\  
\=\+{\rm{t-wire-error}}\,({\it{free-signals\/}}, {\it{t-wire-ins\/}})\index{t-wire-error} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+{\rm{list}}\,(\=\+{\rm{disjoint-or-err}}\,(\=\+{\rm{remove-duplicates}}\,({\it{t-wire-ins\/}})\index{remove-duplicates}, \\ 
{\it{free-signals\/}}, \\ 
{\tt{'}}{\tt{t-wire-ins-used-elsewhere}})\-\index{disjoint-or-err}, \\ 
{\rm{no-duplicates-or-err}}\,(\=\+{\it{t-wire-ins\/}}, \\ 
{\tt{'}}{\tt{duplicate-t-wire-inputs}})\-\index{no-duplicates-or-err})\-, \\ 
{\tt{'}}{\tt{t-wire-errors}})\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable t-wire-error; name this event `t-wire-error-off'.\index{t-wire-error-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{compose-tri-state-data} \\  
\=\+{\rm{compose-tri-state-data}}\,({\it{data\/}}, {\it{io-signals\/}})\index{compose-tri-state-data} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{free-signals}}, \\ 
{\rm{parent-synonyms-list}}\,(\=\+{\rm{value}}\,({\tt{'}}{\tt{free-signals}}, {\it{data\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{synonyms}}, {\it{data\/}})\index{value})\-\index{parent-synonyms-list})\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{t-wire-ins}}, \\ 
{\rm{parent-synonyms-list}}\,(\=\+{\rm{value}}\,({\tt{'}}{\tt{t-wire-ins}}, {\it{data\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{synonyms}}, {\it{data\/}})\index{value})\-\index{parent-synonyms-list})\-, \\ 
{\rm{cons}}\,({\tt{'}}{\tt{synonyms}}, {\rm{value}}\,({\tt{'}}{\tt{synonyms}}, {\it{data\/}})\index{value}), \\ 
{\rm{io-rename-error}}\,({\rm{value}}\,({\tt{'}}{\tt{synonyms}}, {\it{data\/}})\index{value}, {\it{io-signals\/}})\index{io-rename-error}, \\ 
{\rm{t-wire-error}}\,(\=\+{\rm{parent-synonyms-list}}\,(\=\+{\rm{value}}\,({\tt{'}}{\tt{free-signals}}, {\it{data\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{synonyms}}, {\it{data\/}})\index{value})\-\index{parent-synonyms-list}, \\ 
{\rm{parent-synonyms-list}}\,(\=\+{\rm{value}}\,({\tt{'}}{\tt{t-wire-ins}}, {\it{data\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{synonyms}}, {\it{data\/}})\index{value})\-\index{parent-synonyms-list})\-\index{t-wire-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable compose-tri-state-data; name this event `compose-tri-state-data-off'.\index{compose-tri-state-data-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-synonyms} \\  
\=\+{\rm{collect-synonyms}}\,({\it{m-outs\/}}, {\it{synonyms\/}})\index{collect-synonyms} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{m-outs\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{m-outs\/}}) $=$ {\rm{parent-synonym}}\,({\rm{car}}\,({\it{m-outs\/}}), {\it{synonyms\/}})\index{parent-synonym} \\ 
{\bf then }{\rm{collect-synonyms}}\,({\rm{cdr}}\,({\it{m-outs\/}}), {\it{synonyms\/}})\index{collect-synonyms} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{car}}\,({\it{m-outs\/}}), \\ 
{\rm{parent-synonym}}\,({\rm{car}}\,({\it{m-outs\/}}), {\it{synonyms\/}})\index{parent-synonym})\-, \\ 
{\rm{collect-synonyms}}\,({\rm{cdr}}\,({\it{m-outs\/}}), {\it{synonyms\/}})\index{collect-synonyms})\-$\;${\bf  endif}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-synonyms; name this event `collect-synonyms-off'.\index{collect-synonyms-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-tri-state-data} \\  
\=\+{\rm{collect-tri-state-data}}\,({\it{m-ins\/}}, {\it{m-outs\/}}, {\it{data\/}})\index{collect-tri-state-data} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{t-wire-ins}}, \\ 
{\rm{intersection}}\,({\it{m-ins\/}}, {\rm{value}}\,({\tt{'}}{\tt{t-wire-ins}}, {\it{data\/}})\index{value})\index{intersection})\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{synonyms}}, \\ 
{\rm{collect-synonyms}}\,(\=\+{\it{m-outs\/}}, \\ 
{\rm{externalize-parents}}\,(\=\+{\it{m-outs\/}}, \\ 
{\rm{value}}\,(\=\+{\tt{'}}{\tt{synonyms}}, \\ 
{\it{data\/}})\-\index{value}, \\ 
{\it{m-ins\/}}, \\ 
{\it{m-outs\/}})\-\index{externalize-parents})\-\index{collect-synonyms})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-tri-state-data; name this event `collect-tri-state-data-off'.\index{collect-tri-state-data-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tri-state-errors} \\  
\=\+{\rm{tri-state-errors}}\,({\it{data\/}})\index{tri-state-errors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\rm{net-errorp}}\,({\rm{error-entry}}\,({\it{data\/}}, {\tt{'}}{\tt{renamed-io-signals}})\index{error-entry})\index{net-errorp} \\ 
$\wedge$$\;\;\;\;${\rm{net-errorp}}\,({\rm{error-entry}}\,({\it{data\/}}, {\tt{'}}{\tt{t-wire-errors}})\index{error-entry})\index{net-errorp}\- \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{error-entry}}\,({\it{data\/}}, {\tt{'}}{\tt{renamed-io-signals}})\index{error-entry}, \\ 
{\rm{error-entry}}\,({\it{data\/}}, {\tt{'}}{\tt{t-wire-errors}})\index{error-entry})\- \\ 
{\bf elseif }{\rm{net-errorp}}\,({\rm{error-entry}}\,({\it{data\/}}, {\tt{'}}{\tt{renamed-io-signals}})\index{error-entry})\index{net-errorp} \\ 
{\bf then }{\rm{error-entry}}\,({\it{data\/}}, {\tt{'}}{\tt{renamed-io-signals}})\index{error-entry} \\ 
{\bf elseif }{\rm{net-errorp}}\,({\rm{error-entry}}\,({\it{data\/}}, {\tt{'}}{\tt{t-wire-errors}})\index{error-entry})\index{net-errorp} \\ 
{\bf then }{\rm{error-entry}}\,({\it{data\/}}, {\tt{'}}{\tt{t-wire-errors}})\index{error-entry} \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tri-state-errors; name this event `tri-state-errors-off'.\index{tri-state-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{initial-occ-data} \\  
\=\+{\rm{initial-occ-data}}\,({\it{props\/}}, {\it{m-ins\/}}, {\it{m-outs\/}})\index{initial-occ-data} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{props\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,(\=\+{\bf case on }{\rm{car}}\,({\it{props\/}}): \\ 
{\bf case = }{\it{delays\/}} \\ 
{\bf then }{\rm{cons}}\,({\tt{'}}{\tt{delays}}, {\sc{initial-occ-delays}}\index{initial-occ-delays}) \\ 
{\bf case = }{\it{drives\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,({\tt{'}}{\tt{drives}}, {\sc{initial-occ-drives}}\index{initial-occ-drives}) \\ 
{\bf case = }{\it{input-types\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,({\tt{'}}{\tt{input-types}}, {\sc{initial-occ-in-types}}\index{initial-occ-in-types}) \\ 
{\bf case = }{\it{loadings\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,({\tt{'}}{\tt{loadings}}, {\sc{initial-occ-loadings}}\index{initial-occ-loadings}) \\ 
{\bf case = }{\it{out-depends\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,(\=\+{\tt{'}}{\tt{out-depends}}, \\ 
{\rm{initial-occ-out-depends}}\,({\it{m-ins\/}}, {\it{m-outs\/}})\index{initial-occ-out-depends})\- \\ 
{\bf case = }{\it{output-types\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,({\tt{'}}{\tt{output-types}}, {\sc{initial-occ-out-types}}\index{initial-occ-out-types}) \\ 
{\bf case = }{\it{state-types\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,({\tt{'}}{\tt{state-types}}, {\sc{initial-occ-state-types}}\index{initial-occ-state-types}) \\ 
{\bf case = }{\it{tri-state-data\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,(\=\+{\tt{'}}{\tt{tri-state-data}}, \\ 
{\rm{initial-occ-tri-state-data}}\,({\it{m-outs\/}})\index{initial-occ-tri-state-data})\- \\ 
{\bf otherwise }\=\+{\bf if }\=\+{\rm{car}}\,({\it{props\/}}) \\ 
$\in$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{gates}}{\tt{ }}{\tt{pads}}{\tt{ }}{\tt{primitives}} \\ 
{\tt{transistors}}{\tt{)}}\-\- \\ 
{\bf then }{\rm{cons}}\,({\rm{car}}\,({\it{props\/}}), {\tt{0}}) \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-$\;${\bf  endcase}\-) \\ 
{\bf then }{\rm{cons}}\,(\=\+\=\+{\bf case on }{\rm{car}}\,({\it{props\/}}): \\ 
{\bf case = }{\it{delays\/}} \\ 
{\bf then }{\rm{cons}}\,({\tt{'}}{\tt{delays}}, {\sc{initial-occ-delays}}\index{initial-occ-delays}) \\ 
{\bf case = }{\it{drives\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,({\tt{'}}{\tt{drives}}, {\sc{initial-occ-drives}}\index{initial-occ-drives}) \\ 
{\bf case = }{\it{input-types\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,({\tt{'}}{\tt{input-types}}, {\sc{initial-occ-in-types}}\index{initial-occ-in-types}) \\ 
{\bf case = }{\it{loadings\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,({\tt{'}}{\tt{loadings}}, {\sc{initial-occ-loadings}}\index{initial-occ-loadings}) \\ 
{\bf case = }{\it{out-depends\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,(\=\+{\tt{'}}{\tt{out-depends}}, \\ 
{\rm{initial-occ-out-depends}}\,({\it{m-ins\/}}, {\it{m-outs\/}})\index{initial-occ-out-depends})\- \\ 
{\bf case = }{\it{output-types\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,({\tt{'}}{\tt{output-types}}, {\sc{initial-occ-out-types}}\index{initial-occ-out-types}) \\ 
{\bf case = }{\it{state-types\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,({\tt{'}}{\tt{state-types}}, {\sc{initial-occ-state-types}}\index{initial-occ-state-types}) \\ 
{\bf case = }{\it{tri-state-data\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,(\=\+{\tt{'}}{\tt{tri-state-data}}, \\ 
{\rm{initial-occ-tri-state-data}}\,({\it{m-outs\/}})\index{initial-occ-tri-state-data})\- \\ 
{\bf otherwise }\=\+{\bf if }\=\+{\rm{car}}\,({\it{props\/}}) \\ 
$\in$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{gates}}{\tt{ }}{\tt{pads}}{\tt{ }}{\tt{primitives}} \\ 
{\tt{transistors}}{\tt{)}}\-\- \\ 
{\bf then }{\rm{cons}}\,({\rm{car}}\,({\it{props\/}}), {\tt{0}}) \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-$\;${\bf  endcase}\-, \\ 
{\rm{initial-occ-data}}\,({\rm{cdr}}\,({\it{props\/}}), {\it{m-ins\/}}, {\it{m-outs\/}})\index{initial-occ-data})\- \\ 
{\bf else }{\rm{initial-occ-data}}\,({\rm{cdr}}\,({\it{props\/}}), {\it{m-ins\/}}, {\it{m-outs\/}})\index{initial-occ-data}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable initial-occ-data; name this event `initial-occ-data-off'.\index{initial-occ-data-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{update-oprop-binding} \\  
\=\+{\rm{update-oprop-binding}}\,(\=\+{\it{o-name\/}}, \\ 
{\it{o-ins\/}}, \\ 
{\it{o-outs\/}}, \\ 
{\it{o-fn\/}}, \\ 
{\it{o-fn-props\/}}, \\ 
{\it{in-map\/}}, \\ 
{\it{out-map\/}}, \\ 
{\it{binding\/}})\-\index{update-oprop-binding} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{binding\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{car}}\,({\it{binding\/}}), \\ 
\=\+{\bf case on }{\rm{car}}\,({\it{binding\/}}): \\ 
{\bf case = }{\it{delays\/}} \\ 
{\bf then }{\rm{update-delays}}\,(\=\+{\rm{cdr}}\,({\it{binding\/}}), \\ 
{\it{o-outs\/}}, \\ 
{\it{o-fn-props\/}}, \\ 
{\it{in-map\/}}, \\ 
{\it{out-map\/}})\-\index{update-delays} \\ 
{\bf case = }{\it{drives\/}} \\ 
{\bf $\;\;$then }{\rm{update-drives}}\,(\=\+{\rm{cdr}}\,({\it{binding\/}}), \\ 
{\it{o-outs\/}}, \\ 
{\it{o-fn-props\/}}, \\ 
{\it{in-map\/}}, \\ 
{\it{out-map\/}})\-\index{update-drives} \\ 
{\bf case = }{\it{input-types\/}} \\ 
{\bf $\;\;$then }{\rm{update-in-types}}\,({\rm{cdr}}\,({\it{binding\/}}), {\it{o-ins\/}}, {\it{o-fn-props\/}})\index{update-in-types} \\ 
{\bf case = }{\it{loadings\/}} \\ 
{\bf $\;\;$then }{\rm{update-loadings}}\,({\rm{cdr}}\,({\it{binding\/}}), {\it{o-ins\/}}, {\it{o-fn-props\/}})\index{update-loadings} \\ 
{\bf case = }{\it{out-depends\/}} \\ 
{\bf $\;\;$then }{\rm{update-out-depends}}\,(\=\+{\rm{cdr}}\,({\it{binding\/}}), \\ 
{\it{o-outs\/}}, \\ 
{\it{o-fn-props\/}}, \\ 
{\it{o-ins\/}}, \\ 
{\it{in-map\/}})\-\index{update-out-depends} \\ 
{\bf case = }{\it{output-types\/}} \\ 
{\bf $\;\;$then }{\rm{update-out-types}}\,(\=\+{\rm{cdr}}\,({\it{binding\/}}), \\ 
{\it{o-outs\/}}, \\ 
{\it{o-fn-props\/}}, \\ 
{\it{in-map\/}})\-\index{update-out-types} \\ 
{\bf case = }{\it{state-types\/}} \\ 
{\bf $\;\;$then }{\rm{update-state-types}}\,({\rm{cdr}}\,({\it{binding\/}}), {\it{o-name\/}}, {\it{o-fn-props\/}})\index{update-state-types} \\ 
{\bf case = }{\it{tri-state-data\/}} \\ 
{\bf $\;\;$then }{\rm{update-tri-state-data}}\,(\=\+{\rm{cdr}}\,({\it{binding\/}}), \\ 
{\it{o-ins\/}}, \\ 
{\it{o-fn\/}}, \\ 
{\it{o-fn-props\/}}, \\ 
{\it{in-map\/}}, \\ 
{\it{out-map\/}})\-\index{update-tri-state-data} \\ 
{\bf otherwise }\=\+{\bf if }\=\+{\rm{car}}\,({\it{binding\/}}) \\ 
$\in$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{gates}}{\tt{ }}{\tt{pads}}{\tt{ }}{\tt{primitives}} \\ 
{\tt{transistors}}{\tt{)}}\-\- \\ 
{\bf then }\=\+{\rm{value}}\,({\rm{car}}\,({\it{binding\/}}), {\it{o-fn-props\/}})\index{value} \\ 
$+$$\;\;\;\;${\rm{cdr}}\,({\it{binding\/}})\- \\ 
{\bf else }{\rm{cdr}}\,({\it{binding\/}})$\;${\bf  endif}\-$\;${\bf  endcase}\-)\- \\ 
{\bf else }{\it{binding\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable update-oprop-binding; name this event `update-oprop-binding-off'.\index{update-oprop-binding-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{update-occ-bindings} \\  
\=\+{\rm{update-occ-bindings}}\,(\=\+{\it{o-name\/}}, \\ 
{\it{o-ins\/}}, \\ 
{\it{o-outs\/}}, \\ 
{\it{o-fn\/}}, \\ 
{\it{o-fn-props\/}}, \\ 
{\it{in-map\/}}, \\ 
{\it{out-map\/}}, \\ 
{\it{bindings\/}})\-\index{update-occ-bindings} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{bindings\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{update-oprop-binding}}\,(\=\+{\it{o-name\/}}, \\ 
{\it{o-ins\/}}, \\ 
{\it{o-outs\/}}, \\ 
{\it{o-fn\/}}, \\ 
{\it{o-fn-props\/}}, \\ 
{\it{in-map\/}}, \\ 
{\it{out-map\/}}, \\ 
{\rm{car}}\,({\it{bindings\/}}))\-\index{update-oprop-binding}, \\ 
{\rm{update-occ-bindings}}\,(\=\+{\it{o-name\/}}, \\ 
{\it{o-ins\/}}, \\ 
{\it{o-outs\/}}, \\ 
{\it{o-fn\/}}, \\ 
{\it{o-fn-props\/}}, \\ 
{\it{in-map\/}}, \\ 
{\it{out-map\/}}, \\ 
{\rm{cdr}}\,({\it{bindings\/}}))\-\index{update-occ-bindings})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable update-occ-bindings; name this event `update-occ-bindings-off'.\index{update-occ-bindings-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{function-properties} \\  
\=\+{\rm{function-properties}}\,({\it{fn\/}}, {\it{database\/}})\index{function-properties} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{primp}}\,({\it{fn\/}})\index{primp}$\;\;${\bf then }{\rm{cdr}}\,({\rm{primp}}\,({\it{fn\/}})\index{primp}) \\ 
{\bf else }{\rm{value}}\,({\it{fn\/}}, {\it{database\/}})\index{value}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable function-properties; name this event `function-properties-off'.\index{function-properties-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-occurrence-data} \\  
\=\+{\rm{collect-occurrence-data}}\,({\it{body\/}}, {\it{bindings\/}}, {\it{io-outputs\/}}, {\it{io-signals\/}}, {\it{database\/}})\index{collect-occurrence-data} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{body\/}}) \\ 
{\bf then }{\rm{collect-occurrence-data}}\,(\=\+{\rm{cdr}}\,({\it{body\/}}), \\ 
{\rm{update-occ-bindings}}\,(\=\+{\rm{occ-name}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-name}, \\ 
{\rm{mark-io-outs}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-inputs}, \\ 
{\it{io-outputs\/}})\-\index{mark-io-outs}, \\ 
{\rm{mark-io-outs}}\,(\=\+{\rm{occ-outputs}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-outputs}, \\ 
{\it{io-signals\/}})\-\index{mark-io-outs}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-function}, \\ 
{\rm{function-properties}}\,(\=\+{\rm{occ-function}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-function}, \\ 
{\it{database\/}})\-\index{function-properties}, \\ 
{\rm{pairlist}}\,(\=\+{\rm{value}}\,(\=\+{\tt{'}}{\tt{inputs}}, \\ 
{\rm{function-properties}}\,(\=\+{\rm{occ-function}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-function}, \\ 
{\it{database\/}})\-\index{function-properties})\-\index{value}, \\ 
{\rm{mark-io-outs}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-inputs}, \\ 
{\it{io-outputs\/}})\-\index{mark-io-outs})\-, \\ 
{\rm{pairlist}}\,(\=\+{\rm{value}}\,(\=\+{\tt{'}}{\tt{outputs}}, \\ 
{\rm{function-properties}}\,(\=\+{\rm{occ-function}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-function}, \\ 
{\it{database\/}})\-\index{function-properties})\-\index{value}, \\ 
{\rm{mark-io-outs}}\,(\=\+{\rm{occ-outputs}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-outputs}, \\ 
{\it{io-signals\/}})\-\index{mark-io-outs})\-, \\ 
{\it{bindings\/}})\-\index{update-occ-bindings}, \\ 
{\rm{append}}\,(\=\+{\rm{intersection}}\,(\=\+{\it{io-signals\/}}, \\ 
{\rm{occ-outputs}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-outputs})\-\index{intersection}, \\ 
{\it{io-outputs\/}})\-, \\ 
{\it{io-signals\/}}, \\ 
{\it{database\/}})\-\index{collect-occurrence-data} \\ 
{\bf else }{\it{bindings\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-occurrence-data; name this event `collect-occurrence-data-off'.\index{collect-occurrence-data-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{composed-io-types} \\  
\=\+{\rm{composed-io-types}}\,({\it{in-types\/}}, {\it{out-types\/}}, {\it{tri-state-data\/}}, {\it{io-signals\/}})\index{composed-io-types} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{tri-state-data}}, \\ 
{\rm{compose-tri-state-data}}\,({\it{tri-state-data\/}}, {\it{io-signals\/}})\index{compose-tri-state-data})\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{input-types}}, \\ 
{\rm{car}}\,({\rm{compose-io-types}}\,(\=\+{\it{in-types\/}}, \\ 
{\it{out-types\/}}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{t-wire-ins}}, {\it{tri-state-data\/}})\index{value})\-\index{compose-io-types}))\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{output-types}}, \\ 
{\rm{cdr}}\,({\rm{compose-io-types}}\,(\=\+{\it{in-types\/}}, \\ 
{\it{out-types\/}}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{t-wire-ins}}, {\it{tri-state-data\/}})\index{value})\-\index{compose-io-types}))\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable composed-io-types; name this event `composed-io-types-off'.\index{composed-io-types-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{composed-loadings-drives-delays} \\  
\=\+{\rm{composed-loadings-drives-delays}}\,({\it{loadings\/}}, {\it{drives\/}}, {\it{delays\/}})\index{composed-loadings-drives-delays} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{delays}}, \\ 
{\rm{loaded-delays}}\,({\it{delays\/}}, {\rm{transfer-loadings}}\,({\it{loadings\/}}, {\it{drives\/}})\index{transfer-loadings})\index{loaded-delays})\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{drives}}, \\ 
{\rm{net-drives-simple}}\,({\it{drives\/}}, {\rm{transfer-loadings}}\,({\it{loadings\/}}, {\it{drives\/}})\index{transfer-loadings})\index{net-drives-simple})\-, \\ 
{\rm{cons}}\,({\tt{'}}{\tt{loadings}}, {\rm{transfer-loadings}}\,({\it{loadings\/}}, {\it{drives\/}})\index{transfer-loadings}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable composed-loadings-drives-delays; name this event `composed-loadings-drives-delays-off'.\index{composed-loadings-drives-delays!-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{add-composed-data} \\  
\=\+{\rm{add-composed-data}}\,({\it{prop-name\/}}, {\it{bindings\/}}, {\it{io-signals\/}}, {\it{result\/}})\index{add-composed-data} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{boundp}}\,({\it{prop-name\/}}, {\it{result\/}})\index{boundp} $\vee$ ($\neg$ {\rm{boundp}}\,({\it{prop-name\/}}, {\it{bindings\/}})\index{boundp}) \\ 
{\bf then }{\it{result\/}} \\ 
{\bf elseif }{\it{prop-name\/}} $\in$ {\tt{'}}{\tt{(}}\=\+{\tt{input-types}}{\tt{ }}{\tt{output-types}} \\ 
{\tt{tri-state-data}}{\tt{)}}\- \\ 
{\bf then }{\rm{append}}\,(\=\+{\rm{composed-io-types}}\,(\=\+{\rm{value}}\,({\tt{'}}{\tt{input-types}}, {\it{bindings\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{output-types}}, {\it{bindings\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{tri-state-data}}, {\it{bindings\/}})\index{value}, \\ 
{\it{io-signals\/}})\-\index{composed-io-types}, \\ 
{\it{result\/}})\- \\ 
{\bf elseif }{\it{prop-name\/}} $\in$ {\tt{'}}{\tt{(}}{\tt{loadings}}{\tt{ }}{\tt{drives}}{\tt{ }}{\tt{delays}}{\tt{)}} \\ 
{\bf then }{\rm{append}}\,(\=\+{\rm{composed-loadings-drives-delays}}\,(\=\+{\rm{value}}\,(\=\+{\tt{'}}{\tt{loadings}}, \\ 
{\it{bindings\/}})\-\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{drives}}, {\it{bindings\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{delays}}, {\it{bindings\/}})\index{value})\-\index{composed-loadings-drives-delays}, \\ 
{\it{result\/}})\- \\ 
{\bf else }{\rm{cons}}\,({\rm{alist-entry}}\,({\it{prop-name\/}}, {\it{bindings\/}})\index{alist-entry}, {\it{result\/}})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable add-composed-data; name this event `add-composed-data-off'.\index{add-composed-data-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{composed-occurrence-data} \\  
\=\+{\rm{composed-occurrence-data}}\,({\it{bindings\/}}, {\it{io-signals\/}}, {\it{result\/}})\index{composed-occurrence-data} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{bindings\/}}) \\ 
{\bf then }{\rm{composed-occurrence-data}}\,(\=\+{\rm{cdr}}\,({\it{bindings\/}}), \\ 
{\it{io-signals\/}}, \\ 
\=\+{\bf if }{\rm{car}}\,({\it{bindings\/}}) $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }{\rm{cons}}\,({\rm{car}}\,({\it{bindings\/}}), {\it{result\/}}) \\ 
{\bf else }{\rm{add-composed-data}}\,(\=\+{\rm{caar}}\,({\it{bindings\/}}), \\ 
{\it{bindings\/}}, \\ 
{\it{io-signals\/}}, \\ 
{\it{result\/}})\-\index{add-composed-data}$\;${\bf  endif}\-)\-\index{composed-occurrence-data} \\ 
{\bf else }{\it{result\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable composed-occurrence-data; name this event `composed-occurrence-data-off'.\index{composed-occurrence-data-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{compose-occurrence-data} \\  
\=\+{\rm{compose-occurrence-data}}\,({\it{bindings\/}}, {\it{io-signals\/}})\index{compose-occurrence-data} \\ 
$=$$\;\;\;\;${\rm{composed-occurrence-data}}\,({\it{bindings\/}}, {\it{io-signals\/}}, {\bf{nil}})\index{composed-occurrence-data}\-
\end{tabbing}


\noindent{\sc Event}:   Enable compose-occurrence-data; name this event `compose-occurrence-data-off'.\index{compose-occurrence-data-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{occurrence-data} \\  
\=\+{\rm{occurrence-data}}\,({\it{props\/}}, {\it{body\/}}, {\it{m-ins\/}}, {\it{m-outs\/}}, {\it{io-signals\/}}, {\it{database\/}})\index{occurrence-data} \\ 
$=$$\;\;\;\;${\rm{compose-occurrence-data}}\,(\=\+{\rm{collect-occurrence-data}}\,(\=\+{\it{body\/}}, \\ 
{\rm{initial-occ-data}}\,(\=\+{\it{props\/}}, \\ 
{\it{m-ins\/}}, \\ 
{\it{m-outs\/}})\-\index{initial-occ-data}, \\ 
{\bf{nil}}, \\ 
{\it{io-signals\/}}, \\ 
{\it{database\/}})\-\index{collect-occurrence-data}, \\ 
{\it{io-signals\/}})\-\index{compose-occurrence-data}\-
\end{tabbing}


\noindent{\sc Event}:   Enable occurrence-data; name this event `occurrence-data-off'.\index{occurrence-data-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-module-prop} \\  
\=\+{\rm{collect-module-prop}}\,(\=\+{\it{prop-name\/}}, \\ 
{\it{m-ins\/}}, \\ 
{\it{in-types\/}}, \\ 
{\it{m-outs\/}}, \\ 
{\it{out-types\/}}, \\ 
{\it{m-states\/}}, \\ 
{\it{obindings\/}}, \\ 
{\it{approximate-delays-p\/}})\-\index{collect-module-prop} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{prop-name\/}}: \\ 
{\bf case = }{\it{delays\/}} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\tt{'}}{\tt{delays}}, \\ 
{\rm{collect-delays}}\,(\=\+{\it{m-outs\/}}, \\ 
{\it{out-types\/}}, \\ 
{\rm{cdr}}\,({\rm{alist-entry}}\,({\it{prop-name\/}}, {\it{obindings\/}})\index{alist-entry}), \\ 
{\it{m-ins\/}}, \\ 
{\it{approximate-delays-p\/}})\-\index{collect-delays})\- \\ 
{\bf case = }{\it{drives\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,(\=\+{\tt{'}}{\tt{drives}}, \\ 
{\rm{collect-drives}}\,(\=\+{\it{m-outs\/}}, \\ 
{\it{out-types\/}}, \\ 
{\rm{cdr}}\,({\rm{alist-entry}}\,({\it{prop-name\/}}, {\it{obindings\/}})\index{alist-entry}), \\ 
{\it{m-ins\/}})\-\index{collect-drives})\- \\ 
{\bf case = }{\it{input-types\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,({\tt{'}}{\tt{input-types}}, {\it{in-types\/}}) \\ 
{\bf case = }{\it{inputs\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,({\tt{'}}{\tt{inputs}}, {\it{m-ins\/}}) \\ 
{\bf case = }{\it{loadings\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,(\=\+{\tt{'}}{\tt{loadings}}, \\ 
{\rm{collect-loadings}}\,(\=\+{\it{m-ins\/}}, \\ 
{\it{in-types\/}}, \\ 
{\rm{cdr}}\,({\rm{alist-entry}}\,({\it{prop-name\/}}, {\it{obindings\/}})\index{alist-entry}))\-\index{collect-loadings})\- \\ 
{\bf case = }{\it{out-depends\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,(\=\+{\tt{'}}{\tt{out-depends}}, \\ 
{\rm{collect-out-depends}}\,(\=\+{\it{m-outs\/}}, \\ 
{\rm{cdr}}\,({\rm{alist-entry}}\,({\it{prop-name\/}}, {\it{obindings\/}})\index{alist-entry}))\-\index{collect-out-depends})\- \\ 
{\bf case = }{\it{output-types\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,({\tt{'}}{\tt{output-types}}, {\it{out-types\/}}) \\ 
{\bf case = }{\it{outputs\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,({\tt{'}}{\tt{outputs}}, {\rm{unmark-io-outs}}\,({\it{m-outs\/}})\index{unmark-io-outs}) \\ 
{\bf case = }{\it{state-types\/}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\it{m-states\/}} $=$ {\bf{nil}}$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\tt{'}}{\tt{state-types}}, \\ 
{\rm{collect-state-types}}\,(\=\+{\it{m-states\/}}, \\ 
{\rm{cdr}}\,({\rm{alist-entry}}\,(\=\+{\it{prop-name\/}}, \\ 
{\it{obindings\/}})\-\index{alist-entry}))\-\index{collect-state-types})\-$\;${\bf  endif}\- \\ 
{\bf case = }{\it{states\/}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\it{m-states\/}} $=$ {\bf{nil}}$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\tt{'}}{\tt{states}}, {\it{m-states\/}})$\;${\bf  endif}\- \\ 
{\bf case = }{\it{tri-state-data\/}} \\ 
{\bf $\;\;$then }{\rm{cons}}\,(\=\+{\tt{'}}{\tt{tri-state-data}}, \\ 
{\rm{collect-tri-state-data}}\,(\=\+{\it{m-ins\/}}, \\ 
{\it{m-outs\/}}, \\ 
{\rm{cdr}}\,({\rm{alist-entry}}\,(\=\+{\it{prop-name\/}}, \\ 
{\it{obindings\/}})\-\index{alist-entry}))\-\index{collect-tri-state-data})\- \\ 
{\bf otherwise }{\rm{alist-entry}}\,({\it{prop-name\/}}, {\it{obindings\/}})\index{alist-entry}$\;${\bf  endcase}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-module-prop; name this event `collect-module-prop-off'.\index{collect-module-prop-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-module-props} \\  
\=\+{\rm{collect-module-props}}\,(\=\+{\it{props\/}}, \\ 
{\it{m-ins\/}}, \\ 
{\it{in-types\/}}, \\ 
{\it{m-outs\/}}, \\ 
{\it{out-types\/}}, \\ 
{\it{m-states\/}}, \\ 
{\it{obindings\/}}, \\ 
{\it{approximate-delays-p\/}})\-\index{collect-module-props} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{props\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{collect-module-prop}}\,(\=\+{\rm{car}}\,({\it{props\/}}), \\ 
{\it{m-ins\/}}, \\ 
{\it{in-types\/}}, \\ 
{\it{m-outs\/}}, \\ 
{\it{out-types\/}}, \\ 
{\it{m-states\/}}, \\ 
{\it{obindings\/}}, \\ 
{\it{approximate-delays-p\/}})\-\index{collect-module-prop}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{collect-module-prop}}\,(\=\+{\rm{car}}\,({\it{props\/}}), \\ 
{\it{m-ins\/}}, \\ 
{\it{in-types\/}}, \\ 
{\it{m-outs\/}}, \\ 
{\it{out-types\/}}, \\ 
{\it{m-states\/}}, \\ 
{\it{obindings\/}}, \\ 
{\it{approximate-delays-p\/}})\-\index{collect-module-prop}, \\ 
{\rm{collect-module-props}}\,(\=\+{\rm{cdr}}\,({\it{props\/}}), \\ 
{\it{m-ins\/}}, \\ 
{\it{in-types\/}}, \\ 
{\it{m-outs\/}}, \\ 
{\it{out-types\/}}, \\ 
{\it{m-states\/}}, \\ 
{\it{obindings\/}}, \\ 
{\it{approximate-delays-p\/}})\-\index{collect-module-props})\- \\ 
{\bf else }{\rm{collect-module-props}}\,(\=\+{\rm{cdr}}\,({\it{props\/}}), \\ 
{\it{m-ins\/}}, \\ 
{\it{in-types\/}}, \\ 
{\it{m-outs\/}}, \\ 
{\it{out-types\/}}, \\ 
{\it{m-states\/}}, \\ 
{\it{obindings\/}}, \\ 
{\it{approximate-delays-p\/}})\-\index{collect-module-props}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-module-props; name this event `collect-module-props-off'.\index{collect-module-props-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{module-prop-error} \\  
\=\+{\rm{module-prop-error}}\,({\it{obinding\/}}, {\it{m-states\/}})\index{module-prop-error} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{obinding\/}}) \\ 
{\bf then }\=\+{\bf case on }{\rm{car}}\,({\it{obinding\/}}): \\ 
{\bf case = }{\it{delays\/}} \\ 
{\bf then }{\rm{delays-error}}\,({\rm{cdr}}\,({\it{obinding\/}}))\index{delays-error} \\ 
{\bf case = }{\it{drives\/}} \\ 
{\bf $\;\;$then }{\rm{drives-error}}\,({\rm{cdr}}\,({\it{obinding\/}}))\index{drives-error} \\ 
{\bf case = }{\it{input-types\/}} \\ 
{\bf $\;\;$then }{\rm{in-types-error}}\,({\rm{cdr}}\,({\it{obinding\/}}))\index{in-types-error} \\ 
{\bf case = }{\it{loadings\/}} \\ 
{\bf $\;\;$then }{\rm{loadings-error}}\,({\rm{cdr}}\,({\it{obinding\/}}))\index{loadings-error} \\ 
{\bf case = }{\it{out-depends\/}} \\ 
{\bf $\;\;$then }{\rm{out-depends-error}}\,({\rm{cdr}}\,({\it{obinding\/}}))\index{out-depends-error} \\ 
{\bf case = }{\it{output-types\/}} \\ 
{\bf $\;\;$then }{\rm{out-types-error}}\,({\rm{cdr}}\,({\it{obinding\/}}))\index{out-types-error} \\ 
{\bf case = }{\it{state-types\/}} \\ 
{\bf $\;\;$then }{\rm{state-types-error}}\,({\rm{cdr}}\,({\it{obinding\/}}), {\it{m-states\/}})\index{state-types-error} \\ 
{\bf case = }{\it{tri-state-data\/}} \\ 
{\bf $\;\;$then }{\rm{tri-state-errors}}\,({\rm{cdr}}\,({\it{obinding\/}}))\index{tri-state-errors} \\ 
{\bf otherwise }{\bf{nil}}$\;${\bf  endcase}\- \\ 
{\bf else }{\it{obinding\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable module-prop-error; name this event `module-prop-error-off'.\index{module-prop-error-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-module-errors} \\  
\=\+{\rm{collect-module-errors}}\,({\it{obindings\/}}, {\it{m-states\/}})\index{collect-module-errors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{obindings\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{net-errorp}}\,({\rm{module-prop-error}}\,({\rm{car}}\,({\it{obindings\/}}), {\it{m-states\/}})\index{module-prop-error})\index{net-errorp} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{module-prop-error}}\,({\rm{car}}\,({\it{obindings\/}}), {\it{m-states\/}})\index{module-prop-error}, \\ 
{\rm{collect-module-errors}}\,({\rm{cdr}}\,({\it{obindings\/}}), {\it{m-states\/}})\index{collect-module-errors})\- \\ 
{\bf elseif }{\rm{listp}}\,({\rm{module-prop-error}}\,({\rm{car}}\,({\it{obindings\/}}), {\it{m-states\/}})\index{module-prop-error}) \\ 
{\bf then }{\rm{append}}\,(\=\+{\rm{module-prop-error}}\,({\rm{car}}\,({\it{obindings\/}}), {\it{m-states\/}})\index{module-prop-error}, \\ 
{\rm{collect-module-errors}}\,({\rm{cdr}}\,({\it{obindings\/}}), {\it{m-states\/}})\index{collect-module-errors})\- \\ 
{\bf else }{\rm{collect-module-errors}}\,({\rm{cdr}}\,({\it{obindings\/}}), {\it{m-states\/}})\index{collect-module-errors}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-module-errors; name this event `collect-module-errors-off'.\index{collect-module-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{collect-module-data} \\  
\=\+{\rm{collect-module-data}}\,(\=\+{\it{props\/}}, \\ 
{\it{m-name\/}}, \\ 
{\it{m-ins\/}}, \\ 
{\it{m-outs\/}}, \\ 
{\it{m-states\/}}, \\ 
{\it{obindings\/}}, \\ 
{\it{approximate-delays-p\/}})\-\index{collect-module-data} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{net-errorp}}\,({\rm{nlistp-or-err}}\,(\=\+{\rm{collect-module-errors}}\,({\it{obindings\/}}, {\it{m-states\/}})\index{collect-module-errors}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{module}}, {\it{m-name\/}}))\-\index{nlistp-or-err})\index{net-errorp} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\it{m-name\/}}, \\ 
{\rm{cons}}\,(\=\+{\rm{nlistp-or-err}}\,(\=\+{\rm{collect-module-errors}}\,({\it{obindings\/}}, {\it{m-states\/}})\index{collect-module-errors}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{module}}, {\it{m-name\/}}))\-\index{nlistp-or-err}, \\ 
{\rm{collect-module-props}}\,(\=\+{\it{props\/}}, \\ 
{\it{m-ins\/}}, \\ 
\=\+{\bf if }{\tt{'}}{\tt{input-types}} $\in$ {\it{props\/}} \\ 
{\bf then }{\rm{collect-in-types}}\,(\=\+{\it{m-ins\/}}, \\ 
{\rm{value}}\,(\=\+{\tt{'}}{\tt{input-types}}, \\ 
{\it{obindings\/}})\-\index{value})\-\index{collect-in-types} \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-, \\ 
{\it{m-outs\/}}, \\ 
\=\+{\bf if }{\tt{'}}{\tt{output-types}} $\in$ {\it{props\/}} \\ 
{\bf then }{\rm{collect-out-types}}\,(\=\+{\it{m-outs\/}}, \\ 
{\rm{value}}\,(\=\+{\tt{'}}{\tt{output-types}}, \\ 
{\it{obindings\/}})\-\index{value}, \\ 
{\it{m-ins\/}}, \\ 
{\rm{value}}\,(\=\+{\tt{'}}{\tt{input-types}}, \\ 
{\it{obindings\/}})\-\index{value})\-\index{collect-out-types} \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-, \\ 
{\it{m-states\/}}, \\ 
{\it{obindings\/}}, \\ 
{\it{approximate-delays-p\/}})\-\index{collect-module-props})\-)\- \\ 
{\bf else }{\rm{cons}}\,(\=\+{\it{m-name\/}}, \\ 
{\rm{collect-module-props}}\,(\=\+{\it{props\/}}, \\ 
{\it{m-ins\/}}, \\ 
\=\+{\bf if }{\tt{'}}{\tt{input-types}} $\in$ {\it{props\/}} \\ 
{\bf then }{\rm{collect-in-types}}\,(\=\+{\it{m-ins\/}}, \\ 
{\rm{value}}\,(\=\+{\tt{'}}{\tt{input-types}}, \\ 
{\it{obindings\/}})\-\index{value})\-\index{collect-in-types} \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-, \\ 
{\it{m-outs\/}}, \\ 
\=\+{\bf if }{\tt{'}}{\tt{output-types}} $\in$ {\it{props\/}} \\ 
{\bf then }{\rm{collect-out-types}}\,(\=\+{\it{m-outs\/}}, \\ 
{\rm{value}}\,(\=\+{\tt{'}}{\tt{output-types}}, \\ 
{\it{obindings\/}})\-\index{value}, \\ 
{\it{m-ins\/}}, \\ 
{\rm{value}}\,(\=\+{\tt{'}}{\tt{input-types}}, \\ 
{\it{obindings\/}})\-\index{value})\-\index{collect-out-types} \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-, \\ 
{\it{m-states\/}}, \\ 
{\it{obindings\/}}, \\ 
{\it{approximate-delays-p\/}})\-\index{collect-module-props})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable collect-module-data; name this event `collect-module-data-off'.\index{collect-module-data-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{module-data} \\  
\=\+{\rm{module-data}}\,({\it{module\/}}, {\it{props\/}}, {\it{database\/}}, {\it{approximate-delays-p\/}})\index{module-data} \\ 
$=$$\;\;\;\;${\rm{collect-module-data}}\,(\=\+{\it{props\/}}, \\ 
{\rm{module-name}}\,({\it{module\/}})\index{module-name}, \\ 
{\rm{module-inputs}}\,({\it{module\/}})\index{module-inputs}, \\ 
{\rm{mark-io-outs}}\,(\=\+{\rm{module-outputs}}\,({\it{module\/}})\index{module-outputs}, \\ 
{\rm{intersection}}\,(\=\+{\rm{module-inputs}}\,({\it{module\/}})\index{module-inputs}, \\ 
{\rm{module-outputs}}\,({\it{module\/}})\index{module-outputs})\-\index{intersection})\-\index{mark-io-outs}, \\ 
{\rm{module-statenames}}\,({\it{module\/}})\index{module-statenames}, \\ 
{\rm{occurrence-data}}\,(\=\+{\it{props\/}}, \\ 
{\rm{module-occurrences}}\,({\it{module\/}})\index{module-occurrences}, \\ 
{\rm{module-inputs}}\,({\it{module\/}})\index{module-inputs}, \\ 
{\rm{mark-io-outs}}\,(\=\+{\rm{module-outputs}}\,({\it{module\/}})\index{module-outputs}, \\ 
{\rm{intersection}}\,(\=\+{\rm{module-inputs}}\,({\it{module\/}})\index{module-inputs}, \\ 
{\rm{module-outputs}}\,({\it{module\/}})\index{module-outputs})\-\index{intersection})\-\index{mark-io-outs}, \\ 
{\rm{intersection}}\,(\=\+{\rm{module-inputs}}\,({\it{module\/}})\index{module-inputs}, \\ 
{\rm{module-outputs}}\,({\it{module\/}})\index{module-outputs})\-\index{intersection}, \\ 
{\it{database\/}})\-\index{occurrence-data}, \\ 
{\it{approximate-delays-p\/}})\-\index{collect-module-data}\-
\end{tabbing}


\noindent{\sc Event}:   Enable module-data; name this event `module-data-off'.\index{module-data-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{module-database} \\  
\=\+{\rm{module-database}}\,({\it{netlist\/}}, {\it{props\/}}, {\it{approximate-delays-p\/}})\index{module-database} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{netlist\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{module-data}}\,(\=\+{\rm{car}}\,({\it{netlist\/}}), \\ 
{\it{props\/}}, \\ 
{\rm{module-database}}\,(\=\+{\rm{cdr}}\,({\it{netlist\/}}), \\ 
{\it{props\/}}, \\ 
{\it{approximate-delays-p\/}})\-\index{module-database}, \\ 
{\it{approximate-delays-p\/}})\-\index{module-data}, \\ 
{\rm{module-database}}\,({\rm{cdr}}\,({\it{netlist\/}}), {\it{props\/}}, {\it{approximate-delays-p\/}})\index{module-database})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable module-database; name this event `module-database-off'.\index{module-database-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{required-for-prop} \\  
\=\+{\rm{required-for-prop}}\,({\it{prop\/}})\index{required-for-prop} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{prop\/}}: \\ 
{\bf case = }{\it{delays\/}} \\ 
{\bf then }{\tt{'}}{\tt{(}}\=\+{\tt{delays}}{\tt{ }}{\tt{loadings}}{\tt{ }}{\tt{drives}}{\tt{ }}{\tt{input-types}}{\tt{ }}{\tt{output-types}} \\ 
{\tt{inputs}}{\tt{ }}{\tt{outputs}}{\tt{ }}{\tt{tri-state-data}}{\tt{)}}\- \\ 
{\bf case = }{\it{drives\/}} \\ 
{\bf $\;\;$then }{\tt{'}}{\tt{(}}\=\+{\tt{drives}}{\tt{ }}{\tt{loadings}}{\tt{ }}{\tt{input-types}}{\tt{ }}{\tt{output-types}}{\tt{ }}{\tt{inputs}} \\ 
{\tt{outputs}}{\tt{ }}{\tt{tri-state-data}}{\tt{)}}\- \\ 
{\bf case = }{\it{input-types\/}} \\ 
{\bf $\;\;$then }{\tt{'}}{\tt{(}}\=\+{\tt{input-types}}{\tt{ }}{\tt{output-types}}{\tt{ }}{\tt{inputs}}{\tt{ }}{\tt{outputs}} \\ 
{\tt{tri-state-data}}{\tt{)}}\- \\ 
{\bf case = }{\it{loadings\/}} \\ 
{\bf $\;\;$then }{\tt{'}}{\tt{(}}\=\+{\tt{loadings}}{\tt{ }}{\tt{drives}}{\tt{ }}{\tt{input-types}}{\tt{ }}{\tt{output-types}}{\tt{ }}{\tt{inputs}} \\ 
{\tt{outputs}}{\tt{ }}{\tt{tri-state-data}}{\tt{)}}\- \\ 
{\bf case = }{\it{out-depends\/}} \\ 
{\bf $\;\;$then }{\tt{'}}{\tt{(}}{\tt{out-depends}}{\tt{ }}{\tt{inputs}}{\tt{ }}{\tt{outputs}}{\tt{)}} \\ 
{\bf case = }{\it{output-types\/}} \\ 
{\bf $\;\;$then }{\tt{'}}{\tt{(}}\=\+{\tt{output-types}}{\tt{ }}{\tt{input-types}}{\tt{ }}{\tt{inputs}}{\tt{ }}{\tt{outputs}} \\ 
{\tt{tri-state-data}}{\tt{)}}\- \\ 
{\bf otherwise }\=\+{\bf if }{\it{prop\/}} $\in$ {\sc{all-module-props}}\index{all-module-props}$\;\;${\bf then }{\rm{list}}\,({\it{prop\/}}) \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-$\;${\bf  endcase}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable required-for-prop; name this event `required-for-prop-off'.\index{required-for-prop-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{get-required-props} \\  
\=\+{\rm{get-required-props}}\,({\it{props\/}}, {\it{wanted-props\/}})\index{get-required-props} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{props\/}}) \\ 
{\bf then }\=\+{\rm{required-for-prop}}\,({\rm{car}}\,({\it{props\/}}))\index{required-for-prop} \\ 
$\cup$$\;\;\;\;${\rm{get-required-props}}\,({\rm{cdr}}\,({\it{props\/}}), {\it{wanted-props\/}})\index{get-required-props}\- \\ 
{\bf else }{\it{wanted-props\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable get-required-props; name this event `get-required-props-off'.\index{get-required-props-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{required-props} \\  
{\rm{required-props}}\,({\it{props\/}})\index{required-props} $=$ {\rm{get-required-props}}\,({\it{props\/}}, {\it{props\/}})\index{get-required-props}
\end{tabbing}


\noindent{\sc Event}:   Enable required-props; name this event `required-props-off'.\index{required-props-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{unbind-netlist-props-0} \\  
\=\+{\rm{unbind-netlist-props-0}}\,({\it{props\/}}, {\it{database\/}})\index{unbind-netlist-props-0} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{database\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{caar}}\,({\it{database\/}}), \\ 
\=\+{\bf if }{\rm{net-errorp}}\,({\rm{cadar}}\,({\it{database\/}}))\index{net-errorp} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{cadar}}\,({\it{database\/}}), \\ 
{\rm{unbind-list}}\,({\it{props\/}}, {\rm{cddar}}\,({\it{database\/}}))\index{unbind-list})\- \\ 
{\bf else }{\rm{unbind-list}}\,({\it{props\/}}, {\rm{cdar}}\,({\it{database\/}}))\index{unbind-list}$\;${\bf  endif}\-)\-, \\ 
{\rm{unbind-netlist-props-0}}\,({\it{props\/}}, {\rm{cdr}}\,({\it{database\/}}))\index{unbind-netlist-props-0})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable unbind-netlist-props-0; name this event `unbind-netlist-props-0-off'.\index{unbind-netlist-props-0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{unbind-netlist-props} \\  
\=\+{\rm{unbind-netlist-props}}\,({\it{props\/}}, {\it{database\/}})\index{unbind-netlist-props} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{props\/}})$\;\;${\bf then }{\rm{unbind-netlist-props-0}}\,({\rm{reverse}}\,({\it{props\/}})\index{reverse}, {\it{database\/}})\index{unbind-netlist-props-0} \\ 
{\bf else }{\it{database\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable unbind-netlist-props; name this event `unbind-netlist-props-off'.\index{unbind-netlist-props-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{netlist-properties} \\  
\=\+{\rm{netlist-properties}}\,({\it{netlist\/}}, {\it{props\/}}, {\it{approximate-delays-p\/}})\index{netlist-properties} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{net-errorp}}\,({\rm{subset-or-err}}\,(\=\+{\it{props\/}}, \\ 
{\sc{all-module-props}}\index{all-module-props}, \\ 
{\tt{'}}{\tt{unknown-properties}})\-\index{subset-or-err})\index{net-errorp} \\ 
{\bf then }{\rm{subset-or-err}}\,({\it{props\/}}, {\sc{all-module-props}}\index{all-module-props}, {\tt{'}}{\tt{unknown-properties}})\index{subset-or-err} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{collect-net-errors}}\,({\rm{module-database}}\,(\=\+{\it{netlist\/}}, \\ 
{\rm{required-props}}\,({\it{props\/}})\index{required-props}, \\ 
{\it{approximate-delays-p\/}})\-\index{module-database})\index{collect-net-errors}) \\ 
{\bf then }{\rm{pred-error}}\,(\=\+{\tt{'}}{\tt{netlist-errors}}, \\ 
{\rm{collect-net-errors}}\,({\rm{module-database}}\,(\=\+{\it{netlist\/}}, \\ 
{\rm{required-props}}\,({\it{props\/}})\index{required-props}, \\ 
{\it{approximate-delays-p\/}})\-\index{module-database})\index{collect-net-errors})\-\index{pred-error} \\ 
{\bf else }{\rm{unbind-netlist-props}}\,(\=\+{\rm{set-diff}}\,({\rm{required-props}}\,({\it{props\/}})\index{required-props}, {\it{props\/}})\index{set-diff}, \\ 
{\rm{module-database}}\,(\=\+{\it{netlist\/}}, \\ 
{\rm{required-props}}\,({\it{props\/}})\index{required-props}, \\ 
{\it{approximate-delays-p\/}})\-\index{module-database})\-\index{unbind-netlist-props}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable netlist-properties; name this event `netlist-properties-off'.\index{netlist-properties-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{netlist-database} \\  
\=\+{\rm{netlist-database}}\,({\it{netlist\/}}, {\it{approximate-delays-p\/}})\index{netlist-database} \\ 
$=$$\;\;\;\;${\rm{unbind-netlist-props}}\,(\=\+{\rm{set-diff}}\,(\=\+{\rm{required-props}}\,({\sc{all-module-props}}\index{all-module-props})\index{required-props}, \\ 
{\sc{all-module-props}}\index{all-module-props})\-\index{set-diff}, \\ 
{\rm{module-database}}\,(\=\+{\it{netlist\/}}, \\ 
{\rm{required-props}}\,({\sc{all-module-props}}\index{all-module-props})\index{required-props}, \\ 
{\it{approximate-delays-p\/}})\-\index{module-database})\-\index{unbind-netlist-props}\-
\end{tabbing}


\noindent{\sc Event}:   Enable netlist-database; name this event `netlist-database-off'.\index{netlist-database-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{predicate-properties} \\  
\=\+{\sc{predicate-properties}}\index{predicate-properties} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{drives}}{\tt{ }}{\tt{input-types}}{\tt{ }}{\tt{loadings}}{\tt{ }}{\tt{out-depends}}{\tt{ }}{\tt{output-types}} \\ 
{\tt{state-types}}{\tt{)}}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable predicate-properties; name this event `predicate-properties-off'.\index{predicate-properties-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*predicate-properties; name this event `g*1*predicate-properties-off'.\index{g*1*predicate-properties-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{top-level-predicate} \\  
\=\+{\rm{top-level-predicate}}\,({\it{netlist\/}})\index{top-level-predicate} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{net-errorp}}\,({\rm{netlist-syntax-ok}}\,({\it{netlist\/}})\index{netlist-syntax-ok})\index{net-errorp} \\ 
{\bf then }{\rm{netlist-syntax-ok}}\,({\it{netlist\/}})\index{netlist-syntax-ok} \\ 
{\bf elseif }{\rm{net-errorp}}\,({\rm{netlist-properties}}\,({\it{netlist\/}}, {\sc{predicate-properties}}\index{predicate-properties}, {\bf{t}})\index{netlist-properties})\index{net-errorp} \\ 
{\bf then }{\rm{netlist-properties}}\,({\it{netlist\/}}, {\sc{predicate-properties}}\index{predicate-properties}, {\bf{t}})\index{netlist-properties} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable top-level-predicate; name this event `top-level-predicate-off'.\index{top-level-predicate-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{lsi-top-level-predicate} \\  
\=\+{\rm{lsi-top-level-predicate}}\,({\it{netlist\/}}, {\it{token-size\/}}, {\it{max-hierarchical-name-length\/}})\index{lsi-top-level-predicate} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{net-errorp}}\,({\rm{lsi-netlist-syntax-ok}}\,(\=\+{\it{netlist\/}}, \\ 
{\it{token-size\/}}, \\ 
{\it{max-hierarchical-name-length\/}})\-\index{lsi-netlist-syntax-ok})\index{net-errorp} \\ 
{\bf then }{\rm{lsi-netlist-syntax-ok}}\,(\=\+{\it{netlist\/}}, \\ 
{\it{token-size\/}}, \\ 
{\it{max-hierarchical-name-length\/}})\-\index{lsi-netlist-syntax-ok} \\ 
{\bf elseif }{\rm{net-errorp}}\,({\rm{netlist-properties}}\,({\it{netlist\/}}, {\sc{predicate-properties}}\index{predicate-properties}, {\bf{t}})\index{netlist-properties})\index{net-errorp} \\ 
{\bf then }{\rm{netlist-properties}}\,({\it{netlist\/}}, {\sc{predicate-properties}}\index{predicate-properties}, {\bf{t}})\index{netlist-properties} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable lsi-top-level-predicate; name this event `lsi-top-level-predicate-off'.\index{lsi-top-level-predicate-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pname-listp} \\  
\=\+{\rm{pname-listp}}\,({\it{x\/}})\index{pname-listp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\rm{name-okp}}\,({\rm{car}}\,({\it{x\/}}))\index{name-okp} \\ 
$\wedge$$\;\;\;\;$({\rm{car}}\,({\it{x\/}}) $\not\in$ {\rm{cdr}}\,({\it{x\/}})) \\ 
$\wedge$$\;\;\;\;${\rm{pname-listp}}\,({\rm{cdr}}\,({\it{x\/}}))\index{pname-listp}\- \\ 
{\bf else }{\it{x\/}} $=$ {\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable pname-listp; name this event `pname-listp-off'.\index{pname-listp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{function-call-ok} \\  
\=\+{\rm{function-call-ok}}\,({\it{x\/}}, {\it{number-of-args\/}})\index{function-call-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) $\wedge$ {\rm{litatom}}\,({\rm{car}}\,({\it{x\/}})) \\ 
{\bf then }\=\+{\bf if }{\rm{properp}}\,({\it{x\/}})\index{properp} \\ 
{\bf then }\=\+{\bf if }{\it{number-of-args\/}} $\in\;${\bf{N}}${}$ \\ 
{\bf then }{\rm{t-or-err}}\,(\=\+{\rm{length}}\,({\rm{cdr}}\,({\it{x\/}}))\index{length} $=$ {\it{number-of-args\/}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{function}}, \\ 
{\rm{cons}}\,(\=\+{\rm{car}}\,({\it{x\/}}), \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{has}}, \\ 
{\rm{cons}}\,({\it{number-of-args\/}}, {\tt{'}}{\tt{(}}{\tt{args}}{\tt{)}}))\-)\-)\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{it}}, {\tt{'}}{\tt{is}}, {\tt{'}}{\tt{given}}, {\rm{length}}\,({\rm{cdr}}\,({\it{x\/}}))\index{length}, {\tt{'}}{\tt{in}}, {\it{x\/}}))\-\index{t-or-err} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{pred-error}}\,({\tt{'}}{\tt{ill-formed-function-call}}, {\it{x\/}})\index{pred-error}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{pred-error}}\,({\tt{'}}{\tt{not-function-call}}, {\it{x\/}})\index{pred-error}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable function-call-ok; name this event `function-call-ok-off'.\index{function-call-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{io-label} \\  
\=\+{\rm{io-label}}\,({\it{arg\/}}, {\it{what\/}})\index{io-label} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{arg\/}} $\in\;${\bf{N}}${}$$\;\;${\bf then }{\rm{list}}\,({\tt{'}}{\tt{unknown}}, {\it{what\/}}, {\it{arg\/}}) \\ 
{\bf else }{\rm{list}}\,({\it{what\/}}, {\it{arg\/}})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable io-label; name this event `io-label-off'.\index{io-label-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{input-label}$\;\;$
{\rm{input-label}}\,({\it{input\/}})\index{input-label} $=$ {\rm{io-label}}\,({\it{input\/}}, {\tt{'}}{\tt{input}})\index{io-label}
\end{tabbing}


\noindent{\sc Event}:   Enable input-label; name this event `input-label-off'.\index{input-label-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{output-label}$\;\;$
{\rm{output-label}}\,({\it{output\/}})\index{output-label} $=$ {\rm{io-label}}\,({\it{output\/}}, {\tt{'}}{\tt{output}})\index{io-label}
\end{tabbing}


\noindent{\sc Event}:   Enable output-label; name this event `output-label-off'.\index{output-label-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{state-label}$\;\;$
{\rm{state-label}}\,({\it{state\/}})\index{state-label} $=$ {\rm{io-label}}\,({\it{state\/}}, {\tt{'}}{\tt{state}})\index{io-label}
\end{tabbing}


\noindent{\sc Event}:   Enable state-label; name this event `state-label-off'.\index{state-label-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ucar} \\  
\=\+{\rm{ucar}}\,({\it{x\/}})\index{ucar} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}})$\;\;${\bf then }{\rm{car}}\,({\it{x\/}}) \\ 
{\bf else }{\sc{unknown}}\index{unknown}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ucar; name this event `ucar-off'.\index{ucar-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ucdr} \\  
\=\+{\rm{ucdr}}\,({\it{x\/}})\index{ucdr} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}})$\;\;${\bf then }{\rm{cdr}}\,({\it{x\/}}) \\ 
{\bf else }{\sc{unknown}}\index{unknown}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ucdr; name this event `ucdr-off'.\index{ucdr-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{io-car} \\  
\=\+{\rm{io-car}}\,({\it{args\/}})\index{io-car} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{args\/}})$\;\;${\bf then }{\rm{car}}\,({\it{args\/}}) \\ 
{\bf elseif }{\it{args\/}} $\in\;${\bf{N}}${}$$\;\;${\bf then }{\it{args\/}} \\ 
{\bf else }{\tt{1}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable io-car; name this event `io-car-off'.\index{io-car-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{io-cdr} \\  
\=\+{\rm{io-cdr}}\,({\it{args\/}})\index{io-cdr} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{args\/}} $\in\;${\bf{N}}${}$$\;\;${\bf then }$1\;+$ {\it{args\/}} \\ 
{\bf elseif }{\it{args\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\tt{2}} \\ 
{\bf elseif }{\rm{cdr}}\,({\it{args\/}}) $\in\;${\bf{N}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cdr}}\,({\it{args\/}})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable io-cdr; name this event `io-cdr-off'.\index{io-cdr-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{out-prop-signals} \\  
\=\+{\rm{out-prop-signals}}\,({\it{out-depends\/}}, {\it{inputs\/}})\index{out-prop-signals} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{unknownp}}\,({\it{out-depends\/}})\index{unknownp}$\;\;${\bf then }{\it{inputs\/}} \\ 
{\bf else }{\it{out-depends\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable out-prop-signals; name this event `out-prop-signals-off'.\index{out-prop-signals-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{id-out-prop-signals} \\  
\=\+{\rm{id-out-prop-signals}}\,({\it{output-type\/}}, {\it{out-depends\/}}, {\it{inputs\/}})\index{id-out-prop-signals} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{output-type\/}})$\;\;${\bf then }{\it{output-type\/}} \\ 
{\bf else }{\rm{out-prop-signals}}\,({\it{out-depends\/}}, {\it{inputs\/}})\index{out-prop-signals}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable id-out-prop-signals; name this event `id-out-prop-signals-off'.\index{id-out-prop-signals-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{all-input-types} \\  
\=\+{\sc{all-input-types}}\index{all-input-types} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{boolp}}{\tt{ }}{\tt{clk}}{\tt{ }}{\tt{free}}{\tt{ }}{\tt{level}}{\tt{ }}{\tt{parametric}}{\tt{ }}{\tt{tri-state}}{\tt{ }}{\tt{ttl}} \\ 
{\tt{ttl-tri-state}}{\tt{)}}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable all-input-types; name this event `all-input-types-off'.\index{all-input-types-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*all-input-types; name this event `g*1*all-input-types-off'.\index{g*1*all-input-types-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{all-output-types} \\  
\=\+{\rm{all-output-types}}\,({\it{inputs\/}})\index{all-output-types} \\ 
$=$$\;\;\;\;${\rm{append}}\,({\rm{listify}}\,({\it{inputs\/}})\index{listify}, {\rm{delete*}}\,({\tt{'}}{\tt{free}}, {\sc{all-input-types}}\index{all-input-types})\index{delete*})\-
\end{tabbing}


\noindent{\sc Event}:   Enable all-output-types; name this event `all-output-types-off'.\index{all-output-types-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pin-type-ok} \\  
\=\+{\rm{pin-type-ok}}\,({\it{type\/}}, {\it{input\/}}, {\it{io-signals\/}}, {\it{fname\/}})\index{pin-type-ok} \\ 
$=$$\;\;\;\;${\rm{label-error}}\,(\=\+\=\+{\bf if }{\it{fname\/}} $=$ {\tt{'}}{\tt{t-wire}} \\ 
{\bf then }{\rm{t-or-err}}\,(\=\+{\it{type\/}} $=$ {\tt{'}}{\tt{tri-state}}, \\ 
{\tt{'}}{\tt{t-wire-input-type-not-tri-state}}, \\ 
{\it{type\/}})\-\index{t-or-err} \\ 
{\bf elseif }{\it{input\/}} $\in$ {\it{io-signals\/}} \\ 
{\bf then }{\rm{t-or-err}}\,(\=\+{\rm{tri-state-typep}}\,({\it{type\/}})\index{tri-state-typep}, \\ 
{\tt{'}}{\tt{bad-io-signal-type}}, \\ 
{\it{type\/}})\-\index{t-or-err} \\ 
{\bf else }{\rm{t-or-err}}\,(\=\+{\it{type\/}} $\in$ {\sc{all-input-types}}\index{all-input-types}, \\ 
{\tt{'}}{\tt{unknown-type}}, \\ 
{\it{type\/}})\-\index{t-or-err}$\;${\bf  endif}\-, \\ 
{\rm{input-label}}\,({\it{input\/}})\index{input-label})\-\index{label-error}\-
\end{tabbing}


\noindent{\sc Event}:   Enable pin-type-ok; name this event `pin-type-ok-off'.\index{pin-type-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pin-type-errors} \\  
\=\+{\rm{pin-type-errors}}\,({\it{types\/}}, {\it{inputs\/}}, {\it{io-signals\/}}, {\it{fname\/}})\index{pin-type-errors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{types\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{t-or-err}}\,(\=\+{\rm{listp}}\,({\it{inputs\/}}) $\vee$ ({\it{inputs\/}} $\in\;${\bf{N}}${}$), \\ 
{\tt{'}}{\tt{too-many-input-types}}, \\ 
{\rm{cons}}\,({\rm{length}}\,({\it{types\/}})\index{length}, {\tt{'}}{\tt{(}}{\tt{extras}}{\tt{)}}))\-\index{t-or-err}, \\ 
{\rm{cons}}\,(\=\+{\rm{pin-type-ok}}\,({\rm{car}}\,({\it{types\/}}), {\rm{io-car}}\,({\it{inputs\/}})\index{io-car}, {\it{io-signals\/}}, {\it{fname\/}})\index{pin-type-ok}, \\ 
{\rm{pin-type-errors}}\,(\=\+{\rm{cdr}}\,({\it{types\/}}), \\ 
{\rm{io-cdr}}\,({\it{inputs\/}})\index{io-cdr}, \\ 
{\it{io-signals\/}}, \\ 
{\it{fname\/}})\-\index{pin-type-errors})\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{nil-or-err}}\,({\it{types\/}}, {\tt{'}}{\tt{not-proper-list}})\index{nil-or-err}, \\ 
{\rm{nlistp-or-err}}\,({\it{inputs\/}}, {\tt{'}}{\tt{inputs-without-types}})\index{nlistp-or-err})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable pin-type-errors; name this event `pin-type-errors-off'.\index{pin-type-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pin-types-ok} \\  
\=\+{\rm{pin-types-ok}}\,({\it{in-types\/}}, {\it{alist\/}})\index{pin-types-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+{\rm{pin-type-errors}}\,(\=\+{\it{in-types\/}}, \\ 
\=\+{\bf if }{\rm{unknownp}}\,({\rm{value}}\,({\tt{'}}{\tt{inputs}}, {\it{alist\/}})\index{value})\index{unknownp}$\;\;${\bf then }{\tt{1}} \\ 
{\bf else }{\rm{value}}\,({\tt{'}}{\tt{inputs}}, {\it{alist\/}})\index{value}$\;${\bf  endif}\-, \\ 
{\rm{intersection}}\,(\=\+{\rm{value}}\,({\tt{'}}{\tt{inputs}}, {\it{alist\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{outputs}}, {\it{alist\/}})\index{value})\-\index{intersection}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{primp-name}}, {\it{alist\/}})\index{value})\-\index{pin-type-errors}, \\ 
{\tt{'}}{\tt{input-types}})\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable pin-types-ok; name this event `pin-types-ok-off'.\index{pin-types-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pout-type-ok} \\  
\=\+{\rm{pout-type-ok}}\,({\it{type\/}}, {\it{output\/}}, {\it{out-depends\/}}, {\it{inputs\/}}, {\it{io-signals\/}}, {\it{fname\/}}, {\it{in-type-map\/}})\index{pout-type-ok} \\ 
$=$$\;\;\;\;${\rm{label-error}}\,(\=\+\=\+{\bf if }{\it{fname\/}} $=$ {\tt{'}}{\tt{t-wire}} \\ 
{\bf then }{\rm{t-or-err}}\,(\=\+{\it{type\/}} $=$ {\tt{'}}{\tt{tri-state}}, \\ 
{\tt{'}}{\tt{t-wire-output-type-not-tri-state}}, \\ 
{\it{type\/}})\-\index{t-or-err} \\ 
{\bf elseif }{\it{output\/}} $\in$ {\it{io-signals\/}} \\ 
{\bf then }\=\+{\bf if }{\rm{tri-state-typep}}\,({\it{type\/}})\index{tri-state-typep} \\ 
{\bf then }{\rm{t-or-err}}\,(\=\+\=\+($\neg$ {\rm{tri-state-typep}}\,({\rm{value}}\,(\=\+{\it{output\/}}, \\ 
{\it{in-type-map\/}})\-\index{value})\index{tri-state-typep}) \\ 
$\vee$$\;\;\;\;$({\it{type\/}} $=$ {\rm{value}}\,(\=\+{\it{output\/}}, \\ 
{\it{in-type-map\/}})\-\index{value})\-, \\ 
{\tt{'}}{\tt{different-io-signal-in-and-out-types}}, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{input-type}}, \\ 
{\rm{value}}\,({\it{output\/}}, {\it{in-type-map\/}})\index{value})\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{output-type}}, {\it{type\/}}))\-)\-\index{t-or-err} \\ 
{\bf else }{\rm{pred-error}}\,({\tt{'}}{\tt{bad-io-signal-type}}, {\it{type\/}})\index{pred-error}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{listp}}\,({\it{type\/}}) \\ 
{\bf then }{\rm{t-or-err}}\,(\=\+\=\+{\rm{properp}}\,({\it{type\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{type\/}})\index{length} $=$ {\tt{1}}) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{unknownp}}\,({\rm{out-prop-signals}}\,(\=\+{\it{out-depends\/}}, \\ 
{\it{inputs\/}})\-\index{out-prop-signals})\index{unknownp} \\ 
{\bf then }{\rm{name-okp}}\,({\rm{car}}\,({\it{type\/}}))\index{name-okp} \\ 
{\bf else }\=\+{\rm{car}}\,({\it{type\/}}) \\ 
$\in$$\;\;\;\;${\rm{out-prop-signals}}\,(\=\+{\it{out-depends\/}}, \\ 
{\it{inputs\/}})\-\index{out-prop-signals}\-$\;${\bf  endif}\-\-, \\ 
{\tt{'}}{\tt{unknown-type}}, \\ 
{\it{type\/}})\-\index{t-or-err} \\ 
{\bf else }{\rm{t-or-err}}\,(\=\+{\it{type\/}} $\in$ {\rm{all-output-types}}\,({\bf{nil}})\index{all-output-types}, \\ 
{\tt{'}}{\tt{unknown-type}}, \\ 
{\it{type\/}})\-\index{t-or-err}$\;${\bf  endif}\-, \\ 
{\rm{output-label}}\,({\it{output\/}})\index{output-label})\-\index{label-error}\-
\end{tabbing}


\noindent{\sc Event}:   Enable pout-type-ok; name this event `pout-type-ok-off'.\index{pout-type-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pout-type-errors} \\  
\=\+{\rm{pout-type-errors}}\,(\=\+{\it{types\/}}, \\ 
{\it{outputs\/}}, \\ 
{\it{out-depends\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{io-signals\/}}, \\ 
{\it{fname\/}}, \\ 
{\it{in-type-map\/}})\-\index{pout-type-errors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{types\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{t-or-err}}\,(\=\+{\rm{listp}}\,({\it{outputs\/}}) $\vee$ ({\it{outputs\/}} $\in\;${\bf{N}}${}$), \\ 
{\tt{'}}{\tt{too-many-output-types}}, \\ 
{\rm{cons}}\,({\rm{length}}\,({\it{types\/}})\index{length}, {\tt{'}}{\tt{(}}{\tt{extras}}{\tt{)}}))\-\index{t-or-err}, \\ 
{\rm{cons}}\,(\=\+{\rm{pout-type-ok}}\,(\=\+{\rm{car}}\,({\it{types\/}}), \\ 
{\rm{io-car}}\,({\it{outputs\/}})\index{io-car}, \\ 
{\rm{ucar}}\,({\it{out-depends\/}})\index{ucar}, \\ 
{\it{inputs\/}}, \\ 
{\it{io-signals\/}}, \\ 
{\it{fname\/}}, \\ 
{\it{in-type-map\/}})\-\index{pout-type-ok}, \\ 
{\rm{pout-type-errors}}\,(\=\+{\rm{cdr}}\,({\it{types\/}}), \\ 
{\rm{io-cdr}}\,({\it{outputs\/}})\index{io-cdr}, \\ 
{\rm{ucdr}}\,({\it{out-depends\/}})\index{ucdr}, \\ 
{\it{inputs\/}}, \\ 
{\it{io-signals\/}}, \\ 
{\it{fname\/}}, \\ 
{\it{in-type-map\/}})\-\index{pout-type-errors})\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{nil-or-err}}\,({\it{types\/}}, {\tt{'}}{\tt{not-proper-list}})\index{nil-or-err}, \\ 
{\rm{nlistp-or-err}}\,({\it{outputs\/}}, {\tt{'}}{\tt{outputs-without-types}})\index{nlistp-or-err})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable pout-type-errors; name this event `pout-type-errors-off'.\index{pout-type-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pout-types-ok} \\  
\=\+{\rm{pout-types-ok}}\,({\it{out-types\/}}, {\it{alist\/}})\index{pout-types-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+{\rm{pout-type-errors}}\,(\=\+{\it{out-types\/}}, \\ 
\=\+{\bf if }{\rm{unknownp}}\,({\rm{value}}\,({\tt{'}}{\tt{outputs}}, {\it{alist\/}})\index{value})\index{unknownp}$\;\;${\bf then }{\tt{1}} \\ 
{\bf else }{\rm{value}}\,({\tt{'}}{\tt{outputs}}, {\it{alist\/}})\index{value}$\;${\bf  endif}\-, \\ 
{\rm{value}}\,({\tt{'}}{\tt{out-depends}}, {\it{alist\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{inputs}}, {\it{alist\/}})\index{value}, \\ 
{\rm{intersection}}\,(\=\+{\rm{value}}\,({\tt{'}}{\tt{inputs}}, {\it{alist\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{outputs}}, {\it{alist\/}})\index{value})\-\index{intersection}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{primp-name}}, {\it{alist\/}})\index{value}, \\ 
{\rm{pairlist}}\,(\=\+{\rm{value}}\,({\tt{'}}{\tt{inputs}}, {\it{alist\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{input-types}}, {\it{alist\/}})\index{value})\-)\-\index{pout-type-errors}, \\ 
{\tt{'}}{\tt{output-types}})\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable pout-types-ok; name this event `pout-types-ok-off'.\index{pout-types-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{p-name-prop-value-ok} \\  
\=\+{\rm{p-name-prop-value-ok}}\,({\it{name\/}}, {\it{out-type\/}}, {\it{out-depends\/}}, {\it{inputs\/}}, {\it{label\/}})\index{p-name-prop-value-ok} \\ 
$=$$\;\;\;\;${\rm{t-or-err}}\,(\=\+\=\+{\bf if }{\rm{unknownp}}\,({\rm{id-out-prop-signals}}\,({\it{out-type\/}}, {\it{out-depends\/}}, {\it{inputs\/}})\index{id-out-prop-signals})\index{unknownp} \\ 
{\bf then }{\rm{name-okp}}\,({\it{name\/}})\index{name-okp} \\ 
{\bf else }{\it{name\/}} $\in$ {\rm{id-out-prop-signals}}\,(\=\+{\it{out-type\/}}, \\ 
{\it{out-depends\/}}, \\ 
{\it{inputs\/}})\-\index{id-out-prop-signals}$\;${\bf  endif}\-, \\ 
{\it{label\/}}, \\ 
{\it{name\/}})\-\index{t-or-err}\-
\end{tabbing}


\noindent{\sc Event}:   Enable p-name-prop-value-ok; name this event `p-name-prop-value-ok-off'.\index{p-name-prop-value-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{p-t-wire-args-ok} \\  
\=\+{\rm{p-t-wire-args-ok}}\,({\it{args\/}}, {\it{out-depends\/}}, {\it{inputs\/}}, {\it{label\/}})\index{p-t-wire-args-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+\=\+{\bf if }{\rm{unknownp}}\,({\rm{out-prop-signals}}\,({\it{out-depends\/}}, {\it{inputs\/}})\index{out-prop-signals})\index{unknownp} \\ 
{\bf then }{\rm{list}}\,({\rm{name-list-ok}}\,({\it{args\/}}, {\tt{'}}{\tt{ill-formed-args}}, {\bf{f}})\index{name-list-ok}) \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{subset-or-err}}\,(\=\+{\it{args\/}}, \\ 
{\rm{out-prop-signals}}\,(\=\+{\it{out-depends\/}}, \\ 
{\it{inputs\/}})\-\index{out-prop-signals}, \\ 
{\tt{'}}{\tt{unknown-args}})\-\index{subset-or-err}, \\ 
{\rm{no-duplicates-or-err}}\,(\=\+{\it{args\/}}, \\ 
{\tt{'}}{\tt{duplicate-args}})\-\index{no-duplicates-or-err}, \\ 
{\rm{nil-or-err}}\,(\=\+{\rm{last-cdr}}\,({\it{args\/}})\index{last-cdr}, \\ 
{\tt{'}}{\tt{not-proper-list}})\-\index{nil-or-err})\-$\;${\bf  endif}\-, \\ 
{\it{label\/}})\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable p-t-wire-args-ok; name this event `p-t-wire-args-ok-off'.\index{p-t-wire-args-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{phalf-delay-ok} \\  
\=\+{\rm{phalf-delay-ok}}\,({\it{d\/}}, {\it{type\/}}, {\it{label\/}})\index{phalf-delay-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{d\/}})\index{length} $=$ {\tt{2}} \\ 
{\bf then }{\rm{err-and}}\,(\=\+{\rm{list}}\,(\=\+\=\+{\bf if }{\it{type\/}} $\in$ {\tt{'}}{\tt{(}}\=\+{\tt{boolp}}{\tt{ }}{\tt{clk}}{\tt{ }}{\tt{level}}{\tt{ }}{\tt{parametric}} \\ 
{\tt{tri-state}}{\tt{)}}\- \\ 
{\bf then }{\rm{t-or-err}}\,(\=\+{\rm{car}}\,({\it{d\/}}) $\in\;${\bf{N}}${}$, \\ 
{\tt{'}}{\tt{slope-not-number}}, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,({\tt{'}}{\tt{slope}}, {\rm{car}}\,({\it{d\/}})), \\ 
{\rm{list}}\,({\tt{'}}{\tt{output-type}}, {\it{type\/}}))\-)\-\index{t-or-err} \\ 
{\bf elseif }{\it{type\/}} $\in$ {\tt{'}}{\tt{(}}{\tt{ttl}}{\tt{ }}{\tt{ttl-tri-state}}{\tt{)}} \\ 
{\bf then }{\rm{t-or-err}}\,(\=\+{\rm{ps-pfp}}\,({\rm{car}}\,({\it{d\/}}))\index{ps-pfp}, \\ 
{\tt{'}}{\tt{slope-not-ps-pf}}, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,({\tt{'}}{\tt{slope}}, {\rm{car}}\,({\it{d\/}})), \\ 
{\rm{list}}\,({\tt{'}}{\tt{output-type}}, {\it{type\/}}))\-)\-\index{t-or-err} \\ 
{\bf else }{\rm{t-or-err}}\,(\=\+\=\+({\rm{car}}\,({\it{d\/}}) $\in\;${\bf{N}}${}$) \\ 
$\vee$$\;\;\;\;${\rm{ps-pfp}}\,({\rm{car}}\,({\it{d\/}}))\index{ps-pfp}\-, \\ 
{\tt{'}}{\tt{slope-not-number-or-ps-pf}}, \\ 
{\rm{car}}\,({\it{d\/}}))\-\index{t-or-err}$\;${\bf  endif}\-, \\ 
{\rm{t-or-err}}\,(\=\+{\rm{cadr}}\,({\it{d\/}}) $\in\;${\bf{N}}${}$, \\ 
{\tt{'}}{\tt{intercept-not-number}}, \\ 
{\rm{cadr}}\,({\it{d\/}}))\-\index{t-or-err}, \\ 
{\rm{nil-or-err}}\,({\rm{last-cdr}}\,({\it{d\/}})\index{last-cdr}, {\tt{'}}{\tt{not-proper-list}})\index{nil-or-err})\-, \\ 
{\it{label\/}})\-\index{err-and} \\ 
{\bf else }{\rm{pred-error}}\,({\it{label\/}}, {\rm{list}}\,({\tt{'}}{\tt{length-not-2}}, {\it{d\/}}))\index{pred-error}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable phalf-delay-ok; name this event `phalf-delay-ok-off'.\index{phalf-delay-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pdelay-ok} \\  
\=\+{\rm{pdelay-ok}}\,({\it{delay\/}}, {\it{output\/}}, {\it{type\/}}, {\it{out-depends\/}}, {\it{inputs\/}})\index{pdelay-ok} \\ 
$=$$\;\;\;\;${\rm{label-error}}\,(\=\+\=\+{\bf if }{\rm{litatom}}\,({\it{delay\/}}) $\vee$ {\rm{indexp}}\,({\it{delay\/}})\index{indexp} \\ 
{\bf then }{\rm{p-name-prop-value-ok}}\,(\=\+{\it{delay\/}}, \\ 
{\it{type\/}}, \\ 
{\it{out-depends\/}}, \\ 
{\it{inputs\/}}, \\ 
{\tt{'}}{\tt{unknown-delay}})\-\index{p-name-prop-value-ok} \\ 
{\bf elseif }{\rm{listp}}\,({\it{delay\/}}) $\wedge$ ({\rm{car}}\,({\it{delay\/}}) $=$ {\tt{'}}{\tt{or}}) \\ 
{\bf then }{\rm{p-t-wire-args-ok}}\,(\=\+{\rm{cdr}}\,({\it{delay\/}}), \\ 
{\it{out-depends\/}}, \\ 
{\it{inputs\/}}, \\ 
{\tt{'}}{\tt{bad-or-delay}})\-\index{p-t-wire-args-ok} \\ 
{\bf elseif }{\rm{length}}\,({\it{delay\/}})\index{length} $=$ {\tt{2}} \\ 
{\bf then }{\rm{err-and}}\,(\=\+{\rm{list}}\,(\=\+{\rm{nlistp-or-err}}\,(\=\+{\it{type\/}}, \\ 
{\tt{'}}{\tt{expected-literal-type}})\-\index{nlistp-or-err}, \\ 
{\rm{phalf-delay-ok}}\,(\=\+{\rm{car}}\,({\it{delay\/}}), \\ 
{\it{type\/}}, \\ 
{\tt{'}}{\tt{low-to-high}})\-\index{phalf-delay-ok}, \\ 
{\rm{phalf-delay-ok}}\,(\=\+{\rm{cadr}}\,({\it{delay\/}}), \\ 
{\it{type\/}}, \\ 
{\tt{'}}{\tt{high-to-low}})\-\index{phalf-delay-ok}, \\ 
{\rm{nil-or-err}}\,(\=\+{\rm{last-cdr}}\,({\it{delay\/}})\index{last-cdr}, \\ 
{\tt{'}}{\tt{not-proper-list}})\-\index{nil-or-err})\-, \\ 
{\tt{'}}{\tt{bad-literal-delay}})\-\index{err-and} \\ 
{\bf else }{\rm{pred-error}}\,({\tt{'}}{\tt{unknown-delay}}, {\it{delay\/}})\index{pred-error}$\;${\bf  endif}\-, \\ 
{\rm{output-label}}\,({\it{output\/}})\index{output-label})\-\index{label-error}\-
\end{tabbing}


\noindent{\sc Event}:   Enable pdelay-ok; name this event `pdelay-ok-off'.\index{pdelay-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pdelays-errors} \\  
\=\+{\rm{pdelays-errors}}\,({\it{delays\/}}, {\it{outputs\/}}, {\it{types\/}}, {\it{out-depends\/}}, {\it{inputs\/}})\index{pdelays-errors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{delays\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{t-or-err}}\,(\=\+{\rm{listp}}\,({\it{outputs\/}}) $\vee$ ({\it{outputs\/}} $\in\;${\bf{N}}${}$), \\ 
{\tt{'}}{\tt{too-many-delays}}, \\ 
{\rm{cons}}\,({\rm{length}}\,({\it{delays\/}})\index{length}, {\tt{'}}{\tt{(}}{\tt{extras}}{\tt{)}}))\-\index{t-or-err}, \\ 
{\rm{cons}}\,(\=\+{\rm{pdelay-ok}}\,(\=\+{\rm{car}}\,({\it{delays\/}}), \\ 
{\rm{io-car}}\,({\it{outputs\/}})\index{io-car}, \\ 
{\rm{ucar}}\,({\it{types\/}})\index{ucar}, \\ 
{\rm{ucar}}\,({\it{out-depends\/}})\index{ucar}, \\ 
{\it{inputs\/}})\-\index{pdelay-ok}, \\ 
{\rm{pdelays-errors}}\,(\=\+{\rm{cdr}}\,({\it{delays\/}}), \\ 
{\rm{io-cdr}}\,({\it{outputs\/}})\index{io-cdr}, \\ 
{\rm{ucdr}}\,({\it{types\/}})\index{ucdr}, \\ 
{\rm{ucdr}}\,({\it{out-depends\/}})\index{ucdr}, \\ 
{\it{inputs\/}})\-\index{pdelays-errors})\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{nil-or-err}}\,({\it{delays\/}}, {\tt{'}}{\tt{not-proper-list}})\index{nil-or-err}, \\ 
{\rm{nlistp-or-err}}\,({\it{outputs\/}}, {\tt{'}}{\tt{outputs-without-delays}})\index{nlistp-or-err})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable pdelays-errors; name this event `pdelays-errors-off'.\index{pdelays-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pdelays-ok} \\  
\=\+{\rm{pdelays-ok}}\,({\it{delays\/}}, {\it{alist\/}})\index{pdelays-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+{\rm{pdelays-errors}}\,(\=\+{\it{delays\/}}, \\ 
\=\+{\bf if }{\rm{unknownp}}\,({\rm{value}}\,({\tt{'}}{\tt{outputs}}, {\it{alist\/}})\index{value})\index{unknownp}$\;\;${\bf then }{\tt{1}} \\ 
{\bf else }{\rm{value}}\,({\tt{'}}{\tt{outputs}}, {\it{alist\/}})\index{value}$\;${\bf  endif}\-, \\ 
{\rm{value}}\,({\tt{'}}{\tt{output-types}}, {\it{alist\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{out-depends}}, {\it{alist\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{inputs}}, {\it{alist\/}})\index{value})\-\index{pdelays-errors}, \\ 
{\tt{'}}{\tt{delays}})\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable pdelays-ok; name this event `pdelays-ok-off'.\index{pdelays-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pdrive-ok} \\  
\=\+{\rm{pdrive-ok}}\,({\it{drive\/}}, {\it{output\/}}, {\it{type\/}}, {\it{out-depends\/}}, {\it{inputs\/}})\index{pdrive-ok} \\ 
$=$$\;\;\;\;${\rm{label-error}}\,(\=\+\=\+{\bf if }{\rm{litatom}}\,({\it{drive\/}}) $\vee$ {\rm{indexp}}\,({\it{drive\/}})\index{indexp} \\ 
{\bf then }{\rm{p-name-prop-value-ok}}\,(\=\+{\it{drive\/}}, \\ 
{\it{type\/}}, \\ 
{\it{out-depends\/}}, \\ 
{\it{inputs\/}}, \\ 
{\tt{'}}{\tt{unknown-drive}})\-\index{p-name-prop-value-ok} \\ 
{\bf elseif }{\rm{listp}}\,({\it{drive\/}}) $\wedge$ ({\rm{car}}\,({\it{drive\/}}) $=$ {\tt{'}}{\tt{min}}) \\ 
{\bf then }{\rm{p-t-wire-args-ok}}\,(\=\+{\rm{cdr}}\,({\it{drive\/}}), \\ 
{\it{out-depends\/}}, \\ 
{\it{inputs\/}}, \\ 
{\tt{'}}{\tt{bad-min-drive}})\-\index{p-t-wire-args-ok} \\ 
{\bf elseif }{\it{type\/}} $\in$ {\tt{'}}{\tt{(}}\=\+{\tt{boolp}}{\tt{ }}{\tt{clk}}{\tt{ }}{\tt{level}}{\tt{ }}{\tt{parametric}} \\ 
{\tt{tri-state}}{\tt{)}}\- \\ 
{\bf then }{\rm{t-or-err}}\,(\=\+{\it{drive\/}} $\in\;${\bf{N}}${}$, \\ 
{\tt{'}}{\tt{bad-drive}}, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,({\tt{'}}{\tt{drive}}, {\it{drive\/}}), \\ 
{\rm{list}}\,({\tt{'}}{\tt{type}}, {\it{type\/}}))\-)\-\index{t-or-err} \\ 
{\bf elseif }{\it{type\/}} $\in$ {\tt{'}}{\tt{(}}{\tt{ttl}}{\tt{ }}{\tt{ttl-tri-state}}{\tt{)}} \\ 
{\bf then }{\rm{t-or-err}}\,(\=\+{\rm{map}}\,({\it{drive\/}})\index{map}, \\ 
{\tt{'}}{\tt{bad-drive}}, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,({\tt{'}}{\tt{drive}}, {\it{drive\/}}), \\ 
{\rm{list}}\,({\tt{'}}{\tt{type}}, {\it{type\/}}))\-)\-\index{t-or-err} \\ 
{\bf elseif }({\it{drive\/}} $\in\;${\bf{N}}${}$) $\vee$ {\rm{map}}\,({\it{drive\/}})\index{map} \\ 
{\bf then }{\rm{t-or-err}}\,(\=\+{\it{type\/}} $\simeq\;${{\bf{nil}}}${}$, \\ 
{\tt{'}}{\tt{expected-literal-type}}, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,({\tt{'}}{\tt{drive}}, {\it{drive\/}}), \\ 
{\rm{list}}\,({\tt{'}}{\tt{type}}, {\it{type\/}}))\-)\-\index{t-or-err} \\ 
{\bf else }{\rm{pred-error}}\,({\tt{'}}{\tt{unknown-drive}}, {\it{drive\/}})\index{pred-error}$\;${\bf  endif}\-, \\ 
{\rm{output-label}}\,({\it{output\/}})\index{output-label})\-\index{label-error}\-
\end{tabbing}


\noindent{\sc Event}:   Enable pdrive-ok; name this event `pdrive-ok-off'.\index{pdrive-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pdrives-errors} \\  
\=\+{\rm{pdrives-errors}}\,({\it{drives\/}}, {\it{outputs\/}}, {\it{types\/}}, {\it{out-depends\/}}, {\it{inputs\/}})\index{pdrives-errors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{drives\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{t-or-err}}\,(\=\+{\rm{listp}}\,({\it{outputs\/}}) $\vee$ ({\it{outputs\/}} $\in\;${\bf{N}}${}$), \\ 
{\tt{'}}{\tt{too-many-drives}}, \\ 
{\rm{cons}}\,({\rm{length}}\,({\it{drives\/}})\index{length}, {\tt{'}}{\tt{(}}{\tt{extras}}{\tt{)}}))\-\index{t-or-err}, \\ 
{\rm{cons}}\,(\=\+{\rm{pdrive-ok}}\,(\=\+{\rm{car}}\,({\it{drives\/}}), \\ 
{\rm{io-car}}\,({\it{outputs\/}})\index{io-car}, \\ 
{\rm{ucar}}\,({\it{types\/}})\index{ucar}, \\ 
{\rm{ucar}}\,({\it{out-depends\/}})\index{ucar}, \\ 
{\it{inputs\/}})\-\index{pdrive-ok}, \\ 
{\rm{pdrives-errors}}\,(\=\+{\rm{cdr}}\,({\it{drives\/}}), \\ 
{\rm{io-cdr}}\,({\it{outputs\/}})\index{io-cdr}, \\ 
{\rm{ucdr}}\,({\it{types\/}})\index{ucdr}, \\ 
{\rm{ucdr}}\,({\it{out-depends\/}})\index{ucdr}, \\ 
{\it{inputs\/}})\-\index{pdrives-errors})\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{nil-or-err}}\,({\it{drives\/}}, {\tt{'}}{\tt{not-proper-list}})\index{nil-or-err}, \\ 
{\rm{nlistp-or-err}}\,({\it{outputs\/}}, {\tt{'}}{\tt{outputs-without-drives}})\index{nlistp-or-err})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable pdrives-errors; name this event `pdrives-errors-off'.\index{pdrives-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pdrives-ok} \\  
\=\+{\rm{pdrives-ok}}\,({\it{drives\/}}, {\it{alist\/}})\index{pdrives-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+{\rm{pdrives-errors}}\,(\=\+{\it{drives\/}}, \\ 
\=\+{\bf if }{\rm{unknownp}}\,({\rm{value}}\,({\tt{'}}{\tt{outputs}}, {\it{alist\/}})\index{value})\index{unknownp}$\;\;${\bf then }{\tt{1}} \\ 
{\bf else }{\rm{value}}\,({\tt{'}}{\tt{outputs}}, {\it{alist\/}})\index{value}$\;${\bf  endif}\-, \\ 
{\rm{value}}\,({\tt{'}}{\tt{output-types}}, {\it{alist\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{out-depends}}, {\it{alist\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{inputs}}, {\it{alist\/}})\index{value})\-\index{pdrives-errors}, \\ 
{\tt{'}}{\tt{drives}})\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable pdrives-ok; name this event `pdrives-ok-off'.\index{pdrives-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ploading-ok} \\  
\=\+{\rm{ploading-ok}}\,({\it{loading\/}}, {\it{input\/}}, {\it{type\/}})\index{ploading-ok} \\ 
$=$$\;\;\;\;${\rm{label-error}}\,(\=\+{\rm{t-or-err}}\,(\=\+\=\+{\bf if }{\it{type\/}} $\in$ {\tt{'}}{\tt{(}}\=\+{\tt{boolp}}{\tt{ }}{\tt{clk}}{\tt{ }}{\tt{free}}{\tt{ }}{\tt{level}} \\ 
{\tt{parametric}}{\tt{ }}{\tt{tri-state}}{\tt{)}}\- \\ 
{\bf then }{\it{loading\/}} $\in\;${\bf{N}}${}$ \\ 
{\bf elseif }{\it{type\/}} $\in$ {\tt{'}}{\tt{(}}{\tt{ttl}}{\tt{ }}{\tt{ttl-tri-state}}{\tt{)}} \\ 
{\bf then }{\rm{pfp}}\,({\it{loading\/}})\index{pfp} \\ 
{\bf else }({\it{loading\/}} $\in\;${\bf{N}}${}$) $\vee$ {\rm{pfp}}\,({\it{loading\/}})\index{pfp}$\;${\bf  endif}\-, \\ 
{\tt{'}}{\tt{bad-loading}}, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,({\tt{'}}{\tt{loading}}, {\it{loading\/}}), \\ 
{\rm{list}}\,({\tt{'}}{\tt{input-type}}, {\it{type\/}}))\-)\-\index{t-or-err}, \\ 
{\rm{input-label}}\,({\it{input\/}})\index{input-label})\-\index{label-error}\-
\end{tabbing}


\noindent{\sc Event}:   Enable ploading-ok; name this event `ploading-ok-off'.\index{ploading-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ploadings-errors} \\  
\=\+{\rm{ploadings-errors}}\,({\it{loadings\/}}, {\it{inputs\/}}, {\it{types\/}})\index{ploadings-errors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{loadings\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{t-or-err}}\,(\=\+{\rm{listp}}\,({\it{inputs\/}}) $\vee$ ({\it{inputs\/}} $\in\;${\bf{N}}${}$), \\ 
{\tt{'}}{\tt{too-many-loadings}}, \\ 
{\rm{cons}}\,({\rm{length}}\,({\it{loadings\/}})\index{length}, {\tt{'}}{\tt{(}}{\tt{extras}}{\tt{)}}))\-\index{t-or-err}, \\ 
{\rm{cons}}\,(\=\+{\rm{ploading-ok}}\,({\rm{car}}\,({\it{loadings\/}}), {\rm{io-car}}\,({\it{inputs\/}})\index{io-car}, {\rm{ucar}}\,({\it{types\/}})\index{ucar})\index{ploading-ok}, \\ 
{\rm{ploadings-errors}}\,(\=\+{\rm{cdr}}\,({\it{loadings\/}}), \\ 
{\rm{io-cdr}}\,({\it{inputs\/}})\index{io-cdr}, \\ 
{\rm{ucdr}}\,({\it{types\/}})\index{ucdr})\-\index{ploadings-errors})\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{nil-or-err}}\,({\it{loadings\/}}, {\tt{'}}{\tt{not-proper-list}})\index{nil-or-err}, \\ 
{\rm{nlistp-or-err}}\,({\it{inputs\/}}, {\tt{'}}{\tt{inputs-without-loadings}})\index{nlistp-or-err})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ploadings-errors; name this event `ploadings-errors-off'.\index{ploadings-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ploadings-ok} \\  
\=\+{\rm{ploadings-ok}}\,({\it{loadings\/}}, {\it{alist\/}})\index{ploadings-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+{\rm{ploadings-errors}}\,(\=\+{\it{loadings\/}}, \\ 
\=\+{\bf if }{\rm{unknownp}}\,({\rm{value}}\,({\tt{'}}{\tt{inputs}}, {\it{alist\/}})\index{value})\index{unknownp}$\;\;${\bf then }{\tt{1}} \\ 
{\bf else }{\rm{value}}\,({\tt{'}}{\tt{inputs}}, {\it{alist\/}})\index{value}$\;${\bf  endif}\-, \\ 
{\rm{value}}\,({\tt{'}}{\tt{input-types}}, {\it{alist\/}})\index{value})\-\index{ploadings-errors}, \\ 
{\tt{'}}{\tt{loadings}})\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable ploadings-ok; name this event `ploadings-ok-off'.\index{ploadings-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{plsi-name-ok} \\  
\=\+{\rm{plsi-name-ok}}\,({\it{lsi-name-entry\/}}, {\it{alist\/}})\index{plsi-name-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+{\rm{list}}\,(\=\+{\rm{lsi-name-ok}}\,(\=\+\=\+{\bf if }{\rm{listp}}\,({\it{lsi-name-entry\/}}) \\ 
{\bf then }{\rm{car}}\,({\it{lsi-name-entry\/}}) \\ 
{\bf else }{\it{lsi-name-entry\/}}$\;${\bf  endif}\-, \\ 
{\tt{64}})\-\index{lsi-name-ok}, \\ 
\=\+{\bf if }\=\+({\it{lsi-name-entry\/}} $\simeq\;${{\bf{nil}}}${}$) \\ 
$\vee$$\;\;\;\;${\rm{unknownp}}\,({\rm{value}}\,({\tt{'}}{\tt{inputs}}, {\it{alist\/}})\index{value})\index{unknownp}\-$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{t-or-err}}\,(\=\+{\rm{set-equal}}\,(\=\+{\rm{cdr}}\,({\it{lsi-name-entry\/}}), \\ 
{\rm{value}}\,({\tt{'}}{\tt{inputs}}, {\it{alist\/}})\index{value})\-\index{set-equal}, \\ 
{\tt{'}}{\tt{input-conflict}}, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{inputs}}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{inputs}}, {\it{alist\/}})\index{value})\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{lsi-inputs}}, \\ 
{\rm{cdr}}\,({\it{lsi-name-entry\/}}))\-)\-)\-\index{t-or-err}$\;${\bf  endif}\-, \\ 
\=\+{\bf if }\=\+{\rm{unknownp}}\,({\rm{value}}\,({\tt{'}}{\tt{inputs}}, {\it{alist\/}})\index{value})\index{unknownp} \\ 
$\vee$$\;\;\;\;${\rm{unknownp}}\,({\rm{value}}\,({\tt{'}}{\tt{outputs}}, {\it{alist\/}})\index{value})\index{unknownp}\-$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{t-or-err}}\,(\=\+\=\+{\rm{listp}}\,({\rm{intersection}}\,(\=\+{\rm{value}}\,(\=\+{\tt{'}}{\tt{inputs}}, \\ 
{\it{alist\/}})\-\index{value}, \\ 
{\rm{value}}\,(\=\+{\tt{'}}{\tt{outputs}}, \\ 
{\it{alist\/}})\-\index{value})\-\index{intersection}) \\ 
$=$$\;\;\;\;${\rm{is-head}}\,(\=\+{\rm{unpack}}\,({\tt{'}}{\tt{bd}}), \\ 
{\rm{unpack}}\,(\=\+{\bf if }{\rm{listp}}\,({\it{lsi-name-entry\/}}) \\ 
{\bf then }{\rm{car}}\,({\it{lsi-name-entry\/}}) \\ 
{\bf else }{\it{lsi-name-entry\/}}$\;${\bf  endif}\-))\-\index{is-head}\-, \\ 
{\tt{'}}{\tt{bidirect-conflict}}, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{lsi-name}}, \\ 
\=\+{\bf if }{\rm{listp}}\,({\it{lsi-name-entry\/}}) \\ 
{\bf then }{\rm{car}}\,({\it{lsi-name-entry\/}}) \\ 
{\bf else }{\it{lsi-name-entry\/}}$\;${\bf  endif}\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{io-signals}}, \\ 
{\rm{intersection}}\,(\=\+{\rm{value}}\,(\=\+{\tt{'}}{\tt{inputs}}, \\ 
{\it{alist\/}})\-\index{value}, \\ 
{\rm{value}}\,(\=\+{\tt{'}}{\tt{outputs}}, \\ 
{\it{alist\/}})\-\index{value})\-\index{intersection})\-)\-)\-\index{t-or-err}$\;${\bf  endif}\-)\-, \\ 
{\tt{'}}{\tt{lsi-name}})\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable plsi-name-ok; name this event `plsi-name-ok-off'.\index{plsi-name-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pout-depends-one-ok} \\  
\=\+{\rm{pout-depends-one-ok}}\,({\it{out-depends\/}}, {\it{output\/}}, {\it{inputs\/}})\index{pout-depends-one-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{unknownp}}\,({\it{inputs\/}})\index{unknownp} \\ 
{\bf then }{\rm{name-list-ok}}\,({\it{out-depends\/}}, {\rm{output-label}}\,({\it{output\/}})\index{output-label}, {\bf{f}})\index{name-list-ok} \\ 
{\bf else }{\rm{err-and}}\,(\=\+{\rm{list}}\,(\=\+{\rm{subset-or-err}}\,(\=\+{\it{out-depends\/}}, \\ 
{\it{inputs\/}}, \\ 
{\tt{'}}{\tt{unknown-output-dependencies}})\-\index{subset-or-err}, \\ 
{\rm{no-duplicates-or-err}}\,(\=\+{\it{out-depends\/}}, \\ 
{\tt{'}}{\tt{duplicates}})\-\index{no-duplicates-or-err}, \\ 
{\rm{nil-or-err}}\,(\=\+{\rm{last-cdr}}\,({\it{out-depends\/}})\index{last-cdr}, \\ 
{\tt{'}}{\tt{not-proper-list}})\-\index{nil-or-err})\-, \\ 
{\rm{output-label}}\,({\it{output\/}})\index{output-label})\-\index{err-and}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable pout-depends-one-ok; name this event `pout-depends-one-ok-off'.\index{pout-depends-one-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pout-depends-errors} \\  
\=\+{\rm{pout-depends-errors}}\,({\it{out-depends\/}}, {\it{outputs\/}}, {\it{inputs\/}})\index{pout-depends-errors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{out-depends\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{t-or-err}}\,(\=\+{\rm{listp}}\,({\it{outputs\/}}) $\vee$ ({\it{outputs\/}} $\in\;${\bf{N}}${}$), \\ 
{\tt{'}}{\tt{too-many-out-depends}}, \\ 
{\rm{cons}}\,({\rm{length}}\,({\it{out-depends\/}})\index{length}, {\tt{'}}{\tt{(}}{\tt{extras}}{\tt{)}}))\-\index{t-or-err}, \\ 
{\rm{cons}}\,(\=\+{\rm{pout-depends-one-ok}}\,(\=\+{\rm{car}}\,({\it{out-depends\/}}), \\ 
{\rm{io-car}}\,({\it{outputs\/}})\index{io-car}, \\ 
{\it{inputs\/}})\-\index{pout-depends-one-ok}, \\ 
{\rm{pout-depends-errors}}\,(\=\+{\rm{cdr}}\,({\it{out-depends\/}}), \\ 
{\rm{io-cdr}}\,({\it{outputs\/}})\index{io-cdr}, \\ 
{\it{inputs\/}})\-\index{pout-depends-errors})\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{nil-or-err}}\,({\it{out-depends\/}}, {\tt{'}}{\tt{not-proper-list}})\index{nil-or-err}, \\ 
{\rm{nlistp-or-err}}\,(\=\+{\it{outputs\/}}, \\ 
{\tt{'}}{\tt{outputs-without-out-depends}})\-\index{nlistp-or-err})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable pout-depends-errors; name this event `pout-depends-errors-off'.\index{pout-depends-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pout-depends-ok} \\  
\=\+{\rm{pout-depends-ok}}\,({\it{out-depends\/}}, {\it{alist\/}})\index{pout-depends-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+{\rm{pout-depends-errors}}\,(\=\+{\it{out-depends\/}}, \\ 
\=\+{\bf if }{\rm{unknownp}}\,({\rm{value}}\,({\tt{'}}{\tt{outputs}}, {\it{alist\/}})\index{value})\index{unknownp} \\ 
{\bf then }{\tt{1}} \\ 
{\bf else }{\rm{value}}\,({\tt{'}}{\tt{outputs}}, {\it{alist\/}})\index{value}$\;${\bf  endif}\-, \\ 
{\rm{value}}\,({\tt{'}}{\tt{inputs}}, {\it{alist\/}})\index{value})\-\index{pout-depends-errors}, \\ 
{\tt{'}}{\tt{out-depends}})\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable pout-depends-ok; name this event `pout-depends-ok-off'.\index{pout-depends-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pstates-ok} \\  
\=\+{\rm{pstates-ok}}\,({\it{states\/}})\index{pstates-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{states\/}}) \\ 
{\bf then }{\rm{err-and}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{t-or-err}}\,(\=\+{\rm{listp}}\,({\rm{cdr}}\,({\it{states\/}})), \\ 
{\tt{'}}{\tt{list-of-length-1-not-allowed}}, \\ 
{\it{states\/}})\-\index{t-or-err}, \\ 
{\rm{name-list-errors}}\,({\it{states\/}}, {\bf{f}})\index{name-list-errors})\-, \\ 
{\tt{'}}{\tt{states}})\-\index{err-and} \\ 
{\bf elseif }{\it{states\/}} $=$ {\bf{nil}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{t-or-err}}\,(\=\+{\rm{name-okp}}\,({\it{states\/}})\index{name-okp}, \\ 
{\tt{'}}{\tt{states}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{bad-name}}, {\it{states\/}}))\-\index{t-or-err}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable pstates-ok; name this event `pstates-ok-off'.\index{pstates-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{addressed-state} \\  
\=\+{\rm{addressed-state}}\,({\it{address-bits\/}}, {\it{word-value\/}})\index{addressed-state} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{address-bits\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\it{word-value\/}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{addressed-state}}\,({\it{address-bits\/}} $-\;1$, {\it{word-value\/}})\index{addressed-state}, \\ 
{\rm{addressed-state}}\,({\it{address-bits\/}} $-\;1$, {\it{word-value\/}})\index{addressed-state})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable addressed-state; name this event `addressed-state-off'.\index{addressed-state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{boolp-list-ok} \\  
\=\+{\rm{boolp-list-ok}}\,({\it{lst\/}}, {\it{label\/}})\index{boolp-list-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+{\rm{list}}\,(\=\+{\rm{nlistp-or-err}}\,(\=\+{\rm{remove-duplicates}}\,({\rm{delete*}}\,({\tt{'}}{\tt{boolp}}, {\it{lst\/}})\index{delete*})\index{remove-duplicates}, \\ 
{\tt{'}}{\tt{not-boolp}})\-\index{nlistp-or-err}, \\ 
{\rm{nil-or-err}}\,({\rm{last-cdr}}\,({\it{lst\/}})\index{last-cdr}, {\tt{'}}{\tt{not-proper-list}})\index{nil-or-err})\-, \\ 
{\it{label\/}})\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable boolp-list-ok; name this event `boolp-list-ok-off'.\index{boolp-list-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{literal-state-type-ok} \\  
\=\+{\rm{literal-state-type-ok}}\,({\it{type\/}})\index{literal-state-type-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{ramp}}\,({\it{type\/}})\index{ramp}$\;\;${\bf then }{\rm{boolp-list-ok}}\,({\rm{ram-guts}}\,({\it{type\/}})\index{ram-guts}, {\tt{'}}{\tt{bad-ram-type}})\index{boolp-list-ok} \\ 
{\bf elseif }{\rm{romp}}\,({\it{type\/}})\index{romp} \\ 
{\bf then }{\rm{boolp-list-ok}}\,({\rm{rom-guts}}\,({\it{type\/}})\index{rom-guts}, {\tt{'}}{\tt{bad-rom-type}})\index{boolp-list-ok} \\ 
{\bf elseif }{\rm{stubp}}\,({\it{type\/}})\index{stubp} \\ 
{\bf then }{\rm{boolp-list-ok}}\,({\rm{stub-guts}}\,({\it{type\/}})\index{stub-guts}, {\tt{'}}{\tt{bad-stub-type}})\index{boolp-list-ok} \\ 
{\bf else }{\rm{t-or-err}}\,({\it{type\/}} $=$ {\tt{'}}{\tt{boolp}}, {\tt{'}}{\tt{unknown-type}}, {\it{type\/}})\index{t-or-err}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable literal-state-type-ok; name this event `literal-state-type-ok-off'.\index{literal-state-type-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pmemory-word-call-ok} \\  
\=\+{\rm{pmemory-word-call-ok}}\,({\it{type\/}})\index{pmemory-word-call-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{type\/}}) $\wedge$ ({\rm{car}}\,({\it{type\/}}) $\in$ {\tt{'}}{\tt{(}}{\tt{ram}}{\tt{ }}{\tt{rom}}{\tt{ }}{\tt{stub}}{\tt{)}}) \\ 
{\bf then }\=\+{\bf if }{\rm{net-errorp}}\,({\rm{function-call-ok}}\,({\it{type\/}}, {\tt{1}})\index{function-call-ok})\index{net-errorp} \\ 
{\bf then }{\rm{function-call-ok}}\,({\it{type\/}}, {\tt{1}})\index{function-call-ok} \\ 
{\bf else }{\rm{label-error}}\,(\=\+\=\+{\bf if }{\rm{caadr}}\,({\it{type\/}}) $=$ {\tt{'}}{\tt{quote}} \\ 
{\bf then }\=\+{\bf if }{\rm{net-errorp}}\,({\rm{function-call-ok}}\,(\=\+{\rm{cadr}}\,({\it{type\/}}), \\ 
{\tt{1}})\-\index{function-call-ok})\index{net-errorp} \\ 
{\bf then }{\rm{function-call-ok}}\,({\rm{cadr}}\,({\it{type\/}}), {\tt{1}})\index{function-call-ok} \\ 
{\bf else }{\rm{boolp-list-ok}}\,(\=\+{\rm{cadadr}}\,({\it{type\/}}), \\ 
{\tt{'}}{\tt{bad-memory-bit-types}})\-\index{boolp-list-ok}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{pred-error}}\,(\=\+{\tt{'}}{\tt{unknown-memory-bits-call}}, \\ 
{\rm{cadr}}\,({\it{type\/}}))\-\index{pred-error}$\;${\bf  endif}\-, \\ 
{\rm{cons}}\,({\tt{'}}{\tt{bad}}, {\rm{cons}}\,({\rm{car}}\,({\it{type\/}}), {\tt{'}}{\tt{(}}{\tt{call}}{\tt{)}})))\-\index{label-error}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{pred-error}}\,({\tt{'}}{\tt{not-memory-word-call}}, {\it{type\/}})\index{pred-error}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable pmemory-word-call-ok; name this event `pmemory-word-call-ok-off'.\index{pmemory-word-call-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{paddressed-state-call-ok} \\  
\=\+{\rm{paddressed-state-call-ok}}\,({\it{type\/}})\index{paddressed-state-call-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{type\/}}) $\wedge$ ({\rm{car}}\,({\it{type\/}}) $=$ {\tt{'}}{\tt{addressed-state}}) \\ 
{\bf then }\=\+{\bf if }{\rm{net-errorp}}\,({\rm{function-call-ok}}\,({\it{type\/}}, {\tt{2}})\index{function-call-ok})\index{net-errorp} \\ 
{\bf then }{\rm{function-call-ok}}\,({\it{type\/}}, {\tt{2}})\index{function-call-ok} \\ 
{\bf else }{\rm{err-and}}\,(\=\+{\rm{list}}\,(\=\+{\rm{t-or-err}}\,(\=\+{\rm{cadr}}\,({\it{type\/}}) $\in\;${\bf{N}}${}$, \\ 
{\tt{'}}{\tt{address-bits-not-number}}, \\ 
{\rm{cadr}}\,({\it{type\/}}))\-\index{t-or-err}, \\ 
{\rm{pmemory-word-call-ok}}\,({\rm{caddr}}\,({\it{type\/}}))\index{pmemory-word-call-ok})\-, \\ 
{\tt{'}}{\tt{(}}{\tt{bad}}{\tt{ }}{\tt{addressed-state}}{\tt{ }}{\tt{call}}{\tt{)}})\-\index{err-and}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{pred-error}}\,({\tt{'}}{\tt{not-addressed-state-call}}, {\it{type\/}})\index{pred-error}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable paddressed-state-call-ok; name this event `paddressed-state-call-ok-off'.\index{paddressed-state-call-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{one-pstate-type-ok} \\  
\=\+{\rm{one-pstate-type-ok}}\,({\it{type\/}})\index{one-pstate-type-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{type\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{literal-state-type-ok}}\,({\it{type\/}})\index{literal-state-type-ok} \\ 
{\bf elseif }{\rm{car}}\,({\it{type\/}}) $\in$ {\tt{'}}{\tt{(}}{\tt{ram}}{\tt{ }}{\tt{rom}}{\tt{ }}{\tt{stub}}{\tt{)}} \\ 
{\bf then }{\rm{pmemory-word-call-ok}}\,({\it{type\/}})\index{pmemory-word-call-ok} \\ 
{\bf elseif }{\rm{car}}\,({\it{type\/}}) $=$ {\tt{'}}{\tt{addressed-state}} \\ 
{\bf then }{\rm{paddressed-state-call-ok}}\,({\it{type\/}})\index{paddressed-state-call-ok} \\ 
{\bf else }{\rm{boolp-list-ok}}\,({\it{type\/}}, {\tt{'}}{\tt{bad-type-list}})\index{boolp-list-ok}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable one-pstate-type-ok; name this event `one-pstate-type-ok-off'.\index{one-pstate-type-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pstate-type-list-errors} \\  
\=\+{\rm{pstate-type-list-errors}}\,({\it{types\/}}, {\it{fname\/}})\index{pstate-type-list-errors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{types\/}}) \\ 
{\bf then }\=\+{\bf if }\=\+({\it{fname\/}} $=$ {\tt{'}}{\tt{mem-32x32}}) \\ 
$\wedge$$\;\;\;\;$({\rm{car}}\,({\it{types\/}}) $\in$ {\tt{'}}{\tt{(}}{\tt{numberp}}{\tt{ }}{\tt{number-listp}}{\tt{)}})\- \\ 
{\bf then }{\rm{pstate-type-list-errors}}\,({\rm{cdr}}\,({\it{types\/}}), {\it{fname\/}})\index{pstate-type-list-errors} \\ 
{\bf else }{\rm{insert}}\,(\=\+{\rm{one-pstate-type-ok}}\,({\rm{car}}\,({\it{types\/}}))\index{one-pstate-type-ok}, \\ 
{\rm{pstate-type-list-errors}}\,({\rm{cdr}}\,({\it{types\/}}), {\it{fname\/}})\index{pstate-type-list-errors})\-\index{insert}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{list}}\,({\rm{nil-or-err}}\,({\it{types\/}}, {\tt{'}}{\tt{not-proper-list}})\index{nil-or-err})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable pstate-type-list-errors; name this event `pstate-type-list-errors-off'.\index{pstate-type-list-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pstate-type-ok} \\  
\=\+{\rm{pstate-type-ok}}\,({\it{type\/}}, {\it{state\/}}, {\it{fname\/}})\index{pstate-type-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+({\it{type\/}} $\simeq\;${{\bf{nil}}}${}$) \\ 
$\vee$$\;\;\;\;$({\rm{car}}\,({\it{type\/}}) $\in$ {\tt{'}}{\tt{(}}{\tt{ram}}{\tt{ }}{\tt{rom}}{\tt{ }}{\tt{stub}}{\tt{ }}{\tt{addressed-state}}{\tt{)}})\- \\ 
{\bf then }{\rm{label-error}}\,({\rm{one-pstate-type-ok}}\,({\it{type\/}})\index{one-pstate-type-ok}, {\rm{state-label}}\,({\it{state\/}})\index{state-label})\index{label-error} \\ 
{\bf else }{\rm{err-and}}\,(\=\+{\rm{pstate-type-list-errors}}\,({\it{type\/}}, {\it{fname\/}})\index{pstate-type-list-errors}, \\ 
{\rm{state-label}}\,({\it{state\/}})\index{state-label})\-\index{err-and}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable pstate-type-ok; name this event `pstate-type-ok-off'.\index{pstate-type-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pstate-types-errors} \\  
\=\+{\rm{pstate-types-errors}}\,({\it{types\/}}, {\it{states\/}}, {\it{fname\/}})\index{pstate-types-errors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{types\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{t-or-err}}\,(\=\+{\rm{listp}}\,({\it{states\/}}) $\vee$ ({\it{states\/}} $\in\;${\bf{N}}${}$), \\ 
{\tt{'}}{\tt{too-many-state-types}}, \\ 
{\rm{cons}}\,({\rm{length}}\,({\it{types\/}})\index{length}, {\tt{'}}{\tt{(}}{\tt{extras}}{\tt{)}}))\-\index{t-or-err}, \\ 
{\rm{cons}}\,(\=\+{\rm{pstate-type-ok}}\,({\rm{car}}\,({\it{types\/}}), {\rm{io-car}}\,({\it{states\/}})\index{io-car}, {\it{fname\/}})\index{pstate-type-ok}, \\ 
{\rm{pstate-types-errors}}\,({\rm{cdr}}\,({\it{types\/}}), {\rm{io-cdr}}\,({\it{states\/}})\index{io-cdr}, {\it{fname\/}})\index{pstate-types-errors})\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{nil-or-err}}\,({\it{types\/}}, {\tt{'}}{\tt{not-proper-list}})\index{nil-or-err}, \\ 
{\rm{nlistp-or-err}}\,({\it{states\/}}, {\tt{'}}{\tt{states-without-types}})\index{nlistp-or-err})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable pstate-types-errors; name this event `pstate-types-errors-off'.\index{pstate-types-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pstate-types-ok} \\  
\=\+{\rm{pstate-types-ok}}\,({\it{state-types\/}}, {\it{alist\/}})\index{pstate-types-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+\=\+{\bf if }\=\+{\rm{listp}}\,({\rm{value}}\,({\tt{'}}{\tt{states}}, {\it{alist\/}})\index{value}) \\ 
$\vee$$\;\;\;\;$({\rm{value}}\,({\tt{'}}{\tt{states}}, {\it{alist\/}})\index{value} $=$ {\bf{nil}})\- \\ 
{\bf then }{\rm{pstate-types-errors}}\,(\=\+{\it{state-types\/}}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{states}}, {\it{alist\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{primp-name}}, {\it{alist\/}})\index{value})\-\index{pstate-types-errors} \\ 
{\bf else }{\rm{list}}\,({\rm{pstate-type-ok}}\,(\=\+{\it{state-types\/}}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{states}}, {\it{alist\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{primp-name}}, {\it{alist\/}})\index{value})\-\index{pstate-type-ok})$\;${\bf  endif}\-, \\ 
{\tt{'}}{\tt{state-types}})\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable pstate-types-ok; name this event `pstate-types-ok-off'.\index{pstate-types-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{unknown-args} \\  
\=\+{\rm{unknown-args}}\,({\it{x\/}}, {\it{signals\/}}, {\it{states\/}}, {\it{arg-listp\/}})\index{unknown-args} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{arg-listp\/}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\rm{unknown-args}}\,({\rm{car}}\,({\it{x\/}}), {\it{signals\/}}, {\it{states\/}}, {\bf{f}})\index{unknown-args} \\ 
$\cup$$\;\;\;\;${\rm{unknown-args}}\,({\rm{cdr}}\,({\it{x\/}}), {\it{signals\/}}, {\it{states\/}}, {\bf{t}})\index{unknown-args}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }\=\+{\bf if }({\it{x\/}} $\in$ {\it{signals\/}}) $\vee$ ({\it{x\/}} $\in$ {\it{states\/}})$\;\;${\bf then }{\bf{nil}} \\ 
{\bf elseif }{\rm{unknownp}}\,({\it{signals\/}})\index{unknownp} $\vee$ {\rm{unknownp}}\,({\it{states\/}})\index{unknownp} \\ 
{\bf then }\=\+{\bf if }{\rm{name-okp}}\,({\it{x\/}})\index{name-okp}$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{list}}\,({\it{x\/}})$\;${\bf  endif}\- \\ 
{\bf else }{\rm{list}}\,({\it{x\/}})$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{quote}}$\;\;${\bf then }{\bf{nil}} \\ 
{\bf elseif }{\rm{litatom}}\,({\rm{car}}\,({\it{x\/}}))$\;\;${\bf then }{\rm{unknown-args}}\,({\rm{cdr}}\,({\it{x\/}}), {\it{signals\/}}, {\it{states\/}}, {\bf{t}})\index{unknown-args} \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable unknown-args; name this event `unknown-args-off'.\index{unknown-args-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{presult-form-errors} \\  
\=\+{\rm{presult-form-errors}}\,({\it{x\/}}, {\it{arg-listp\/}})\index{presult-form-errors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{arg-listp\/}} \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{net-errorp}}\,({\rm{presult-form-errors}}\,({\rm{car}}\,({\it{x\/}}), {\bf{f}})\index{presult-form-errors})\index{net-errorp} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{presult-form-errors}}\,({\rm{car}}\,({\it{x\/}}), {\bf{f}})\index{presult-form-errors}, \\ 
{\rm{presult-form-errors}}\,({\rm{cdr}}\,({\it{x\/}}), {\bf{t}})\index{presult-form-errors})\- \\ 
{\bf else }{\rm{append}}\,(\=\+{\rm{presult-form-errors}}\,({\rm{car}}\,({\it{x\/}}), {\bf{f}})\index{presult-form-errors}, \\ 
{\rm{presult-form-errors}}\,({\rm{cdr}}\,({\it{x\/}}), {\bf{t}})\index{presult-form-errors})\-$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{x\/}} $=$ {\bf{nil}}$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{list}}\,({\rm{pred-error}}\,({\tt{'}}{\tt{not-proper-list}}, {\it{x\/}})\index{pred-error})$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{net-errorp}}\,({\rm{function-call-ok}}\,(\=\+{\it{x\/}}, \\ 
\=\+{\bf case on }{\rm{car}}\,({\it{x\/}}): \\ 
{\bf case = }{\it{quote\/}} \\ 
{\bf then }{\tt{1}} \\ 
{\bf case = }{\it{cons\/}} \\ 
{\bf $\;\;$then }{\tt{2}} \\ 
{\bf otherwise }{\sc{unknown}}\index{unknown}$\;${\bf  endcase}\-)\-\index{function-call-ok})\index{net-errorp} \\ 
{\bf then }{\rm{function-call-ok}}\,(\=\+{\it{x\/}}, \\ 
\=\+{\bf case on }{\rm{car}}\,({\it{x\/}}): \\ 
{\bf case = }{\it{quote\/}} \\ 
{\bf then }{\tt{1}} \\ 
{\bf case = }{\it{cons\/}} \\ 
{\bf $\;\;$then }{\tt{2}} \\ 
{\bf otherwise }{\sc{unknown}}\index{unknown}$\;${\bf  endcase}\-)\-\index{function-call-ok} \\ 
{\bf elseif }{\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{quote}}$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{presult-form-errors}}\,({\rm{cdr}}\,({\it{x\/}}), {\bf{t}})\index{presult-form-errors}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable presult-form-errors; name this event `presult-form-errors-off'.\index{presult-form-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{presult-ok} \\  
\=\+{\rm{presult-ok}}\,({\it{result\/}}, {\it{signals\/}}, {\it{states\/}}, {\it{label\/}})\index{presult-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{nlistp-or-err}}\,(\=\+{\rm{unknown-args}}\,({\it{result\/}}, {\it{signals\/}}, {\it{states\/}}, {\bf{f}})\index{unknown-args}, \\ 
{\tt{'}}{\tt{unknown-args}})\-\index{nlistp-or-err}, \\ 
{\rm{presult-form-errors}}\,({\rm{list}}\,({\it{result\/}}), {\bf{t}})\index{presult-form-errors})\-, \\ 
{\it{label\/}})\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable presult-ok; name this event `presult-ok-off'.\index{presult-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{results-length} \\  
\=\+{\rm{results-length}}\,({\it{x\/}})\index{results-length} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf elseif }{\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{cons}}$\;\;${\bf then }$1\;+$ {\rm{results-length}}\,({\rm{caddr}}\,({\it{x\/}}))\index{results-length} \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable results-length; name this event `results-length-off'.\index{results-length-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{presults-errors} \\  
\=\+{\rm{presults-errors}}\,({\it{results\/}}, {\it{outputs\/}}, {\it{out-depends\/}}, {\it{inputs\/}}, {\it{states\/}}, {\it{label\/}})\index{presults-errors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{results\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }{\rm{list}}\,({\rm{pred-error}}\,({\tt{'}}{\tt{unknown-dual-eval-form}}, {\it{results\/}})\index{pred-error}) \\ 
{\bf elseif }{\it{results\/}} $=$ {\tt{'}}{\tt{'}}{\tt{nil}} \\ 
{\bf then }{\rm{list}}\,({\rm{nlistp-or-err}}\,(\=\+{\it{outputs\/}}, \\ 
{\rm{cons}}\,({\tt{'}}{\tt{missing}}, {\rm{cons}}\,({\it{label\/}}, {\tt{'}}{\tt{(}}{\tt{values}}{\tt{)}})))\-\index{nlistp-or-err}) \\ 
{\bf elseif }{\rm{car}}\,({\it{results\/}}) $=$ {\tt{'}}{\tt{cons}} \\ 
{\bf then }\=\+{\bf if }{\rm{net-errorp}}\,({\rm{function-call-ok}}\,({\it{results\/}}, {\tt{2}})\index{function-call-ok})\index{net-errorp} \\ 
{\bf then }{\rm{list}}\,({\rm{function-call-ok}}\,({\it{results\/}}, {\tt{2}})\index{function-call-ok}) \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{t-or-err}}\,(\=\+{\rm{listp}}\,({\it{outputs\/}}) $\vee$ ({\it{outputs\/}} $\in\;${\bf{N}}${}$), \\ 
{\tt{'}}{\tt{too-many-values}}, \\ 
{\rm{cons}}\,(\=\+{\rm{results-length}}\,({\it{results\/}})\index{results-length}, \\ 
{\tt{'}}{\tt{(}}{\tt{or}}{\tt{ }}{\tt{more}}{\tt{ }}{\tt{extras}}{\tt{)}})\-)\-\index{t-or-err}, \\ 
{\rm{cons}}\,(\=\+{\rm{presult-ok}}\,(\=\+{\rm{cadr}}\,({\it{results\/}}), \\ 
{\rm{out-prop-signals}}\,(\=\+{\rm{ucar}}\,({\it{out-depends\/}})\index{ucar}, \\ 
{\it{inputs\/}})\-\index{out-prop-signals}, \\ 
{\it{states\/}}, \\ 
{\rm{io-label}}\,({\rm{io-car}}\,({\it{outputs\/}})\index{io-car}, {\it{label\/}})\index{io-label})\-\index{presult-ok}, \\ 
{\rm{presults-errors}}\,(\=\+{\rm{caddr}}\,({\it{results\/}}), \\ 
{\rm{io-cdr}}\,({\it{outputs\/}})\index{io-cdr}, \\ 
{\rm{ucdr}}\,({\it{out-depends\/}})\index{ucdr}, \\ 
{\it{inputs\/}}, \\ 
{\it{states\/}}, \\ 
{\it{label\/}})\-\index{presults-errors})\-)\-$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{listp}}\,({\it{outputs\/}}) $\vee$ ({\it{outputs\/}} $=$ {\bf{nil}}) \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{pred-error}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{evaluation}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{should}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{return}}, \\ 
{\rm{cons}}\,(\=\+{\rm{length}}\,({\it{outputs\/}})\index{length}, \\ 
{\tt{'}}{\tt{(}}{\tt{results}}{\tt{)}})\-)\-)\-)\-, \\ 
{\it{results\/}})\-\index{pred-error}, \\ 
{\rm{presult-ok}}\,(\=\+{\it{results\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{states\/}}, \\ 
{\rm{list}}\,({\it{label\/}}, {\tt{'}}{\tt{list}}, {\it{outputs\/}}))\-\index{presult-ok})\- \\ 
{\bf else }{\rm{list}}\,({\rm{presult-ok}}\,(\=\+{\it{results\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{states\/}}, \\ 
{\tt{'}}{\tt{unknown-outputs}})\-\index{presult-ok})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable presults-errors; name this event `presults-errors-off'.\index{presults-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{presults-ok} \\  
\=\+{\rm{presults-ok}}\,({\it{results\/}}, {\it{alist\/}})\index{presults-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+{\rm{presults-errors}}\,(\=\+{\it{results\/}}, \\ 
\=\+{\bf if }{\rm{unknownp}}\,({\rm{value}}\,({\tt{'}}{\tt{outputs}}, {\it{alist\/}})\index{value})\index{unknownp}$\;\;${\bf then }{\tt{1}} \\ 
{\bf else }{\rm{value}}\,({\tt{'}}{\tt{outputs}}, {\it{alist\/}})\index{value}$\;${\bf  endif}\-, \\ 
{\rm{value}}\,({\tt{'}}{\tt{out-depends}}, {\it{alist\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{inputs}}, {\it{alist\/}})\index{value}, \\ 
\=\+{\bf if }{\rm{unknownp}}\,({\rm{value}}\,({\tt{'}}{\tt{states}}, {\it{alist\/}})\index{value})\index{unknownp} \\ 
{\bf then }{\rm{value}}\,({\tt{'}}{\tt{states}}, {\it{alist\/}})\index{value} \\ 
{\bf else }{\rm{m-states-list}}\,({\rm{value}}\,(\=\+{\tt{'}}{\tt{states}}, \\ 
{\it{alist\/}})\-\index{value})\index{m-states-list}$\;${\bf  endif}\-, \\ 
{\tt{'}}{\tt{output}})\-\index{presults-errors}, \\ 
{\tt{'}}{\tt{results}})\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable presults-ok; name this event `presults-ok-off'.\index{presults-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pnew-states-ok} \\  
\=\+{\rm{pnew-states-ok}}\,({\it{new-states\/}}, {\it{alist\/}})\index{pnew-states-ok} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+\=\+{\bf if }\=\+{\rm{listp}}\,({\rm{value}}\,({\tt{'}}{\tt{states}}, {\it{alist\/}})\index{value}) \\ 
$\vee$$\;\;\;\;$({\rm{value}}\,({\tt{'}}{\tt{states}}, {\it{alist\/}})\index{value} $=$ {\bf{nil}})\- \\ 
{\bf then }{\rm{presults-errors}}\,(\=\+{\it{new-states\/}}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{states}}, {\it{alist\/}})\index{value}, \\ 
{\sc{unknown}}\index{unknown}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{inputs}}, {\it{alist\/}})\index{value}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{states}}, {\it{alist\/}})\index{value}, \\ 
{\tt{'}}{\tt{state}})\-\index{presults-errors} \\ 
{\bf elseif }\=\+{\rm{litatom}}\,({\rm{value}}\,({\tt{'}}{\tt{states}}, {\it{alist\/}})\index{value}) \\ 
$\vee$$\;\;\;\;${\rm{indexp}}\,({\rm{value}}\,({\tt{'}}{\tt{states}}, {\it{alist\/}})\index{value})\index{indexp}\- \\ 
{\bf then }{\rm{list}}\,({\rm{presult-ok}}\,(\=\+{\it{new-states\/}}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{inputs}}, {\it{alist\/}})\index{value}, \\ 
{\rm{list}}\,({\rm{value}}\,({\tt{'}}{\tt{states}}, {\it{alist\/}})\index{value}), \\ 
{\rm{state-label}}\,({\rm{value}}\,({\tt{'}}{\tt{states}}, {\it{alist\/}})\index{value})\index{state-label})\-\index{presult-ok}) \\ 
{\bf else }{\rm{presults-errors}}\,(\=\+{\it{new-states\/}}, \\ 
{\tt{1}}, \\ 
{\sc{unknown}}\index{unknown}, \\ 
{\rm{value}}\,({\tt{'}}{\tt{inputs}}, {\it{alist\/}})\index{value}, \\ 
{\sc{unknown}}\index{unknown}, \\ 
{\tt{'}}{\tt{state}})\-\index{presults-errors}$\;${\bf  endif}\-, \\ 
{\tt{'}}{\tt{new-states}})\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable pnew-states-ok; name this event `pnew-states-ok-off'.\index{pnew-states-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{primitive-prop-ok} \\  
\=\+{\rm{primitive-prop-ok}}\,({\it{prop\/}}, {\it{alist\/}}, {\it{keys\/}})\index{primitive-prop-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{prop\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\it{prop\/}}) $\in$ {\it{keys\/}} \\ 
{\bf then }{\rm{pred-error}}\,({\tt{'}}{\tt{duplicate-property}}, {\it{prop\/}})\index{pred-error} \\ 
{\bf elseif }{\rm{car}}\,({\it{prop\/}}) $=$ {\tt{'}}{\tt{delays}}$\;\;${\bf then }{\rm{pdelays-ok}}\,({\rm{cdr}}\,({\it{prop\/}}), {\it{alist\/}})\index{pdelays-ok} \\ 
{\bf elseif }{\rm{car}}\,({\it{prop\/}}) $=$ {\tt{'}}{\tt{drives}}$\;\;${\bf then }{\rm{pdrives-ok}}\,({\rm{cdr}}\,({\it{prop\/}}), {\it{alist\/}})\index{pdrives-ok} \\ 
{\bf elseif }{\rm{car}}\,({\it{prop\/}}) $=$ {\tt{'}}{\tt{input-types}} \\ 
{\bf then }{\rm{pin-types-ok}}\,({\rm{cdr}}\,({\it{prop\/}}), {\it{alist\/}})\index{pin-types-ok} \\ 
{\bf elseif }{\rm{car}}\,({\it{prop\/}}) $=$ {\tt{'}}{\tt{inputs}} \\ 
{\bf then }{\rm{name-list-ok}}\,({\rm{cdr}}\,({\it{prop\/}}), {\tt{'}}{\tt{inputs}}, {\bf{f}})\index{name-list-ok} \\ 
{\bf elseif }{\rm{car}}\,({\it{prop\/}}) $=$ {\tt{'}}{\tt{loadings}} \\ 
{\bf then }{\rm{ploadings-ok}}\,({\rm{cdr}}\,({\it{prop\/}}), {\it{alist\/}})\index{ploadings-ok} \\ 
{\bf elseif }{\rm{car}}\,({\it{prop\/}}) $=$ {\tt{'}}{\tt{lsi-name}} \\ 
{\bf then }{\rm{plsi-name-ok}}\,({\rm{cdr}}\,({\it{prop\/}}), {\it{alist\/}})\index{plsi-name-ok} \\ 
{\bf elseif }{\rm{car}}\,({\it{prop\/}}) $=$ {\tt{'}}{\tt{new-states}} \\ 
{\bf then }{\rm{pnew-states-ok}}\,({\rm{cdr}}\,({\it{prop\/}}), {\it{alist\/}})\index{pnew-states-ok} \\ 
{\bf elseif }{\rm{car}}\,({\it{prop\/}}) $=$ {\tt{'}}{\tt{out-depends}} \\ 
{\bf then }{\rm{pout-depends-ok}}\,({\rm{cdr}}\,({\it{prop\/}}), {\it{alist\/}})\index{pout-depends-ok} \\ 
{\bf elseif }{\rm{car}}\,({\it{prop\/}}) $=$ {\tt{'}}{\tt{output-types}} \\ 
{\bf then }{\rm{pout-types-ok}}\,({\rm{cdr}}\,({\it{prop\/}}), {\it{alist\/}})\index{pout-types-ok} \\ 
{\bf elseif }{\rm{car}}\,({\it{prop\/}}) $=$ {\tt{'}}{\tt{outputs}} \\ 
{\bf then }{\rm{name-list-ok}}\,({\rm{cdr}}\,({\it{prop\/}}), {\tt{'}}{\tt{outputs}}, {\bf{f}})\index{name-list-ok} \\ 
{\bf elseif }{\rm{car}}\,({\it{prop\/}}) $=$ {\tt{'}}{\tt{results}} \\ 
{\bf then }{\rm{presults-ok}}\,({\rm{cdr}}\,({\it{prop\/}}), {\it{alist\/}})\index{presults-ok} \\ 
{\bf elseif }{\rm{car}}\,({\it{prop\/}}) $=$ {\tt{'}}{\tt{state-types}} \\ 
{\bf then }{\rm{pstate-types-ok}}\,({\rm{cdr}}\,({\it{prop\/}}), {\it{alist\/}})\index{pstate-types-ok} \\ 
{\bf elseif }{\rm{car}}\,({\it{prop\/}}) $=$ {\tt{'}}{\tt{states}}$\;\;${\bf then }{\rm{pstates-ok}}\,({\rm{cdr}}\,({\it{prop\/}}))\index{pstates-ok} \\ 
{\bf elseif }\=\+{\rm{car}}\,({\it{prop\/}}) \\ 
$\in$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{gates}}{\tt{ }}{\tt{pads}}{\tt{ }}{\tt{primitives}}{\tt{ }}{\tt{transistors}}{\tt{)}}\- \\ 
{\bf then }{\rm{t-or-err}}\,(\=\+{\rm{cdr}}\,({\it{prop\/}}) $\in\;${\bf{N}}${}$, \\ 
{\rm{car}}\,({\it{prop\/}}), \\ 
{\rm{list}}\,({\tt{'}}{\tt{value-not-number}}, {\rm{cdr}}\,({\it{prop\/}})))\-\index{t-or-err} \\ 
{\bf else }{\rm{pred-error}}\,({\tt{'}}{\tt{unknown-property}}, {\rm{car}}\,({\it{prop\/}}))\index{pred-error}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{pred-error}}\,({\tt{'}}{\tt{not-key-value-pair}}, {\it{prop\/}})\index{pred-error}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable primitive-prop-ok; name this event `primitive-prop-ok-off'.\index{primitive-prop-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{primitive-prop-errors} \\  
\=\+{\rm{primitive-prop-errors}}\,({\it{props\/}}, {\it{alist\/}}, {\it{keys\/}})\index{primitive-prop-errors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{props\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{primitive-prop-ok}}\,({\rm{car}}\,({\it{props\/}}), {\it{alist\/}}, {\it{keys\/}})\index{primitive-prop-ok}, \\ 
{\rm{primitive-prop-errors}}\,(\=\+{\rm{cdr}}\,({\it{props\/}}), \\ 
{\it{alist\/}}, \\ 
{\rm{cons}}\,({\rm{caar}}\,({\it{props\/}}), {\it{keys\/}}))\-\index{primitive-prop-errors})\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{nlistp-or-err}}\,(\=\+{\rm{delete*}}\,(\=\+{\tt{'}}{\tt{pads}}, \\ 
\=\+{\bf if }{\rm{subset}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{new-states}} \\ 
{\tt{state-types}} \\ 
{\tt{states}}{\tt{)}}\-, \\ 
{\rm{set-diff}}\,(\=\+{\sc{primitive-properties}}\index{primitive-properties}, \\ 
{\it{keys\/}})\-\index{set-diff})\-\index{subset} \\ 
{\bf then }{\rm{set-diff}}\,(\=\+{\rm{set-diff}}\,(\=\+{\sc{primitive-properties}}\index{primitive-properties}, \\ 
{\it{keys\/}})\-\index{set-diff}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{new-states}} \\ 
{\tt{state-types}} \\ 
{\tt{states}}{\tt{)}}\-)\-\index{set-diff} \\ 
{\bf else }{\rm{set-diff}}\,(\=\+{\sc{primitive-properties}}\index{primitive-properties}, \\ 
{\it{keys\/}})\-\index{set-diff}$\;${\bf  endif}\-)\-\index{delete*}, \\ 
{\tt{'}}{\tt{missing-properties}})\-\index{nlistp-or-err}, \\ 
{\rm{nil-or-err}}\,({\it{props\/}}, {\tt{'}}{\tt{not-proper-list}})\index{nil-or-err})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable primitive-prop-errors; name this event `primitive-prop-errors-off'.\index{primitive-prop-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ok-name-list} \\  
\=\+{\rm{ok-name-list}}\,({\it{pname\/}}, {\it{props\/}})\index{ok-name-list} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{pname-listp}}\,({\rm{value-or-unknown}}\,({\it{pname\/}}, {\it{props\/}})\index{value-or-unknown})\index{pname-listp} \\ 
{\bf then }{\rm{value-or-unknown}}\,({\it{pname\/}}, {\it{props\/}})\index{value-or-unknown} \\ 
{\bf else }{\sc{unknown}}\index{unknown}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ok-name-list; name this event `ok-name-list-off'.\index{ok-name-list-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ok-states} \\  
\=\+{\rm{ok-states}}\,({\it{props\/}})\index{ok-states} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{boundp}}\,({\tt{'}}{\tt{states}}, {\it{props\/}})\index{boundp} \\ 
{\bf then }\=\+{\bf if }\=\+{\rm{listp}}\,({\rm{value}}\,({\tt{'}}{\tt{states}}, {\it{props\/}})\index{value}) \\ 
$\vee$$\;\;\;\;$({\rm{value}}\,({\tt{'}}{\tt{states}}, {\it{props\/}})\index{value} $=$ {\bf{nil}})\- \\ 
{\bf then }\=\+{\bf if }{\rm{pname-listp}}\,({\rm{value}}\,({\tt{'}}{\tt{states}}, {\it{props\/}})\index{value})\index{pname-listp} \\ 
{\bf then }{\rm{value}}\,({\tt{'}}{\tt{states}}, {\it{props\/}})\index{value} \\ 
{\bf else }{\sc{unknown}}\index{unknown}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{name-okp}}\,({\rm{value}}\,({\tt{'}}{\tt{states}}, {\it{props\/}})\index{value})\index{name-okp} \\ 
{\bf then }{\rm{value}}\,({\tt{'}}{\tt{states}}, {\it{props\/}})\index{value} \\ 
{\bf else }{\sc{unknown}}\index{unknown}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ok-states; name this event `ok-states-off'.\index{ok-states-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ok-out-depends} \\  
\=\+{\rm{ok-out-depends}}\,({\it{ods\/}}, {\it{inputs\/}})\index{ok-out-depends} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{ods\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+\=\+{\bf if }\=\+{\rm{pname-listp}}\,({\rm{car}}\,({\it{ods\/}}))\index{pname-listp} \\ 
$\wedge$$\;\;\;\;$({\rm{unknownp}}\,({\it{inputs\/}})\index{unknownp} $\vee$ {\rm{subset}}\,({\rm{car}}\,({\it{ods\/}}), {\it{inputs\/}})\index{subset})\- \\ 
{\bf then }{\rm{car}}\,({\it{ods\/}}) \\ 
{\bf else }{\sc{unknown}}\index{unknown}$\;${\bf  endif}\-, \\ 
{\rm{ok-out-depends}}\,({\rm{cdr}}\,({\it{ods\/}}), {\it{inputs\/}})\index{ok-out-depends})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ok-out-depends; name this event `ok-out-depends-off'.\index{ok-out-depends-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ok-input-types} \\  
\=\+{\rm{ok-input-types}}\,({\it{types\/}})\index{ok-input-types} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{types\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+\=\+{\bf if }{\rm{car}}\,({\it{types\/}}) $\in$ {\sc{all-input-types}}\index{all-input-types}$\;\;${\bf then }{\rm{car}}\,({\it{types\/}}) \\ 
{\bf else }{\sc{unknown}}\index{unknown}$\;${\bf  endif}\-, \\ 
{\rm{ok-input-types}}\,({\rm{cdr}}\,({\it{types\/}}))\index{ok-input-types})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ok-input-types; name this event `ok-input-types-off'.\index{ok-input-types-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ok-output-types} \\  
\=\+{\rm{ok-output-types}}\,({\it{out-types\/}}, {\it{out-depends\/}}, {\it{inputs\/}})\index{ok-output-types} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{out-types\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+\=\+{\bf if }\=\+{\bf if }{\rm{listp}}\,({\rm{car}}\,({\it{out-types\/}})) \\ 
{\bf then }\=\+{\rm{properp}}\,({\rm{car}}\,({\it{out-types\/}}))\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{car}}\,({\it{out-types\/}}))\index{length} $=$ {\tt{1}}) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{unknownp}}\,({\rm{out-prop-signals}}\,(\=\+{\rm{ucar}}\,({\it{out-depends\/}})\index{ucar}, \\ 
{\it{inputs\/}})\-\index{out-prop-signals})\index{unknownp} \\ 
{\bf then }{\rm{name-okp}}\,({\rm{caar}}\,({\it{out-types\/}}))\index{name-okp} \\ 
{\bf else }\=\+{\rm{caar}}\,({\it{out-types\/}}) \\ 
$\in$$\;\;\;\;${\rm{out-prop-signals}}\,(\=\+{\rm{ucar}}\,({\it{out-depends\/}})\index{ucar}, \\ 
{\it{inputs\/}})\-\index{out-prop-signals}\-$\;${\bf  endif}\-\- \\ 
{\bf else }{\rm{car}}\,({\it{out-types\/}}) $\in$ {\rm{all-output-types}}\,({\bf{nil}})\index{all-output-types}$\;${\bf  endif}\- \\ 
{\bf then }{\rm{car}}\,({\it{out-types\/}}) \\ 
{\bf else }{\sc{unknown}}\index{unknown}$\;${\bf  endif}\-, \\ 
{\rm{ok-output-types}}\,({\rm{cdr}}\,({\it{out-types\/}}), {\rm{ucdr}}\,({\it{out-depends\/}})\index{ucdr}, {\it{inputs\/}})\index{ok-output-types})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ok-output-types; name this event `ok-output-types-off'.\index{ok-output-types-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{parent-props-alist} \\  
\=\+{\rm{parent-props-alist}}\,({\it{primp-entry\/}})\index{parent-props-alist} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{cons}}\,({\tt{'}}{\tt{primp-name}}, {\rm{car}}\,({\it{primp-entry\/}})), \\ 
{\rm{cons}}\,({\tt{'}}{\tt{inputs}}, {\rm{ok-name-list}}\,({\tt{'}}{\tt{inputs}}, {\rm{cdr}}\,({\it{primp-entry\/}}))\index{ok-name-list}), \\ 
{\rm{cons}}\,({\tt{'}}{\tt{outputs}}, {\rm{ok-name-list}}\,({\tt{'}}{\tt{outputs}}, {\rm{cdr}}\,({\it{primp-entry\/}}))\index{ok-name-list}), \\ 
{\rm{cons}}\,({\tt{'}}{\tt{states}}, {\rm{ok-states}}\,({\rm{cdr}}\,({\it{primp-entry\/}}))\index{ok-states}), \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{out-depends}}, \\ 
{\rm{ok-out-depends}}\,(\=\+{\rm{value}}\,({\tt{'}}{\tt{out-depends}}, {\rm{cdr}}\,({\it{primp-entry\/}}))\index{value}, \\ 
{\rm{ok-name-list}}\,({\tt{'}}{\tt{inputs}}, {\rm{cdr}}\,({\it{primp-entry\/}}))\index{ok-name-list})\-\index{ok-out-depends})\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{input-types}}, \\ 
{\rm{ok-input-types}}\,({\rm{value}}\,({\tt{'}}{\tt{input-types}}, {\rm{cdr}}\,({\it{primp-entry\/}}))\index{value})\index{ok-input-types})\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{output-types}}, \\ 
{\rm{ok-output-types}}\,(\=\+{\rm{value}}\,({\tt{'}}{\tt{output-types}}, {\rm{cdr}}\,({\it{primp-entry\/}}))\index{value}, \\ 
{\rm{ok-out-depends}}\,(\=\+{\rm{value}}\,(\=\+{\tt{'}}{\tt{out-depends}}, \\ 
{\rm{cdr}}\,({\it{primp-entry\/}}))\-\index{value}, \\ 
{\rm{ok-name-list}}\,(\=\+{\tt{'}}{\tt{inputs}}, \\ 
{\rm{cdr}}\,({\it{primp-entry\/}}))\-\index{ok-name-list})\-\index{ok-out-depends}, \\ 
{\rm{ok-name-list}}\,({\tt{'}}{\tt{inputs}}, {\rm{cdr}}\,({\it{primp-entry\/}}))\index{ok-name-list})\-\index{ok-output-types})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable parent-props-alist; name this event `parent-props-alist-off'.\index{parent-props-alist-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{primitive-ok} \\  
\=\+{\rm{primitive-ok}}\,({\it{p\/}})\index{primitive-ok} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{p\/}}) \\ 
{\bf then }{\rm{err-and}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{t-or-err}}\,(\=\+{\rm{name-okp}}\,({\rm{car}}\,({\it{p\/}}))\index{name-okp}, \\ 
{\tt{'}}{\tt{bad-primitive-name}}, \\ 
{\rm{car}}\,({\it{p\/}}))\-\index{t-or-err}, \\ 
{\rm{primitive-prop-errors}}\,(\=\+{\rm{cdr}}\,({\it{p\/}}), \\ 
{\rm{parent-props-alist}}\,({\it{p\/}})\index{parent-props-alist}, \\ 
{\bf{nil}})\-\index{primitive-prop-errors})\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{primitive}}, {\rm{car}}\,({\it{p\/}})))\-\index{err-and} \\ 
{\bf else }{\rm{pred-error}}\,({\tt{'}}{\tt{not-a-primitive}}, {\it{p\/}})\index{pred-error}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable primitive-ok; name this event `primitive-ok-off'.\index{primitive-ok-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{primp-database-errors} \\  
\=\+{\rm{primp-database-errors}}\,({\it{d\/}})\index{primp-database-errors} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{d\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{primitive-ok}}\,({\rm{car}}\,({\it{d\/}}))\index{primitive-ok}, {\rm{primp-database-errors}}\,({\rm{cdr}}\,({\it{d\/}}))\index{primp-database-errors})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable primp-database-errors; name this event `primp-database-errors-off'.\index{primp-database-errors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{primp-database-predicate} \\  
\=\+{\sc{primp-database-predicate}}\index{primp-database-predicate} \\ 
$=$$\;\;\;\;${\rm{err-and}}\,(\=\+{\rm{primp-database-errors}}\,({\sc{primp-database}}\index{primp-database})\index{primp-database-errors}, \\ 
{\tt{'}}{\tt{primp-database-errors}})\-\index{err-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable primp-database-predicate; name this event `primp-database-predicate-off'.\index{primp-database-predicate-off}

\addvspace{18pt}


\noindent{\sc Event}:   Disable boundp; name this event `boundp-on'.\index{boundp-on}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{subnet0} \\  
\=\+{\rm{subnet0}}\,({\it{flg\/}}, {\it{x0\/}}, {\it{netlist\/}}, {\it{used-modules\/}}, {\it{result\/}})\index{subnet0} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{flg\/}}: \\ 
{\bf case = }{\tt{0}} \\ 
{\bf then }\=\+{\bf if }{\rm{lookup-module}}\,({\it{x0\/}}, {\it{result\/}})\index{lookup-module} $\vee$ ({\it{x0\/}} $\in$ {\it{used-modules\/}}) \\ 
{\bf then }{\it{result\/}} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{lookup-module}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{lookup-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{lookup-module}, \\ 
{\rm{subnet0}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{lookup-module})\index{module-occurrences}, \\ 
{\it{netlist\/}}, \\ 
{\rm{cons}}\,({\it{x0\/}}, {\it{used-modules\/}}), \\ 
{\it{result\/}})\-\index{subnet0})\- \\ 
{\bf else }{\it{result\/}}$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{1}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\it{x0\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{result\/}} \\ 
{\bf else }{\rm{subnet0}}\,(\=\+{\tt{1}}, \\ 
{\rm{cdr}}\,({\it{x0\/}}), \\ 
{\it{netlist\/}}, \\ 
{\it{used-modules\/}}, \\ 
{\rm{subnet0}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-function}, \\ 
{\it{netlist\/}}, \\ 
{\it{used-modules\/}}, \\ 
{\it{result\/}})\-\index{subnet0})\-\index{subnet0}$\;${\bf  endif}\- \\ 
{\bf otherwise }{\bf{f}}$\;${\bf  endcase}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable boundp; name this event `boundp-off1'.\index{boundp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable subnet0; name this event `subnet0-off'.\index{subnet0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{subnet} \\  
{\rm{subnet}}\,({\it{flg\/}}, {\it{x0\/}}, {\it{netlist\/}})\index{subnet} $=$ {\rm{subnet0}}\,({\it{flg\/}}, {\it{x0\/}}, {\it{netlist\/}}, {\bf{nil}}, {\bf{nil}})\index{subnet0}
\end{tabbing}


\noindent{\sc Event}:   Enable subnet; name this event `subnet-off'.\index{subnet-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{delete-null-entries} \\  
\=\+{\rm{delete-null-entries}}\,({\it{database\/}})\index{delete-null-entries} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{database\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{cdar}}\,({\it{database\/}})) \\ 
{\bf then }{\rm{cons}}\,({\rm{car}}\,({\it{database\/}}), {\rm{delete-null-entries}}\,({\rm{cdr}}\,({\it{database\/}}))\index{delete-null-entries}) \\ 
{\bf else }{\rm{delete-null-entries}}\,({\rm{cdr}}\,({\it{database\/}}))\index{delete-null-entries}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable delete-null-entries; name this event `delete-null-entries-off'.\index{delete-null-entries-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{primitive-count} \\  
\=\+{\rm{primitive-count}}\,({\it{flg\/}}, {\it{x0\/}}, {\it{type\/}}, {\it{netlist\/}})\index{primitive-count} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{flg\/}}: \\ 
{\bf case = }{\tt{0}} \\ 
{\bf then }\=\+{\bf if }{\rm{primp}}\,({\it{x0\/}})\index{primp}$\;\;${\bf then }{\rm{primp2}}\,({\it{x0\/}}, {\it{type\/}})\index{primp2} \\ 
{\bf elseif }{\rm{lookup-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{lookup-module} \\ 
{\bf then }\=\+{\bf if }{\rm{net-errorp}}\,({\rm{netlist-properties}}\,(\=\+{\rm{subnet}}\,({\tt{0}}, {\it{x0\/}}, {\it{netlist\/}})\index{subnet}, \\ 
{\rm{list}}\,({\it{type\/}}), \\ 
{\bf{t}})\-\index{netlist-properties})\index{net-errorp} \\ 
{\bf then }{\rm{netlist-properties}}\,({\rm{subnet}}\,({\tt{0}}, {\it{x0\/}}, {\it{netlist\/}})\index{subnet}, {\rm{list}}\,({\it{type\/}}), {\bf{t}})\index{netlist-properties} \\ 
{\bf else }{\rm{value}}\,(\=\+{\it{type\/}}, \\ 
{\rm{value}}\,(\=\+{\it{x0\/}}, \\ 
{\rm{netlist-properties}}\,(\=\+{\rm{subnet}}\,(\=\+{\tt{0}}, \\ 
{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{subnet}, \\ 
{\rm{list}}\,({\it{type\/}}), \\ 
{\bf{t}})\-\index{netlist-properties})\-\index{value})\-\index{value}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{pred-error}}\,({\tt{'}}{\tt{unknown-module}}, {\it{x0\/}})\index{pred-error}$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{1}} \\ 
{\bf $\;\;$then }{\rm{value}}\,(\=\+{\it{type\/}}, \\ 
{\rm{occurrence-data}}\,(\=\+{\rm{required-props}}\,({\rm{list}}\,({\it{type\/}}))\index{required-props}, \\ 
{\it{x0\/}}, \\ 
{\bf{nil}}, \\ 
{\bf{nil}}, \\ 
{\bf{nil}}, \\ 
{\rm{module-database}}\,(\=\+{\rm{subnet}}\,({\tt{1}}, {\it{x0\/}}, {\it{netlist\/}})\index{subnet}, \\ 
{\rm{required-props}}\,({\rm{list}}\,({\it{type\/}}))\index{required-props}, \\ 
{\bf{t}})\-\index{module-database})\-\index{occurrence-data})\-\index{value} \\ 
{\bf otherwise }{\rm{pred-error}}\,(\=\+{\tt{'}}{\tt{unknown-flag}}, \\ 
{\rm{list}}\,({\rm{list}}\,({\tt{'}}{\tt{flg}}, {\it{flg\/}}), {\rm{list}}\,({\tt{'}}{\tt{x0}}, {\it{x0\/}})))\-\index{pred-error}$\;${\bf  endcase}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable primitive-count; name this event `primitive-count-off'.\index{primitive-count-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{out-depends} \\  
\=\+{\rm{out-depends}}\,({\it{flg\/}}, {\it{x0\/}}, {\it{x1\/}}, {\it{x2\/}}, {\it{netlist\/}})\index{out-depends} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{flg\/}}: \\ 
{\bf case = }{\tt{0}} \\ 
{\bf then }\=\+{\bf if }{\rm{primp}}\,({\it{x0\/}})\index{primp} \\ 
{\bf then }{\rm{list-union-values}}\,(\=\+{\rm{primp2}}\,({\it{x0\/}}, {\tt{'}}{\tt{out-depends}})\index{primp2}, \\ 
{\rm{pairlist}}\,({\rm{primp2}}\,({\it{x0\/}}, {\tt{'}}{\tt{inputs}})\index{primp2}, {\it{x1\/}}))\-\index{list-union-values} \\ 
{\bf elseif }{\rm{lookup-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{lookup-module} \\ 
{\bf then }\=\+{\bf if }{\rm{net-errorp}}\,({\rm{netlist-properties}}\,(\=\+{\rm{subnet}}\,({\tt{0}}, {\it{x0\/}}, {\it{netlist\/}})\index{subnet}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{out-depends}}{\tt{ }}{\tt{inputs}}{\tt{)}}\-, \\ 
{\bf{t}})\-\index{netlist-properties})\index{net-errorp} \\ 
{\bf then }{\rm{netlist-properties}}\,(\=\+{\rm{subnet}}\,({\tt{0}}, {\it{x0\/}}, {\it{netlist\/}})\index{subnet}, \\ 
{\tt{'}}{\tt{(}}{\tt{out-depends}}{\tt{ }}{\tt{inputs}}{\tt{)}}, \\ 
{\bf{t}})\-\index{netlist-properties} \\ 
{\bf else }{\rm{list-union-values}}\,(\=\+{\rm{value}}\,(\=\+{\tt{'}}{\tt{out-depends}}, \\ 
{\rm{value}}\,(\=\+{\it{x0\/}}, \\ 
{\rm{netlist-properties}}\,(\=\+{\rm{subnet}}\,(\=\+{\tt{0}}, \\ 
{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{subnet}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{out-depends}} \\ 
{\tt{inputs}}{\tt{)}}\-, \\ 
{\bf{t}})\-\index{netlist-properties})\-\index{value})\-\index{value}, \\ 
{\rm{pairlist}}\,(\=\+{\rm{value}}\,(\=\+{\tt{'}}{\tt{inputs}}, \\ 
{\rm{value}}\,(\=\+{\it{x0\/}}, \\ 
{\rm{netlist-properties}}\,(\=\+{\rm{subnet}}\,(\=\+{\tt{0}}, \\ 
{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{subnet}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{out-depends}} \\ 
{\tt{inputs}}{\tt{)}}\-, \\ 
{\bf{t}})\-\index{netlist-properties})\-\index{value})\-\index{value}, \\ 
{\it{x1\/}})\-)\-\index{list-union-values}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{pred-error}}\,({\tt{'}}{\tt{unknown-module}}, {\it{x0\/}})\index{pred-error}$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{1}} \\ 
{\bf $\;\;$then }{\rm{value}}\,(\=\+{\tt{'}}{\tt{out-depends}}, \\ 
{\rm{occurrence-data}}\,(\=\+{\rm{required-props}}\,({\tt{'}}{\tt{(}}{\tt{out-depends}}{\tt{)}})\index{required-props}, \\ 
{\it{x0\/}}, \\ 
{\it{x1\/}}, \\ 
{\rm{mark-io-outs}}\,({\it{x2\/}}, {\rm{intersection}}\,({\it{x1\/}}, {\it{x2\/}})\index{intersection})\index{mark-io-outs}, \\ 
{\rm{intersection}}\,({\it{x1\/}}, {\it{x2\/}})\index{intersection}, \\ 
{\rm{module-database}}\,(\=\+{\rm{subnet}}\,({\tt{1}}, {\it{x0\/}}, {\it{netlist\/}})\index{subnet}, \\ 
{\rm{required-props}}\,({\tt{'}}{\tt{(}}\=\+{\tt{out-depends}}{\tt{)}}\-)\index{required-props}, \\ 
{\bf{t}})\-\index{module-database})\-\index{occurrence-data})\-\index{value} \\ 
{\bf otherwise }{\rm{pred-error}}\,(\=\+{\tt{'}}{\tt{unknown-flag}}, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,({\tt{'}}{\tt{flg}}, {\it{flg\/}}), \\ 
{\rm{list}}\,({\tt{'}}{\tt{x0}}, {\it{x0\/}}), \\ 
{\rm{list}}\,({\tt{'}}{\tt{x1}}, {\it{x1\/}}), \\ 
{\rm{list}}\,({\tt{'}}{\tt{x2}}, {\it{x2\/}}))\-)\-\index{pred-error}$\;${\bf  endcase}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable out-depends; name this event `out-depends-off'.\index{out-depends-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{dependency-table} \\  
\=\+{\rm{dependency-table}}\,({\it{netlist\/}})\index{dependency-table} \\ 
$=$$\;\;\;\;${\rm{netlist-properties}}\,({\it{netlist\/}}, {\tt{'}}{\tt{(}}{\tt{out-depends}}{\tt{)}}, {\bf{t}})\index{netlist-properties}\-
\end{tabbing}


\noindent{\sc Event}:   Enable dependency-table; name this event `dependency-table-off'.\index{dependency-table-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{output-dependencies} \\  
\=\+{\rm{output-dependencies}}\,({\it{module-name\/}}, {\it{args\/}}, {\it{netlist\/}})\index{output-dependencies} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{net-errorp}}\,(\=\+{\bf if }{\rm{primp}}\,({\it{module-name\/}})\index{primp} \\ 
{\bf then }{\rm{length}}\,({\rm{primp2}}\,({\it{module-name\/}}, {\tt{'}}{\tt{inputs}})\index{primp2})\index{length} \\ 
{\bf elseif }{\rm{lookup-module}}\,({\it{module-name\/}}, {\it{netlist\/}})\index{lookup-module} \\ 
{\bf then }{\rm{length}}\,({\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{module-name\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs})\index{length} \\ 
{\bf else }{\rm{pred-error}}\,({\tt{'}}{\tt{unknown-module}}, {\it{module-name\/}})\index{pred-error}$\;${\bf  endif}\-)\index{net-errorp} \\ 
{\bf then }\=\+{\bf if }{\rm{primp}}\,({\it{module-name\/}})\index{primp} \\ 
{\bf then }{\rm{length}}\,({\rm{primp2}}\,({\it{module-name\/}}, {\tt{'}}{\tt{inputs}})\index{primp2})\index{length} \\ 
{\bf elseif }{\rm{lookup-module}}\,({\it{module-name\/}}, {\it{netlist\/}})\index{lookup-module} \\ 
{\bf then }{\rm{length}}\,({\rm{module-inputs}}\,({\rm{lookup-module}}\,({\it{module-name\/}}, {\it{netlist\/}})\index{lookup-module})\index{module-inputs})\index{length} \\ 
{\bf else }{\rm{pred-error}}\,({\tt{'}}{\tt{unknown-module}}, {\it{module-name\/}})\index{pred-error}$\;${\bf  endif}\- \\ 
{\bf elseif }\=\+{\rm{length}}\,({\it{args\/}})\index{length} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{primp}}\,({\it{module-name\/}})\index{primp} \\ 
{\bf then }{\rm{length}}\,({\rm{primp2}}\,({\it{module-name\/}}, {\tt{'}}{\tt{inputs}})\index{primp2})\index{length} \\ 
{\bf elseif }{\rm{lookup-module}}\,({\it{module-name\/}}, {\it{netlist\/}})\index{lookup-module} \\ 
{\bf then }{\rm{length}}\,({\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{module-name\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs})\index{length} \\ 
{\bf else }{\rm{pred-error}}\,({\tt{'}}{\tt{unknown-module}}, {\it{module-name\/}})\index{pred-error}$\;${\bf  endif}\-\- \\ 
{\bf then }\=\+{\bf if }{\rm{net-errorp}}\,({\rm{out-depends}}\,({\tt{0}}, {\it{module-name\/}}, {\it{args\/}}, {\bf{nil}}, {\it{netlist\/}})\index{out-depends})\index{net-errorp} \\ 
{\bf then }{\rm{out-depends}}\,({\tt{0}}, {\it{module-name\/}}, {\it{args\/}}, {\bf{nil}}, {\it{netlist\/}})\index{out-depends} \\ 
{\bf else }{\rm{list-list-sort}}\,({\rm{out-depends}}\,(\=\+{\tt{0}}, \\ 
{\it{module-name\/}}, \\ 
{\it{args\/}}, \\ 
{\bf{nil}}, \\ 
{\it{netlist\/}})\-\index{out-depends})\index{list-list-sort}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{pred-error}}\,(\=\+{\tt{'}}{\tt{wrong-number-of-args}}, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{module-name\/}}, \\ 
{\tt{'}}{\tt{expects}}, \\ 
\=\+{\bf if }{\rm{primp}}\,({\it{module-name\/}})\index{primp} \\ 
{\bf then }{\rm{length}}\,({\rm{primp2}}\,(\=\+{\it{module-name\/}}, \\ 
{\tt{'}}{\tt{inputs}})\-\index{primp2})\index{length} \\ 
{\bf elseif }{\rm{lookup-module}}\,(\=\+{\it{module-name\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module} \\ 
{\bf then }{\rm{length}}\,({\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{module-name\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs})\index{length} \\ 
{\bf else }{\rm{pred-error}}\,(\=\+{\tt{'}}{\tt{unknown-module}}, \\ 
{\it{module-name\/}})\-\index{pred-error}$\;${\bf  endif}\-)\-, \\ 
{\rm{list}}\,({\tt{'}}{\tt{got}}, {\rm{length}}\,({\it{args\/}})\index{length}, {\it{args\/}}))\-)\-\index{pred-error}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable output-dependencies; name this event `output-dependencies-off'.\index{output-dependencies-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{io-types-collector} \\  
\=\+{\rm{io-types-collector}}\,({\it{types\/}}, {\it{alist\/}})\index{io-types-collector} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{types\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+\=\+{\bf if }{\rm{listp}}\,({\rm{car}}\,({\it{types\/}}))$\;\;${\bf then }{\rm{value}}\,({\rm{caar}}\,({\it{types\/}}), {\it{alist\/}})\index{value} \\ 
{\bf else }{\rm{car}}\,({\it{types\/}})$\;${\bf  endif}\-, \\ 
{\rm{io-types-collector}}\,({\rm{cdr}}\,({\it{types\/}}), {\it{alist\/}})\index{io-types-collector})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable io-types-collector; name this event `io-types-collector-off'.\index{io-types-collector-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{io-types} \\  
\=\+{\rm{io-types}}\,({\it{flg\/}}, {\it{x0\/}}, {\it{x1\/}}, {\it{x2\/}}, {\it{netlist\/}})\index{io-types} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{flg\/}}: \\ 
{\bf case = }{\tt{0}} \\ 
{\bf then }\=\+{\bf if }{\rm{primp}}\,({\it{x0\/}})\index{primp} \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{primp-lookup}}\,({\it{x0\/}}, {\tt{'}}{\tt{input-types}})\index{primp-lookup}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{output-types}}, \\ 
{\rm{io-types-collector}}\,(\=\+{\rm{primp2}}\,({\it{x0\/}}, {\tt{'}}{\tt{output-types}})\index{primp2}, \\ 
{\rm{pairlist}}\,(\=\+{\rm{primp2}}\,({\it{x0\/}}, {\tt{'}}{\tt{inputs}})\index{primp2}, \\ 
{\it{x1\/}})\-)\-\index{io-types-collector})\-)\- \\ 
{\bf elseif }{\rm{lookup-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{lookup-module} \\ 
{\bf then }\=\+{\bf if }{\rm{net-errorp}}\,({\rm{netlist-properties}}\,(\=\+{\rm{subnet}}\,({\tt{0}}, {\it{x0\/}}, {\it{netlist\/}})\index{subnet}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{input-types}} \\ 
{\tt{output-types}}{\tt{ }}{\tt{inputs}}{\tt{)}}\-, \\ 
{\bf{t}})\-\index{netlist-properties})\index{net-errorp} \\ 
{\bf then }{\rm{netlist-properties}}\,(\=\+{\rm{subnet}}\,({\tt{0}}, {\it{x0\/}}, {\it{netlist\/}})\index{subnet}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{input-types}}{\tt{ }}{\tt{output-types}} \\ 
{\tt{inputs}}{\tt{)}}\-, \\ 
{\bf{t}})\-\index{netlist-properties} \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{alist-entry}}\,(\=\+{\tt{'}}{\tt{input-types}}, \\ 
{\rm{value}}\,(\=\+{\it{x0\/}}, \\ 
{\rm{netlist-properties}}\,(\=\+{\rm{subnet}}\,(\=\+{\tt{0}}, \\ 
{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{subnet}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{input-types}} \\ 
{\tt{output-types}} \\ 
{\tt{inputs}}{\tt{)}}\-, \\ 
{\bf{t}})\-\index{netlist-properties})\-\index{value})\-\index{alist-entry}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{output-types}}, \\ 
{\rm{io-types-collector}}\,(\=\+{\rm{value}}\,(\=\+{\tt{'}}{\tt{output-types}}, \\ 
{\rm{value}}\,(\=\+{\it{x0\/}}, \\ 
{\rm{netlist-properties}}\,(\=\+{\rm{subnet}}\,(\=\+{\tt{0}}, \\ 
{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{subnet}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{input-types}} \\ 
{\tt{output-types}} \\ 
{\tt{inputs}}{\tt{)}}\-, \\ 
{\bf{t}})\-\index{netlist-properties})\-\index{value})\-\index{value}, \\ 
{\rm{pairlist}}\,(\=\+{\rm{value}}\,(\=\+{\tt{'}}{\tt{inputs}}, \\ 
{\rm{value}}\,(\=\+{\it{x0\/}}, \\ 
{\rm{netlist-properties}}\,(\=\+{\rm{subnet}}\,(\=\+{\tt{0}}, \\ 
{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{subnet}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{input-types}} \\ 
{\tt{output-types}} \\ 
{\tt{inputs}}{\tt{)}}\-, \\ 
{\bf{t}})\-\index{netlist-properties})\-\index{value})\-\index{value}, \\ 
{\it{x1\/}})\-)\-\index{io-types-collector})\-)\-$\;${\bf  endif}\- \\ 
{\bf else }{\rm{pred-error}}\,({\tt{'}}{\tt{unknown-module}}, {\it{x0\/}})\index{pred-error}$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{1}} \\ 
{\bf $\;\;$then }{\rm{list}}\,(\=\+{\rm{alist-entry}}\,(\=\+{\tt{'}}{\tt{input-types}}, \\ 
{\rm{occurrence-data}}\,(\=\+{\rm{required-props}}\,({\tt{'}}{\tt{(}}\=\+{\tt{input-types}} \\ 
{\tt{output-types}}{\tt{)}}\-)\index{required-props}, \\ 
{\it{x0\/}}, \\ 
{\it{x1\/}}, \\ 
{\rm{mark-io-outs}}\,(\=\+{\it{x2\/}}, \\ 
{\rm{intersection}}\,(\=\+{\it{x1\/}}, \\ 
{\it{x2\/}})\-\index{intersection})\-\index{mark-io-outs}, \\ 
{\rm{intersection}}\,({\it{x1\/}}, {\it{x2\/}})\index{intersection}, \\ 
{\rm{module-database}}\,(\=\+{\rm{subnet}}\,(\=\+{\tt{1}}, \\ 
{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{subnet}, \\ 
{\rm{required-props}}\,({\tt{'}}{\tt{(}}\=\+{\tt{input-types}} \\ 
{\tt{output-types}}{\tt{)}}\-)\index{required-props}, \\ 
{\bf{t}})\-\index{module-database})\-\index{occurrence-data})\-\index{alist-entry}, \\ 
{\rm{alist-entry}}\,(\=\+{\tt{'}}{\tt{output-types}}, \\ 
{\rm{occurrence-data}}\,(\=\+{\rm{required-props}}\,({\tt{'}}{\tt{(}}\=\+{\tt{input-types}} \\ 
{\tt{output-types}}{\tt{)}}\-)\index{required-props}, \\ 
{\it{x0\/}}, \\ 
{\it{x1\/}}, \\ 
{\rm{mark-io-outs}}\,(\=\+{\it{x2\/}}, \\ 
{\rm{intersection}}\,(\=\+{\it{x1\/}}, \\ 
{\it{x2\/}})\-\index{intersection})\-\index{mark-io-outs}, \\ 
{\rm{intersection}}\,({\it{x1\/}}, {\it{x2\/}})\index{intersection}, \\ 
{\rm{module-database}}\,(\=\+{\rm{subnet}}\,(\=\+{\tt{1}}, \\ 
{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{subnet}, \\ 
{\rm{required-props}}\,({\tt{'}}{\tt{(}}\=\+{\tt{input-types}} \\ 
{\tt{output-types}}{\tt{)}}\-)\index{required-props}, \\ 
{\bf{t}})\-\index{module-database})\-\index{occurrence-data})\-\index{alist-entry})\- \\ 
{\bf otherwise }{\rm{pred-error}}\,(\=\+{\tt{'}}{\tt{unknown-flag}}, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,({\tt{'}}{\tt{flg}}, {\it{flg\/}}), \\ 
{\rm{list}}\,({\tt{'}}{\tt{x0}}, {\it{x0\/}}), \\ 
{\rm{list}}\,({\tt{'}}{\tt{x1}}, {\it{x1\/}}), \\ 
{\rm{list}}\,({\tt{'}}{\tt{x2}}, {\it{x2\/}}))\-)\-\index{pred-error}$\;${\bf  endcase}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable io-types; name this event `io-types-off'.\index{io-types-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{netlist-type-table} \\  
\=\+{\rm{netlist-type-table}}\,({\it{netlist\/}})\index{netlist-type-table} \\ 
$=$$\;\;\;\;${\rm{netlist-properties}}\,({\it{netlist\/}}, {\tt{'}}{\tt{(}}{\tt{input-types}}{\tt{ }}{\tt{output-types}}{\tt{)}}, {\bf{t}})\index{netlist-properties}\-
\end{tabbing}


\noindent{\sc Event}:   Enable netlist-type-table; name this event `netlist-type-table-off'.\index{netlist-type-table-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{arg-types-matchp} \\  
\=\+{\rm{arg-types-matchp}}\,({\it{actuals\/}}, {\it{formals\/}})\index{arg-types-matchp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{actuals\/}} $\simeq\;${{\bf{nil}}}${}$) $\vee$ ({\it{formals\/}} $\simeq\;${{\bf{nil}}}${}$)$\;\;${\bf then }{\it{actuals\/}} $=$ {\it{formals\/}} \\ 
{\bf elseif }{\rm{unknownp}}\,({\rm{car}}\,({\it{actuals\/}}))\index{unknownp} $\vee$ {\rm{unknownp}}\,({\rm{car}}\,({\it{formals\/}}))\index{unknownp}$\;\;${\bf then }{\bf{f}} \\ 
{\bf elseif }{\rm{types-compatiblep}}\,({\rm{car}}\,({\it{actuals\/}}), {\rm{car}}\,({\it{formals\/}}))\index{types-compatiblep} \\ 
{\bf then }{\rm{arg-types-matchp}}\,({\rm{cdr}}\,({\it{actuals\/}}), {\rm{cdr}}\,({\it{formals\/}}))\index{arg-types-matchp} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable arg-types-matchp; name this event `arg-types-matchp-off'.\index{arg-types-matchp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{arg-types-okp} \\  
\=\+{\rm{arg-types-okp}}\,({\it{fn\/}}, {\it{arg-types\/}}, {\it{netlist\/}})\index{arg-types-okp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{boundp}}\,({\tt{'}}{\tt{input-types}}, {\rm{io-types}}\,({\tt{0}}, {\it{fn\/}}, {\it{arg-types\/}}, {\bf{nil}}, {\it{netlist\/}})\index{io-types})\index{boundp} \\ 
{\bf then }{\rm{arg-types-matchp}}\,(\=\+{\it{arg-types\/}}, \\ 
{\rm{value}}\,(\=\+{\tt{'}}{\tt{input-types}}, \\ 
{\rm{io-types}}\,({\tt{0}}, {\it{fn\/}}, {\it{arg-types\/}}, {\bf{nil}}, {\it{netlist\/}})\index{io-types})\-\index{value})\-\index{arg-types-matchp} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable arg-types-okp; name this event `arg-types-okp-off'.\index{arg-types-okp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{state-type-requirement} \\  
\=\+{\rm{state-type-requirement}}\,({\it{flg\/}}, {\it{x0\/}}, {\it{netlist\/}})\index{state-type-requirement} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{flg\/}}: \\ 
{\bf case = }{\tt{0}} \\ 
{\bf then }\=\+{\bf if }{\rm{primp}}\,({\it{x0\/}})\index{primp} \\ 
{\bf then }\=\+{\bf if }{\rm{primp-lookup}}\,({\it{x0\/}}, {\tt{'}}{\tt{state-types}})\index{primp-lookup} \\ 
{\bf then }{\rm{primp2}}\,({\it{x0\/}}, {\tt{'}}{\tt{state-types}})\index{primp2} \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{lookup-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{lookup-module} \\ 
{\bf then }\=\+{\bf if }{\rm{net-errorp}}\,({\rm{netlist-properties}}\,(\=\+{\rm{subnet}}\,({\tt{0}}, {\it{x0\/}}, {\it{netlist\/}})\index{subnet}, \\ 
{\tt{'}}{\tt{(}}{\tt{state-types}}{\tt{)}}, \\ 
{\bf{t}})\-\index{netlist-properties})\index{net-errorp} \\ 
{\bf then }{\rm{netlist-properties}}\,(\=\+{\rm{subnet}}\,({\tt{0}}, {\it{x0\/}}, {\it{netlist\/}})\index{subnet}, \\ 
{\tt{'}}{\tt{(}}{\tt{state-types}}{\tt{)}}, \\ 
{\bf{t}})\-\index{netlist-properties} \\ 
{\bf elseif }{\rm{boundp}}\,(\=\+{\tt{'}}{\tt{state-types}}, \\ 
{\rm{value}}\,(\=\+{\it{x0\/}}, \\ 
{\rm{netlist-properties}}\,(\=\+{\rm{subnet}}\,({\tt{0}}, {\it{x0\/}}, {\it{netlist\/}})\index{subnet}, \\ 
{\tt{'}}{\tt{(}}{\tt{state-types}}{\tt{)}}, \\ 
{\bf{t}})\-\index{netlist-properties})\-\index{value})\-\index{boundp} \\ 
{\bf then }{\rm{value}}\,(\=\+{\tt{'}}{\tt{state-types}}, \\ 
{\rm{value}}\,(\=\+{\it{x0\/}}, \\ 
{\rm{netlist-properties}}\,(\=\+{\rm{subnet}}\,({\tt{0}}, {\it{x0\/}}, {\it{netlist\/}})\index{subnet}, \\ 
{\tt{'}}{\tt{(}}{\tt{state-types}}{\tt{)}}, \\ 
{\bf{t}})\-\index{netlist-properties})\-\index{value})\-\index{value} \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{pred-error}}\,({\tt{'}}{\tt{unknown-module}}, {\it{x0\/}})\index{pred-error}$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{1}} \\ 
{\bf $\;\;$then }{\rm{value}}\,(\=\+{\tt{'}}{\tt{state-types}}, \\ 
{\rm{occurrence-data}}\,(\=\+{\rm{required-props}}\,({\tt{'}}{\tt{(}}{\tt{state-types}}{\tt{)}})\index{required-props}, \\ 
{\it{x0\/}}, \\ 
{\bf{nil}}, \\ 
{\bf{nil}}, \\ 
{\bf{nil}}, \\ 
{\rm{module-database}}\,(\=\+{\rm{subnet}}\,({\tt{1}}, {\it{x0\/}}, {\it{netlist\/}})\index{subnet}, \\ 
{\rm{required-props}}\,({\tt{'}}{\tt{(}}\=\+{\tt{state-types}}{\tt{)}}\-)\index{required-props}, \\ 
{\bf{t}})\-\index{module-database})\-\index{occurrence-data})\-\index{value} \\ 
{\bf otherwise }{\rm{pred-error}}\,(\=\+{\tt{'}}{\tt{unknown-flag}}, \\ 
{\rm{list}}\,({\rm{list}}\,({\tt{'}}{\tt{flg}}, {\it{flg\/}}), {\rm{list}}\,({\tt{'}}{\tt{x0}}, {\it{x0\/}})))\-\index{pred-error}$\;${\bf  endcase}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable state-type-requirement; name this event `state-type-requirement-off'.\index{state-type-requirement-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{netlist-state-types} \\  
\=\+{\rm{netlist-state-types}}\,({\it{netlist\/}})\index{netlist-state-types} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{net-errorp}}\,({\rm{netlist-properties}}\,({\it{netlist\/}}, {\tt{'}}{\tt{(}}{\tt{state-types}}{\tt{)}}, {\bf{t}})\index{netlist-properties})\index{net-errorp} \\ 
{\bf then }{\rm{netlist-properties}}\,({\it{netlist\/}}, {\tt{'}}{\tt{(}}{\tt{state-types}}{\tt{)}}, {\bf{t}})\index{netlist-properties} \\ 
{\bf else }{\rm{delete-null-entries}}\,({\rm{netlist-properties}}\,(\=\+{\it{netlist\/}}, \\ 
{\tt{'}}{\tt{(}}{\tt{state-types}}{\tt{)}}, \\ 
{\bf{t}})\-\index{netlist-properties})\index{delete-null-entries}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable netlist-state-types; name this event `netlist-state-types-off'.\index{netlist-state-types-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{type-count} \\  
{\rm{type-count}}\,({\it{type\/}}, {\it{word-type\/}})\index{type-count} $=$ ({\rm{count}}\,({\it{type\/}}) $+$ {\rm{count}}\,({\it{word-type\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  type-count-lessp1 \\ \index{type-count-lessp1}
{\rm{listp}}\,({\it{type\/}}) $\rightarrow$ ({\rm{type-count}}\,({\rm{car}}\,({\it{type\/}}), {\rm{caddr}}\,({\it{type\/}}))\index{type-count} $<$ {\rm{type-count}}\,({\it{type\/}}, {\it{x\/}})\index{type-count})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  type-count-lessp2 \\ \index{type-count-lessp2}
{\rm{listp}}\,({\it{type\/}}) $\rightarrow$ ({\rm{type-count}}\,({\rm{cadr}}\,({\it{type\/}}), {\bf{f}})\index{type-count} $<$ {\rm{type-count}}\,({\it{type\/}}, {\it{x\/}})\index{type-count})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  type-count-lessp3 \\ \index{type-count-lessp3}
\=\+({\rm{count}}\,({\it{t2\/}}) $<$ {\rm{count}}\,({\it{t1\/}})) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{type-count}}\,({\it{wtype\/}}, {\it{t2\/}})\index{type-count} $<$ {\rm{type-count}}\,({\it{t1\/}}, {\it{wtype\/}})\index{type-count}) $=$ {\bf{t}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable type-count; name this event `type-count-off'.\index{type-count-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{state-okp-0} \\  
\=\+{\rm{state-okp-0}}\,({\it{state\/}}, {\it{type\/}}, {\it{address-bits\/}}, {\it{word-type\/}})\index{state-okp-0} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{type\/}}: \\ 
{\bf case = }{\bf{nil}} \\ 
{\bf then }{\it{state\/}} $=$ {\bf{nil}} \\ 
{\bf case = }{\it{boolp\/}} \\ 
{\bf $\;\;$then }{\rm{boolp}}\,({\it{state\/}})\index{boolp} \\ 
{\bf otherwise }\=\+{\bf if }{\rm{listp}}\,({\it{type\/}}) \\ 
{\bf then }\=\+{\bf case on }{\rm{car}}\,({\it{type\/}}): \\ 
{\bf case = }{\it{addressed-state\/}} \\ 
{\bf then }{\rm{state-okp-0}}\,(\=\+{\it{state\/}}, \\ 
{\rm{car}}\,({\it{type\/}}), \\ 
{\rm{cadr}}\,({\it{type\/}}), \\ 
{\rm{caddr}}\,({\it{type\/}}))\-\index{state-okp-0} \\ 
{\bf case = }{\it{ram\/}} \\ 
{\bf $\;\;$then }\=\+{\rm{ramp}}\,({\it{state\/}})\index{ramp} \\ 
$\wedge$$\;\;\;\;${\rm{state-okp-0}}\,(\=\+{\rm{ram-guts}}\,({\it{state\/}})\index{ram-guts}, \\ 
{\rm{cadr}}\,({\it{type\/}}), \\ 
{\tt{0}}, \\ 
{\bf{f}})\-\index{state-okp-0}\- \\ 
{\bf case = }{\it{rom\/}} \\ 
{\bf $\;\;$then }\=\+{\rm{romp}}\,({\it{state\/}})\index{romp} \\ 
$\wedge$$\;\;\;\;${\rm{state-okp-0}}\,(\=\+{\rm{rom-guts}}\,({\it{state\/}})\index{rom-guts}, \\ 
{\rm{cadr}}\,({\it{type\/}}), \\ 
{\tt{0}}, \\ 
{\bf{f}})\-\index{state-okp-0}\- \\ 
{\bf case = }{\it{stub\/}} \\ 
{\bf $\;\;$then }\=\+{\rm{stubp}}\,({\it{state\/}})\index{stubp} \\ 
$\wedge$$\;\;\;\;${\rm{state-okp-0}}\,(\=\+{\rm{stub-guts}}\,({\it{state\/}})\index{stub-guts}, \\ 
{\rm{cadr}}\,({\it{type\/}}), \\ 
{\tt{0}}, \\ 
{\bf{f}})\-\index{state-okp-0}\- \\ 
{\bf case = }{\it{quote\/}} \\ 
{\bf $\;\;$then }{\rm{state-okp-0}}\,({\it{state\/}}, {\rm{cadr}}\,({\it{type\/}}), {\tt{0}}, {\bf{f}})\index{state-okp-0} \\ 
{\bf otherwise }\=\+{\bf if }{\rm{listp}}\,({\it{state\/}}) \\ 
{\bf then }\=\+{\rm{state-okp-0}}\,({\rm{car}}\,({\it{state\/}}), {\rm{car}}\,({\it{type\/}}), {\tt{0}}, {\bf{f}})\index{state-okp-0} \\ 
$\wedge$$\;\;\;\;${\rm{state-okp-0}}\,(\=\+{\rm{cdr}}\,({\it{state\/}}), \\ 
{\rm{cdr}}\,({\it{type\/}}), \\ 
{\tt{0}}, \\ 
{\bf{f}})\-\index{state-okp-0}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-$\;${\bf  endcase}\- \\ 
{\bf elseif }{\it{type\/}} $=$ {\tt{'}}{\tt{addressed-state}} \\ 
{\bf then }\=\+{\bf if }{\it{address-bits\/}} $\simeq {\tt{0}}$ \\ 
{\bf then }{\rm{state-okp-0}}\,({\it{state\/}}, {\it{word-type\/}}, {\tt{0}}, {\bf{f}})\index{state-okp-0} \\ 
{\bf elseif }{\rm{listp}}\,({\it{state\/}}) \\ 
{\bf then }\=\+{\rm{state-okp-0}}\,(\=\+{\rm{car}}\,({\it{state\/}}), \\ 
{\it{type\/}}, \\ 
{\it{address-bits\/}} $-\;1$, \\ 
{\it{word-type\/}})\-\index{state-okp-0} \\ 
$\wedge$$\;\;\;\;${\rm{state-okp-0}}\,(\=\+{\rm{cdr}}\,({\it{state\/}}), \\ 
{\it{type\/}}, \\ 
{\it{address-bits\/}} $-\;1$, \\ 
{\it{word-type\/}})\-\index{state-okp-0}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{type\/}} $=$ {\tt{'}}{\tt{numberp}}$\;\;${\bf then }{\it{state\/}} $\in\;${\bf{N}}${}$ \\ 
{\bf elseif }{\it{type\/}} $=$ {\tt{'}}{\tt{number-listp}} \\ 
{\bf then }\=\+{\bf if }{\it{state\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{state\/}} $=$ {\bf{nil}} \\ 
{\bf elseif }{\rm{car}}\,({\it{state\/}}) $\in\;${\bf{N}}${}$ \\ 
{\bf then }{\rm{state-okp-0}}\,({\rm{cdr}}\,({\it{state\/}}), {\it{type\/}}, {\tt{0}}, {\bf{f}})\index{state-okp-0} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{ramp}}\,({\it{type\/}})\index{ramp} \\ 
{\bf then }\=\+{\bf if }{\rm{ramp}}\,({\it{state\/}})\index{ramp} \\ 
{\bf then }{\rm{state-okp-0}}\,({\rm{ram-guts}}\,({\it{state\/}})\index{ram-guts}, {\rm{ram-guts}}\,({\it{type\/}})\index{ram-guts}, {\tt{0}}, {\bf{f}})\index{state-okp-0} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{romp}}\,({\it{type\/}})\index{romp} \\ 
{\bf then }\=\+{\bf if }{\rm{romp}}\,({\it{state\/}})\index{romp} \\ 
{\bf then }{\rm{state-okp-0}}\,({\rm{rom-guts}}\,({\it{state\/}})\index{rom-guts}, {\rm{rom-guts}}\,({\it{type\/}})\index{rom-guts}, {\tt{0}}, {\bf{f}})\index{state-okp-0} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{stubp}}\,({\it{type\/}})\index{stubp} \\ 
{\bf then }\=\+{\bf if }{\rm{stubp}}\,({\it{state\/}})\index{stubp} \\ 
{\bf then }{\rm{state-okp-0}}\,({\rm{stub-guts}}\,({\it{state\/}})\index{stub-guts}, {\rm{stub-guts}}\,({\it{type\/}})\index{stub-guts}, {\tt{0}}, {\bf{f}})\index{state-okp-0} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-$\;${\bf  endcase}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable state-okp-0; name this event `state-okp-0-off'.\index{state-okp-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable type-count-lessp1; name this event `type-count-lessp1-off'.\index{type-count-lessp1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable type-count-lessp2; name this event `type-count-lessp2-off'.\index{type-count-lessp2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable type-count-lessp3; name this event `type-count-lessp3-off'.\index{type-count-lessp3-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{state-okp} \\  
\=\+{\rm{state-okp}}\,({\it{fn\/}}, {\it{state\/}}, {\it{netlist\/}})\index{state-okp} \\ 
$=$$\;\;\;\;${\rm{state-okp-0}}\,({\it{state\/}}, {\rm{state-type-requirement}}\,({\tt{0}}, {\it{fn\/}}, {\it{netlist\/}})\index{state-type-requirement}, {\tt{0}}, {\bf{f}})\index{state-okp-0}\-
\end{tabbing}


\noindent{\sc Event}:   Enable state-okp; name this event `state-okp-off'.\index{state-okp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fix-dependent-drs} \\  
\=\+{\rm{fix-dependent-drs}}\,({\it{drs\/}}, {\it{alist\/}})\index{fix-dependent-drs} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{drs\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+\=\+{\bf if }{\rm{signal-namep}}\,({\rm{car}}\,({\it{drs\/}}))\index{signal-namep}$\;\;${\bf then }{\rm{value}}\,({\rm{car}}\,({\it{drs\/}}), {\it{alist\/}})\index{value} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{car}}\,({\it{drs\/}})) $\wedge$ ({\rm{caar}}\,({\it{drs\/}}) $=$ {\tt{'}}{\tt{min}}) \\ 
{\bf then }{\rm{cons}}\,({\tt{'}}{\tt{min}}, {\rm{fix-dependent-drs}}\,({\rm{cdar}}\,({\it{drs\/}}), {\it{alist\/}})\index{fix-dependent-drs}) \\ 
{\bf else }{\rm{car}}\,({\it{drs\/}})$\;${\bf  endif}\-, \\ 
{\rm{fix-dependent-drs}}\,({\rm{cdr}}\,({\it{drs\/}}), {\it{alist\/}})\index{fix-dependent-drs})\- \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fix-dependent-drs; name this event `fix-dependent-drs-off'.\index{fix-dependent-drs-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN LOADINGS-AND-DRIVES
 (FLG X0 X1 X2 NETLIST)
 (CASE FLG
  (0
   (COND
    ((PRIMP X0)
     (LIST (PRIMP-LOOKUP X0 'LOADINGS)
           (CONS 'DRIVES
                 (FIX-DEPENDENT-DRS (PRIMP2 X0 'DRIVES)
                                    (APPEND (PAIRLIST (PRIMP2 X0 'INPUTS) X1)
                                            (PAIRLIST (PRIMP2 X0 'OUTPUTS)
                                                      X2))))))
    ((LOOKUP-MODULE X0 NETLIST)
     (IF
      (NET-ERRORP (NETLIST-PROPERTIES (SUBNET 0 X0 NETLIST)
                                      '(LOADINGS DRIVES INPUTS OUTPUTS)
                                      T))
      (NETLIST-PROPERTIES (SUBNET 0 X0 NETLIST)
                          '(LOADINGS DRIVES INPUTS OUTPUTS)
                          T)
      (LIST
       (ALIST-ENTRY 'LOADINGS
                   (VALUE X0
                          (NETLIST-PROPERTIES (SUBNET 0 X0 NETLIST)
                                              '(LOADINGS DRIVES INPUTS OUTPUTS)
                                              T)))
       (CONS 'DRIVES
        (FIX-DEPENDENT-DRS
         (VALUE 'DRIVES
                (VALUE X0
                       (NETLIST-PROPERTIES (SUBNET 0 X0 NETLIST)
                                           '(LOADINGS DRIVES INPUTS OUTPUTS)
                                           T)))
         (APPEND
          (PAIRLIST
            (VALUE 'INPUTS
                   (VALUE X0
                          (NETLIST-PROPERTIES (SUBNET 0 X0 NETLIST)
                                              '(LOADINGS DRIVES INPUTS OUTPUTS)
                                              T)))
            X1)
          (PAIRLIST
            (VALUE 'OUTPUTS
                   (VALUE X0
                          (NETLIST-PROPERTIES (SUBNET 0 X0 NETLIST)
                                              '(LOADINGS DRIVES INPUTS OUTPUTS)
                                              T)))
            X2)))))))
    (T (PRED-ERROR 'UNKNOWN-MODULE X0))))
  (1
   (LIST
    (ALIST-ENTRY 'LOADINGS
          (OCCURRENCE-DATA (REQUIRED-PROPS '(LOADINGS DRIVES))
                           X0 X1
                           (MARK-IO-OUTS X2 (INTERSECTION X1 X2))
                           (INTERSECTION X1 X2)
                           (MODULE-DATABASE (SUBNET 1 X0 NETLIST)
                                            (REQUIRED-PROPS '(LOADINGS DRIVES))
                                            T)))
    (ALIST-ENTRY 'DRIVES
          (OCCURRENCE-DATA (REQUIRED-PROPS '(LOADINGS DRIVES))
                           X0 X1
                           (MARK-IO-OUTS X2 (INTERSECTION X1 X2))
                           (INTERSECTION X1 X2)
                           (MODULE-DATABASE (SUBNET 1 X0 NETLIST)
                                            (REQUIRED-PROPS '(LOADINGS DRIVES))
                                            T)))))
  (OTHERWISE (PRED-ERROR 'UNKNOWN-FLAG
                         (LIST (LIST 'FLG FLG)
                               (LIST 'X0 X0)
                               (LIST 'X1 X1)
                               (LIST 'X2 X2))))))
\end{verbatim}



\noindent{\sc Event}:   Enable loadings-and-drives; name this event `loadings-and-drives-off'.\index{loadings-and-drives-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{netlist-loadings-and-drives} \\  
\=\+{\rm{netlist-loadings-and-drives}}\,({\it{netlist\/}})\index{netlist-loadings-and-drives} \\ 
$=$$\;\;\;\;${\rm{netlist-properties}}\,({\it{netlist\/}}, {\tt{'}}{\tt{(}}{\tt{loadings}}{\tt{ }}{\tt{drives}}{\tt{)}}, {\bf{t}})\index{netlist-properties}\-
\end{tabbing}


\noindent{\sc Event}:   Enable netlist-loadings-and-drives; name this event `netlist-loadings-and-drives-off'.\index{netlist-loadings-and-drives-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ao2\&}$\;\;$
{\rm{ao2\&}}\,({\it{netlist\/}})\index{ao2\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable ao2\&; name this event `ao2\&-off'.\index{ao2\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ao2\$netlist}$\;\;$
{\sc{ao2\$netlist}}\index{ao2\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ao2\$value \\ \index{ao2\$value}
\=\+{\rm{ao2\&}}\,({\it{netlist\/}})\index{ao2\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ao2}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nor}}\,({\rm{f-and}}\,({\it{a\/}}, {\it{b\/}})\index{f-and}, {\rm{f-and}}\,({\it{c\/}}, {\it{d\/}})\index{f-and})\index{f-nor}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ao2\$value; name this event `ao2\$value-off'.\index{ao2\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ao4\&}$\;\;$
{\rm{ao4\&}}\,({\it{netlist\/}})\index{ao4\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable ao4\&; name this event `ao4\&-off'.\index{ao4\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ao4\$netlist}$\;\;$
{\sc{ao4\$netlist}}\index{ao4\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ao4\$value \\ \index{ao4\$value}
\=\+{\rm{ao4\&}}\,({\it{netlist\/}})\index{ao4\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ao4}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nand}}\,({\rm{f-or}}\,({\it{a\/}}, {\it{b\/}})\index{f-or}, {\rm{f-or}}\,({\it{c\/}}, {\it{d\/}})\index{f-or})\index{f-nand}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ao4\$value; name this event `ao4\$value-off'.\index{ao4\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ao6\&}$\;\;$
{\rm{ao6\&}}\,({\it{netlist\/}})\index{ao6\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable ao6\&; name this event `ao6\&-off'.\index{ao6\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ao6\$netlist}$\;\;$
{\sc{ao6\$netlist}}\index{ao6\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ao6\$value \\ \index{ao6\$value}
\=\+{\rm{ao6\&}}\,({\it{netlist\/}})\index{ao6\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ao6}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nor}}\,({\rm{f-and}}\,({\it{a\/}}, {\it{b\/}})\index{f-and}, {\it{c\/}})\index{f-nor}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ao6\$value; name this event `ao6\$value-off'.\index{ao6\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ao7\&}$\;\;$
{\rm{ao7\&}}\,({\it{netlist\/}})\index{ao7\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable ao7\&; name this event `ao7\&-off'.\index{ao7\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ao7\$netlist}$\;\;$
{\sc{ao7\$netlist}}\index{ao7\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ao7\$value \\ \index{ao7\$value}
\=\+{\rm{ao7\&}}\,({\it{netlist\/}})\index{ao7\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ao7}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nand}}\,({\rm{f-or}}\,({\it{a\/}}, {\it{b\/}})\index{f-or}, {\it{c\/}})\index{f-nand}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ao7\$value; name this event `ao7\$value-off'.\index{ao7\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-and\&}$\;\;$
{\rm{b-and\&}}\,({\it{netlist\/}})\index{b-and\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-and\&; name this event `b-and\&-off'.\index{b-and\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-and\$netlist}$\;\;$
{\sc{b-and\$netlist}}\index{b-and\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-and\$value \\ \index{b-and\$value}
\=\+{\rm{b-and\&}}\,({\it{netlist\/}})\index{b-and\&} \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-and}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{f-and}}\,({\it{a\/}}, {\it{b\/}})\index{f-and}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-and\$value; name this event `b-and\$value-off'.\index{b-and\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-and3\&}$\;\;$
{\rm{b-and3\&}}\,({\it{netlist\/}})\index{b-and3\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-and3\&; name this event `b-and3\&-off'.\index{b-and3\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-and3\$netlist}$\;\;$
{\sc{b-and3\$netlist}}\index{b-and3\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-and3\$value \\ \index{b-and3\$value}
\=\+{\rm{b-and3\&}}\,({\it{netlist\/}})\index{b-and3\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-and3}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-and3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-and3}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-and3\$value; name this event `b-and3\$value-off'.\index{b-and3\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-and4\&}$\;\;$
{\rm{b-and4\&}}\,({\it{netlist\/}})\index{b-and4\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-and4\&; name this event `b-and4\&-off'.\index{b-and4\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-and4\$netlist}$\;\;$
{\sc{b-and4\$netlist}}\index{b-and4\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-and4\$value \\ \index{b-and4\$value}
\=\+{\rm{b-and4\&}}\,({\it{netlist\/}})\index{b-and4\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-and4}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-and4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-and4}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-and4\$value; name this event `b-and4\$value-off'.\index{b-and4\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-equv\&}$\;\;$
{\rm{b-equv\&}}\,({\it{netlist\/}})\index{b-equv\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-equv\&; name this event `b-equv\&-off'.\index{b-equv\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-equv\$netlist}$\;\;$
{\sc{b-equv\$netlist}}\index{b-equv\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-equv\$value \\ \index{b-equv\$value}
\=\+{\rm{b-equv\&}}\,({\it{netlist\/}})\index{b-equv\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-equv}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-equv}}\,({\it{a\/}}, {\it{b\/}})\index{f-equv}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-equv\$value; name this event `b-equv\$value-off'.\index{b-equv\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-equv3\&}$\;\;$
{\rm{b-equv3\&}}\,({\it{netlist\/}})\index{b-equv3\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-equv3\&; name this event `b-equv3\&-off'.\index{b-equv3\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-equv3\$netlist}$\;\;$
{\sc{b-equv3\$netlist}}\index{b-equv3\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-equv3\$value \\ \index{b-equv3\$value}
\=\+{\rm{b-equv3\&}}\,({\it{netlist\/}})\index{b-equv3\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-equv3}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-equv3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-equv3}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-equv3\$value; name this event `b-equv3\$value-off'.\index{b-equv3\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-if\&}$\;\;$
{\rm{b-if\&}}\,({\it{netlist\/}})\index{b-if\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-if\&; name this event `b-if\&-off'.\index{b-if\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-if\$netlist}$\;\;$
{\sc{b-if\$netlist}}\index{b-if\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-if\$value \\ \index{b-if\$value}
\=\+{\rm{b-if\&}}\,({\it{netlist\/}})\index{b-if\&} \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-if}}, {\rm{list}}\,({\it{s\/}}, {\it{a\/}}, {\it{b\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{f-if}}\,({\it{s\/}}, {\it{a\/}}, {\it{b\/}})\index{f-if}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-if\$value; name this event `b-if\$value-off'.\index{b-if\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nand\&}$\;\;$
{\rm{b-nand\&}}\,({\it{netlist\/}})\index{b-nand\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-nand\&; name this event `b-nand\&-off'.\index{b-nand\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nand\$netlist}$\;\;$
{\sc{b-nand\$netlist}}\index{b-nand\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nand\$value \\ \index{b-nand\$value}
\=\+{\rm{b-nand\&}}\,({\it{netlist\/}})\index{b-nand\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nand}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nand}}\,({\it{a\/}}, {\it{b\/}})\index{f-nand}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-nand\$value; name this event `b-nand\$value-off'.\index{b-nand\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nand3\&}$\;\;$
{\rm{b-nand3\&}}\,({\it{netlist\/}})\index{b-nand3\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-nand3\&; name this event `b-nand3\&-off'.\index{b-nand3\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nand3\$netlist}$\;\;$
{\sc{b-nand3\$netlist}}\index{b-nand3\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nand3\$value \\ \index{b-nand3\$value}
\=\+{\rm{b-nand3\&}}\,({\it{netlist\/}})\index{b-nand3\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nand3}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nand3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-nand3}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-nand3\$value; name this event `b-nand3\$value-off'.\index{b-nand3\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nand4\&}$\;\;$
{\rm{b-nand4\&}}\,({\it{netlist\/}})\index{b-nand4\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-nand4\&; name this event `b-nand4\&-off'.\index{b-nand4\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nand4\$netlist}$\;\;$
{\sc{b-nand4\$netlist}}\index{b-nand4\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nand4\$value \\ \index{b-nand4\$value}
\=\+{\rm{b-nand4\&}}\,({\it{netlist\/}})\index{b-nand4\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nand4}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nand4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nand4}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-nand4\$value; name this event `b-nand4\$value-off'.\index{b-nand4\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nand5\&}$\;\;$
{\rm{b-nand5\&}}\,({\it{netlist\/}})\index{b-nand5\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-nand5\&; name this event `b-nand5\&-off'.\index{b-nand5\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nand5\$netlist}$\;\;$
{\sc{b-nand5\$netlist}}\index{b-nand5\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nand5\$value \\ \index{b-nand5\$value}
\=\+{\rm{b-nand5\&}}\,({\it{netlist\/}})\index{b-nand5\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nand5}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nand5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nand5}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-nand5\$value; name this event `b-nand5\$value-off'.\index{b-nand5\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nand6\&}$\;\;$
{\rm{b-nand6\&}}\,({\it{netlist\/}})\index{b-nand6\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-nand6\&; name this event `b-nand6\&-off'.\index{b-nand6\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nand6\$netlist}$\;\;$
{\sc{b-nand6\$netlist}}\index{b-nand6\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nand6\$value \\ \index{b-nand6\$value}
\=\+{\rm{b-nand6\&}}\,({\it{netlist\/}})\index{b-nand6\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nand6}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nand6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nand6}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-nand6\$value; name this event `b-nand6\$value-off'.\index{b-nand6\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nand8\&}$\;\;$
{\rm{b-nand8\&}}\,({\it{netlist\/}})\index{b-nand8\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-nand8\&; name this event `b-nand8\&-off'.\index{b-nand8\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nand8\$netlist}$\;\;$
{\sc{b-nand8\$netlist}}\index{b-nand8\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nand8\$value \\ \index{b-nand8\$value}
\=\+{\rm{b-nand8\&}}\,({\it{netlist\/}})\index{b-nand8\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nand8}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nand8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nand8}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-nand8\$value; name this event `b-nand8\$value-off'.\index{b-nand8\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nbuf\&}$\;\;$
{\rm{b-nbuf\&}}\,({\it{netlist\/}})\index{b-nbuf\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-nbuf\&; name this event `b-nbuf\&-off'.\index{b-nbuf\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nbuf\$netlist}$\;\;$
{\sc{b-nbuf\$netlist}}\index{b-nbuf\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nbuf\$value \\ \index{b-nbuf\$value}
\=\+{\rm{b-nbuf\&}}\,({\it{netlist\/}})\index{b-nbuf\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nbuf}}, {\rm{list}}\,({\it{a\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-not}}\,({\it{a\/}})\index{f-not}, {\rm{f-buf}}\,({\it{a\/}})\index{f-buf}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-nbuf\$value; name this event `b-nbuf\$value-off'.\index{b-nbuf\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nor\&}$\;\;$
{\rm{b-nor\&}}\,({\it{netlist\/}})\index{b-nor\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-nor\&; name this event `b-nor\&-off'.\index{b-nor\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nor\$netlist}$\;\;$
{\sc{b-nor\$netlist}}\index{b-nor\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nor\$value \\ \index{b-nor\$value}
\=\+{\rm{b-nor\&}}\,({\it{netlist\/}})\index{b-nor\&} \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nor}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{f-nor}}\,({\it{a\/}}, {\it{b\/}})\index{f-nor}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-nor\$value; name this event `b-nor\$value-off'.\index{b-nor\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nor3\&}$\;\;$
{\rm{b-nor3\&}}\,({\it{netlist\/}})\index{b-nor3\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-nor3\&; name this event `b-nor3\&-off'.\index{b-nor3\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nor3\$netlist}$\;\;$
{\sc{b-nor3\$netlist}}\index{b-nor3\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nor3\$value \\ \index{b-nor3\$value}
\=\+{\rm{b-nor3\&}}\,({\it{netlist\/}})\index{b-nor3\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nor3}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-nor3}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-nor3\$value; name this event `b-nor3\$value-off'.\index{b-nor3\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nor4\&}$\;\;$
{\rm{b-nor4\&}}\,({\it{netlist\/}})\index{b-nor4\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-nor4\&; name this event `b-nor4\&-off'.\index{b-nor4\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nor4\$netlist}$\;\;$
{\sc{b-nor4\$netlist}}\index{b-nor4\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nor4\$value \\ \index{b-nor4\$value}
\=\+{\rm{b-nor4\&}}\,({\it{netlist\/}})\index{b-nor4\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nor4}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nor4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-nor4}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-nor4\$value; name this event `b-nor4\$value-off'.\index{b-nor4\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nor5\&}$\;\;$
{\rm{b-nor5\&}}\,({\it{netlist\/}})\index{b-nor5\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-nor5\&; name this event `b-nor5\&-off'.\index{b-nor5\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nor5\$netlist}$\;\;$
{\sc{b-nor5\$netlist}}\index{b-nor5\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nor5\$value \\ \index{b-nor5\$value}
\=\+{\rm{b-nor5\&}}\,({\it{netlist\/}})\index{b-nor5\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nor5}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nor5}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}})\index{f-nor5}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-nor5\$value; name this event `b-nor5\$value-off'.\index{b-nor5\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nor6\&}$\;\;$
{\rm{b-nor6\&}}\,({\it{netlist\/}})\index{b-nor6\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-nor6\&; name this event `b-nor6\&-off'.\index{b-nor6\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nor6\$netlist}$\;\;$
{\sc{b-nor6\$netlist}}\index{b-nor6\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nor6\$value \\ \index{b-nor6\$value}
\=\+{\rm{b-nor6\&}}\,({\it{netlist\/}})\index{b-nor6\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nor6}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nor6}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}})\index{f-nor6}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-nor6\$value; name this event `b-nor6\$value-off'.\index{b-nor6\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nor8\&}$\;\;$
{\rm{b-nor8\&}}\,({\it{netlist\/}})\index{b-nor8\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-nor8\&; name this event `b-nor8\&-off'.\index{b-nor8\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-nor8\$netlist}$\;\;$
{\sc{b-nor8\$netlist}}\index{b-nor8\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nor8\$value \\ \index{b-nor8\$value}
\=\+{\rm{b-nor8\&}}\,({\it{netlist\/}})\index{b-nor8\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nor8}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nor8}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}, {\it{e\/}}, {\it{g\/}}, {\it{h\/}}, {\it{i\/}})\index{f-nor8}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-nor8\$value; name this event `b-nor8\$value-off'.\index{b-nor8\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-not\&}$\;\;$
{\rm{b-not\&}}\,({\it{netlist\/}})\index{b-not\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-not\&; name this event `b-not\&-off'.\index{b-not\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-not\$netlist}$\;\;$
{\sc{b-not\$netlist}}\index{b-not\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-not\$value \\ \index{b-not\$value}
\=\+{\rm{b-not\&}}\,({\it{netlist\/}})\index{b-not\&} \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-not}}, {\rm{list}}\,({\it{a\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{f-not}}\,({\it{a\/}})\index{f-not}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-not\$value; name this event `b-not\$value-off'.\index{b-not\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-not-b4ip\&}$\;\;$
{\rm{b-not-b4ip\&}}\,({\it{netlist\/}})\index{b-not-b4ip\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-not-b4ip\&; name this event `b-not-b4ip\&-off'.\index{b-not-b4ip\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-not-b4ip\$netlist}$\;\;$
{\sc{b-not-b4ip\$netlist}}\index{b-not-b4ip\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-not-b4ip\$value \\ \index{b-not-b4ip\$value}
\=\+{\rm{b-not-b4ip\&}}\,({\it{netlist\/}})\index{b-not-b4ip\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-not-b4ip}}, {\rm{list}}\,({\it{a\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-not}}\,({\it{a\/}})\index{f-not}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-not-b4ip\$value; name this event `b-not-b4ip\$value-off'.\index{b-not-b4ip\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-not-ivap\&}$\;\;$
{\rm{b-not-ivap\&}}\,({\it{netlist\/}})\index{b-not-ivap\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-not-ivap\&; name this event `b-not-ivap\&-off'.\index{b-not-ivap\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-not-ivap\$netlist}$\;\;$
{\sc{b-not-ivap\$netlist}}\index{b-not-ivap\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-not-ivap\$value \\ \index{b-not-ivap\$value}
\=\+{\rm{b-not-ivap\&}}\,({\it{netlist\/}})\index{b-not-ivap\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-not-ivap}}, {\rm{list}}\,({\it{a\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-not}}\,({\it{a\/}})\index{f-not}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-not-ivap\$value; name this event `b-not-ivap\$value-off'.\index{b-not-ivap\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-or\&}$\;\;$
{\rm{b-or\&}}\,({\it{netlist\/}})\index{b-or\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-or\&; name this event `b-or\&-off'.\index{b-or\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-or\$netlist}$\;\;$
{\sc{b-or\$netlist}}\index{b-or\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-or\$value \\ \index{b-or\$value}
\=\+{\rm{b-or\&}}\,({\it{netlist\/}})\index{b-or\&} \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-or}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{f-or}}\,({\it{a\/}}, {\it{b\/}})\index{f-or}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-or\$value; name this event `b-or\$value-off'.\index{b-or\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-or3\&}$\;\;$
{\rm{b-or3\&}}\,({\it{netlist\/}})\index{b-or3\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-or3\&; name this event `b-or3\&-off'.\index{b-or3\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-or3\$netlist}$\;\;$
{\sc{b-or3\$netlist}}\index{b-or3\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-or3\$value \\ \index{b-or3\$value}
\=\+{\rm{b-or3\&}}\,({\it{netlist\/}})\index{b-or3\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-or3}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-or3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-or3}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-or3\$value; name this event `b-or3\$value-off'.\index{b-or3\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-or4\&}$\;\;$
{\rm{b-or4\&}}\,({\it{netlist\/}})\index{b-or4\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-or4\&; name this event `b-or4\&-off'.\index{b-or4\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-or4\$netlist}$\;\;$
{\sc{b-or4\$netlist}}\index{b-or4\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-or4\$value \\ \index{b-or4\$value}
\=\+{\rm{b-or4\&}}\,({\it{netlist\/}})\index{b-or4\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-or4}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-or4}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{f-or4}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-or4\$value; name this event `b-or4\$value-off'.\index{b-or4\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-xor\&}$\;\;$
{\rm{b-xor\&}}\,({\it{netlist\/}})\index{b-xor\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-xor\&; name this event `b-xor\&-off'.\index{b-xor\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-xor\$netlist}$\;\;$
{\sc{b-xor\$netlist}}\index{b-xor\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-xor\$value \\ \index{b-xor\$value}
\=\+{\rm{b-xor\&}}\,({\it{netlist\/}})\index{b-xor\&} \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-xor}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{f-xor}}\,({\it{a\/}}, {\it{b\/}})\index{f-xor}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-xor\$value; name this event `b-xor\$value-off'.\index{b-xor\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-xor3\&}$\;\;$
{\rm{b-xor3\&}}\,({\it{netlist\/}})\index{b-xor3\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable b-xor3\&; name this event `b-xor3\&-off'.\index{b-xor3\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-xor3\$netlist}$\;\;$
{\sc{b-xor3\$netlist}}\index{b-xor3\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-xor3\$value \\ \index{b-xor3\$value}
\=\+{\rm{b-xor3\&}}\,({\it{netlist\/}})\index{b-xor3\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-xor3}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-xor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f-xor3}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-xor3\$value; name this event `b-xor3\$value-off'.\index{b-xor3\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{del2\&}$\;\;$
{\rm{del2\&}}\,({\it{netlist\/}})\index{del2\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable del2\&; name this event `del2\&-off'.\index{del2\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{del2\$netlist}$\;\;$
{\sc{del2\$netlist}}\index{del2\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  del2\$value \\ \index{del2\$value}
\=\+{\rm{del2\&}}\,({\it{netlist\/}})\index{del2\&} \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{del2}}, {\rm{list}}\,({\it{a\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{f-buf}}\,({\it{a\/}})\index{f-buf}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable del2\$value; name this event `del2\$value-off'.\index{del2\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{del4\&}$\;\;$
{\rm{del4\&}}\,({\it{netlist\/}})\index{del4\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable del4\&; name this event `del4\&-off'.\index{del4\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{del4\$netlist}$\;\;$
{\sc{del4\$netlist}}\index{del4\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  del4\$value \\ \index{del4\$value}
\=\+{\rm{del4\&}}\,({\it{netlist\/}})\index{del4\&} \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{del4}}, {\rm{list}}\,({\it{a\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{f-buf}}\,({\it{a\/}})\index{f-buf}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable del4\$value; name this event `del4\$value-off'.\index{del4\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{del10\&}$\;\;$
{\rm{del10\&}}\,({\it{netlist\/}})\index{del10\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable del10\&; name this event `del10\&-off'.\index{del10\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{del10\$netlist}$\;\;$
{\sc{del10\$netlist}}\index{del10\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  del10\$value \\ \index{del10\$value}
\=\+{\rm{del10\&}}\,({\it{netlist\/}})\index{del10\&} \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{del10}}, {\rm{list}}\,({\it{a\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{f-buf}}\,({\it{a\/}})\index{f-buf}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable del10\$value; name this event `del10\$value-off'.\index{del10\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{procmon\&}$\;\;$
{\rm{procmon\&}}\,({\it{netlist\/}})\index{procmon\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable procmon\&; name this event `procmon\&-off'.\index{procmon\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{procmon\$netlist}$\;\;$
{\sc{procmon\$netlist}}\index{procmon\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  procmon\$value \\ \index{procmon\$value}
\=\+{\rm{procmon\&}}\,({\it{netlist\/}})\index{procmon\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{procmon}}, {\rm{list}}\,({\it{a\/}}, {\it{e\/}}, {\it{s\/}}, {\it{n\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-if}}\,({\it{s\/}}, {\rm{f-if}}\,({\it{e\/}}, {\rm{f-if}}\,({\it{a\/}}, {\bf{f}}, {\bf{f}})\index{f-if}, {\it{a\/}})\index{f-if}, {\it{n\/}})\index{f-if}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable procmon\$value; name this event `procmon\$value-off'.\index{procmon\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{dp-ram-16x32\&}$\;\;$
{\rm{dp-ram-16x32\&}}\,({\it{netlist\/}})\index{dp-ram-16x32\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable dp-ram-16x32\&; name this event `dp-ram-16x32\&-off'.\index{dp-ram-16x32\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{dp-ram-16x32\$netlist}$\;\;$
{\sc{dp-ram-16x32\$netlist}}\index{dp-ram-16x32\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dp-ram-16x32\$value \\ \index{dp-ram-16x32\$value}
\=\+{\rm{dp-ram-16x32\&}}\,({\it{netlist\/}})\index{dp-ram-16x32\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{dp-ram-16x32}}, \\ 
{\rm{list}}\,(\=\+{\it{read-a0\/}}, \\ 
{\it{read-a1\/}}, \\ 
{\it{read-a2\/}}, \\ 
{\it{read-a3\/}}, \\ 
{\it{write-b0\/}}, \\ 
{\it{write-b1\/}}, \\ 
{\it{write-b2\/}}, \\ 
{\it{write-b3\/}}, \\ 
{\it{wen\/}}, \\ 
{\it{d0\/}}, \\ 
{\it{d1\/}}, \\ 
{\it{d2\/}}, \\ 
{\it{d3\/}}, \\ 
{\it{d4\/}}, \\ 
{\it{d5\/}}, \\ 
{\it{d6\/}}, \\ 
{\it{d7\/}}, \\ 
{\it{d8\/}}, \\ 
{\it{d9\/}}, \\ 
{\it{d10\/}}, \\ 
{\it{d11\/}}, \\ 
{\it{d12\/}}, \\ 
{\it{d13\/}}, \\ 
{\it{d14\/}}, \\ 
{\it{d15\/}}, \\ 
{\it{d16\/}}, \\ 
{\it{d17\/}}, \\ 
{\it{d18\/}}, \\ 
{\it{d19\/}}, \\ 
{\it{d20\/}}, \\ 
{\it{d21\/}}, \\ 
{\it{d22\/}}, \\ 
{\it{d23\/}}, \\ 
{\it{d24\/}}, \\ 
{\it{d25\/}}, \\ 
{\it{d26\/}}, \\ 
{\it{d27\/}}, \\ 
{\it{d28\/}}, \\ 
{\it{d29\/}}, \\ 
{\it{d30\/}}, \\ 
{\it{d31\/}})\-, \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{dual-port-ram-value}}\,(\=\+{\tt{32}}, \\ 
{\tt{4}}, \\ 
{\rm{list}}\,(\=\+{\it{read-a0\/}}, \\ 
{\it{read-a1\/}}, \\ 
{\it{read-a2\/}}, \\ 
{\it{read-a3\/}}, \\ 
{\it{write-b0\/}}, \\ 
{\it{write-b1\/}}, \\ 
{\it{write-b2\/}}, \\ 
{\it{write-b3\/}}, \\ 
{\it{wen\/}}, \\ 
{\it{d0\/}}, \\ 
{\it{d1\/}}, \\ 
{\it{d2\/}}, \\ 
{\it{d3\/}}, \\ 
{\it{d4\/}}, \\ 
{\it{d5\/}}, \\ 
{\it{d6\/}}, \\ 
{\it{d7\/}}, \\ 
{\it{d8\/}}, \\ 
{\it{d9\/}}, \\ 
{\it{d10\/}}, \\ 
{\it{d11\/}}, \\ 
{\it{d12\/}}, \\ 
{\it{d13\/}}, \\ 
{\it{d14\/}}, \\ 
{\it{d15\/}}, \\ 
{\it{d16\/}}, \\ 
{\it{d17\/}}, \\ 
{\it{d18\/}}, \\ 
{\it{d19\/}}, \\ 
{\it{d20\/}}, \\ 
{\it{d21\/}}, \\ 
{\it{d22\/}}, \\ 
{\it{d23\/}}, \\ 
{\it{d24\/}}, \\ 
{\it{d25\/}}, \\ 
{\it{d26\/}}, \\ 
{\it{d27\/}}, \\ 
{\it{d28\/}}, \\ 
{\it{d29\/}}, \\ 
{\it{d30\/}}, \\ 
{\it{d31\/}})\-, \\ 
{\it{state\/}})\-\index{dual-port-ram-value})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable dp-ram-16x32\$value; name this event `dp-ram-16x32\$value-off'.\index{dp-ram-16x32\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fd1\&}$\;\;$
{\rm{fd1\&}}\,({\it{netlist\/}})\index{fd1\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable fd1\&; name this event `fd1\&-off'.\index{fd1\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fd1\$netlist}$\;\;$
{\sc{fd1\$netlist}}\index{fd1\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fd1\$value \\ \index{fd1\$value}
\=\+{\rm{fd1\&}}\,({\it{netlist\/}})\index{fd1\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{fd1}}, {\rm{list}}\,({\it{d\/}}, {\it{cp\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-buf}}\,({\it{state\/}})\index{f-buf}, {\rm{f-not}}\,({\it{state\/}})\index{f-not}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fd1\$value; name this event `fd1\$value-off'.\index{fd1\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fd1s\&}$\;\;$
{\rm{fd1s\&}}\,({\it{netlist\/}})\index{fd1s\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable fd1s\&; name this event `fd1s\&-off'.\index{fd1s\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fd1s\$netlist}$\;\;$
{\sc{fd1s\$netlist}}\index{fd1s\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fd1s\$value \\ \index{fd1s\$value}
\=\+{\rm{fd1s\&}}\,({\it{netlist\/}})\index{fd1s\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{fd1s}}, {\rm{list}}\,({\it{d\/}}, {\it{cp\/}}, {\it{ti\/}}, {\it{te\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-buf}}\,({\it{state\/}})\index{f-buf}, {\rm{f-not}}\,({\it{state\/}})\index{f-not}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fd1s\$value; name this event `fd1s\$value-off'.\index{fd1s\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fd1sp\&}$\;\;$
{\rm{fd1sp\&}}\,({\it{netlist\/}})\index{fd1sp\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable fd1sp\&; name this event `fd1sp\&-off'.\index{fd1sp\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fd1sp\$netlist}$\;\;$
{\sc{fd1sp\$netlist}}\index{fd1sp\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fd1sp\$value \\ \index{fd1sp\$value}
\=\+{\rm{fd1sp\&}}\,({\it{netlist\/}})\index{fd1sp\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{fd1sp}}, {\rm{list}}\,({\it{d\/}}, {\it{cp\/}}, {\it{ti\/}}, {\it{te\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-buf}}\,({\it{state\/}})\index{f-buf}, {\rm{f-not}}\,({\it{state\/}})\index{f-not}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fd1sp\$value; name this event `fd1sp\$value-off'.\index{fd1sp\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fd1slp\&}$\;\;$
{\rm{fd1slp\&}}\,({\it{netlist\/}})\index{fd1slp\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable fd1slp\&; name this event `fd1slp\&-off'.\index{fd1slp\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fd1slp\$netlist}$\;\;$
{\sc{fd1slp\$netlist}}\index{fd1slp\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fd1slp\$value \\ \index{fd1slp\$value}
\=\+{\rm{fd1slp\&}}\,({\it{netlist\/}})\index{fd1slp\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{fd1slp}}, {\rm{list}}\,({\it{d\/}}, {\it{cp\/}}, {\it{ld\/}}, {\it{ti\/}}, {\it{te\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-buf}}\,({\it{state\/}})\index{f-buf}, {\rm{f-not}}\,({\it{state\/}})\index{f-not}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fd1slp\$value; name this event `fd1slp\$value-off'.\index{fd1slp\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{id\&}$\;\;$
{\rm{id\&}}\,({\it{netlist\/}})\index{id\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable id\&; name this event `id\&-off'.\index{id\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{id\$netlist}$\;\;$
{\sc{id\$netlist}}\index{id\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  id\$value \\ \index{id\$value}
{\rm{id\&}}\,({\it{netlist\/}})\index{id\&} $\rightarrow$ ({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{id}}, {\rm{list}}\,({\it{a\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\it{a\/}}))
\end{tabbing}


\noindent{\sc Event}:   Enable id\$value; name this event `id\$value-off'.\index{id\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{mem-32x32\&}$\;\;$
{\rm{mem-32x32\&}}\,({\it{netlist\/}})\index{mem-32x32\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable mem-32x32\&; name this event `mem-32x32\&-off'.\index{mem-32x32\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{mem-32x32\$netlist}$\;\;$
{\sc{mem-32x32\$netlist}}\index{mem-32x32\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  mem-32x32\$value \\ \index{mem-32x32\$value}
\=\+{\rm{mem-32x32\&}}\,({\it{netlist\/}})\index{mem-32x32\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{mem-32x32}}, \\ 
{\rm{list}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{strobe-\/}}, \\ 
{\it{a0\/}}, \\ 
{\it{a1\/}}, \\ 
{\it{a2\/}}, \\ 
{\it{a3\/}}, \\ 
{\it{a4\/}}, \\ 
{\it{a5\/}}, \\ 
{\it{a6\/}}, \\ 
{\it{a7\/}}, \\ 
{\it{a8\/}}, \\ 
{\it{a9\/}}, \\ 
{\it{a10\/}}, \\ 
{\it{a11\/}}, \\ 
{\it{a12\/}}, \\ 
{\it{a13\/}}, \\ 
{\it{a14\/}}, \\ 
{\it{a15\/}}, \\ 
{\it{a16\/}}, \\ 
{\it{a17\/}}, \\ 
{\it{a18\/}}, \\ 
{\it{a19\/}}, \\ 
{\it{a20\/}}, \\ 
{\it{a21\/}}, \\ 
{\it{a22\/}}, \\ 
{\it{a23\/}}, \\ 
{\it{a24\/}}, \\ 
{\it{a25\/}}, \\ 
{\it{a26\/}}, \\ 
{\it{a27\/}}, \\ 
{\it{a28\/}}, \\ 
{\it{a29\/}}, \\ 
{\it{a30\/}}, \\ 
{\it{a31\/}}, \\ 
{\it{d0\/}}, \\ 
{\it{d1\/}}, \\ 
{\it{d2\/}}, \\ 
{\it{d3\/}}, \\ 
{\it{d4\/}}, \\ 
{\it{d5\/}}, \\ 
{\it{d6\/}}, \\ 
{\it{d7\/}}, \\ 
{\it{d8\/}}, \\ 
{\it{d9\/}}, \\ 
{\it{d10\/}}, \\ 
{\it{d11\/}}, \\ 
{\it{d12\/}}, \\ 
{\it{d13\/}}, \\ 
{\it{d14\/}}, \\ 
{\it{d15\/}}, \\ 
{\it{d16\/}}, \\ 
{\it{d17\/}}, \\ 
{\it{d18\/}}, \\ 
{\it{d19\/}}, \\ 
{\it{d20\/}}, \\ 
{\it{d21\/}}, \\ 
{\it{d22\/}}, \\ 
{\it{d23\/}}, \\ 
{\it{d24\/}}, \\ 
{\it{d25\/}}, \\ 
{\it{d26\/}}, \\ 
{\it{d27\/}}, \\ 
{\it{d28\/}}, \\ 
{\it{d29\/}}, \\ 
{\it{d30\/}}, \\ 
{\it{d31\/}})\-, \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{mem-value}}\,(\=\+{\rm{list}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{strobe-\/}}, \\ 
{\it{a0\/}}, \\ 
{\it{a1\/}}, \\ 
{\it{a2\/}}, \\ 
{\it{a3\/}}, \\ 
{\it{a4\/}}, \\ 
{\it{a5\/}}, \\ 
{\it{a6\/}}, \\ 
{\it{a7\/}}, \\ 
{\it{a8\/}}, \\ 
{\it{a9\/}}, \\ 
{\it{a10\/}}, \\ 
{\it{a11\/}}, \\ 
{\it{a12\/}}, \\ 
{\it{a13\/}}, \\ 
{\it{a14\/}}, \\ 
{\it{a15\/}}, \\ 
{\it{a16\/}}, \\ 
{\it{a17\/}}, \\ 
{\it{a18\/}}, \\ 
{\it{a19\/}}, \\ 
{\it{a20\/}}, \\ 
{\it{a21\/}}, \\ 
{\it{a22\/}}, \\ 
{\it{a23\/}}, \\ 
{\it{a24\/}}, \\ 
{\it{a25\/}}, \\ 
{\it{a26\/}}, \\ 
{\it{a27\/}}, \\ 
{\it{a28\/}}, \\ 
{\it{a29\/}}, \\ 
{\it{a30\/}}, \\ 
{\it{a31\/}}, \\ 
{\it{d0\/}}, \\ 
{\it{d1\/}}, \\ 
{\it{d2\/}}, \\ 
{\it{d3\/}}, \\ 
{\it{d4\/}}, \\ 
{\it{d5\/}}, \\ 
{\it{d6\/}}, \\ 
{\it{d7\/}}, \\ 
{\it{d8\/}}, \\ 
{\it{d9\/}}, \\ 
{\it{d10\/}}, \\ 
{\it{d11\/}}, \\ 
{\it{d12\/}}, \\ 
{\it{d13\/}}, \\ 
{\it{d14\/}}, \\ 
{\it{d15\/}}, \\ 
{\it{d16\/}}, \\ 
{\it{d17\/}}, \\ 
{\it{d18\/}}, \\ 
{\it{d19\/}}, \\ 
{\it{d20\/}}, \\ 
{\it{d21\/}}, \\ 
{\it{d22\/}}, \\ 
{\it{d23\/}}, \\ 
{\it{d24\/}}, \\ 
{\it{d25\/}}, \\ 
{\it{d26\/}}, \\ 
{\it{d27\/}}, \\ 
{\it{d28\/}}, \\ 
{\it{d29\/}}, \\ 
{\it{d30\/}}, \\ 
{\it{d31\/}})\-, \\ 
{\it{state\/}})\-\index{mem-value})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable mem-32x32\$value; name this event `mem-32x32\$value-off'.\index{mem-32x32\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ram-enable-circuit\&}$\;\;$
{\rm{ram-enable-circuit\&}}\,({\it{netlist\/}})\index{ram-enable-circuit\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable ram-enable-circuit\&; name this event `ram-enable-circuit\&-off'.\index{ram-enable-circuit\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ram-enable-circuit\$netlist}$\;\;$
{\sc{ram-enable-circuit\$netlist}}\index{ram-enable-circuit\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ram-enable-circuit\$value \\ \index{ram-enable-circuit\$value}
\=\+{\rm{ram-enable-circuit\&}}\,({\it{netlist\/}})\index{ram-enable-circuit\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{ram-enable-circuit}}, \\ 
{\rm{list}}\,({\it{clk\/}}, {\it{test-regfile-\/}}, {\it{disable-regfile-\/}}, {\it{we\/}}), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nand}}\,({\it{disable-regfile-\/}}, {\it{we\/}})\index{f-nand}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ram-enable-circuit\$value; name this event `ram-enable-circuit\$value-off'.\index{ram-enable-circuit\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{t-buf\&}$\;\;$
{\rm{t-buf\&}}\,({\it{netlist\/}})\index{t-buf\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable t-buf\&; name this event `t-buf\&-off'.\index{t-buf\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{t-buf\$netlist}$\;\;$
{\sc{t-buf\$netlist}}\index{t-buf\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  t-buf\$value \\ \index{t-buf\$value}
\=\+{\rm{t-buf\&}}\,({\it{netlist\/}})\index{t-buf\&} \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{t-buf}}, {\rm{list}}\,({\it{e\/}}, {\it{a\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{ft-buf}}\,({\it{e\/}}, {\it{a\/}})\index{ft-buf}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable t-buf\$value; name this event `t-buf\$value-off'.\index{t-buf\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{t-wire\&}$\;\;$
{\rm{t-wire\&}}\,({\it{netlist\/}})\index{t-wire\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable t-wire\&; name this event `t-wire\&-off'.\index{t-wire\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{t-wire\$netlist}$\;\;$
{\sc{t-wire\$netlist}}\index{t-wire\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  t-wire\$value \\ \index{t-wire\$value}
\=\+{\rm{t-wire\&}}\,({\it{netlist\/}})\index{t-wire\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{t-wire}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{ft-wire}}\,({\it{a\/}}, {\it{b\/}})\index{ft-wire}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable t-wire\$value; name this event `t-wire\$value-off'.\index{t-wire\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pullup\&}$\;\;$
{\rm{pullup\&}}\,({\it{netlist\/}})\index{pullup\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable pullup\&; name this event `pullup\&-off'.\index{pullup\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{pullup\$netlist}$\;\;$
{\sc{pullup\$netlist}}\index{pullup\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  pullup\$value \\ \index{pullup\$value}
\=\+{\rm{pullup\&}}\,({\it{netlist\/}})\index{pullup\&} \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{pullup}}, {\rm{list}}\,({\it{a\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{f-pullup}}\,({\it{a\/}})\index{f-pullup}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable pullup\$value; name this event `pullup\$value-off'.\index{pullup\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-bidirect\&}$\;\;$
{\rm{ttl-bidirect\&}}\,({\it{netlist\/}})\index{ttl-bidirect\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-bidirect\&; name this event `ttl-bidirect\&-off'.\index{ttl-bidirect\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-bidirect\$netlist}$\;\;$
{\sc{ttl-bidirect\$netlist}}\index{ttl-bidirect\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-bidirect\$value \\ \index{ttl-bidirect\$value}
\=\+{\rm{ttl-bidirect\&}}\,({\it{netlist\/}})\index{ttl-bidirect\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-bidirect}}, {\rm{list}}\,({\it{io\/}}, {\it{a\/}}, {\it{en\/}}, {\it{pi\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{ft-buf}}\,({\rm{f-not}}\,({\it{en\/}})\index{f-not}, {\it{a\/}})\index{ft-buf}, \\ 
{\rm{f-buf}}\,({\rm{ft-wire}}\,({\it{io\/}}, {\rm{ft-buf}}\,({\rm{f-not}}\,({\it{en\/}})\index{f-not}, {\it{a\/}})\index{ft-buf})\index{ft-wire})\index{f-buf}, \\ 
{\rm{f-nand}}\,({\rm{ft-wire}}\,({\it{io\/}}, {\rm{ft-buf}}\,({\rm{f-not}}\,({\it{en\/}})\index{f-not}, {\it{a\/}})\index{ft-buf})\index{ft-wire}, {\it{pi\/}})\index{f-nand})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-bidirect\$value; name this event `ttl-bidirect\$value-off'.\index{ttl-bidirect\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-clk-input\&}$\;\;$
{\rm{ttl-clk-input\&}}\,({\it{netlist\/}})\index{ttl-clk-input\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-clk-input\&; name this event `ttl-clk-input\&-off'.\index{ttl-clk-input\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-clk-input\$netlist}$\;\;$
{\sc{ttl-clk-input\$netlist}}\index{ttl-clk-input\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-clk-input\$value \\ \index{ttl-clk-input\$value}
\=\+{\rm{ttl-clk-input\&}}\,({\it{netlist\/}})\index{ttl-clk-input\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-clk-input}}, {\rm{list}}\,({\it{a\/}}, {\it{pi\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-buf}}\,({\it{a\/}})\index{f-buf}, {\rm{f-nand}}\,({\it{a\/}}, {\it{pi\/}})\index{f-nand}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-clk-input\$value; name this event `ttl-clk-input\$value-off'.\index{ttl-clk-input\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-input\&}$\;\;$
{\rm{ttl-input\&}}\,({\it{netlist\/}})\index{ttl-input\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-input\&; name this event `ttl-input\&-off'.\index{ttl-input\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-input\$netlist}$\;\;$
{\sc{ttl-input\$netlist}}\index{ttl-input\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-input\$value \\ \index{ttl-input\$value}
\=\+{\rm{ttl-input\&}}\,({\it{netlist\/}})\index{ttl-input\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-input}}, {\rm{list}}\,({\it{a\/}}, {\it{pi\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-buf}}\,({\it{a\/}})\index{f-buf}, {\rm{f-nand}}\,({\it{a\/}}, {\it{pi\/}})\index{f-nand}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-input\$value; name this event `ttl-input\$value-off'.\index{ttl-input\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-output\&}$\;\;$
{\rm{ttl-output\&}}\,({\it{netlist\/}})\index{ttl-output\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-output\&; name this event `ttl-output\&-off'.\index{ttl-output\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-output\$netlist}$\;\;$
{\sc{ttl-output\$netlist}}\index{ttl-output\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-output\$value \\ \index{ttl-output\$value}
\=\+{\rm{ttl-output\&}}\,({\it{netlist\/}})\index{ttl-output\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-output}}, {\rm{list}}\,({\it{a\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-buf}}\,({\it{a\/}})\index{f-buf}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-output\$value; name this event `ttl-output\$value-off'.\index{ttl-output\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-output-parametric\&}$\;\;$
{\rm{ttl-output-parametric\&}}\,({\it{netlist\/}})\index{ttl-output-parametric\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-output-parametric\&; name this event `ttl-output-parametric\&-off'.\index{ttl-output-parametric\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-output-parametric\$netlist}$\;\;$
{\sc{ttl-output-parametric\$netlist}}\index{ttl-output-parametric\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-output-parametric\$value \\ \index{ttl-output-parametric\$value}
\=\+{\rm{ttl-output-parametric\&}}\,({\it{netlist\/}})\index{ttl-output-parametric\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-output-parametric}}, {\rm{list}}\,({\it{a\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-buf}}\,({\it{a\/}})\index{f-buf}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-output-parametric\$value; name this event `ttl-output-parametric\$value-off'.\index{ttl-output-parametric\$value-of!f}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-output-fast\&}$\;\;$
{\rm{ttl-output-fast\&}}\,({\it{netlist\/}})\index{ttl-output-fast\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-output-fast\&; name this event `ttl-output-fast\&-off'.\index{ttl-output-fast\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-output-fast\$netlist}$\;\;$
{\sc{ttl-output-fast\$netlist}}\index{ttl-output-fast\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-output-fast\$value \\ \index{ttl-output-fast\$value}
\=\+{\rm{ttl-output-fast\&}}\,({\it{netlist\/}})\index{ttl-output-fast\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-output-fast}}, {\rm{list}}\,({\it{a\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-buf}}\,({\it{a\/}})\index{f-buf}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-output-fast\$value; name this event `ttl-output-fast\$value-off'.\index{ttl-output-fast\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-tri-output\&}$\;\;$
{\rm{ttl-tri-output\&}}\,({\it{netlist\/}})\index{ttl-tri-output\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-tri-output\&; name this event `ttl-tri-output\&-off'.\index{ttl-tri-output\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-tri-output\$netlist}$\;\;$
{\sc{ttl-tri-output\$netlist}}\index{ttl-tri-output\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-tri-output\$value \\ \index{ttl-tri-output\$value}
\=\+{\rm{ttl-tri-output\&}}\,({\it{netlist\/}})\index{ttl-tri-output\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-tri-output}}, {\rm{list}}\,({\it{a\/}}, {\it{en\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{ft-buf}}\,({\rm{f-not}}\,({\it{en\/}})\index{f-not}, {\it{a\/}})\index{ft-buf}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-tri-output\$value; name this event `ttl-tri-output\$value-off'.\index{ttl-tri-output\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-tri-output-fast\&}$\;\;$
{\rm{ttl-tri-output-fast\&}}\,({\it{netlist\/}})\index{ttl-tri-output-fast\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-tri-output-fast\&; name this event `ttl-tri-output-fast\&-off'.\index{ttl-tri-output-fast\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-tri-output-fast\$netlist}$\;\;$
{\sc{ttl-tri-output-fast\$netlist}}\index{ttl-tri-output-fast\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-tri-output-fast\$value \\ \index{ttl-tri-output-fast\$value}
\=\+{\rm{ttl-tri-output-fast\&}}\,({\it{netlist\/}})\index{ttl-tri-output-fast\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-tri-output-fast}}, {\rm{list}}\,({\it{a\/}}, {\it{en\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{ft-buf}}\,({\rm{f-not}}\,({\it{en\/}})\index{f-not}, {\it{a\/}})\index{ft-buf}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-tri-output-fast\$value; name this event `ttl-tri-output-fast\$value-off'.\index{ttl-tri-output-fast\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{vdd\&}$\;\;$
{\rm{vdd\&}}\,({\it{netlist\/}})\index{vdd\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable vdd\&; name this event `vdd\&-off'.\index{vdd\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{vdd\$netlist}$\;\;$
{\sc{vdd\$netlist}}\index{vdd\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  vdd\$value \\ \index{vdd\$value}
{\rm{vdd\&}}\,({\it{netlist\/}})\index{vdd\&} $\rightarrow$ ({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{vdd}}, {\bf{nil}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\bf{t}}))
\end{tabbing}


\noindent{\sc Event}:   Enable vdd\$value; name this event `vdd\$value-off'.\index{vdd\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{vdd-parametric\&}$\;\;$
{\rm{vdd-parametric\&}}\,({\it{netlist\/}})\index{vdd-parametric\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable vdd-parametric\&; name this event `vdd-parametric\&-off'.\index{vdd-parametric\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{vdd-parametric\$netlist}$\;\;$
{\sc{vdd-parametric\$netlist}}\index{vdd-parametric\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  vdd-parametric\$value \\ \index{vdd-parametric\$value}
\=\+{\rm{vdd-parametric\&}}\,({\it{netlist\/}})\index{vdd-parametric\&} \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{vdd-parametric}}, {\bf{nil}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\bf{t}}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable vdd-parametric\$value; name this event `vdd-parametric\$value-off'.\index{vdd-parametric\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{vss\&}$\;\;$
{\rm{vss\&}}\,({\it{netlist\/}})\index{vss\&} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable vss\&; name this event `vss\&-off'.\index{vss\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{vss\$netlist}$\;\;$
{\sc{vss\$netlist}}\index{vss\$netlist} $=$ {\bf{nil}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  vss\$value \\ \index{vss\$value}
{\rm{vss\&}}\,({\it{netlist\/}})\index{vss\&} $\rightarrow$ ({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{vss}}, {\bf{nil}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\bf{f}}))
\end{tabbing}


\noindent{\sc Event}:   Enable vss\$value; name this event `vss\$value-off'.\index{vss\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  dp-ram-16x32\$state \\ \index{dp-ram-16x32\$state}
\=\+{\rm{dp-ram-16x32\&}}\,({\it{netlist\/}})\index{dp-ram-16x32\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\tt{'}}{\tt{dp-ram-16x32}}, \\ 
{\rm{list}}\,(\=\+{\it{read-a0\/}}, \\ 
{\it{read-a1\/}}, \\ 
{\it{read-a2\/}}, \\ 
{\it{read-a3\/}}, \\ 
{\it{write-b0\/}}, \\ 
{\it{write-b1\/}}, \\ 
{\it{write-b2\/}}, \\ 
{\it{write-b3\/}}, \\ 
{\it{wen\/}}, \\ 
{\it{d0\/}}, \\ 
{\it{d1\/}}, \\ 
{\it{d2\/}}, \\ 
{\it{d3\/}}, \\ 
{\it{d4\/}}, \\ 
{\it{d5\/}}, \\ 
{\it{d6\/}}, \\ 
{\it{d7\/}}, \\ 
{\it{d8\/}}, \\ 
{\it{d9\/}}, \\ 
{\it{d10\/}}, \\ 
{\it{d11\/}}, \\ 
{\it{d12\/}}, \\ 
{\it{d13\/}}, \\ 
{\it{d14\/}}, \\ 
{\it{d15\/}}, \\ 
{\it{d16\/}}, \\ 
{\it{d17\/}}, \\ 
{\it{d18\/}}, \\ 
{\it{d19\/}}, \\ 
{\it{d20\/}}, \\ 
{\it{d21\/}}, \\ 
{\it{d22\/}}, \\ 
{\it{d23\/}}, \\ 
{\it{d24\/}}, \\ 
{\it{d25\/}}, \\ 
{\it{d26\/}}, \\ 
{\it{d27\/}}, \\ 
{\it{d28\/}}, \\ 
{\it{d29\/}}, \\ 
{\it{d30\/}}, \\ 
{\it{d31\/}})\-, \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{dual-port-ram-state}}\,(\=\+{\tt{32}}, \\ 
{\tt{4}}, \\ 
{\rm{list}}\,(\=\+{\it{read-a0\/}}, \\ 
{\it{read-a1\/}}, \\ 
{\it{read-a2\/}}, \\ 
{\it{read-a3\/}}, \\ 
{\it{write-b0\/}}, \\ 
{\it{write-b1\/}}, \\ 
{\it{write-b2\/}}, \\ 
{\it{write-b3\/}}, \\ 
{\it{wen\/}}, \\ 
{\it{d0\/}}, \\ 
{\it{d1\/}}, \\ 
{\it{d2\/}}, \\ 
{\it{d3\/}}, \\ 
{\it{d4\/}}, \\ 
{\it{d5\/}}, \\ 
{\it{d6\/}}, \\ 
{\it{d7\/}}, \\ 
{\it{d8\/}}, \\ 
{\it{d9\/}}, \\ 
{\it{d10\/}}, \\ 
{\it{d11\/}}, \\ 
{\it{d12\/}}, \\ 
{\it{d13\/}}, \\ 
{\it{d14\/}}, \\ 
{\it{d15\/}}, \\ 
{\it{d16\/}}, \\ 
{\it{d17\/}}, \\ 
{\it{d18\/}}, \\ 
{\it{d19\/}}, \\ 
{\it{d20\/}}, \\ 
{\it{d21\/}}, \\ 
{\it{d22\/}}, \\ 
{\it{d23\/}}, \\ 
{\it{d24\/}}, \\ 
{\it{d25\/}}, \\ 
{\it{d26\/}}, \\ 
{\it{d27\/}}, \\ 
{\it{d28\/}}, \\ 
{\it{d29\/}}, \\ 
{\it{d30\/}}, \\ 
{\it{d31\/}})\-, \\ 
{\it{state\/}})\-\index{dual-port-ram-state})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable dp-ram-16x32\$state; name this event `dp-ram-16x32\$state-off'.\index{dp-ram-16x32\$state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  fd1\$state \\ \index{fd1\$state}
\=\+{\rm{fd1\&}}\,({\it{netlist\/}})\index{fd1\&} \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{fd1}}, {\rm{list}}\,({\it{d\/}}, {\it{cp\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{f-buf}}\,({\it{d\/}})\index{f-buf})\-
\end{tabbing}


\noindent{\sc Event}:   Enable fd1\$state; name this event `fd1\$state-off'.\index{fd1\$state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  fd1s\$state \\ \index{fd1s\$state}
\=\+{\rm{fd1s\&}}\,({\it{netlist\/}})\index{fd1s\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{fd1s}}, {\rm{list}}\,({\it{d\/}}, {\it{cp\/}}, {\it{ti\/}}, {\it{te\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f-if}}\,({\it{te\/}}, {\it{ti\/}}, {\it{d\/}})\index{f-if})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fd1s\$state; name this event `fd1s\$state-off'.\index{fd1s\$state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  fd1sp\$state \\ \index{fd1sp\$state}
\=\+{\rm{fd1sp\&}}\,({\it{netlist\/}})\index{fd1sp\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{fd1sp}}, {\rm{list}}\,({\it{d\/}}, {\it{cp\/}}, {\it{ti\/}}, {\it{te\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f-if}}\,({\it{te\/}}, {\it{ti\/}}, {\it{d\/}})\index{f-if})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fd1sp\$state; name this event `fd1sp\$state-off'.\index{fd1sp\$state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  fd1slp\$state \\ \index{fd1slp\$state}
\=\+{\rm{fd1slp\&}}\,({\it{netlist\/}})\index{fd1slp\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{fd1slp}}, {\rm{list}}\,({\it{d\/}}, {\it{cp\/}}, {\it{ld\/}}, {\it{ti\/}}, {\it{te\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f-if}}\,({\it{te\/}}, {\it{ti\/}}, {\rm{f-if}}\,({\it{ld\/}}, {\it{d\/}}, {\it{state\/}})\index{f-if})\index{f-if})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fd1slp\$state; name this event `fd1slp\$state-off'.\index{fd1slp\$state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mem-32x32\$state \\ \index{mem-32x32\$state}
\=\+{\rm{mem-32x32\&}}\,({\it{netlist\/}})\index{mem-32x32\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\tt{'}}{\tt{mem-32x32}}, \\ 
{\rm{list}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{strobe-\/}}, \\ 
{\it{a0\/}}, \\ 
{\it{a1\/}}, \\ 
{\it{a2\/}}, \\ 
{\it{a3\/}}, \\ 
{\it{a4\/}}, \\ 
{\it{a5\/}}, \\ 
{\it{a6\/}}, \\ 
{\it{a7\/}}, \\ 
{\it{a8\/}}, \\ 
{\it{a9\/}}, \\ 
{\it{a10\/}}, \\ 
{\it{a11\/}}, \\ 
{\it{a12\/}}, \\ 
{\it{a13\/}}, \\ 
{\it{a14\/}}, \\ 
{\it{a15\/}}, \\ 
{\it{a16\/}}, \\ 
{\it{a17\/}}, \\ 
{\it{a18\/}}, \\ 
{\it{a19\/}}, \\ 
{\it{a20\/}}, \\ 
{\it{a21\/}}, \\ 
{\it{a22\/}}, \\ 
{\it{a23\/}}, \\ 
{\it{a24\/}}, \\ 
{\it{a25\/}}, \\ 
{\it{a26\/}}, \\ 
{\it{a27\/}}, \\ 
{\it{a28\/}}, \\ 
{\it{a29\/}}, \\ 
{\it{a30\/}}, \\ 
{\it{a31\/}}, \\ 
{\it{d0\/}}, \\ 
{\it{d1\/}}, \\ 
{\it{d2\/}}, \\ 
{\it{d3\/}}, \\ 
{\it{d4\/}}, \\ 
{\it{d5\/}}, \\ 
{\it{d6\/}}, \\ 
{\it{d7\/}}, \\ 
{\it{d8\/}}, \\ 
{\it{d9\/}}, \\ 
{\it{d10\/}}, \\ 
{\it{d11\/}}, \\ 
{\it{d12\/}}, \\ 
{\it{d13\/}}, \\ 
{\it{d14\/}}, \\ 
{\it{d15\/}}, \\ 
{\it{d16\/}}, \\ 
{\it{d17\/}}, \\ 
{\it{d18\/}}, \\ 
{\it{d19\/}}, \\ 
{\it{d20\/}}, \\ 
{\it{d21\/}}, \\ 
{\it{d22\/}}, \\ 
{\it{d23\/}}, \\ 
{\it{d24\/}}, \\ 
{\it{d25\/}}, \\ 
{\it{d26\/}}, \\ 
{\it{d27\/}}, \\ 
{\it{d28\/}}, \\ 
{\it{d29\/}}, \\ 
{\it{d30\/}}, \\ 
{\it{d31\/}})\-, \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{mem-state}}\,(\=\+{\rm{list}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{strobe-\/}}, \\ 
{\it{a0\/}}, \\ 
{\it{a1\/}}, \\ 
{\it{a2\/}}, \\ 
{\it{a3\/}}, \\ 
{\it{a4\/}}, \\ 
{\it{a5\/}}, \\ 
{\it{a6\/}}, \\ 
{\it{a7\/}}, \\ 
{\it{a8\/}}, \\ 
{\it{a9\/}}, \\ 
{\it{a10\/}}, \\ 
{\it{a11\/}}, \\ 
{\it{a12\/}}, \\ 
{\it{a13\/}}, \\ 
{\it{a14\/}}, \\ 
{\it{a15\/}}, \\ 
{\it{a16\/}}, \\ 
{\it{a17\/}}, \\ 
{\it{a18\/}}, \\ 
{\it{a19\/}}, \\ 
{\it{a20\/}}, \\ 
{\it{a21\/}}, \\ 
{\it{a22\/}}, \\ 
{\it{a23\/}}, \\ 
{\it{a24\/}}, \\ 
{\it{a25\/}}, \\ 
{\it{a26\/}}, \\ 
{\it{a27\/}}, \\ 
{\it{a28\/}}, \\ 
{\it{a29\/}}, \\ 
{\it{a30\/}}, \\ 
{\it{a31\/}}, \\ 
{\it{d0\/}}, \\ 
{\it{d1\/}}, \\ 
{\it{d2\/}}, \\ 
{\it{d3\/}}, \\ 
{\it{d4\/}}, \\ 
{\it{d5\/}}, \\ 
{\it{d6\/}}, \\ 
{\it{d7\/}}, \\ 
{\it{d8\/}}, \\ 
{\it{d9\/}}, \\ 
{\it{d10\/}}, \\ 
{\it{d11\/}}, \\ 
{\it{d12\/}}, \\ 
{\it{d13\/}}, \\ 
{\it{d14\/}}, \\ 
{\it{d15\/}}, \\ 
{\it{d16\/}}, \\ 
{\it{d17\/}}, \\ 
{\it{d18\/}}, \\ 
{\it{d19\/}}, \\ 
{\it{d20\/}}, \\ 
{\it{d21\/}}, \\ 
{\it{d22\/}}, \\ 
{\it{d23\/}}, \\ 
{\it{d24\/}}, \\ 
{\it{d25\/}}, \\ 
{\it{d26\/}}, \\ 
{\it{d27\/}}, \\ 
{\it{d28\/}}, \\ 
{\it{d29\/}}, \\ 
{\it{d30\/}}, \\ 
{\it{d31\/}})\-, \\ 
{\it{state\/}})\-\index{mem-state})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable mem-32x32\$state; name this event `mem-32x32\$state-off'.\index{mem-32x32\$state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-buf*} \\  
\=\+{\sc{b-buf*}}\index{b-buf*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{b-buf}} \\ 
{\tt{(}}{\tt{in}}{\tt{)}} \\ 
{\tt{(}}{\tt{out}}{\tt{)}} \\ 
{\tt{(}}{\tt{(}}{\tt{g0}}{\tt{ }}{\tt{(}}{\tt{out-}}{\tt{ }}{\tt{out}}{\tt{)}}{\tt{ }}{\tt{b-nbuf}}{\tt{ }}{\tt{(}}{\tt{in}}{\tt{)}}{\tt{)}}{\tt{)}} \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-buf\&} \\  
\=\+{\rm{b-buf\&}}\,({\it{netlist\/}})\index{b-buf\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{b-buf}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{b-buf*}}\index{b-buf*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-nbuf\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{b-buf}}, {\it{netlist\/}})\index{delete-module})\index{b-nbuf\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-buf\&; name this event `b-buf\&-off'.\index{b-buf\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-buf\$netlist}$\;\;$
{\sc{b-buf\$netlist}}\index{b-buf\$netlist} $=$ {\rm{cons}}\,({\sc{b-buf*}}\index{b-buf*}, {\sc{b-nbuf\$netlist}}\index{b-nbuf\$netlist})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-buf\$value \\ \index{b-buf\$value}
\=\+{\rm{b-buf\&}}\,({\it{netlist\/}})\index{b-buf\&} \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-buf}}, {\rm{list}}\,({\it{in\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{f-buf}}\,({\it{in\/}})\index{f-buf}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-buf\$value; name this event `b-buf\$value-off'.\index{b-buf\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-buf-pwr*} \\  
\=\+{\sc{b-buf-pwr*}}\index{b-buf-pwr*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{b-buf-pwr}} \\ 
{\tt{(}}{\tt{in}}{\tt{)}} \\ 
{\tt{(}}{\tt{out}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{g0}}{\tt{ }}{\tt{(}}{\tt{out-}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{in}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g1}}{\tt{ }}{\tt{(}}{\tt{out}}{\tt{)}}{\tt{ }}{\tt{b-not-b4ip}}{\tt{ }}{\tt{(}}{\tt{out-}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-buf-pwr\&} \\  
\=\+{\rm{b-buf-pwr\&}}\,({\it{netlist\/}})\index{b-buf-pwr\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{b-buf-pwr}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{b-buf-pwr*}}\index{b-buf-pwr*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{b-buf-pwr}}, {\it{netlist\/}})\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-not-b4ip\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{b-buf-pwr}}, {\it{netlist\/}})\index{delete-module})\index{b-not-b4ip\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-buf-pwr\&; name this event `b-buf-pwr\&-off'.\index{b-buf-pwr\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-buf-pwr\$netlist} \\  
{\sc{b-buf-pwr\$netlist}}\index{b-buf-pwr\$netlist} $=$ {\rm{cons}}\,({\sc{b-buf-pwr*}}\index{b-buf-pwr*}, {\sc{b-not\$netlist}}\index{b-not\$netlist} $\cup$ {\sc{b-not-b4ip\$netlist}}\index{b-not-b4ip\$netlist})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-buf-pwr\$value \\ \index{b-buf-pwr\$value}
\=\+{\rm{b-buf-pwr\&}}\,({\it{netlist\/}})\index{b-buf-pwr\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-buf-pwr}}, {\rm{list}}\,({\it{in\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-buf}}\,({\it{in\/}})\index{f-buf}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-buf-pwr\$value; name this event `b-buf-pwr\$value-off'.\index{b-buf-pwr\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  dp-ram-16x32-args-crock \\ \index{dp-ram-16x32-args-crock}
\=\+(\=\+({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{a\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{b\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{c\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{c\/}})\index{properp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{append}}\,({\it{a\/}}, {\rm{append}}\,({\it{b\/}}, {\rm{cons}}\,({\it{x\/}}, {\it{c\/}}))) \\ 
$=$$\;\;\;\;${\rm{append}}\,(\=\+{\rm{list-as-collected-nth}}\,({\it{a\/}}, {\tt{4}}, {\tt{0}})\index{list-as-collected-nth}, \\ 
{\rm{append}}\,(\=\+{\rm{list-as-collected-nth}}\,({\it{b\/}}, {\tt{4}}, {\tt{0}})\index{list-as-collected-nth}, \\ 
{\rm{cons}}\,({\it{x\/}}, {\rm{list-as-collected-nth}}\,({\it{c\/}}, {\tt{32}}, {\tt{0}})\index{list-as-collected-nth}))\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable dp-ram-16x32-args-crock; name this event `dp-ram-16x32-args-crock-off'.\index{dp-ram-16x32-args-crock-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  dp-ram-16x32\$structured-value \\ \index{dp-ram-16x32\$structured-value}
\=\+(\=\+{\rm{dp-ram-16x32\&}}\,({\it{netlist\/}})\index{dp-ram-16x32\&} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{a\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{b\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{c\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{c\/}})\index{properp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{dp-ram-16x32}}, \\ 
{\rm{append}}\,({\it{a\/}}, {\rm{append}}\,({\it{b\/}}, {\rm{cons}}\,({\it{x\/}}, {\it{c\/}}))), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{dual-port-ram-value}}\,({\tt{32}}, {\tt{4}}, {\rm{append}}\,({\it{a\/}}, {\rm{append}}\,({\it{b\/}}, {\rm{cons}}\,({\it{x\/}}, {\it{c\/}}))), {\it{state\/}})\index{dual-port-ram-value})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable dp-ram-16x32\$structured-value; name this event `dp-ram-16x32\$structured-value-off'.\index{dp-ram-16x32\$structured-value-!off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  dp-ram-16x32\$structured-state \\ \index{dp-ram-16x32\$structured-state}
\=\+(\=\+{\rm{dp-ram-16x32\&}}\,({\it{netlist\/}})\index{dp-ram-16x32\&} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{a\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{b\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{c\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{c\/}})\index{properp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\tt{'}}{\tt{dp-ram-16x32}}, \\ 
{\rm{append}}\,({\it{a\/}}, {\rm{append}}\,({\it{b\/}}, {\rm{cons}}\,({\it{x\/}}, {\it{c\/}}))), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{dual-port-ram-state}}\,({\tt{32}}, {\tt{4}}, {\rm{append}}\,({\it{a\/}}, {\rm{append}}\,({\it{b\/}}, {\rm{cons}}\,({\it{x\/}}, {\it{c\/}}))), {\it{state\/}})\index{dual-port-ram-state})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable dp-ram-16x32\$structured-state; name this event `dp-ram-16x32\$structured-state-off'.\index{dp-ram-16x32\$structured-state-!off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mem-32x32-args-crock \\ \index{mem-32x32-args-crock}
\=\+(\=\+({\rm{length}}\,({\it{addr\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{addr\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{data\/}})\index{properp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{cons}}\,({\it{rw-\/}}, {\rm{cons}}\,({\it{strobe-\/}}, {\rm{append}}\,({\it{addr\/}}, {\it{data\/}}))) \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\it{rw-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{strobe-\/}}, \\ 
{\rm{append}}\,(\=\+{\rm{list-as-collected-nth}}\,({\it{addr\/}}, {\tt{32}}, {\tt{0}})\index{list-as-collected-nth}, \\ 
{\rm{list-as-collected-nth}}\,({\it{data\/}}, {\tt{32}}, {\tt{0}})\index{list-as-collected-nth})\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable mem-32x32-args-crock; name this event `mem-32x32-args-crock-off'.\index{mem-32x32-args-crock-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  list-32-nth-collapse \\ \index{list-32-nth-collapse}
\=\+({\rm{properp}}\,({\it{args\/}})\index{properp} $\wedge$ ({\rm{length}}\,({\it{args\/}})\index{length} $=$ {\tt{32}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{list}}\,(\=\+{\rm{nth}}\,({\tt{0}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{1}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{2}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{3}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{4}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{5}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{6}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{7}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{8}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{9}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{10}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{11}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{12}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{13}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{14}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{15}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{16}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{17}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{18}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{19}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{20}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{21}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{22}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{23}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{24}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{25}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{26}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{27}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{28}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{29}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{30}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{31}}, {\it{args\/}})\index{nth})\- \\ 
$=$$\;\;\;\;${\it{args\/}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable list-32-nth-collapse; name this event `list-32-nth-collapse-off'.\index{list-32-nth-collapse-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mem-32x32\$structured-value-1 \\ \index{mem-32x32\$structured-value-1}
\=\+(\=\+{\rm{mem-32x32\&}}\,({\it{netlist\/}})\index{mem-32x32\&} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{addr\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{data\/}})\index{properp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{mem-32x32}}, \\ 
{\rm{cons}}\,({\it{rw-\/}}, {\rm{cons}}\,({\it{strobe-\/}}, {\rm{append}}\,({\it{addr\/}}, {\it{data\/}}))), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{memory-value}}\,(\=\+{\it{state\/}}, \\ 
{\it{strobe-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\rm{list}}\,(\=\+{\rm{nth}}\,({\tt{0}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{1}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{2}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{3}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{4}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{5}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{6}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{7}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{8}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{9}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{10}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{11}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{12}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{13}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{14}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{15}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{16}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{17}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{18}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{19}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{20}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{21}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{22}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{23}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{24}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{25}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{26}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{27}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{28}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{29}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{30}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{31}}, {\it{addr\/}})\index{nth})\-, \\ 
{\rm{list}}\,(\=\+{\rm{nth}}\,({\tt{0}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{1}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{2}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{3}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{4}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{5}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{6}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{7}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{8}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{9}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{10}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{11}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{12}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{13}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{14}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{15}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{16}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{17}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{18}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{19}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{20}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{21}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{22}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{23}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{24}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{25}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{26}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{27}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{28}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{29}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{30}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{31}}, {\it{data\/}})\index{nth})\-)\-\index{memory-value})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable mem-32x32\$structured-value-1; name this event `mem-32x32\$structured-value-1-off'.\index{mem-32x32\$structured-value-1-o!ff}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mem-32x32\$structured-value \\ \index{mem-32x32\$structured-value}
\=\+(\=\+{\rm{mem-32x32\&}}\,({\it{netlist\/}})\index{mem-32x32\&} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{addr\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{data\/}})\index{properp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{mem-32x32}}, \\ 
{\rm{cons}}\,({\it{rw-\/}}, {\rm{cons}}\,({\it{strobe-\/}}, {\rm{append}}\,({\it{addr\/}}, {\it{data\/}}))), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{memory-value}}\,({\it{state\/}}, {\it{strobe-\/}}, {\it{rw-\/}}, {\it{addr\/}}, {\it{data\/}})\index{memory-value})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable mem-32x32\$structured-value; name this event `mem-32x32\$structured-value-off'.\index{mem-32x32\$structured-value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mem-32x32\$structured-state-1 \\ \index{mem-32x32\$structured-state-1}
\=\+(\=\+{\rm{mem-32x32\&}}\,({\it{netlist\/}})\index{mem-32x32\&} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{addr\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{data\/}})\index{properp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\tt{'}}{\tt{mem-32x32}}, \\ 
{\rm{cons}}\,({\it{rw-\/}}, {\rm{cons}}\,({\it{strobe-\/}}, {\rm{append}}\,({\it{addr\/}}, {\it{data\/}}))), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{next-memory-state}}\,(\=\+{\it{state\/}}, \\ 
{\it{strobe-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\rm{list}}\,(\=\+{\rm{nth}}\,({\tt{0}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{1}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{2}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{3}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{4}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{5}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{6}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{7}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{8}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{9}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{10}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{11}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{12}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{13}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{14}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{15}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{16}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{17}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{18}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{19}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{20}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{21}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{22}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{23}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{24}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{25}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{26}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{27}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{28}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{29}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{30}}, {\it{addr\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{31}}, {\it{addr\/}})\index{nth})\-, \\ 
{\rm{list}}\,(\=\+{\rm{nth}}\,({\tt{0}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{1}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{2}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{3}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{4}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{5}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{6}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{7}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{8}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{9}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{10}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{11}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{12}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{13}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{14}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{15}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{16}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{17}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{18}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{19}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{20}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{21}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{22}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{23}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{24}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{25}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{26}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{27}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{28}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{29}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{30}}, {\it{data\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{31}}, {\it{data\/}})\index{nth})\-)\-\index{next-memory-state})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable mem-32x32\$structured-state-1; name this event `mem-32x32\$structured-state-1-off'.\index{mem-32x32\$structured-state-1-o!ff}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mem-32x32\$structured-state \\ \index{mem-32x32\$structured-state}
\=\+(\=\+{\rm{mem-32x32\&}}\,({\it{netlist\/}})\index{mem-32x32\&} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{addr\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{data\/}})\index{properp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\tt{'}}{\tt{mem-32x32}}, \\ 
{\rm{cons}}\,({\it{rw-\/}}, {\rm{cons}}\,({\it{strobe-\/}}, {\rm{append}}\,({\it{addr\/}}, {\it{data\/}}))), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{next-memory-state}}\,({\it{state\/}}, {\it{strobe-\/}}, {\it{rw-\/}}, {\it{addr\/}}, {\it{data\/}})\index{next-memory-state})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable mem-32x32\$structured-state; name this event `mem-32x32\$structured-state-off'.\index{mem-32x32\$structured-state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{unbound-in-body} \\  
\=\+{\rm{unbound-in-body}}\,({\it{name\/}}, {\it{body\/}})\index{unbound-in-body} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{body\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }\=\+({\it{name\/}} $\not\in$ {\rm{occ-outputs}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-outputs}) \\ 
$\wedge$$\;\;\;\;${\rm{unbound-in-body}}\,({\it{name\/}}, {\rm{cdr}}\,({\it{body\/}}))\index{unbound-in-body}\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable unbound-in-body; name this event `unbound-in-body-off'.\index{unbound-in-body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  unbound-in-body-nlistp \\ \index{unbound-in-body-nlistp}
({\it{body\/}} $\simeq\;${{\bf{nil}}}${}$) $\rightarrow$ {\rm{unbound-in-body}}\,({\it{name\/}}, {\it{body\/}})\index{unbound-in-body}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  unbound-in-body-listp \\ \index{unbound-in-body-listp}
\=\+{\rm{unbound-in-body}}\,({\it{name\/}}, {\rm{cons}}\,({\it{occurrence\/}}, {\it{rest\/}}))\index{unbound-in-body} \\ 
$=$$\;\;\;\;$(({\it{name\/}} $\not\in$ {\rm{occ-outputs}}\,({\it{occurrence\/}})\index{occ-outputs}) $\wedge$ {\rm{unbound-in-body}}\,({\it{name\/}}, {\it{rest\/}})\index{unbound-in-body})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{all-unbound-in-body} \\  
\=\+{\rm{all-unbound-in-body}}\,({\it{names\/}}, {\it{body\/}})\index{all-unbound-in-body} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{body\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }\=\+{\rm{disjoint}}\,({\it{names\/}}, {\rm{occ-outputs}}\,({\rm{car}}\,({\it{body\/}}))\index{occ-outputs})\index{disjoint} \\ 
$\wedge$$\;\;\;\;${\rm{all-unbound-in-body}}\,({\it{names\/}}, {\rm{cdr}}\,({\it{body\/}}))\index{all-unbound-in-body}\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable all-unbound-in-body; name this event `all-unbound-in-body-off'.\index{all-unbound-in-body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  all-unbound-in-body-nlistp \\ \index{all-unbound-in-body-nlistp}
({\it{body\/}} $\simeq\;${{\bf{nil}}}${}$) $\rightarrow$ {\rm{all-unbound-in-body}}\,({\it{names\/}}, {\it{body\/}})\index{all-unbound-in-body}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  all-unbound-in-body-listp \\ \index{all-unbound-in-body-listp}
\=\+{\rm{all-unbound-in-body}}\,({\it{names\/}}, {\rm{cons}}\,({\it{occurrence\/}}, {\it{rest\/}}))\index{all-unbound-in-body} \\ 
$=$$\;\;\;\;$(\=\+{\rm{disjoint}}\,({\it{names\/}}, {\rm{occ-outputs}}\,({\it{occurrence\/}})\index{occ-outputs})\index{disjoint} \\ 
$\wedge$$\;\;\;\;${\rm{all-unbound-in-body}}\,({\it{names\/}}, {\it{rest\/}})\index{all-unbound-in-body})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  all-unbound-in-body-append \\ \index{all-unbound-in-body-append}
\=\+{\rm{all-unbound-in-body}}\,({\rm{append}}\,({\it{names1\/}}, {\it{names2\/}}), {\it{body\/}})\index{all-unbound-in-body} \\ 
$=$$\;\;\;\;$(\=\+{\rm{all-unbound-in-body}}\,({\it{names1\/}}, {\it{body\/}})\index{all-unbound-in-body} \\ 
$\wedge$$\;\;\;\;${\rm{all-unbound-in-body}}\,({\it{names2\/}}, {\it{body\/}})\index{all-unbound-in-body})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  all-unbound-in-body-cons \\ \index{all-unbound-in-body-cons}
\=\+{\rm{all-unbound-in-body}}\,({\rm{cons}}\,({\it{name\/}}, {\it{names\/}}), {\it{body\/}})\index{all-unbound-in-body} \\ 
$=$$\;\;\;\;$({\rm{unbound-in-body}}\,({\it{name\/}}, {\it{body\/}})\index{unbound-in-body} $\wedge$ {\rm{all-unbound-in-body}}\,({\it{names\/}}, {\it{body\/}})\index{all-unbound-in-body})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  all-unbound-in-body-nlistp-names \\ \index{all-unbound-in-body-nlistp-name!s}
({\it{names\/}} $\simeq\;${{\bf{nil}}}${}$) $\rightarrow$ {\rm{all-unbound-in-body}}\,({\it{names\/}}, {\it{body\/}})\index{all-unbound-in-body}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  unbound-in-body-dual-eval-1 \\ \index{unbound-in-body-dual-eval-1}
\=\+(({\it{flag\/}} $=$ {\tt{1}}) $\wedge$ {\rm{unbound-in-body}}\,({\it{name\/}}, {\it{body\/}})\index{unbound-in-body}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{value}}\,({\it{name\/}}, {\rm{dual-eval}}\,({\it{flag\/}}, {\it{body\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{dual-eval})\index{value} \\ 
$=$$\;\;\;\;${\rm{value}}\,({\it{name\/}}, {\it{bindings\/}})\index{value})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  all-unbound-in-body-dual-eval-1 \\ \index{all-unbound-in-body-dual-eval-1}
\=\+(({\it{flag\/}} $=$ {\tt{1}}) $\wedge$ {\rm{all-unbound-in-body}}\,({\it{names\/}}, {\it{body\/}})\index{all-unbound-in-body}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,(\=\+{\it{names\/}}, \\ 
{\rm{dual-eval}}\,({\it{flag\/}}, {\it{body\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{dual-eval})\-\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{collect-value}}\,({\it{names\/}}, {\it{bindings\/}})\index{collect-value})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{vector-module-induction} \\  
\=\+{\rm{vector-module-induction}}\,({\it{body\/}}, {\it{m\/}}, {\it{n\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{vector-module-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{vector-module-induction}}\,(\=\+{\rm{cdr}}\,({\it{body\/}}), \\ 
$1\;+$ {\it{m\/}}, \\ 
{\it{n\/}} $-\;1$, \\ 
{\rm{dual-eval-body-bindings}}\,(\=\+{\tt{1}}, \\ 
{\it{body\/}}, \\ 
{\it{bindings\/}}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval-body-bindings}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{vector-module-induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-buf\$body} \\  
\=\+{\rm{v-buf\$body}}\,({\it{m\/}}, {\it{n\/}})\index{v-buf\$body} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{g}}, {\it{m\/}})\index{index}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{y}}, {\it{m\/}})\index{index}), \\ 
{\tt{'}}{\tt{b-buf}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{a}}, {\it{m\/}})\index{index}))\-, \\ 
{\rm{v-buf\$body}}\,($1\;+$ {\it{m\/}}, {\it{n\/}} $-\;1$)\index{v-buf\$body})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-buf\$body; name this event `v-buf\$body-off'.\index{v-buf\$body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-buf*} \\  
\=\+{\rm{v-buf*}}\,({\it{n\/}})\index{v-buf*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{v-buf}}, {\it{n\/}})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}, \\ 
{\rm{cons}}\,({\rm{indices}}\,({\tt{'}}{\tt{y}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{cons}}\,({\rm{v-buf\$body}}\,({\tt{0}}, {\it{n\/}})\index{v-buf\$body}, {\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}})))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-buf*\$destructure \\ \index{v-buf*\$destructure}
\=\+({\rm{car}}\,({\rm{v-buf*}}\,({\it{n\/}})\index{v-buf*}) $=$ {\rm{index}}\,({\tt{'}}{\tt{v-buf}}, {\it{n\/}})\index{index}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadr}}\,({\rm{v-buf*}}\,({\it{n\/}})\index{v-buf*}) $=$ {\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\rm{v-buf*}}\,({\it{n\/}})\index{v-buf*}) $=$ {\rm{indices}}\,({\tt{'}}{\tt{y}}, {\tt{0}}, {\it{n\/}})\index{indices}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadddr}}\,({\rm{v-buf*}}\,({\it{n\/}})\index{v-buf*}) $=$ {\rm{v-buf\$body}}\,({\tt{0}}, {\it{n\/}})\index{v-buf\$body}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{v-buf*}}\,({\it{n\/}})\index{v-buf*}) $=$ {\bf{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-buf*; name this event `v-buf*-off'.\index{v-buf*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-buf*\$destructure; name this event `v-buf*\$destructure-off'.\index{v-buf*\$destructure-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-buf\&} \\  
\=\+{\rm{v-buf\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{v-buf\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\rm{index}}\,({\tt{'}}{\tt{v-buf}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{lookup-module} $=$ {\rm{v-buf*}}\,({\it{n\/}})\index{v-buf*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-buf\&}}\,({\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{v-buf}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{delete-module})\index{b-buf\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-buf\&; name this event `v-buf\&-off'.\index{v-buf\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-buf\$netlist}$\;\;$
{\rm{v-buf\$netlist}}\,({\it{n\/}})\index{v-buf\$netlist} $=$ {\rm{cons}}\,({\rm{v-buf*}}\,({\it{n\/}})\index{v-buf*}, {\sc{b-buf\$netlist}}\index{b-buf\$netlist})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-buf\$unbound-in-body \\ \index{v-buf\$unbound-in-body}
({\it{l\/}} $<$ {\it{m\/}}) $\rightarrow$ {\rm{unbound-in-body}}\,({\rm{index}}\,({\tt{'}}{\tt{y}}, {\it{l\/}})\index{index}, {\rm{v-buf\$body}}\,({\it{m\/}}, {\it{n\/}})\index{v-buf\$body})\index{unbound-in-body}
\end{tabbing}


\noindent{\sc Event}:   Enable v-buf\$unbound-in-body; name this event `v-buf\$unbound-in-body-off'.\index{v-buf\$unbound-in-body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-buf\$body-value \\ \index{v-buf\$body-value}
\=\+({\rm{b-buf\&}}\,({\it{netlist\/}})\index{b-buf\&} $\wedge$ ({\it{body\/}} $=$ {\rm{v-buf\$body}}\,({\it{m\/}}, {\it{n\/}})\index{v-buf\$body})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{y}}, {\it{m\/}}, {\it{n\/}})\index{indices}, \\ 
{\rm{dual-eval}}\,({\tt{1}}, {\it{body\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{dual-eval})\-\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{v-threefix}}\,({\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\it{m\/}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value})\index{v-threefix})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-buf\$body-value; name this event `v-buf\$body-value-off'.\index{v-buf\$body-value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-buf\$value \\ \index{v-buf\$value}
\=\+({\rm{v-buf\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{v-buf\&} $\wedge$ {\rm{properp}}\,({\it{a\/}})\index{properp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\it{n\/}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\rm{index}}\,({\tt{'}}{\tt{v-buf}}, {\it{n\/}})\index{index}, {\it{a\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{v-threefix}}\,({\it{a\/}})\index{v-threefix})\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-buf\$value; name this event `v-buf\$value-off'.\index{v-buf\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-or\$body} \\  
\=\+{\rm{v-or\$body}}\,({\it{m\/}}, {\it{n\/}})\index{v-or\$body} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{g}}, {\it{m\/}})\index{index}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{y}}, {\it{m\/}})\index{index}), \\ 
{\tt{'}}{\tt{b-or}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{a}}, {\it{m\/}})\index{index}, {\rm{index}}\,({\tt{'}}{\tt{b}}, {\it{m\/}})\index{index}))\-, \\ 
{\rm{v-or\$body}}\,($1\;+$ {\it{m\/}}, {\it{n\/}} $-\;1$)\index{v-or\$body})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-or\$body; name this event `v-or\$body-off'.\index{v-or\$body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-or*} \\  
\=\+{\rm{v-or*}}\,({\it{n\/}})\index{v-or*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{v-or}}, {\it{n\/}})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\rm{append}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{indices}}\,({\tt{'}}{\tt{b}}, {\tt{0}}, {\it{n\/}})\index{indices}), \\ 
{\rm{cons}}\,({\rm{indices}}\,({\tt{'}}{\tt{y}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{cons}}\,({\rm{v-or\$body}}\,({\tt{0}}, {\it{n\/}})\index{v-or\$body}, {\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}})))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-or*\$destructure \\ \index{v-or*\$destructure}
\=\+({\rm{car}}\,({\rm{v-or*}}\,({\it{n\/}})\index{v-or*}) $=$ {\rm{index}}\,({\tt{'}}{\tt{v-or}}, {\it{n\/}})\index{index}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadr}}\,({\rm{v-or*}}\,({\it{n\/}})\index{v-or*}) $=$ {\rm{append}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{indices}}\,({\tt{'}}{\tt{b}}, {\tt{0}}, {\it{n\/}})\index{indices})) \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\rm{v-or*}}\,({\it{n\/}})\index{v-or*}) $=$ {\rm{indices}}\,({\tt{'}}{\tt{y}}, {\tt{0}}, {\it{n\/}})\index{indices}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadddr}}\,({\rm{v-or*}}\,({\it{n\/}})\index{v-or*}) $=$ {\rm{v-or\$body}}\,({\tt{0}}, {\it{n\/}})\index{v-or\$body}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{v-or*}}\,({\it{n\/}})\index{v-or*}) $=$ {\bf{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-or*; name this event `v-or*-off'.\index{v-or*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-or*\$destructure; name this event `v-or*\$destructure-off'.\index{v-or*\$destructure-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-or\&} \\  
\=\+{\rm{v-or\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{v-or\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\rm{index}}\,({\tt{'}}{\tt{v-or}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{lookup-module} $=$ {\rm{v-or*}}\,({\it{n\/}})\index{v-or*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-or\&}}\,({\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{v-or}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{delete-module})\index{b-or\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-or\&; name this event `v-or\&-off'.\index{v-or\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-or\$netlist}$\;\;$
{\rm{v-or\$netlist}}\,({\it{n\/}})\index{v-or\$netlist} $=$ {\rm{cons}}\,({\rm{v-or*}}\,({\it{n\/}})\index{v-or*}, {\sc{b-or\$netlist}}\index{b-or\$netlist})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-or\$unbound-in-body \\ \index{v-or\$unbound-in-body}
({\it{l\/}} $<$ {\it{m\/}}) $\rightarrow$ {\rm{unbound-in-body}}\,({\rm{index}}\,({\tt{'}}{\tt{y}}, {\it{l\/}})\index{index}, {\rm{v-or\$body}}\,({\it{m\/}}, {\it{n\/}})\index{v-or\$body})\index{unbound-in-body}
\end{tabbing}


\noindent{\sc Event}:   Enable v-or\$unbound-in-body; name this event `v-or\$unbound-in-body-off'.\index{v-or\$unbound-in-body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-or\$body-value \\ \index{v-or\$body-value}
\=\+({\rm{b-or\&}}\,({\it{netlist\/}})\index{b-or\&} $\wedge$ ({\it{body\/}} $=$ {\rm{v-or\$body}}\,({\it{m\/}}, {\it{n\/}})\index{v-or\$body})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{y}}, {\it{m\/}}, {\it{n\/}})\index{indices}, \\ 
{\rm{dual-eval}}\,({\tt{1}}, {\it{body\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{dual-eval})\-\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{fv-or}}\,(\=\+{\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\it{m\/}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value}, \\ 
{\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{b}}, {\it{m\/}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value})\-\index{fv-or})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-or\$body-value; name this event `v-or\$body-value-off'.\index{v-or\$body-value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-or\$value \\ \index{v-or\$value}
\=\+(\=\+{\rm{v-or\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{v-or\&} \\ 
$\wedge$$\;\;\;\;$({\rm{properp}}\,({\it{a\/}})\index{properp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\it{n\/}})) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{b\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\it{n\/}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\rm{index}}\,({\tt{'}}{\tt{v-or}}, {\it{n\/}})\index{index}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{fv-or}}\,({\it{a\/}}, {\it{b\/}})\index{fv-or})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-or\$value; name this event `v-or\$value-off'.\index{v-or\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-xor\$body} \\  
\=\+{\rm{v-xor\$body}}\,({\it{m\/}}, {\it{n\/}})\index{v-xor\$body} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{g}}, {\it{m\/}})\index{index}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{y}}, {\it{m\/}})\index{index}), \\ 
{\tt{'}}{\tt{b-xor}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{a}}, {\it{m\/}})\index{index}, {\rm{index}}\,({\tt{'}}{\tt{b}}, {\it{m\/}})\index{index}))\-, \\ 
{\rm{v-xor\$body}}\,($1\;+$ {\it{m\/}}, {\it{n\/}} $-\;1$)\index{v-xor\$body})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-xor\$body; name this event `v-xor\$body-off'.\index{v-xor\$body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-xor*} \\  
\=\+{\rm{v-xor*}}\,({\it{n\/}})\index{v-xor*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{v-xor}}, {\it{n\/}})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\rm{append}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{indices}}\,({\tt{'}}{\tt{b}}, {\tt{0}}, {\it{n\/}})\index{indices}), \\ 
{\rm{cons}}\,({\rm{indices}}\,({\tt{'}}{\tt{y}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{cons}}\,({\rm{v-xor\$body}}\,({\tt{0}}, {\it{n\/}})\index{v-xor\$body}, {\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}})))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-xor*\$destructure \\ \index{v-xor*\$destructure}
\=\+({\rm{car}}\,({\rm{v-xor*}}\,({\it{n\/}})\index{v-xor*}) $=$ {\rm{index}}\,({\tt{'}}{\tt{v-xor}}, {\it{n\/}})\index{index}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadr}}\,({\rm{v-xor*}}\,({\it{n\/}})\index{v-xor*}) $=$ {\rm{append}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{indices}}\,({\tt{'}}{\tt{b}}, {\tt{0}}, {\it{n\/}})\index{indices})) \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\rm{v-xor*}}\,({\it{n\/}})\index{v-xor*}) $=$ {\rm{indices}}\,({\tt{'}}{\tt{y}}, {\tt{0}}, {\it{n\/}})\index{indices}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadddr}}\,({\rm{v-xor*}}\,({\it{n\/}})\index{v-xor*}) $=$ {\rm{v-xor\$body}}\,({\tt{0}}, {\it{n\/}})\index{v-xor\$body}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{v-xor*}}\,({\it{n\/}})\index{v-xor*}) $=$ {\bf{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-xor*; name this event `v-xor*-off'.\index{v-xor*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-xor*\$destructure; name this event `v-xor*\$destructure-off'.\index{v-xor*\$destructure-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-xor\&} \\  
\=\+{\rm{v-xor\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{v-xor\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\rm{index}}\,({\tt{'}}{\tt{v-xor}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{lookup-module} $=$ {\rm{v-xor*}}\,({\it{n\/}})\index{v-xor*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-xor\&}}\,({\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{v-xor}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{delete-module})\index{b-xor\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-xor\&; name this event `v-xor\&-off'.\index{v-xor\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-xor\$netlist}$\;\;$
{\rm{v-xor\$netlist}}\,({\it{n\/}})\index{v-xor\$netlist} $=$ {\rm{cons}}\,({\rm{v-xor*}}\,({\it{n\/}})\index{v-xor*}, {\sc{b-xor\$netlist}}\index{b-xor\$netlist})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-xor\$unbound-in-body \\ \index{v-xor\$unbound-in-body}
({\it{l\/}} $<$ {\it{m\/}}) $\rightarrow$ {\rm{unbound-in-body}}\,({\rm{index}}\,({\tt{'}}{\tt{y}}, {\it{l\/}})\index{index}, {\rm{v-xor\$body}}\,({\it{m\/}}, {\it{n\/}})\index{v-xor\$body})\index{unbound-in-body}
\end{tabbing}


\noindent{\sc Event}:   Enable v-xor\$unbound-in-body; name this event `v-xor\$unbound-in-body-off'.\index{v-xor\$unbound-in-body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-xor\$body-value \\ \index{v-xor\$body-value}
\=\+({\rm{b-xor\&}}\,({\it{netlist\/}})\index{b-xor\&} $\wedge$ ({\it{body\/}} $=$ {\rm{v-xor\$body}}\,({\it{m\/}}, {\it{n\/}})\index{v-xor\$body})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{y}}, {\it{m\/}}, {\it{n\/}})\index{indices}, \\ 
{\rm{dual-eval}}\,({\tt{1}}, {\it{body\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{dual-eval})\-\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{fv-xor}}\,(\=\+{\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\it{m\/}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value}, \\ 
{\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{b}}, {\it{m\/}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value})\-\index{fv-xor})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-xor\$body-value; name this event `v-xor\$body-value-off'.\index{v-xor\$body-value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-xor\$value \\ \index{v-xor\$value}
\=\+(\=\+{\rm{v-xor\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{v-xor\&} \\ 
$\wedge$$\;\;\;\;$({\rm{properp}}\,({\it{a\/}})\index{properp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\it{n\/}})) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{b\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\it{n\/}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\rm{index}}\,({\tt{'}}{\tt{v-xor}}, {\it{n\/}})\index{index}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{fv-xor}}\,({\it{a\/}}, {\it{b\/}})\index{fv-xor})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-xor\$value; name this event `v-xor\$value-off'.\index{v-xor\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-pullup\$body} \\  
\=\+{\rm{v-pullup\$body}}\,({\it{m\/}}, {\it{n\/}})\index{v-pullup\$body} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{g}}, {\it{m\/}})\index{index}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{y}}, {\it{m\/}})\index{index}), \\ 
{\tt{'}}{\tt{pullup}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{a}}, {\it{m\/}})\index{index}))\-, \\ 
{\rm{v-pullup\$body}}\,($1\;+$ {\it{m\/}}, {\it{n\/}} $-\;1$)\index{v-pullup\$body})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-pullup\$body; name this event `v-pullup\$body-off'.\index{v-pullup\$body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-pullup*} \\  
\=\+{\rm{v-pullup*}}\,({\it{n\/}})\index{v-pullup*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{v-pullup}}, {\it{n\/}})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}, \\ 
{\rm{cons}}\,({\rm{indices}}\,({\tt{'}}{\tt{y}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{cons}}\,({\rm{v-pullup\$body}}\,({\tt{0}}, {\it{n\/}})\index{v-pullup\$body}, {\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}})))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-pullup*\$destructure \\ \index{v-pullup*\$destructure}
\=\+({\rm{car}}\,({\rm{v-pullup*}}\,({\it{n\/}})\index{v-pullup*}) $=$ {\rm{index}}\,({\tt{'}}{\tt{v-pullup}}, {\it{n\/}})\index{index}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadr}}\,({\rm{v-pullup*}}\,({\it{n\/}})\index{v-pullup*}) $=$ {\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\rm{v-pullup*}}\,({\it{n\/}})\index{v-pullup*}) $=$ {\rm{indices}}\,({\tt{'}}{\tt{y}}, {\tt{0}}, {\it{n\/}})\index{indices}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadddr}}\,({\rm{v-pullup*}}\,({\it{n\/}})\index{v-pullup*}) $=$ {\rm{v-pullup\$body}}\,({\tt{0}}, {\it{n\/}})\index{v-pullup\$body}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{v-pullup*}}\,({\it{n\/}})\index{v-pullup*}) $=$ {\bf{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-pullup*; name this event `v-pullup*-off'.\index{v-pullup*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-pullup*\$destructure; name this event `v-pullup*\$destructure-off'.\index{v-pullup*\$destructure-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-pullup\&} \\  
\=\+{\rm{v-pullup\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{v-pullup\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\rm{index}}\,({\tt{'}}{\tt{v-pullup}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{lookup-module} $=$ {\rm{v-pullup*}}\,({\it{n\/}})\index{v-pullup*}) \\ 
$\wedge$$\;\;\;\;${\rm{pullup\&}}\,({\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{v-pullup}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{delete-module})\index{pullup\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-pullup\&; name this event `v-pullup\&-off'.\index{v-pullup\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-pullup\$netlist} \\  
{\rm{v-pullup\$netlist}}\,({\it{n\/}})\index{v-pullup\$netlist} $=$ {\rm{cons}}\,({\rm{v-pullup*}}\,({\it{n\/}})\index{v-pullup*}, {\sc{pullup\$netlist}}\index{pullup\$netlist})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-pullup\$unbound-in-body \\ \index{v-pullup\$unbound-in-body}
({\it{l\/}} $<$ {\it{m\/}}) $\rightarrow$ {\rm{unbound-in-body}}\,({\rm{index}}\,({\tt{'}}{\tt{y}}, {\it{l\/}})\index{index}, {\rm{v-pullup\$body}}\,({\it{m\/}}, {\it{n\/}})\index{v-pullup\$body})\index{unbound-in-body}
\end{tabbing}


\noindent{\sc Event}:   Enable v-pullup\$unbound-in-body; name this event `v-pullup\$unbound-in-body-off'.\index{v-pullup\$unbound-in-body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-pullup\$body-value \\ \index{v-pullup\$body-value}
\=\+({\rm{pullup\&}}\,({\it{netlist\/}})\index{pullup\&} $\wedge$ ({\it{body\/}} $=$ {\rm{v-pullup\$body}}\,({\it{m\/}}, {\it{n\/}})\index{v-pullup\$body})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{y}}, {\it{m\/}}, {\it{n\/}})\index{indices}, \\ 
{\rm{dual-eval}}\,({\tt{1}}, {\it{body\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{dual-eval})\-\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{v-pullup}}\,({\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\it{m\/}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value})\index{v-pullup})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-pullup\$body-value; name this event `v-pullup\$body-value-off'.\index{v-pullup\$body-value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-pullup\$value \\ \index{v-pullup\$value}
\=\+({\rm{v-pullup\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{v-pullup\&} $\wedge$ {\rm{properp}}\,({\it{a\/}})\index{properp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\it{n\/}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\rm{index}}\,({\tt{'}}{\tt{v-pullup}}, {\it{n\/}})\index{index}, {\it{a\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{v-pullup}}\,({\it{a\/}})\index{v-pullup})\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-pullup\$value; name this event `v-pullup\$value-off'.\index{v-pullup\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-wire\$body} \\  
\=\+{\rm{v-wire\$body}}\,({\it{m\/}}, {\it{n\/}})\index{v-wire\$body} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{g}}, {\it{m\/}})\index{index}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{y}}, {\it{m\/}})\index{index}), \\ 
{\tt{'}}{\tt{t-wire}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{a}}, {\it{m\/}})\index{index}, {\rm{index}}\,({\tt{'}}{\tt{b}}, {\it{m\/}})\index{index}))\-, \\ 
{\rm{v-wire\$body}}\,($1\;+$ {\it{m\/}}, {\it{n\/}} $-\;1$)\index{v-wire\$body})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-wire\$body; name this event `v-wire\$body-off'.\index{v-wire\$body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-wire*} \\  
\=\+{\rm{v-wire*}}\,({\it{n\/}})\index{v-wire*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{v-wire}}, {\it{n\/}})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\rm{append}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{indices}}\,({\tt{'}}{\tt{b}}, {\tt{0}}, {\it{n\/}})\index{indices}), \\ 
{\rm{cons}}\,({\rm{indices}}\,({\tt{'}}{\tt{y}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{cons}}\,({\rm{v-wire\$body}}\,({\tt{0}}, {\it{n\/}})\index{v-wire\$body}, {\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}})))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-wire*\$destructure \\ \index{v-wire*\$destructure}
\=\+({\rm{car}}\,({\rm{v-wire*}}\,({\it{n\/}})\index{v-wire*}) $=$ {\rm{index}}\,({\tt{'}}{\tt{v-wire}}, {\it{n\/}})\index{index}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadr}}\,({\rm{v-wire*}}\,({\it{n\/}})\index{v-wire*}) $=$ {\rm{append}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{indices}}\,({\tt{'}}{\tt{b}}, {\tt{0}}, {\it{n\/}})\index{indices})) \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\rm{v-wire*}}\,({\it{n\/}})\index{v-wire*}) $=$ {\rm{indices}}\,({\tt{'}}{\tt{y}}, {\tt{0}}, {\it{n\/}})\index{indices}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadddr}}\,({\rm{v-wire*}}\,({\it{n\/}})\index{v-wire*}) $=$ {\rm{v-wire\$body}}\,({\tt{0}}, {\it{n\/}})\index{v-wire\$body}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{v-wire*}}\,({\it{n\/}})\index{v-wire*}) $=$ {\bf{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-wire*; name this event `v-wire*-off'.\index{v-wire*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-wire*\$destructure; name this event `v-wire*\$destructure-off'.\index{v-wire*\$destructure-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-wire\&} \\  
\=\+{\rm{v-wire\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{v-wire\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\rm{index}}\,({\tt{'}}{\tt{v-wire}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{lookup-module} $=$ {\rm{v-wire*}}\,({\it{n\/}})\index{v-wire*}) \\ 
$\wedge$$\;\;\;\;${\rm{t-wire\&}}\,({\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{v-wire}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{delete-module})\index{t-wire\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-wire\&; name this event `v-wire\&-off'.\index{v-wire\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-wire\$netlist}$\;\;$
{\rm{v-wire\$netlist}}\,({\it{n\/}})\index{v-wire\$netlist} $=$ {\rm{cons}}\,({\rm{v-wire*}}\,({\it{n\/}})\index{v-wire*}, {\sc{t-wire\$netlist}}\index{t-wire\$netlist})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-wire\$unbound-in-body \\ \index{v-wire\$unbound-in-body}
({\it{l\/}} $<$ {\it{m\/}}) $\rightarrow$ {\rm{unbound-in-body}}\,({\rm{index}}\,({\tt{'}}{\tt{y}}, {\it{l\/}})\index{index}, {\rm{v-wire\$body}}\,({\it{m\/}}, {\it{n\/}})\index{v-wire\$body})\index{unbound-in-body}
\end{tabbing}


\noindent{\sc Event}:   Enable v-wire\$unbound-in-body; name this event `v-wire\$unbound-in-body-off'.\index{v-wire\$unbound-in-body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-wire\$body-value \\ \index{v-wire\$body-value}
\=\+({\rm{t-wire\&}}\,({\it{netlist\/}})\index{t-wire\&} $\wedge$ ({\it{body\/}} $=$ {\rm{v-wire\$body}}\,({\it{m\/}}, {\it{n\/}})\index{v-wire\$body})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{y}}, {\it{m\/}}, {\it{n\/}})\index{indices}, \\ 
{\rm{dual-eval}}\,({\tt{1}}, {\it{body\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{dual-eval})\-\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{v-wire}}\,(\=\+{\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\it{m\/}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value}, \\ 
{\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{b}}, {\it{m\/}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value})\-\index{v-wire})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-wire\$body-value; name this event `v-wire\$body-value-off'.\index{v-wire\$body-value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-wire\$value \\ \index{v-wire\$value}
\=\+(\=\+{\rm{v-wire\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{v-wire\&} \\ 
$\wedge$$\;\;\;\;$({\rm{properp}}\,({\it{a\/}})\index{properp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\it{n\/}})) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{b\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\it{n\/}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\rm{index}}\,({\tt{'}}{\tt{v-wire}}, {\it{n\/}})\index{index}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{v-wire}}\,({\it{a\/}}, {\it{b\/}})\index{v-wire})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-wire\$value; name this event `v-wire\$value-off'.\index{v-wire\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{rev-0}$\;\;$
{\rm{rev-0}}\,({\it{x\/}})\index{rev-0} $=$ {\rm{rev1}}\,({\it{x\/}}, {\tt{0}})\index{rev1}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{number-to-digit} \\  
{\rm{number-to-digit}}\,({\it{number\/}})\index{number-to-digit} $=$ {\rm{nth}}\,({\it{number\/}}, {\rm{cdr}}\,({\rm{unpack}}\,({\tt{'}}{\tt{a0123456789}})))\index{nth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{number-to-list1} \\  
\=\+{\rm{number-to-list1}}\,({\it{number\/}})\index{number-to-list1} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{number\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{number-to-digit}}\,({\it{number\/}} ${}${\bf{mod}}${}$ {\tt{10}})\index{number-to-digit}, \\ 
{\rm{number-to-list1}}\,({\it{number\/}} $\div$ {\tt{10}})\index{number-to-list1})\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{number-to-list} \\  
\=\+{\rm{number-to-list}}\,({\it{number\/}})\index{number-to-list} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{number\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\rm{cons}}\,({\rm{cadr}}\,({\rm{unpack}}\,({\tt{'}}{\tt{a0}})), {\tt{0}}) \\ 
{\bf else }{\rm{rev-0}}\,({\rm{number-to-list1}}\,({\it{number\/}})\index{number-to-list1})\index{rev-0}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{lisp-netlist} \\  
\=\+{\rm{lisp-netlist}}\,({\it{netlist\/}})\index{lisp-netlist} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{indexp}}\,({\it{netlist\/}})\index{indexp} \\ 
{\bf then }{\rm{pack}}\,({\rm{append}}\,(\=\+{\rm{unpack}}\,({\rm{i-name}}\,({\it{netlist\/}})\index{i-name}), \\ 
{\rm{cons}}\,(\=\+{\rm{cadr}}\,({\rm{unpack}}\,({\tt{'}}{\tt{a\_}})), \\ 
{\rm{number-to-list}}\,({\rm{i-num}}\,({\it{netlist\/}})\index{i-num})\index{number-to-list})\-)\-) \\ 
{\bf elseif }{\it{netlist\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{netlist\/}} \\ 
{\bf else }{\rm{cons}}\,({\rm{lisp-netlist}}\,({\rm{car}}\,({\it{netlist\/}}))\index{lisp-netlist}, {\rm{lisp-netlist}}\,({\rm{cdr}}\,({\it{netlist\/}}))\index{lisp-netlist})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{collect-primitives} \\  
\=\+{\rm{collect-primitives}}\,({\it{flg\/}}, {\it{x0\/}}, {\it{netlist\/}})\index{collect-primitives} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{flg\/}}: \\ 
{\bf case = }{\tt{0}} \\ 
{\bf then }\=\+{\bf if }{\rm{primp}}\,({\it{x0\/}})\index{primp} $\vee$ ($\neg$ {\rm{lookup-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{lookup-module})$\;\;${\bf then }{\rm{list}}\,({\it{x0\/}}) \\ 
{\bf else }{\rm{flatten-list}}\,({\rm{collect-primitives}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\rm{delete-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{delete-module})\-\index{collect-primitives})\index{flatten-list}$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{1}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\it{x0\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{collect-primitives}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-function}, \\ 
{\it{netlist\/}})\-\index{collect-primitives}, \\ 
{\rm{collect-primitives}}\,({\tt{1}}, {\rm{cdr}}\,({\it{x0\/}}), {\it{netlist\/}})\index{collect-primitives})\-$\;${\bf  endif}\- \\ 
{\bf otherwise }{\bf{f}}$\;${\bf  endcase}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{count-primitives} \\  
\=\+{\rm{count-primitives}}\,({\it{flg\/}}, {\it{x0\/}}, {\it{x1\/}}, {\it{type\/}}, {\it{netlist\/}})\index{count-primitives} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{flg\/}}: \\ 
{\bf case = }{\tt{0}} \\ 
{\bf then }\=\+{\bf if }{\rm{primp}}\,({\it{x0\/}})\index{primp} \\ 
{\bf then }\=\+{\bf if }{\rm{primp-lookup}}\,({\it{x0\/}}, {\it{type\/}})\index{primp-lookup}$\;\;${\bf then }{\rm{primp2}}\,({\it{x0\/}}, {\it{type\/}})\index{primp2} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{listp}}\,({\rm{lookup-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{lookup-module}) \\ 
{\bf then }{\rm{count-primitives}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{x0\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\tt{0}}, \\ 
{\it{type\/}}, \\ 
{\rm{delete-module}}\,({\it{x0\/}}, {\it{netlist\/}})\index{delete-module})\-\index{count-primitives} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{1}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\it{x0\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{x1\/}} \\ 
{\bf elseif }{\rm{count-primitives}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-function}, \\ 
{\bf{nil}}, \\ 
{\it{type\/}}, \\ 
{\it{netlist\/}})\-\index{count-primitives} \\ 
{\bf then }{\rm{count-primitives}}\,(\=\+{\tt{1}}, \\ 
{\rm{cdr}}\,({\it{x0\/}}), \\ 
{\it{x1\/}} $+$ {\rm{count-primitives}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{x0\/}}))\index{occ-function}, \\ 
{\bf{nil}}, \\ 
{\it{type\/}}, \\ 
{\it{netlist\/}})\-\index{count-primitives}, \\ 
{\it{type\/}}, \\ 
{\it{netlist\/}})\-\index{count-primitives} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf otherwise }{\bf{f}}$\;${\bf  endcase}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable count-primitives; name this event `count-primitives-off'.\index{count-primitives-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{half-adder*} \\  
\=\+{\sc{half-adder*}}\index{half-adder*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{half-adder}} \\ 
{\tt{(}}{\tt{a}}{\tt{ }}{\tt{b}}{\tt{)}} \\ 
{\tt{(}}{\tt{sum}}{\tt{ }}{\tt{carry}}{\tt{)}} \\ 
{\tt{(}}{\tt{(}}{\tt{g0}}{\tt{ }}{\tt{(}}{\tt{sum}}{\tt{)}}{\tt{ }}{\tt{b-xor}}{\tt{ }}{\tt{(}}{\tt{a}}{\tt{ }}{\tt{b}}{\tt{)}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{g1}}{\tt{ }}{\tt{(}}{\tt{carry}}{\tt{)}}{\tt{ }}{\tt{b-and}}{\tt{ }}{\tt{(}}{\tt{a}}{\tt{ }}{\tt{b}}{\tt{)}}{\tt{)}}{\tt{)}} \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{half-adder\$netlist} \\  
{\sc{half-adder\$netlist}}\index{half-adder\$netlist} $=$ {\rm{cons}}\,({\sc{half-adder*}}\index{half-adder*}, {\sc{b-xor\$netlist}}\index{b-xor\$netlist} $\cup$ {\sc{b-and\$netlist}}\index{b-and\$netlist})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{half-adder\&} \\  
\=\+{\rm{half-adder\&}}\,({\it{netlist\/}})\index{half-adder\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{half-adder}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{half-adder*}}\index{half-adder*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-xor\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{half-adder}}, {\it{netlist\/}})\index{delete-module})\index{b-xor\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-and\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{half-adder}}, {\it{netlist\/}})\index{delete-module})\index{b-and\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable half-adder\&; name this event `half-adder\&-off'.\index{half-adder\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  half-adder\$value \\ \index{half-adder\$value}
\=\+{\rm{half-adder\&}}\,({\it{netlist\/}})\index{half-adder\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{half-adder}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-xor}}\,({\it{a\/}}, {\it{b\/}})\index{f-xor}, {\rm{f-and}}\,({\it{a\/}}, {\it{b\/}})\index{f-and}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable half-adder\$value; name this event `half-adder\$value-off'.\index{half-adder\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{full-adder*} \\  
\=\+{\sc{full-adder*}}\index{full-adder*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{full-adder}} \\ 
{\tt{(}}{\tt{a}}{\tt{ }}{\tt{b}}{\tt{ }}{\tt{c}}{\tt{)}} \\ 
{\tt{(}}{\tt{sum}}{\tt{ }}{\tt{carry}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{t0}}{\tt{ }}{\tt{(}}{\tt{sum1}}{\tt{ }}{\tt{carry1}}{\tt{)}}{\tt{ }}{\tt{half-adder}}{\tt{ }}{\tt{(}}{\tt{a}}{\tt{ }}{\tt{b}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{t1}}{\tt{ }}{\tt{(}}{\tt{sum}}{\tt{ }}{\tt{carry2}}{\tt{)}}{\tt{ }}{\tt{half-adder}}{\tt{ }}{\tt{(}}{\tt{sum1}}{\tt{ }}{\tt{c}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{t2}}{\tt{ }}{\tt{(}}{\tt{carry}}{\tt{)}}{\tt{ }}{\tt{b-or}}{\tt{ }}{\tt{(}}{\tt{carry1}}{\tt{ }}{\tt{carry2}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{full-adder\$netlist} \\  
\=\+{\sc{full-adder\$netlist}}\index{full-adder\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\sc{full-adder*}}\index{full-adder*}, {\sc{half-adder\$netlist}}\index{half-adder\$netlist} $\cup$ {\sc{b-or\$netlist}}\index{b-or\$netlist})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{full-adder\&} \\  
\=\+{\rm{full-adder\&}}\,({\it{netlist\/}})\index{full-adder\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{full-adder}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{full-adder*}}\index{full-adder*}) \\ 
$\wedge$$\;\;\;\;${\rm{half-adder\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{full-adder}}, {\it{netlist\/}})\index{delete-module})\index{half-adder\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-or\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{full-adder}}, {\it{netlist\/}})\index{delete-module})\index{b-or\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable full-adder\&; name this event `full-adder\&-off'.\index{full-adder\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{f\$full-adder} \\  
\=\+{\rm{f\$full-adder}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f\$full-adder} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-xor}}\,({\rm{f-xor}}\,({\it{a\/}}, {\it{b\/}})\index{f-xor}, {\it{c\/}})\index{f-xor}, {\rm{f-or}}\,({\rm{f-and}}\,({\it{a\/}}, {\it{b\/}})\index{f-and}, {\rm{f-and}}\,({\rm{f-xor}}\,({\it{a\/}}, {\it{b\/}})\index{f-xor}, {\it{c\/}})\index{f-and})\index{f-or})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  full-adder\$value \\ \index{full-adder\$value}
\=\+{\rm{full-adder\&}}\,({\it{netlist\/}})\index{full-adder\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{full-adder}}, {\rm{list}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$full-adder}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f\$full-adder})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{full-adder} \\  
\=\+{\rm{full-adder}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{full-adder} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{b-xor3}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{b-xor3}, {\rm{b-or}}\,({\rm{b-and}}\,({\it{a\/}}, {\rm{b-or}}\,({\it{b\/}}, {\it{c\/}})\index{b-or})\index{b-and}, {\rm{b-and}}\,({\it{b\/}}, {\it{c\/}})\index{b-and})\index{b-or})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f\$full-adder=full-adder \\ \index{f\$full-adder=full-adder}
\=\+({\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f\$full-adder}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{f\$full-adder} $=$ {\rm{full-adder}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{full-adder})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{m1*} \\  
\=\+{\sc{m1*}}\index{m1*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{m1}} \\ 
{\tt{(}}{\tt{clk}}{\tt{ }}{\tt{en}}{\tt{ }}{\tt{sel}}{\tt{ }}{\tt{d}}{\tt{ }}{\tt{q}}{\tt{)}} \\ 
{\tt{(}}{\tt{q}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{mux}}{\tt{ }}{\tt{(}}{\tt{b}}{\tt{)}}{\tt{ }}{\tt{b-if}}{\tt{ }}{\tt{(}}{\tt{sel}}{\tt{ }}{\tt{d}}{\tt{ }}{\tt{q}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{latch}}{\tt{ }}{\tt{(}}{\tt{a}}{\tt{ }}{\tt{an}}{\tt{)}}{\tt{ }}{\tt{fd1}}{\tt{ }}{\tt{(}}{\tt{b}}{\tt{ }}{\tt{clk}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{tbuf}}{\tt{ }}{\tt{(}}{\tt{q}}{\tt{)}}{\tt{ }}{\tt{t-buf}}{\tt{ }}{\tt{(}}{\tt{en}}{\tt{ }}{\tt{a}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{latch}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{m1\$netlist} \\  
{\sc{m1\$netlist}}\index{m1\$netlist} $=$ {\rm{cons}}\,({\sc{m1*}}\index{m1*}, ({\sc{b-if\$netlist}}\index{b-if\$netlist} $\cup$ {\sc{fd1\$netlist}}\index{fd1\$netlist}) $\cup$ {\sc{t-buf\$netlist}}\index{t-buf\$netlist})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{m1\&} \\  
\=\+{\rm{m1\&}}\,({\it{netlist\/}})\index{m1\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{m1}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{m1*}}\index{m1*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-if\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{m1}}, {\it{netlist\/}})\index{delete-module})\index{b-if\&} \\ 
$\wedge$$\;\;\;\;${\rm{fd1\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{m1}}, {\it{netlist\/}})\index{delete-module})\index{fd1\&} \\ 
$\wedge$$\;\;\;\;${\rm{t-buf\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{m1}}, {\it{netlist\/}})\index{delete-module})\index{t-buf\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable m1\&; name this event `m1\&-off'.\index{m1\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  m1\$value \\ \index{m1\$value}
\=\+{\rm{m1\&}}\,({\it{netlist\/}})\index{m1\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{m1}}, {\rm{list}}\,({\it{clk\/}}, {\it{en\/}}, {\it{sel\/}}, {\it{d\/}}, {\it{q\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{ft-buf}}\,({\it{en\/}}, {\it{state\/}})\index{ft-buf}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable m1\$value; name this event `m1\$value-off'.\index{m1\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  m1\$state \\ \index{m1\$state}
\=\+{\rm{m1\&}}\,({\it{netlist\/}})\index{m1\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{m1}}, {\rm{list}}\,({\it{clk\/}}, {\it{en\/}}, {\it{sel\/}}, {\it{d\/}}, {\it{q\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f-if}}\,({\it{sel\/}}, {\it{d\/}}, {\it{q\/}})\index{f-if})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable m1\$state; name this event `m1\$state-off'.\index{m1\$state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{m2*} \\  
\=\+{\sc{m2*}}\index{m2*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{m2}} \\ 
{\tt{(}}{\tt{clk}}{\tt{ }}{\tt{en0}}{\tt{ }}{\tt{en1}}{\tt{ }}{\tt{sel0}}{\tt{ }}{\tt{sel1}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{)}} \\ 
{\tt{(}}{\tt{q}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{occ0}}{\tt{ }}{\tt{(}}{\tt{q0}}{\tt{)}}{\tt{ }}{\tt{m1}}{\tt{ }}{\tt{(}}{\tt{clk}}{\tt{ }}{\tt{en0}}{\tt{ }}{\tt{sel0}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{q}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{occ1}}{\tt{ }}{\tt{(}}{\tt{q1}}{\tt{)}}{\tt{ }}{\tt{m1}}{\tt{ }}{\tt{(}}{\tt{clk}}{\tt{ }}{\tt{en1}}{\tt{ }}{\tt{sel1}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{q}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{wire}}{\tt{ }}{\tt{(}}{\tt{q}}{\tt{)}}{\tt{ }}{\tt{t-wire}}{\tt{ }}{\tt{(}}{\tt{q0}}{\tt{ }}{\tt{q1}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{occ0}}{\tt{ }}{\tt{occ1}}{\tt{)}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{m2\$netlist} \\  
{\sc{m2\$netlist}}\index{m2\$netlist} $=$ {\rm{cons}}\,({\sc{m2*}}\index{m2*}, {\sc{m1\$netlist}}\index{m1\$netlist} $\cup$ {\sc{t-wire\$netlist}}\index{t-wire\$netlist})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{m2\&} \\  
\=\+{\rm{m2\&}}\,({\it{netlist\/}})\index{m2\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{m2}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{m2*}}\index{m2*}) \\ 
$\wedge$$\;\;\;\;${\rm{m1\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{m2}}, {\it{netlist\/}})\index{delete-module})\index{m1\&} \\ 
$\wedge$$\;\;\;\;${\rm{t-wire\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{m2}}, {\it{netlist\/}})\index{delete-module})\index{t-wire\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable m2\&; name this event `m2\&-off'.\index{m2\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  m2\$value \\ \index{m2\$value}
\=\+{\rm{m2\&}}\,({\it{netlist\/}})\index{m2\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{m2}}, {\rm{list}}\,({\it{clk\/}}, {\it{en0\/}}, {\it{en1\/}}, {\it{sel0\/}}, {\it{sel1\/}}, {\it{d0\/}}, {\it{d1\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{ft-wire}}\,({\rm{ft-buf}}\,({\it{en0\/}}, {\rm{car}}\,({\it{state\/}}))\index{ft-buf}, {\rm{ft-buf}}\,({\it{en1\/}}, {\rm{cadr}}\,({\it{state\/}}))\index{ft-buf})\index{ft-wire}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable m2\$value; name this event `m2\$value-off'.\index{m2\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  m2\$state \\ \index{m2\$state}
\=\+{\rm{m2\&}}\,({\it{netlist\/}})\index{m2\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{m2}}, {\rm{list}}\,({\it{clk\/}}, {\it{en0\/}}, {\it{en1\/}}, {\it{sel0\/}}, {\it{sel1\/}}, {\it{d0\/}}, {\it{d1\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{f-if}}\,(\=\+{\it{sel0\/}}, \\ 
{\it{d0\/}}, \\ 
{\rm{ft-wire}}\,(\=\+{\rm{ft-buf}}\,({\it{en0\/}}, {\rm{car}}\,({\it{state\/}}))\index{ft-buf}, \\ 
{\rm{ft-buf}}\,({\it{en1\/}}, {\rm{cadr}}\,({\it{state\/}}))\index{ft-buf})\-\index{ft-wire})\-\index{f-if}, \\ 
{\rm{f-if}}\,(\=\+{\it{sel1\/}}, \\ 
{\it{d1\/}}, \\ 
{\rm{ft-wire}}\,(\=\+{\rm{ft-buf}}\,({\it{en0\/}}, {\rm{car}}\,({\it{state\/}}))\index{ft-buf}, \\ 
{\rm{ft-buf}}\,({\it{en1\/}}, {\rm{cadr}}\,({\it{state\/}}))\index{ft-buf})\-\index{ft-wire})\-\index{f-if})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable m2\$state; name this event `m2\$state-off'.\index{m2\$state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{bv-adder} \\  
\=\+{\rm{bv-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{bv-adder} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{list}}\,({\it{c\/}}) \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{xor}}\,({\it{c\/}}, {\rm{xor}}\,({\rm{car}}\,({\it{a\/}}), {\rm{car}}\,({\it{b\/}}))\index{xor})\index{xor}, \\ 
{\rm{bv-adder}}\,(\=\+\=\+({\rm{car}}\,({\it{a\/}}) $\wedge$ {\rm{car}}\,({\it{b\/}})) \\ 
$\vee$$\;\;\;\;$({\rm{car}}\,({\it{a\/}}) $\wedge$ {\it{c\/}}) \\ 
$\vee$$\;\;\;\;$({\rm{car}}\,({\it{b\/}}) $\wedge$ {\it{c\/}})\-, \\ 
{\rm{cdr}}\,({\it{a\/}}), \\ 
{\rm{cdr}}\,({\it{b\/}}))\-\index{bv-adder})\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{bv-adder-body} \\  
\=\+{\rm{bv-adder-body}}\,({\it{m\/}}, {\it{n\/}})\index{bv-adder-body} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{g}}, {\it{m\/}})\index{index}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{sum}}, {\it{m\/}})\index{index}, {\rm{index}}\,({\tt{'}}{\tt{carry}}, $1\;+$ {\it{m\/}})\index{index}), \\ 
{\tt{'}}{\tt{full-adder}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{a}}, {\it{m\/}})\index{index}, {\rm{index}}\,({\tt{'}}{\tt{b}}, {\it{m\/}})\index{index}, {\rm{index}}\,({\tt{'}}{\tt{carry}}, {\it{m\/}})\index{index}))\-, \\ 
{\rm{bv-adder-body}}\,($1\;+$ {\it{m\/}}, {\it{n\/}} $-\;1$)\index{bv-adder-body})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable bv-adder-body; name this event `bv-adder-body-off'.\index{bv-adder-body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{bv-adder*} \\  
\=\+{\rm{bv-adder*}}\,({\it{n\/}})\index{bv-adder*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{bv-adder}}, {\it{n\/}})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{carry}}, {\tt{0}})\index{index}, \\ 
{\rm{append}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{indices}}\,({\tt{'}}{\tt{b}}, {\tt{0}}, {\it{n\/}})\index{indices}))\-, \\ 
{\rm{cons}}\,(\=\+{\rm{append}}\,({\rm{indices}}\,({\tt{'}}{\tt{sum}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{carry}}, {\it{n\/}})\index{index})), \\ 
{\rm{cons}}\,({\rm{bv-adder-body}}\,({\tt{0}}, {\it{n\/}})\index{bv-adder-body}, {\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}}))\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bv-adder*\$destructure \\ \index{bv-adder*\$destructure}
\=\+({\rm{car}}\,({\rm{bv-adder*}}\,({\it{n\/}})\index{bv-adder*}) $=$ {\rm{index}}\,({\tt{'}}{\tt{bv-adder}}, {\it{n\/}})\index{index}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadr}}\,({\rm{bv-adder*}}\,({\it{n\/}})\index{bv-adder*}) \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{carry}}, {\tt{0}})\index{index}, \\ 
{\rm{append}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{indices}}\,({\tt{'}}{\tt{b}}, {\tt{0}}, {\it{n\/}})\index{indices}))\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{caddr}}\,({\rm{bv-adder*}}\,({\it{n\/}})\index{bv-adder*}) \\ 
$=$$\;\;\;\;${\rm{append}}\,({\rm{indices}}\,({\tt{'}}{\tt{sum}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{carry}}, {\it{n\/}})\index{index})))\- \\ 
$\wedge$$\;\;\;\;$({\rm{cadddr}}\,({\rm{bv-adder*}}\,({\it{n\/}})\index{bv-adder*}) $=$ {\rm{bv-adder-body}}\,({\tt{0}}, {\it{n\/}})\index{bv-adder-body}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{bv-adder*}}\,({\it{n\/}})\index{bv-adder*}) $=$ {\bf{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable bv-adder*; name this event `bv-adder*-off'.\index{bv-adder*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable bv-adder*\$destructure; name this event `bv-adder*\$destructure-off'.\index{bv-adder*\$destructure-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{bv-adder\&} \\  
\=\+{\rm{bv-adder\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{bv-adder\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\rm{index}}\,({\tt{'}}{\tt{bv-adder}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{lookup-module} $=$ {\rm{bv-adder*}}\,({\it{n\/}})\index{bv-adder*}) \\ 
$\wedge$$\;\;\;\;${\rm{full-adder\&}}\,({\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{bv-adder}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{delete-module})\index{full-adder\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable bv-adder\&; name this event `bv-adder\&-off'.\index{bv-adder\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{bv-adder\$netlist} \\  
{\rm{bv-adder\$netlist}}\,({\it{n\/}})\index{bv-adder\$netlist} $=$ {\rm{cons}}\,({\rm{bv-adder*}}\,({\it{n\/}})\index{bv-adder*}, {\sc{full-adder\$netlist}}\index{full-adder\$netlist})
\end{tabbing}


\noindent{\sc Event}:   Enable bv-adder\$netlist; name this event `bv-adder\$netlist-off'.\index{bv-adder\$netlist-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{bv-adder-body\$induction} \\  
\=\+{\rm{bv-adder-body\$induction}}\,({\it{m\/}}, {\it{n\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{bv-adder-body\$induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\it{bindings\/}} \\ 
{\bf else }{\rm{bv-adder-body\$induction}}\,(\=\+$1\;+$ {\it{m\/}}, \\ 
{\it{n\/}} $-\;1$, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\rm{list}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{sum}}, \\ 
{\it{m\/}})\-\index{index}, \\ 
{\rm{index}}\,(\=\+{\tt{'}}{\tt{carry}}, \\ 
$1\;+$ {\it{m\/}})\-\index{index})\-, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{full-adder}}, \\ 
{\rm{collect-value}}\,(\=\+{\rm{list}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{a}}, \\ 
{\it{m\/}})\-\index{index}, \\ 
{\rm{index}}\,(\=\+{\tt{'}}{\tt{b}}, \\ 
{\it{m\/}})\-\index{index}, \\ 
{\rm{index}}\,(\=\+{\tt{'}}{\tt{carry}}, \\ 
{\it{m\/}})\-\index{index})\-, \\ 
{\it{bindings\/}})\-\index{collect-value}, \\ 
{\rm{value}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{g}}, \\ 
{\it{m\/}})\-\index{index}, \\ 
{\it{state-bindings\/}})\-\index{value}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-, \\ 
{\it{bindings\/}})\-, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{bv-adder-body\$induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bv-adder\$unbound-in-body-sum \\ \index{bv-adder\$unbound-in-body-sum}
({\it{l\/}} $<$ {\it{m\/}}) $\rightarrow$ {\rm{unbound-in-body}}\,({\rm{index}}\,({\tt{'}}{\tt{sum}}, {\it{l\/}})\index{index}, {\rm{bv-adder-body}}\,({\it{m\/}}, {\it{n\/}})\index{bv-adder-body})\index{unbound-in-body}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bv-adder\$unbound-in-body-carry \\ \index{bv-adder\$unbound-in-body-carry}
({\it{l\/}} $<$ ($1\;+$ {\it{m\/}})) $\rightarrow$ {\rm{unbound-in-body}}\,({\rm{index}}\,({\tt{'}}{\tt{carry}}, {\it{l\/}})\index{index}, {\rm{bv-adder-body}}\,({\it{m\/}}, {\it{n\/}})\index{bv-adder-body})\index{unbound-in-body}
\end{tabbing}


\noindent{\sc Event}:   Enable bv-adder\$unbound-in-body-sum; name this event `bv-adder\$unbound-in-body-sum-off'.\index{bv-adder\$unbound-in-body-sum-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable bv-adder\$unbound-in-body-carry; name this event `bv-adder\$unbound-in-body-carry-off'.\index{bv-adder\$unbound-in-body-carry!-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  bv-adder-body\$value \\ \index{bv-adder-body\$value}
\=\+(\=\+{\rm{full-adder\&}}\,({\it{netlist\/}})\index{full-adder\&} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{value}}\,({\rm{index}}\,({\tt{'}}{\tt{carry}}, {\it{m\/}})\index{index}, {\it{bindings\/}})\index{value})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\it{m\/}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{b}}, {\it{m\/}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value})\index{bvp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,(\=\+{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{sum}}, {\it{m\/}}, {\it{n\/}})\index{indices}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{carry}}, {\it{n\/}} $+$ {\it{m\/}})\index{index}))\-, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{1}}, \\ 
{\rm{bv-adder-body}}\,({\it{m\/}}, {\it{n\/}})\index{bv-adder-body}, \\ 
{\it{bindings\/}}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{bv-adder}}\,(\=\+{\rm{value}}\,({\rm{index}}\,({\tt{'}}{\tt{carry}}, {\it{m\/}})\index{index}, {\it{bindings\/}})\index{value}, \\ 
{\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\it{m\/}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value}, \\ 
{\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{b}}, {\it{m\/}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value})\-\index{bv-adder})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bv-adder-body-special-case\$value \\ \index{bv-adder-body-special-case\$val!ue}
\=\+(\=\+{\rm{full-adder\&}}\,({\it{netlist\/}})\index{full-adder\&} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{value}}\,({\rm{index}}\,({\tt{'}}{\tt{carry}}, {\tt{0}})\index{index}, {\it{bindings\/}})\index{value})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{b}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value})\index{bvp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,(\=\+{\rm{append}}\,({\rm{indices}}\,({\tt{'}}{\tt{sum}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{carry}}, {\it{n\/}})\index{index})), \\ 
{\rm{dual-eval}}\,(\=\+{\tt{1}}, \\ 
{\rm{bv-adder-body}}\,({\tt{0}}, {\it{n\/}})\index{bv-adder-body}, \\ 
{\it{bindings\/}}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{bv-adder}}\,(\=\+{\rm{value}}\,({\rm{index}}\,({\tt{'}}{\tt{carry}}, {\tt{0}})\index{index}, {\it{bindings\/}})\index{value}, \\ 
{\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value}, \\ 
{\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{b}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value})\-\index{bv-adder})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bv-adder\$value \\ \index{bv-adder\$value}
\=\+(\=\+{\rm{bv-adder\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{bv-adder\&} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{c\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\it{n\/}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\it{n\/}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\rm{index}}\,({\tt{'}}{\tt{bv-adder}}, {\it{n\/}})\index{index}, {\rm{cons}}\,({\it{c\/}}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}})), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{bv-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{bv-adder})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable bv-adder-body-special-case\$value; name this event `bv-adder-body-special-case\$value-off'.\index{bv-adder-body-special-case\$val!ue-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable bv-adder-body\$value; name this event `bv-adder-body\$value-off'.\index{bv-adder-body\$value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable bv-adder\$value; name this event `bv-adder\$value-off'.\index{bv-adder\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-sum} \\  
\=\+{\rm{v-sum}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-sum} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{b-xor}}\,({\it{c\/}}, {\rm{b-xor}}\,({\rm{car}}\,({\it{a\/}}), {\rm{car}}\,({\it{b\/}}))\index{b-xor})\index{b-xor}, \\ 
{\rm{v-sum}}\,(\=\+{\rm{b-or3}}\,(\=\+{\rm{b-and}}\,({\rm{car}}\,({\it{a\/}}), {\rm{car}}\,({\it{b\/}}))\index{b-and}, \\ 
{\rm{b-and}}\,({\rm{car}}\,({\it{a\/}}), {\it{c\/}})\index{b-and}, \\ 
{\rm{b-and}}\,({\rm{car}}\,({\it{b\/}}), {\it{c\/}})\index{b-and})\-\index{b-or3}, \\ 
{\rm{cdr}}\,({\it{a\/}}), \\ 
{\rm{cdr}}\,({\it{b\/}}))\-\index{v-sum})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-sum; name this event `v-sum-off'.\index{v-sum-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  bvp-sum \\ \index{bvp-sum}
{\rm{bvp}}\,({\rm{v-sum}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-sum})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-sum \\ \index{length-sum}
{\rm{length}}\,({\rm{v-sum}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-sum})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-sum-congruence \\ \index{v-sum-congruence}
{\it{c\/}} $\rightarrow$ (({\rm{v-sum}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-sum} $=$ {\rm{v-sum}}\,({\bf{t}}, {\it{a\/}}, {\it{b\/}})\index{v-sum}) $=$ {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  a-1+1=a \\ \index{a-1+1=a}
({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ {\it{c\/}}) $\rightarrow$ ({\rm{v-sum}}\,({\it{c\/}}, {\rm{v-not}}\,({\rm{nat-to-v}}\,({\tt{0}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{nat-to-v})\index{v-not}, {\it{a\/}})\index{v-sum} $=$ {\it{a\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-carry} \\  
\=\+{\rm{v-carry}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-carry} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{boolfix}}\,({\it{c\/}})\index{boolfix} \\ 
{\bf else }{\rm{v-carry}}\,(\=\+\=\+({\rm{car}}\,({\it{a\/}}) $\wedge$ {\rm{car}}\,({\it{b\/}})) \\ 
$\vee$$\;\;\;\;$(({\rm{car}}\,({\it{a\/}}) $\vee$ {\rm{car}}\,({\it{b\/}})) $\wedge$ {\it{c\/}})\-, \\ 
{\rm{cdr}}\,({\it{a\/}}), \\ 
{\rm{cdr}}\,({\it{b\/}}))\-\index{v-carry}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-carry; name this event `v-carry-off'.\index{v-carry-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-propagate} \\  
\=\+{\rm{v-propagate}}\,({\it{a\/}}, {\it{b\/}})\index{v-propagate} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }({\rm{car}}\,({\it{a\/}}) $\vee$ {\rm{car}}\,({\it{b\/}})) $\wedge$ {\rm{v-propagate}}\,({\rm{cdr}}\,({\it{a\/}}), {\rm{cdr}}\,({\it{b\/}}))\index{v-propagate}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-propagate; name this event `v-propagate-off'.\index{v-propagate-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-generate} \\  
\=\+{\rm{v-generate}}\,({\it{a\/}}, {\it{b\/}})\index{v-generate} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }\=\+{\rm{v-generate}}\,({\rm{cdr}}\,({\it{a\/}}), {\rm{cdr}}\,({\it{b\/}}))\index{v-generate} \\ 
$\vee$$\;\;\;\;$({\rm{car}}\,({\it{a\/}}) $\wedge$ {\rm{car}}\,({\it{b\/}}) $\wedge$ {\rm{v-propagate}}\,({\rm{cdr}}\,({\it{a\/}}), {\rm{cdr}}\,({\it{b\/}}))\index{v-propagate})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-generate; name this event `v-generate-off'.\index{v-generate-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{f\$t-carry}$\;\;$
{\rm{f\$t-carry}}\,({\it{c\/}}, {\it{prop\/}}, {\it{gen\/}})\index{f\$t-carry} $=$ {\rm{f-or}}\,({\rm{f-and}}\,({\it{c\/}}, {\it{prop\/}})\index{f-and}, {\it{gen\/}})\index{f-or}
\end{tabbing}


\noindent{\sc Event}:   Enable f\$t-carry; name this event `f\$t-carry-off'.\index{f\$t-carry-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{t-carry}$\;\;$
{\rm{t-carry}}\,({\it{c\/}}, {\it{prop\/}}, {\it{gen\/}})\index{t-carry} $=$ {\rm{b-not}}\,({\rm{ao6}}\,({\it{c\/}}, {\it{prop\/}}, {\it{gen\/}})\index{ao6})\index{b-not}
\end{tabbing}


\noindent{\sc Event}:   Enable t-carry; name this event `t-carry-off'.\index{t-carry-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$t-carry=t-carry \\ \index{f\$t-carry=t-carry}
\=\+({\rm{boolp}}\,({\it{c\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{prop\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{gen\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f\$t-carry}}\,({\it{c\/}}, {\it{prop\/}}, {\it{gen\/}})\index{f\$t-carry} $=$ {\rm{t-carry}}\,({\it{c\/}}, {\it{prop\/}}, {\it{gen\/}})\index{t-carry})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  t-carry-congruence \\ \index{t-carry-congruence}
{\it{x\/}} $\rightarrow$ (({\rm{t-carry}}\,({\it{x\/}}, {\it{p\/}}, {\it{g\/}})\index{t-carry} $=$ {\rm{t-carry}}\,({\bf{t}}, {\it{p\/}}, {\it{g\/}})\index{t-carry}) $=$ {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{t-carry*} \\  
\=\+{\sc{t-carry*}}\index{t-carry*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{t-carry}} \\ 
{\tt{(}}{\tt{c}}{\tt{ }}{\tt{prop}}{\tt{ }}{\tt{gen}}{\tt{)}} \\ 
{\tt{(}}{\tt{z}}{\tt{)}} \\ 
{\tt{(}}{\tt{(}}{\tt{g0}}{\tt{ }}{\tt{(}}{\tt{z-}}{\tt{)}}{\tt{ }}{\tt{ao6}}{\tt{ }}{\tt{(}}{\tt{c}}{\tt{ }}{\tt{prop}}{\tt{ }}{\tt{gen}}{\tt{)}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{g1}}{\tt{ }}{\tt{(}}{\tt{z}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{z-}}{\tt{)}}{\tt{)}}{\tt{)}} \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{t-carry\&} \\  
\=\+{\rm{t-carry\&}}\,({\it{netlist\/}})\index{t-carry\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{t-carry}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{t-carry*}}\index{t-carry*}) \\ 
$\wedge$$\;\;\;\;${\rm{ao6\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{t-carry}}, {\it{netlist\/}})\index{delete-module})\index{ao6\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{t-carry}}, {\it{netlist\/}})\index{delete-module})\index{b-not\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable t-carry\&; name this event `t-carry\&-off'.\index{t-carry\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{t-carry\$netlist} \\  
{\sc{t-carry\$netlist}}\index{t-carry\$netlist} $=$ {\rm{cons}}\,({\sc{t-carry*}}\index{t-carry*}, {\sc{ao6\$netlist}}\index{ao6\$netlist} $\cup$ {\sc{b-not\$netlist}}\index{b-not\$netlist})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  t-carry\$value \\ \index{t-carry\$value}
\=\+{\rm{t-carry\&}}\,({\it{netlist\/}})\index{t-carry\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{t-carry}}, {\rm{list}}\,({\it{c\/}}, {\it{prop\/}}, {\it{gen\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f\$t-carry}}\,({\it{c\/}}, {\it{prop\/}}, {\it{gen\/}})\index{f\$t-carry}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable t-carry\$value; name this event `t-carry\$value-off'.\index{t-carry\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-append-propagate \\ \index{v-append-propagate}
\=\+({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{length}}\,({\it{c\/}})\index{length}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-propagate}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}), {\rm{append}}\,({\it{c\/}}, {\it{d\/}}))\index{v-propagate} \\ 
$=$$\;\;\;\;$({\rm{v-propagate}}\,({\it{a\/}}, {\it{c\/}})\index{v-propagate} $\wedge$ {\rm{v-propagate}}\,({\it{b\/}}, {\it{d\/}})\index{v-propagate}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-propagate-append \\ \index{v-propagate-append}
\=\+({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{length}}\,({\it{c\/}})\index{length}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{b-and}}\,({\rm{v-propagate}}\,({\it{a\/}}, {\it{c\/}})\index{v-propagate}, {\rm{v-propagate}}\,({\it{b\/}}, {\it{d\/}})\index{v-propagate})\index{b-and} \\ 
$=$$\;\;\;\;${\rm{v-propagate}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}), {\rm{append}}\,({\it{c\/}}, {\it{d\/}}))\index{v-propagate})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-propagate-append; name this event `v-propagate-append-off'.\index{v-propagate-append-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  generate-append \\ \index{generate-append}
\=\+({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{length}}\,({\it{c\/}})\index{length}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{t-carry}}\,({\rm{v-generate}}\,({\it{a\/}}, {\it{c\/}})\index{v-generate}, {\rm{v-propagate}}\,({\it{b\/}}, {\it{d\/}})\index{v-propagate}, {\rm{v-generate}}\,({\it{b\/}}, {\it{d\/}})\index{v-generate})\index{t-carry} \\ 
$=$$\;\;\;\;${\rm{v-generate}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}), {\rm{append}}\,({\it{c\/}}, {\it{d\/}}))\index{v-generate})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  append-sum \\ \index{append-sum}
\=\+(({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{length}}\,({\it{b\/}})\index{length}) $\wedge$ ({\it{c2\/}} $=$ {\rm{v-carry}}\,({\it{c1\/}}, {\it{a\/}}, {\it{b\/}})\index{v-carry})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{append}}\,({\rm{v-sum}}\,({\it{c1\/}}, {\it{a\/}}, {\it{b\/}})\index{v-sum}, {\rm{v-sum}}\,({\it{c2\/}}, {\it{c\/}}, {\it{d\/}})\index{v-sum}) \\ 
$=$$\;\;\;\;${\rm{v-sum}}\,({\it{c1\/}}, {\rm{append}}\,({\it{a\/}}, {\it{c\/}}), {\rm{append}}\,({\it{b\/}}, {\it{d\/}}))\index{v-sum})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  t-carry-p-g-carry \\ \index{t-carry-p-g-carry}
{\rm{t-carry}}\,({\it{c\/}}, {\rm{v-propagate}}\,({\it{a\/}}, {\it{b\/}})\index{v-propagate}, {\rm{v-generate}}\,({\it{a\/}}, {\it{b\/}})\index{v-generate})\index{t-carry} $=$ {\rm{v-carry}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-carry}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-adder-output=v-sum \\ \index{v-adder-output=v-sum}
{\rm{v-adder-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder-output} $=$ {\rm{v-sum}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-sum}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-adder-carry-out=v-carry \\ \index{v-adder-carry-out=v-carry}
{\rm{v-adder-carry-out}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder-carry-out} $=$ {\rm{v-carry}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-carry}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tv-adder} \\  
\=\+{\rm{tv-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{tree\/}})\index{tv-adder} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }{\rm{list}}\,(\=\+{\rm{b-or}}\,({\rm{car}}\,({\it{a\/}}), {\rm{car}}\,({\it{b\/}}))\index{b-or}, \\ 
{\rm{b-and}}\,({\rm{car}}\,({\it{a\/}}), {\rm{car}}\,({\it{b\/}}))\index{b-and}, \\ 
{\rm{b-xor}}\,({\rm{car}}\,({\it{a\/}}), {\rm{b-xor}}\,({\rm{car}}\,({\it{b\/}}), {\it{c\/}})\index{b-xor})\index{b-xor})\- \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{b-and}}\,(\=\+{\rm{car}}\,({\rm{tv-adder}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\rm{tfirstn}}\,({\it{b\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-adder}), \\ 
{\rm{car}}\,({\rm{tv-adder}}\,(\=\+{\rm{t-carry}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{tv-adder}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-adder}), \\ 
{\rm{cadr}}\,({\rm{tv-adder}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-adder}))\-\index{t-carry}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{trestn}}\,({\it{b\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{cdr}}\,({\it{tree\/}}))\-\index{tv-adder}))\-\index{b-and}, \\ 
{\rm{cons}}\,(\=\+{\rm{t-carry}}\,(\=\+{\rm{cadr}}\,({\rm{tv-adder}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\rm{tfirstn}}\,({\it{b\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-adder}), \\ 
{\rm{car}}\,({\rm{tv-adder}}\,(\=\+{\rm{t-carry}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{tv-adder}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-adder}), \\ 
{\rm{cadr}}\,({\rm{tv-adder}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-adder}))\-\index{t-carry}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{trestn}}\,({\it{b\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{cdr}}\,({\it{tree\/}}))\-\index{tv-adder}), \\ 
{\rm{cadr}}\,({\rm{tv-adder}}\,(\=\+{\rm{t-carry}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{tv-adder}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-adder}), \\ 
{\rm{cadr}}\,({\rm{tv-adder}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-adder}))\-\index{t-carry}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{trestn}}\,({\it{b\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{cdr}}\,({\it{tree\/}}))\-\index{tv-adder}))\-\index{t-carry}, \\ 
{\rm{append}}\,(\=\+{\rm{cddr}}\,({\rm{tv-adder}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\rm{tfirstn}}\,({\it{b\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-adder}), \\ 
{\rm{cddr}}\,({\rm{tv-adder}}\,(\=\+{\rm{t-carry}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{tv-adder}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-adder}), \\ 
{\rm{cadr}}\,({\rm{tv-adder}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-adder}))\-\index{t-carry}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{trestn}}\,({\it{b\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{cdr}}\,({\it{tree\/}}))\-\index{tv-adder}))\-)\-)\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-adder; name this event `tv-adder-off'.\index{tv-adder-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  car-tv-adder-as-p \\ \index{car-tv-adder-as-p}
\=\+(({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ ({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{car}}\,({\rm{tv-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{tree\/}})\index{tv-adder}) $=$ {\rm{v-propagate}}\,({\it{a\/}}, {\it{b\/}})\index{v-propagate})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  cadr-tv-adder-as-g \\ \index{cadr-tv-adder-as-g}
\=\+(({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ ({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{cadr}}\,({\rm{tv-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{tree\/}})\index{tv-adder}) $=$ {\rm{v-generate}}\,({\it{a\/}}, {\it{b\/}})\index{v-generate})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  cddr-tv-adder-as-sum \\ \index{cddr-tv-adder-as-sum}
\=\+(({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ ({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{cddr}}\,({\rm{tv-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{tree\/}})\index{tv-adder}) $=$ {\rm{v-sum}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-sum})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equality-of-three-element-lists \\ \index{equality-of-three-element-lists}
\=\+(({\it{x\/}} $\not=$ {\tt{0}}) $\wedge$ ({\it{y\/}} $\not=$ {\tt{0}}) $\wedge$ ({\it{z\/}} $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\it{w\/}} $=$ {\rm{cons}}\,({\it{x\/}}, {\rm{cons}}\,({\it{y\/}}, {\it{z\/}}))) \\ 
$=$$\;\;\;\;$(({\rm{car}}\,({\it{w\/}}) $=$ {\it{x\/}}) $\wedge$ ({\rm{cadr}}\,({\it{w\/}}) $=$ {\it{y\/}}) $\wedge$ ({\rm{cddr}}\,({\it{w\/}}) $=$ {\it{z\/}})))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tv-adder-as-p-g-sum \\ \index{tv-adder-as-p-g-sum}
\=\+(({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ ({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tv-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{tree\/}})\index{tv-adder} \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\rm{v-propagate}}\,({\it{a\/}}, {\it{b\/}})\index{v-propagate}, {\rm{cons}}\,({\rm{v-generate}}\,({\it{a\/}}, {\it{b\/}})\index{v-generate}, {\rm{v-sum}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-sum})))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable car-tv-adder-as-p; name this event `car-tv-adder-as-p-off'.\index{car-tv-adder-as-p-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cadr-tv-adder-as-g; name this event `cadr-tv-adder-as-g-off'.\index{cadr-tv-adder-as-g-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cddr-tv-adder-as-sum; name this event `cddr-tv-adder-as-sum-off'.\index{cddr-tv-adder-as-sum-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable tv-adder-as-p-g-sum; name this event `tv-adder-as-p-g-sum-off'.\index{tv-adder-as-p-g-sum-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tv-if-body} \\  
\=\+{\rm{tv-if-body}}\,({\it{tree\/}})\index{tv-if-body} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }{\rm{list}}\,({\rm{list}}\,(\=\+{\tt{'}}{\tt{leaf}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{out}}, {\tt{0}})\index{index}), \\ 
{\tt{'}}{\tt{b-if}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{c}}, {\rm{index}}\,({\tt{'}}{\tt{a}}, {\tt{0}})\index{index}, {\rm{index}}\,({\tt{'}}{\tt{b}}, {\tt{0}})\index{index}))\-) \\ 
{\bf else }{\rm{append}}\,(\=\+\=\+{\bf if }({\rm{tree-height}}\,({\it{tree\/}})\index{tree-height} ${}${\bf{mod}}${}$ {\tt{3}}) $\simeq {\tt{0}}$ \\ 
{\bf then }{\tt{'}}{\tt{(}}{\tt{(}}{\tt{c-buf}}{\tt{ }}{\tt{(}}{\tt{c-buf}}{\tt{)}}{\tt{ }}{\tt{b-buf}}{\tt{ }}{\tt{(}}{\tt{c}}{\tt{)}}{\tt{)}}{\tt{)}} \\ 
{\bf else }{\bf{nil}}$\;${\bf  endif}\-, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{left}}, \\ 
{\rm{tfirstn}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{tv-if}}, {\rm{tree-number}}\,({\rm{car}}\,({\it{tree\/}}))\index{tree-number})\index{index}, \\ 
{\rm{cons}}\,(\=\+\=\+{\bf if }({\rm{tree-height}}\,({\it{tree\/}})\index{tree-height} ${}${\bf{mod}}${}$ {\tt{3}}) $\simeq {\tt{0}}$ \\ 
{\bf then }{\tt{'}}{\tt{c-buf}} \\ 
{\bf else }{\tt{'}}{\tt{c}}$\;${\bf  endif}\-, \\ 
{\rm{append}}\,(\=\+{\rm{tfirstn}}\,(\=\+{\rm{indices}}\,(\=\+{\tt{'}}{\tt{a}}, \\ 
{\tt{0}}, \\ 
{\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\-\index{indices}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\rm{indices}}\,(\=\+{\tt{'}}{\tt{b}}, \\ 
{\tt{0}}, \\ 
{\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\-\index{indices}, \\ 
{\it{tree\/}})\-\index{tfirstn})\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{right}}, \\ 
{\rm{trestn}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\it{tree\/}})\-\index{trestn}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{tv-if}}, {\rm{tree-number}}\,({\rm{cdr}}\,({\it{tree\/}}))\index{tree-number})\index{index}, \\ 
{\rm{cons}}\,(\=\+\=\+{\bf if }({\rm{tree-height}}\,({\it{tree\/}})\index{tree-height} ${}${\bf{mod}}${}$ {\tt{3}}) $\simeq {\tt{0}}$ \\ 
{\bf then }{\tt{'}}{\tt{c-buf}} \\ 
{\bf else }{\tt{'}}{\tt{c}}$\;${\bf  endif}\-, \\ 
{\rm{append}}\,(\=\+{\rm{trestn}}\,(\=\+{\rm{indices}}\,(\=\+{\tt{'}}{\tt{a}}, \\ 
{\tt{0}}, \\ 
{\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\-\index{indices}, \\ 
{\it{tree\/}})\-\index{trestn}, \\ 
{\rm{trestn}}\,(\=\+{\rm{indices}}\,(\=\+{\tt{'}}{\tt{b}}, \\ 
{\tt{0}}, \\ 
{\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\-\index{indices}, \\ 
{\it{tree\/}})\-\index{trestn})\-)\-)\-)\-)\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tv-if*} \\  
\=\+{\rm{tv-if*}}\,({\it{tree\/}})\index{tv-if*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{tv-if}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{c}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{b}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices})\-)\-, \\ 
{\rm{cons}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{cons}}\,({\rm{tv-if-body}}\,({\it{tree\/}})\index{tv-if-body}, {\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}}))\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tv-if*\$destructure \\ \index{tv-if*\$destructure}
\=\+({\rm{car}}\,({\rm{tv-if*}}\,({\it{tree\/}})\index{tv-if*}) $=$ {\rm{index}}\,({\tt{'}}{\tt{tv-if}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadr}}\,({\rm{tv-if*}}\,({\it{tree\/}})\index{tv-if*}) \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\tt{'}}{\tt{c}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{b}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices})\-)\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\rm{tv-if*}}\,({\it{tree\/}})\index{tv-if*}) $=$ {\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadddr}}\,({\rm{tv-if*}}\,({\it{tree\/}})\index{tv-if*}) $=$ {\rm{tv-if-body}}\,({\it{tree\/}})\index{tv-if-body}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{tv-if*}}\,({\it{tree\/}})\index{tv-if*}) $=$ {\bf{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-if*; name this event `tv-if*-off'.\index{tv-if*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable tv-if*\$destructure; name this event `tv-if*\$destructure-off'.\index{tv-if*\$destructure-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tv-if\&} \\  
\=\+{\rm{tv-if\&}}\,({\it{netlist\/}}, {\it{tree\/}})\index{tv-if\&} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }\=\+(\=\+{\rm{lookup-module}}\,({\rm{index}}\,({\tt{'}}{\tt{tv-if}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, {\it{netlist\/}})\index{lookup-module} \\ 
$=$$\;\;\;\;${\rm{tv-if*}}\,({\it{tree\/}})\index{tv-if*})\- \\ 
$\wedge$$\;\;\;\;${\rm{b-if\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{tv-if}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{b-if\&}\- \\ 
{\bf else }\=\+(\=\+{\rm{lookup-module}}\,({\rm{index}}\,({\tt{'}}{\tt{tv-if}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, {\it{netlist\/}})\index{lookup-module} \\ 
$=$$\;\;\;\;${\rm{tv-if*}}\,({\it{tree\/}})\index{tv-if*})\- \\ 
$\wedge$$\;\;\;\;${\rm{b-buf\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-if}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{b-buf\&} \\ 
$\wedge$$\;\;\;\;${\rm{tv-if\&}}\,(\=\+{\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-if}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-if\&} \\ 
$\wedge$$\;\;\;\;${\rm{tv-if\&}}\,(\=\+{\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-if}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\rm{cdr}}\,({\it{tree\/}}))\-\index{tv-if\&}\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-if\&; name this event `tv-if\&-off'.\index{tv-if\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tv-if\$netlist} \\  
\=\+{\rm{tv-if\$netlist}}\,({\it{tree\/}})\index{tv-if\$netlist} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{cons}}\,({\rm{tv-if*}}\,({\it{tree\/}})\index{tv-if*}, {\sc{b-if\$netlist}}\index{b-if\$netlist}) \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{tv-if*}}\,({\it{tree\/}})\index{tv-if*}, \\ 
\=\+{\rm{tv-if\$netlist}}\,({\rm{car}}\,({\it{tree\/}}))\index{tv-if\$netlist} \\ 
$\cup$$\;\;\;\;$({\rm{tv-if\$netlist}}\,({\rm{cdr}}\,({\it{tree\/}}))\index{tv-if\$netlist} $\cup$ {\sc{b-buf\$netlist}}\index{b-buf\$netlist})\-)\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tv-if-induction} \\  
\=\+{\rm{tv-if-induction}}\,({\it{tree\/}}, {\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{state\/}}, {\it{netlist\/}})\index{tv-if-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }\=\+{\rm{tv-if-induction}}\,(\=\+{\rm{car}}\,({\it{tree\/}}), \\ 
{\it{c\/}}, \\ 
{\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\rm{tfirstn}}\,({\it{b\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\tt{0}}, \\ 
{\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-if}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\-\index{tv-if-induction} \\ 
$\wedge$$\;\;\;\;${\rm{tv-if-induction}}\,(\=\+{\rm{car}}\,({\it{tree\/}}), \\ 
{\sc{x}}\index{x}, \\ 
{\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\rm{tfirstn}}\,({\it{b\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\tt{0}}, \\ 
{\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-if}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\-\index{tv-if-induction} \\ 
$\wedge$$\;\;\;\;${\rm{tv-if-induction}}\,(\=\+{\rm{cdr}}\,({\it{tree\/}}), \\ 
{\it{c\/}}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{trestn}}\,({\it{b\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\tt{0}}, \\ 
{\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-if}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\-\index{tv-if-induction} \\ 
$\wedge$$\;\;\;\;${\rm{tv-if-induction}}\,(\=\+{\rm{cdr}}\,({\it{tree\/}}), \\ 
{\sc{x}}\index{x}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{trestn}}\,({\it{b\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\tt{0}}, \\ 
{\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-if}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\-\index{tv-if-induction}\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tv-if-lemma-crock \\ \index{tv-if-lemma-crock}
\=\+{\rm{tv-if\&}}\,({\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{tv-if}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, {\it{netlist\/}})\index{delete-module}, {\rm{car}}\,({\it{tree\/}}))\index{tv-if\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\it{alist\/}})\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{append}}\,(\=\+{\rm{collect-value}}\,(\=\+{\rm{firstn}}\,(\=\+{\rm{tree-size}}\,({\rm{car}}\,({\it{tree\/}}))\index{tree-size}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\it{n\/}})\index{indices})\-\index{firstn}, \\ 
{\it{alist\/}})\-\index{collect-value}, \\ 
{\rm{collect-value}}\,(\=\+{\rm{restn}}\,(\=\+{\rm{tree-size}}\,({\rm{car}}\,({\it{tree\/}}))\index{tree-size}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\it{n\/}})\index{indices})\-\index{restn}, \\ 
{\it{alist\/}})\-\index{collect-value})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-if-lemma-crock; name this event `tv-if-lemma-crock-off'.\index{tv-if-lemma-crock-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tv-if\$value \\ \index{tv-if\$value}
\=\+(\=\+{\rm{tv-if\&}}\,({\it{netlist\/}}, {\it{tree\/}})\index{tv-if\&} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{a\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{b\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{tv-if}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\rm{cons}}\,({\it{c\/}}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}})), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{fv-if}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{fv-if})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-if\$value; name this event `tv-if\$value-off'.\index{tv-if\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{t-or-nor-body} \\  
\=\+{\rm{t-or-nor-body}}\,({\it{tree\/}}, {\it{parity\/}})\index{t-or-nor-body} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }{\rm{list}}\,({\rm{list}}\,(\=\+{\tt{'}}{\tt{leaf}}, \\ 
{\tt{'}}{\tt{(}}{\tt{out}}{\tt{)}}, \\ 
\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{b-not}} \\ 
{\bf else }{\tt{'}}{\tt{b-buf}}$\;${\bf  endif}\-, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{a}}, {\tt{0}})\index{index}))\-) \\ 
{\bf elseif }({\rm{car}}\,({\it{tree\/}}) $\simeq\;${{\bf{nil}}}${}$) $\wedge$ ({\rm{cdr}}\,({\it{tree\/}}) $\simeq\;${{\bf{nil}}}${}$) \\ 
{\bf then }{\rm{list}}\,({\rm{list}}\,(\=\+{\tt{'}}{\tt{leaf}}, \\ 
{\tt{'}}{\tt{(}}{\tt{out}}{\tt{)}}, \\ 
\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{b-nor}} \\ 
{\bf else }{\tt{'}}{\tt{b-or}}$\;${\bf  endif}\-, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{a}}, {\tt{0}})\index{index}, {\rm{index}}\,({\tt{'}}{\tt{a}}, {\tt{1}})\index{index}))\-) \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{left}}, \\ 
{\tt{'}}{\tt{(}}{\tt{left-out}}{\tt{)}}, \\ 
{\rm{index}}\,(\=\+\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{t-or}} \\ 
{\bf else }{\tt{'}}{\tt{t-nor}}$\;${\bf  endif}\-, \\ 
{\rm{tree-number}}\,({\rm{car}}\,({\it{tree\/}}))\index{tree-number})\-\index{index}, \\ 
{\rm{tfirstn}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, {\it{tree\/}})\index{tfirstn})\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{right}}, \\ 
{\tt{'}}{\tt{(}}{\tt{right-out}}{\tt{)}}, \\ 
{\rm{index}}\,(\=\+\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{t-or}} \\ 
{\bf else }{\tt{'}}{\tt{t-nor}}$\;${\bf  endif}\-, \\ 
{\rm{tree-number}}\,({\rm{cdr}}\,({\it{tree\/}}))\index{tree-number})\-\index{index}, \\ 
{\rm{trestn}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, {\it{tree\/}})\index{trestn})\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{output}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{out}}{\tt{)}}, \\ 
{\rm{cons}}\,(\=\+\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{b-nor}} \\ 
{\bf else }{\tt{'}}{\tt{b-nand}}$\;${\bf  endif}\-, \\ 
{\tt{'}}{\tt{(}}{\tt{(}}{\tt{left-out}}{\tt{ }}{\tt{right-out}}{\tt{)}}{\tt{)}})\-)\-)\-)\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{t-or-nor*} \\  
\=\+{\rm{t-or-nor*}}\,({\it{tree\/}}, {\it{parity\/}})\index{t-or-nor*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{index}}\,(\=\+\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{t-nor}} \\ 
{\bf else }{\tt{'}}{\tt{t-or}}$\;${\bf  endif}\-, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\rm{cons}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{cons}}\,({\tt{'}}{\tt{(}}{\tt{out}}{\tt{)}}, {\rm{cons}}\,({\rm{t-or-nor-body}}\,({\it{tree\/}}, {\it{parity\/}})\index{t-or-nor-body}, {\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}})))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  t-or-nor*\$destructure \\ \index{t-or-nor*\$destructure}
\=\+(\=\+{\rm{car}}\,({\rm{t-or-nor*}}\,({\it{tree\/}}, {\it{parity\/}})\index{t-or-nor*}) \\ 
$=$$\;\;\;\;${\rm{index}}\,(\=\+\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{t-nor}} \\ 
{\bf else }{\tt{'}}{\tt{t-or}}$\;${\bf  endif}\-, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index})\- \\ 
$\wedge$$\;\;\;\;$({\rm{cadr}}\,({\rm{t-or-nor*}}\,({\it{tree\/}}, {\it{parity\/}})\index{t-or-nor*}) $=$ {\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\rm{t-or-nor*}}\,({\it{tree\/}}, {\it{parity\/}})\index{t-or-nor*}) $=$ {\tt{'}}{\tt{(}}{\tt{out}}{\tt{)}}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadddr}}\,({\rm{t-or-nor*}}\,({\it{tree\/}}, {\it{parity\/}})\index{t-or-nor*}) $=$ {\rm{t-or-nor-body}}\,({\it{tree\/}}, {\it{parity\/}})\index{t-or-nor-body}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{t-or-nor*}}\,({\it{tree\/}}, {\it{parity\/}})\index{t-or-nor*}) $=$ {\bf{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable t-or-nor*; name this event `t-or-nor*-off'.\index{t-or-nor*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable t-or-nor*\$destructure; name this event `t-or-nor*\$destructure-off'.\index{t-or-nor*\$destructure-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{t-or-nor\&} \\  
\=\+{\rm{t-or-nor\&}}\,({\it{netlist\/}}, {\it{tree\/}}, {\it{parity\/}})\index{t-or-nor\&} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$) $\vee$ (({\rm{car}}\,({\it{tree\/}}) $\simeq\;${{\bf{nil}}}${}$) $\wedge$ ({\rm{cdr}}\,({\it{tree\/}}) $\simeq\;${{\bf{nil}}}${}$)) \\ 
{\bf then }\=\+(\=\+{\rm{lookup-module}}\,(\=\+{\rm{index}}\,(\=\+\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{t-nor}} \\ 
{\bf else }{\tt{'}}{\tt{t-or}}$\;${\bf  endif}\-, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{lookup-module} \\ 
$=$$\;\;\;\;${\rm{t-or-nor*}}\,({\it{tree\/}}, {\it{parity\/}})\index{t-or-nor*})\- \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{t-nor}} \\ 
{\bf else }{\tt{'}}{\tt{t-or}}$\;${\bf  endif}\-, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-buf\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{t-nor}} \\ 
{\bf else }{\tt{'}}{\tt{t-or}}$\;${\bf  endif}\-, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{b-buf\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nor\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{t-nor}} \\ 
{\bf else }{\tt{'}}{\tt{t-or}}$\;${\bf  endif}\-, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{b-nor\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-or\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{t-nor}} \\ 
{\bf else }{\tt{'}}{\tt{t-or}}$\;${\bf  endif}\-, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{b-or\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{t-nor}} \\ 
{\bf else }{\tt{'}}{\tt{t-or}}$\;${\bf  endif}\-, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{b-nand\&}\- \\ 
{\bf else }\=\+(\=\+{\rm{lookup-module}}\,(\=\+{\rm{index}}\,(\=\+\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{t-nor}} \\ 
{\bf else }{\tt{'}}{\tt{t-or}}$\;${\bf  endif}\-, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{lookup-module} \\ 
$=$$\;\;\;\;${\rm{t-or-nor*}}\,({\it{tree\/}}, {\it{parity\/}})\index{t-or-nor*})\- \\ 
$\wedge$$\;\;\;\;${\rm{t-or-nor\&}}\,(\=\+{\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+\=\+{\bf if }{\it{parity\/}} \\ 
{\bf then }{\tt{'}}{\tt{t-nor}} \\ 
{\bf else }{\tt{'}}{\tt{t-or}}$\;${\bf  endif}\-, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\rm{car}}\,({\it{tree\/}}), \\ 
$\neg$ {\it{parity\/}})\-\index{t-or-nor\&} \\ 
$\wedge$$\;\;\;\;${\rm{t-or-nor\&}}\,(\=\+{\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+\=\+{\bf if }{\it{parity\/}} \\ 
{\bf then }{\tt{'}}{\tt{t-nor}} \\ 
{\bf else }{\tt{'}}{\tt{t-or}}$\;${\bf  endif}\-, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\rm{cdr}}\,({\it{tree\/}}), \\ 
$\neg$ {\it{parity\/}})\-\index{t-or-nor\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{t-nor}} \\ 
{\bf else }{\tt{'}}{\tt{t-or}}$\;${\bf  endif}\-, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-buf\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{t-nor}} \\ 
{\bf else }{\tt{'}}{\tt{t-or}}$\;${\bf  endif}\-, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{b-buf\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nor\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{t-nor}} \\ 
{\bf else }{\tt{'}}{\tt{t-or}}$\;${\bf  endif}\-, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{b-nor\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-or\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{t-nor}} \\ 
{\bf else }{\tt{'}}{\tt{t-or}}$\;${\bf  endif}\-, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{b-or\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{t-nor}} \\ 
{\bf else }{\tt{'}}{\tt{t-or}}$\;${\bf  endif}\-, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{b-nand\&}\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable t-or-nor\&; name this event `t-or-nor\&-off'.\index{t-or-nor\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{t-or-nor\$netlist} \\  
\=\+{\rm{t-or-nor\$netlist}}\,({\it{tree\/}}, {\it{parity\/}})\index{t-or-nor\$netlist} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$) $\vee$ (({\rm{car}}\,({\it{tree\/}}) $\simeq\;${{\bf{nil}}}${}$) $\wedge$ ({\rm{cdr}}\,({\it{tree\/}}) $\simeq\;${{\bf{nil}}}${}$)) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{t-or-nor*}}\,({\it{tree\/}}, {\it{parity\/}})\index{t-or-nor*}, \\ 
\=\+(\=\+({\sc{b-not\$netlist}}\index{b-not\$netlist} $\cup$ {\sc{b-buf\$netlist}}\index{b-buf\$netlist}) \\ 
$\cup$$\;\;\;\;$({\sc{b-nor\$netlist}}\index{b-nor\$netlist} $\cup$ {\sc{b-or\$netlist}}\index{b-or\$netlist}))\- \\ 
$\cup$$\;\;\;\;${\sc{b-nand\$netlist}}\index{b-nand\$netlist}\-)\- \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{t-or-nor*}}\,({\it{tree\/}}, {\it{parity\/}})\index{t-or-nor*}, \\ 
\=\+{\rm{t-or-nor\$netlist}}\,({\rm{car}}\,({\it{tree\/}}), $\neg$ {\it{parity\/}})\index{t-or-nor\$netlist} \\ 
$\cup$$\;\;\;\;${\rm{t-or-nor\$netlist}}\,({\rm{cdr}}\,({\it{tree\/}}), $\neg$ {\it{parity\/}})\index{t-or-nor\$netlist}\-)\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{t-or-nor-induction} \\  
\=\+{\rm{t-or-nor-induction}}\,({\it{tree\/}}, {\it{parity\/}}, {\it{call-name\/}}, {\it{a\/}}, {\it{state\/}}, {\it{netlist\/}})\index{t-or-nor-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$) $\vee$ (({\rm{car}}\,({\it{tree\/}}) $\simeq\;${{\bf{nil}}}${}$) $\wedge$ ({\rm{cdr}}\,({\it{tree\/}}) $\simeq\;${{\bf{nil}}}${}$))$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }\=\+{\rm{t-or-nor-induction}}\,(\=\+{\rm{car}}\,({\it{tree\/}}), \\ 
$\neg$ {\it{parity\/}}, \\ 
\=\+{\bf if }$\neg$ {\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{t-nor}} \\ 
{\bf else }{\tt{'}}{\tt{t-or}}$\;${\bf  endif}\-, \\ 
{\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\tt{0}}, \\ 
{\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+\=\+{\bf if }{\it{parity\/}} \\ 
{\bf then }{\tt{'}}{\tt{t-nor}} \\ 
{\bf else }{\tt{'}}{\tt{t-or}}$\;${\bf  endif}\-, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\-\index{t-or-nor-induction} \\ 
$\wedge$$\;\;\;\;${\rm{t-or-nor-induction}}\,(\=\+{\rm{cdr}}\,({\it{tree\/}}), \\ 
$\neg$ {\it{parity\/}}, \\ 
\=\+{\bf if }$\neg$ {\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{t-nor}} \\ 
{\bf else }{\tt{'}}{\tt{t-or}}$\;${\bf  endif}\-, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\tt{0}}, \\ 
{\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+\=\+{\bf if }{\it{parity\/}} \\ 
{\bf then }{\tt{'}}{\tt{t-nor}} \\ 
{\bf else }{\tt{'}}{\tt{t-or}}$\;${\bf  endif}\-, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\-\index{t-or-nor-induction}\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tr-or-nor} \\  
\=\+{\rm{tr-or-nor}}\,({\it{a\/}}, {\it{parity\/}}, {\it{tree\/}})\index{tr-or-nor} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\rm{f-not}}\,({\rm{car}}\,({\it{a\/}}))\index{f-not} \\ 
{\bf else }{\rm{f-buf}}\,({\rm{car}}\,({\it{a\/}}))\index{f-buf}$\;${\bf  endif}\- \\ 
{\bf elseif }({\rm{car}}\,({\it{tree\/}}) $\simeq\;${{\bf{nil}}}${}$) $\wedge$ ({\rm{cdr}}\,({\it{tree\/}}) $\simeq\;${{\bf{nil}}}${}$) \\ 
{\bf then }\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\rm{f-nor}}\,({\rm{car}}\,({\it{a\/}}), {\rm{cadr}}\,({\it{a\/}}))\index{f-nor} \\ 
{\bf else }{\rm{f-or}}\,({\rm{car}}\,({\it{a\/}}), {\rm{cadr}}\,({\it{a\/}}))\index{f-or}$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{parity\/}} \\ 
{\bf then }{\rm{f-nor}}\,(\=\+{\rm{tr-or-nor}}\,({\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, $\neg$ {\it{parity\/}}, {\rm{car}}\,({\it{tree\/}}))\index{tr-or-nor}, \\ 
{\rm{tr-or-nor}}\,({\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, $\neg$ {\it{parity\/}}, {\rm{cdr}}\,({\it{tree\/}}))\index{tr-or-nor})\-\index{f-nor} \\ 
{\bf else }{\rm{f-nand}}\,(\=\+{\rm{tr-or-nor}}\,({\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, $\neg$ {\it{parity\/}}, {\rm{car}}\,({\it{tree\/}}))\index{tr-or-nor}, \\ 
{\rm{tr-or-nor}}\,({\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, $\neg$ {\it{parity\/}}, {\rm{cdr}}\,({\it{tree\/}}))\index{tr-or-nor})\-\index{f-nand}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tr-or-nor; name this event `tr-or-nor-off'.\index{tr-or-nor-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  t-or-nor\$value \\ \index{t-or-nor\$value}
\=\+(\=\+{\rm{t-or-nor\&}}\,({\it{netlist\/}}, {\it{tree\/}}, {\it{parity\/}})\index{t-or-nor\&} \\ 
$\wedge$$\;\;\;\;$({\it{call-name\/}} $=$ \=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\tt{'}}{\tt{t-nor}} \\ 
{\bf else }{\tt{'}}{\tt{t-or}}$\;${\bf  endif}\-) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{a\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\rm{index}}\,({\it{call-name\/}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, {\it{a\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{tr-or-nor}}\,({\it{a\/}}, {\it{parity\/}}, {\it{tree\/}})\index{tr-or-nor}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable t-or-nor\$value; name this event `t-or-nor\$value-off'.\index{t-or-nor\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{btr-or-nor} \\  
\=\+{\rm{btr-or-nor}}\,({\it{a\/}}, {\it{parity\/}}, {\it{tree\/}})\index{btr-or-nor} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\rm{b-not}}\,({\rm{car}}\,({\it{a\/}}))\index{b-not} \\ 
{\bf else }{\rm{b-buf}}\,({\rm{car}}\,({\it{a\/}}))\index{b-buf}$\;${\bf  endif}\- \\ 
{\bf elseif }({\rm{car}}\,({\it{tree\/}}) $\simeq\;${{\bf{nil}}}${}$) $\wedge$ ({\rm{cdr}}\,({\it{tree\/}}) $\simeq\;${{\bf{nil}}}${}$) \\ 
{\bf then }\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\rm{b-nor}}\,({\rm{car}}\,({\it{a\/}}), {\rm{cadr}}\,({\it{a\/}}))\index{b-nor} \\ 
{\bf else }{\rm{b-or}}\,({\rm{car}}\,({\it{a\/}}), {\rm{cadr}}\,({\it{a\/}}))\index{b-or}$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{parity\/}} \\ 
{\bf then }{\rm{b-nor}}\,(\=\+{\rm{btr-or-nor}}\,({\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, $\neg$ {\it{parity\/}}, {\rm{car}}\,({\it{tree\/}}))\index{btr-or-nor}, \\ 
{\rm{btr-or-nor}}\,({\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, $\neg$ {\it{parity\/}}, {\rm{cdr}}\,({\it{tree\/}}))\index{btr-or-nor})\-\index{b-nor} \\ 
{\bf else }{\rm{b-nand}}\,(\=\+{\rm{btr-or-nor}}\,({\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, $\neg$ {\it{parity\/}}, {\rm{car}}\,({\it{tree\/}}))\index{btr-or-nor}, \\ 
{\rm{btr-or-nor}}\,({\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, $\neg$ {\it{parity\/}}, {\rm{cdr}}\,({\it{tree\/}}))\index{btr-or-nor})\-\index{b-nand}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable btr-or-nor; name this event `btr-or-nor-off'.\index{btr-or-nor-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tr-or-nor=btr-or-nor \\ \index{tr-or-nor=btr-or-nor}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tr-or-nor}}\,({\it{a\/}}, {\it{parity\/}}, {\it{tree\/}})\index{tr-or-nor} $=$ {\rm{btr-or-nor}}\,({\it{a\/}}, {\it{parity\/}}, {\it{tree\/}})\index{btr-or-nor})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  btr-or-is-v-nzerop \\ \index{btr-or-is-v-nzerop}
\=\+({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{btr-or-nor}}\,({\it{a\/}}, {\it{parity\/}}, {\it{tree\/}})\index{btr-or-nor} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{parity\/}}$\;\;${\bf then }{\rm{v-zerop}}\,({\it{a\/}})\index{v-zerop} \\ 
{\bf else }{\rm{v-nzerop}}\,({\it{a\/}})\index{v-nzerop}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tv-zerop*} \\  
\=\+{\rm{tv-zerop*}}\,({\it{tree\/}})\index{tv-zerop*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{tv-zerop}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{in}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{out}}{\tt{)}}, \\ 
{\rm{cons}}\,(\=\+\=\+{\bf if }({\rm{tree-height}}\,({\it{tree\/}})\index{tree-height} ${}${\bf{mod}}${}$ {\tt{2}}) $=$ {\tt{1}} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{g0}}, \\ 
{\tt{'}}{\tt{(}}{\tt{out-}}{\tt{)}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{t-or}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{in}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices})\-, \\ 
{\tt{'}}{\tt{(}}{\tt{(}}{\tt{g1}}{\tt{ }}{\tt{(}}{\tt{out}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{out-}}{\tt{)}}{\tt{)}}{\tt{)}})\- \\ 
{\bf else }{\rm{list}}\,({\rm{list}}\,(\=\+{\tt{'}}{\tt{g0}}, \\ 
{\tt{'}}{\tt{(}}{\tt{out}}{\tt{)}}, \\ 
{\rm{index}}\,(\=\+{\tt{'}}{\tt{t-nor}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\rm{indices}}\,(\=\+{\tt{'}}{\tt{in}}, \\ 
{\tt{0}}, \\ 
{\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\-\index{indices})\-)$\;${\bf  endif}\-, \\ 
{\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}})\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tv-zerop*\$destructure \\ \index{tv-zerop*\$destructure}
\=\+({\rm{car}}\,({\rm{tv-zerop*}}\,({\it{tree\/}})\index{tv-zerop*}) $=$ {\rm{index}}\,({\tt{'}}{\tt{tv-zerop}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadr}}\,({\rm{tv-zerop*}}\,({\it{tree\/}})\index{tv-zerop*}) $=$ {\rm{indices}}\,({\tt{'}}{\tt{in}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\rm{tv-zerop*}}\,({\it{tree\/}})\index{tv-zerop*}) $=$ {\tt{'}}{\tt{(}}{\tt{out}}{\tt{)}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadddr}}\,({\rm{tv-zerop*}}\,({\it{tree\/}})\index{tv-zerop*}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\rm{tree-height}}\,({\it{tree\/}})\index{tree-height} ${}${\bf{mod}}${}$ {\tt{2}}) $=$ {\tt{1}} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{g0}}, \\ 
{\tt{'}}{\tt{(}}{\tt{out-}}{\tt{)}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{t-or}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{in}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices})\-, \\ 
{\tt{'}}{\tt{(}}{\tt{(}}{\tt{g1}}{\tt{ }}{\tt{(}}{\tt{out}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{out-}}{\tt{)}}{\tt{)}}{\tt{)}})\- \\ 
{\bf else }{\rm{list}}\,({\rm{list}}\,(\=\+{\tt{'}}{\tt{g0}}, \\ 
{\tt{'}}{\tt{(}}{\tt{out}}{\tt{)}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{t-nor}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{in}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices})\-)$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{tv-zerop*}}\,({\it{tree\/}})\index{tv-zerop*}) $=$ {\bf{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-zerop*; name this event `tv-zerop*-off'.\index{tv-zerop*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable tv-zerop*\$destructure; name this event `tv-zerop*\$destructure-off'.\index{tv-zerop*\$destructure-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tv-zerop\&} \\  
\=\+{\rm{tv-zerop\&}}\,({\it{netlist\/}}, {\it{tree\/}})\index{tv-zerop\&} \\ 
$=$$\;\;\;\;$(\=\+(\=\+{\rm{lookup-module}}\,({\rm{index}}\,({\tt{'}}{\tt{tv-zerop}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, {\it{netlist\/}})\index{lookup-module} \\ 
$=$$\;\;\;\;${\rm{tv-zerop*}}\,({\it{tree\/}})\index{tv-zerop*})\- \\ 
$\wedge$$\;\;\;\;${\rm{t-or-nor\&}}\,(\=\+{\rm{delete-module}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{tv-zerop}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\it{tree\/}}, \\ 
({\rm{tree-height}}\,({\it{tree\/}})\index{tree-height} ${}${\bf{mod}}${}$ {\tt{2}}) $\not=$ {\tt{1}})\-\index{t-or-nor\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{tv-zerop}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{b-not\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-zerop\&; name this event `tv-zerop\&-off'.\index{tv-zerop\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tv-zerop\$netlist} \\  
\=\+{\rm{tv-zerop\$netlist}}\,({\it{tree\/}})\index{tv-zerop\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{tv-zerop*}}\,({\it{tree\/}})\index{tv-zerop*}, \\ 
\=\+{\rm{t-or-nor\$netlist}}\,({\it{tree\/}}, ({\rm{tree-height}}\,({\it{tree\/}})\index{tree-height} ${}${\bf{mod}}${}$ {\tt{2}}) $\not=$ {\tt{1}})\index{t-or-nor\$netlist} \\ 
$\cup$$\;\;\;\;${\sc{b-not\$netlist}}\index{b-not\$netlist}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$tv-zerop} \\  
\=\+{\rm{f\$tv-zerop}}\,({\it{a\/}}, {\it{tree\/}})\index{f\$tv-zerop} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\rm{tree-height}}\,({\it{tree\/}})\index{tree-height} ${}${\bf{mod}}${}$ {\tt{2}}) $=$ {\tt{1}}$\;\;${\bf then }{\rm{f-not}}\,({\rm{tr-or-nor}}\,({\it{a\/}}, {\bf{f}}, {\it{tree\/}})\index{tr-or-nor})\index{f-not} \\ 
{\bf else }{\rm{tr-or-nor}}\,({\it{a\/}}, {\bf{t}}, {\it{tree\/}})\index{tr-or-nor}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$tv-zerop; name this event `f\$tv-zerop-off'.\index{f\$tv-zerop-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tv-zerop\$value \\ \index{tv-zerop\$value}
\=\+({\rm{tv-zerop\&}}\,({\it{netlist\/}}, {\it{tree\/}})\index{tv-zerop\&} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{properp}}\,({\it{a\/}})\index{properp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\rm{index}}\,({\tt{'}}{\tt{tv-zerop}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, {\it{a\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f\$tv-zerop}}\,({\it{a\/}}, {\it{tree\/}})\index{f\$tv-zerop}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-zerop\$value; name this event `tv-zerop\$value-off'.\index{tv-zerop\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$tv-zerop=v-zerop \\ \index{f\$tv-zerop=v-zerop}
\=\+(({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{bvp}}\,({\it{a\/}})\index{bvp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f\$tv-zerop}}\,({\it{a\/}}, {\it{tree\/}})\index{f\$tv-zerop} $=$ {\rm{v-zerop}}\,({\it{a\/}})\index{v-zerop})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$fast-zero} \\  
\=\+{\rm{f\$fast-zero}}\,({\it{v\/}})\index{f\$fast-zero} \\ 
$=$$\;\;\;\;${\rm{f-nor3}}\,(\=\+{\rm{tr-or-nor}}\,(\=\+{\rm{firstn}}\,(({\rm{length}}\,({\it{v\/}})\index{length} $-\;1$) $-\;1$, {\it{v\/}})\index{firstn}, \\ 
{\bf{f}}, \\ 
{\rm{make-tree}}\,(({\rm{length}}\,({\it{v\/}})\index{length} $-\;1$) $-\;1$)\index{make-tree})\-\index{tr-or-nor}, \\ 
{\rm{nth}}\,(({\rm{length}}\,({\it{v\/}})\index{length} $-\;1$) $-\;1$, {\it{v\/}})\index{nth}, \\ 
{\rm{nth}}\,({\rm{length}}\,({\it{v\/}})\index{length} $-\;1$, {\it{v\/}})\index{nth})\-\index{f-nor3}\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$fast-zero; name this event `f\$fast-zero-off'.\index{f\$fast-zero-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$fast-zero=tr-or-nor \\ \index{f\$fast-zero=tr-or-nor}
\=\+(\=\+{\rm{properp}}\,({\it{v\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{v\/}})\index{length} $<$ {\tt{3}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$fast-zero}}\,({\it{v\/}})\index{f\$fast-zero} \\ 
$=$$\;\;\;\;${\rm{tr-or-nor}}\,(\=\+{\it{v\/}}, \\ 
{\bf{t}}, \\ 
{\rm{cons}}\,({\rm{make-tree}}\,(({\rm{length}}\,({\it{v\/}})\index{length} $-\;1$) $-\;1$)\index{make-tree}, {\tt{'}}{\tt{(}}{\tt{0}}{\tt{ .\ }}{\tt{0}}{\tt{)}}))\-\index{tr-or-nor})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f\$fast-zero=v-zerop \\ \index{f\$fast-zero=v-zerop}
\=\+(\=\+{\rm{bvp}}\,({\it{v\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{v\/}})\index{length} $<$ {\tt{3}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{f\$fast-zero}}\,({\it{v\/}})\index{f\$fast-zero} $=$ {\rm{v-zerop}}\,({\it{v\/}})\index{v-zerop})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fast-zero*} \\  
\=\+{\rm{fast-zero*}}\,({\it{n\/}})\index{fast-zero*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{fast-zero}}, {\it{n\/}})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{z}}{\tt{)}}, \\ 
{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{front}}, \\ 
{\tt{'}}{\tt{(}}{\tt{zfront}}{\tt{)}}, \\ 
{\rm{index}}\,(\=\+{\tt{'}}{\tt{t-or}}, \\ 
{\rm{tree-number}}\,({\rm{make-tree}}\,(({\it{n\/}} $-\;1$) $-\;1$)\index{make-tree})\index{tree-number})\-\index{index}, \\ 
{\rm{firstn}}\,(({\it{n\/}} $-\;1$) $-\;1$, {\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices})\index{firstn})\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{result}}, \\ 
{\tt{'}}{\tt{(}}{\tt{z}}{\tt{)}}, \\ 
{\tt{'}}{\tt{b-nor3}}, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{zfront}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{a}}, ({\it{n\/}} $-\;1$) $-\;1$)\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{a}}, {\it{n\/}} $-\;1$)\index{index})\-)\-)\-, \\ 
{\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}})\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fast-zero*\$destructure \\ \index{fast-zero*\$destructure}
\=\+({\rm{car}}\,({\rm{fast-zero*}}\,({\it{n\/}})\index{fast-zero*}) $=$ {\rm{index}}\,({\tt{'}}{\tt{fast-zero}}, {\it{n\/}})\index{index}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadr}}\,({\rm{fast-zero*}}\,({\it{n\/}})\index{fast-zero*}) $=$ {\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\rm{fast-zero*}}\,({\it{n\/}})\index{fast-zero*}) $=$ {\tt{'}}{\tt{(}}{\tt{z}}{\tt{)}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadddr}}\,({\rm{fast-zero*}}\,({\it{n\/}})\index{fast-zero*}) \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{front}}, \\ 
{\tt{'}}{\tt{(}}{\tt{zfront}}{\tt{)}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{t-or}}, {\rm{tree-number}}\,({\rm{make-tree}}\,(({\it{n\/}} $-\;1$) $-\;1$)\index{make-tree})\index{tree-number})\index{index}, \\ 
{\rm{firstn}}\,(({\it{n\/}} $-\;1$) $-\;1$, {\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices})\index{firstn})\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{result}}, \\ 
{\tt{'}}{\tt{(}}{\tt{z}}{\tt{)}}, \\ 
{\tt{'}}{\tt{b-nor3}}, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{zfront}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{a}}, ({\it{n\/}} $-\;1$) $-\;1$)\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{a}}, {\it{n\/}} $-\;1$)\index{index})\-)\-)\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{fast-zero*}}\,({\it{n\/}})\index{fast-zero*}) $=$ {\bf{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable fast-zero*; name this event `fast-zero*-off'.\index{fast-zero*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fast-zero*\$destructure; name this event `fast-zero*\$destructure-off'.\index{fast-zero*\$destructure-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fast-zero\&} \\  
\=\+{\rm{fast-zero\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{fast-zero\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\rm{index}}\,({\tt{'}}{\tt{fast-zero}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{lookup-module} $=$ {\rm{fast-zero*}}\,({\it{n\/}})\index{fast-zero*}) \\ 
$\wedge$$\;\;\;\;${\rm{t-or-nor\&}}\,(\=\+{\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{fast-zero}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{delete-module}, \\ 
{\rm{make-tree}}\,(({\it{n\/}} $-\;1$) $-\;1$)\index{make-tree}, \\ 
{\bf{f}})\-\index{t-or-nor\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nor3\&}}\,({\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{fast-zero}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{delete-module})\index{b-nor3\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fast-zero\&; name this event `fast-zero\&-off'.\index{fast-zero\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fast-zero\$netlist} \\  
\=\+{\rm{fast-zero\$netlist}}\,({\it{n\/}})\index{fast-zero\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{fast-zero*}}\,({\it{n\/}})\index{fast-zero*}, \\ 
{\rm{t-or-nor\$netlist}}\,({\rm{make-tree}}\,(({\it{n\/}} $-\;1$) $-\;1$)\index{make-tree}, {\bf{f}})\index{t-or-nor\$netlist} $\cup$ {\sc{b-nor3\$netlist}}\index{b-nor3\$netlist})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  check-fast-zero\$netlist \\ \index{check-fast-zero\$netlist}
{\rm{fast-zero\&}}\,({\rm{fast-zero\$netlist}}\,({\tt{5}})\index{fast-zero\$netlist}, {\tt{5}})\index{fast-zero\&}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fast-zero\$value \\ \index{fast-zero\$value}
\=\+(\=\+{\rm{fast-zero\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{fast-zero\&} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{v\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{v\/}})\index{length} $=$ {\it{n\/}}) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $<$ {\tt{3}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\rm{index}}\,({\tt{'}}{\tt{fast-zero}}, {\it{n\/}})\index{index}, {\it{v\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f\$fast-zero}}\,({\it{v\/}})\index{f\$fast-zero}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-equal*} \\  
\=\+{\rm{v-equal*}}\,({\it{n\/}})\index{v-equal*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{v-equal}}, {\it{n\/}})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\rm{append}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{indices}}\,({\tt{'}}{\tt{b}}, {\tt{0}}, {\it{n\/}})\index{indices}), \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{equal}}{\tt{)}}, \\ 
{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{g0}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{x}}, {\tt{0}}, {\it{n\/}})\index{indices}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{v-xor}}, {\it{n\/}})\index{index}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{b}}, {\tt{0}}, {\it{n\/}})\index{indices})\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g1}}, \\ 
{\tt{'}}{\tt{(}}{\tt{equal}}{\tt{)}}, \\ 
{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-zerop}}, \\ 
{\rm{tree-number}}\,({\rm{make-tree}}\,({\it{n\/}})\index{make-tree})\index{tree-number})\-\index{index}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{x}}, {\tt{0}}, {\it{n\/}})\index{indices})\-)\-, \\ 
{\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}})\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-equal*\$destructure \\ \index{v-equal*\$destructure}
\=\+({\rm{car}}\,({\rm{v-equal*}}\,({\it{n\/}})\index{v-equal*}) $=$ {\rm{index}}\,({\tt{'}}{\tt{v-equal}}, {\it{n\/}})\index{index}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadr}}\,({\rm{v-equal*}}\,({\it{n\/}})\index{v-equal*}) $=$ {\rm{append}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{indices}}\,({\tt{'}}{\tt{b}}, {\tt{0}}, {\it{n\/}})\index{indices})) \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\rm{v-equal*}}\,({\it{n\/}})\index{v-equal*}) $=$ {\tt{'}}{\tt{(}}{\tt{equal}}{\tt{)}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadddr}}\,({\rm{v-equal*}}\,({\it{n\/}})\index{v-equal*}) \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{g0}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{x}}, {\tt{0}}, {\it{n\/}})\index{indices}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{v-xor}}, {\it{n\/}})\index{index}, \\ 
{\rm{append}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{indices}}\,({\tt{'}}{\tt{b}}, {\tt{0}}, {\it{n\/}})\index{indices}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g1}}, \\ 
{\tt{'}}{\tt{(}}{\tt{equal}}{\tt{)}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{tv-zerop}}, {\rm{tree-number}}\,({\rm{make-tree}}\,({\it{n\/}})\index{make-tree})\index{tree-number})\index{index}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{x}}, {\tt{0}}, {\it{n\/}})\index{indices})\-)\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{v-equal*}}\,({\it{n\/}})\index{v-equal*}) $=$ {\bf{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-equal*; name this event `v-equal*-off'.\index{v-equal*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-equal*\$destructure; name this event `v-equal*\$destructure-off'.\index{v-equal*\$destructure-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-equal\&} \\  
\=\+{\rm{v-equal\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{v-equal\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\rm{index}}\,({\tt{'}}{\tt{v-equal}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{lookup-module} $=$ {\rm{v-equal*}}\,({\it{n\/}})\index{v-equal*}) \\ 
$\wedge$$\;\;\;\;${\rm{v-xor\&}}\,({\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{v-equal}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{delete-module}, {\it{n\/}})\index{v-xor\&} \\ 
$\wedge$$\;\;\;\;${\rm{tv-zerop\&}}\,(\=\+{\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{v-equal}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{delete-module}, \\ 
{\rm{make-tree}}\,({\it{n\/}})\index{make-tree})\-\index{tv-zerop\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-equal\&; name this event `v-equal\&-off'.\index{v-equal\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-equal\$netlist} \\  
\=\+{\rm{v-equal\$netlist}}\,({\it{n\/}})\index{v-equal\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\rm{v-equal*}}\,({\it{n\/}})\index{v-equal*}, {\rm{v-xor\$netlist}}\,({\it{n\/}})\index{v-xor\$netlist} $\cup$ {\rm{tv-zerop\$netlist}}\,({\rm{make-tree}}\,({\it{n\/}})\index{make-tree})\index{tv-zerop\$netlist})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$v-equal} \\  
{\rm{f\$v-equal}}\,({\it{a\/}}, {\it{b\/}})\index{f\$v-equal} $=$ {\rm{f\$tv-zerop}}\,({\rm{fv-xor}}\,({\it{a\/}}, {\it{b\/}})\index{fv-xor}, {\rm{make-tree}}\,({\rm{length}}\,({\it{a\/}})\index{length})\index{make-tree})\index{f\$tv-zerop}
\end{tabbing}


\noindent{\sc Event}:   Enable f\$v-equal; name this event `f\$v-equal-off'.\index{f\$v-equal-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-equal\$value \\ \index{v-equal\$value}
\=\+(\=\+{\rm{v-equal\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{v-equal\&} \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{a\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{b\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\it{n\/}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\it{n\/}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\rm{index}}\,({\tt{'}}{\tt{v-equal}}, {\it{n\/}})\index{index}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f\$v-equal}}\,({\it{a\/}}, {\it{b\/}})\index{f\$v-equal}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-equal\$value; name this event `v-equal\$value-off'.\index{v-equal\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$v-equal=equal* \\ \index{f\$v-equal=equal*}
\=\+(({\rm{length}}\,({\it{a\/}})\index{length} $\not\simeq {\tt{0}}$) $\wedge$ {\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ {\rm{bvp}}\,({\it{b\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{length}}\,({\it{b\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f\$v-equal}}\,({\it{a\/}}, {\it{b\/}})\index{f\$v-equal} $=$ ({\it{a\/}} $=$ {\it{b\/}}))\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-inc4} \\  
\=\+{\rm{v-inc4}}\,({\it{a0\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{a3\/}})\index{v-inc4} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{b-not}}\,({\it{a0\/}})\index{b-not}, \\ 
{\rm{b-xor}}\,({\rm{b-not}}\,({\it{a1\/}})\index{b-not}, {\rm{b-not}}\,({\it{a0\/}})\index{b-not})\index{b-xor}, \\ 
{\rm{b-equv}}\,({\rm{b-not}}\,({\it{a2\/}})\index{b-not}, {\rm{b-nor}}\,({\rm{b-not}}\,({\it{a0\/}})\index{b-not}, {\rm{b-not}}\,({\it{a1\/}})\index{b-not})\index{b-nor})\index{b-equv}, \\ 
{\rm{b-equv}}\,({\rm{b-not}}\,({\it{a3\/}})\index{b-not}, {\rm{b-nor3}}\,({\rm{b-not}}\,({\it{a0\/}})\index{b-not}, {\rm{b-not}}\,({\it{a1\/}})\index{b-not}, {\rm{b-not}}\,({\it{a2\/}})\index{b-not})\index{b-nor3})\index{b-equv})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$v-inc4} \\  
\=\+{\rm{f\$v-inc4}}\,({\it{a0\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{a3\/}})\index{f\$v-inc4} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{f-not}}\,({\it{a0\/}})\index{f-not}, \\ 
{\rm{f-xor}}\,({\rm{f-not}}\,({\it{a1\/}})\index{f-not}, {\rm{f-not}}\,({\it{a0\/}})\index{f-not})\index{f-xor}, \\ 
{\rm{f-equv}}\,({\rm{f-not}}\,({\it{a2\/}})\index{f-not}, {\rm{f-nor}}\,({\rm{f-not}}\,({\it{a0\/}})\index{f-not}, {\rm{f-not}}\,({\it{a1\/}})\index{f-not})\index{f-nor})\index{f-equv}, \\ 
{\rm{f-equv}}\,({\rm{f-not}}\,({\it{a3\/}})\index{f-not}, {\rm{f-nor3}}\,({\rm{f-not}}\,({\it{a0\/}})\index{f-not}, {\rm{f-not}}\,({\it{a1\/}})\index{f-not}, {\rm{f-not}}\,({\it{a2\/}})\index{f-not})\index{f-nor3})\index{f-equv})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$v-inc4; name this event `f\$v-inc4-off'.\index{f\$v-inc4-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-inc4*} \\  
\=\+{\sc{v-inc4*}}\index{v-inc4*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{v-inc4}} \\ 
{\tt{(}}{\tt{a0}}{\tt{ }}{\tt{a1}}{\tt{ }}{\tt{a2}}{\tt{ }}{\tt{a3}}{\tt{)}} \\ 
{\tt{(}}{\tt{w-10}}{\tt{ }}{\tt{w-3}}{\tt{ }}{\tt{w-8}}{\tt{ }}{\tt{w-14}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{g-12}}{\tt{ }}{\tt{(}}{\tt{w-12}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{a2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-11}}{\tt{ }}{\tt{(}}{\tt{w-11}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{a1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-10}}{\tt{ }}{\tt{(}}{\tt{w-10}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{a0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-13}}{\tt{ }}{\tt{(}}{\tt{w-13}}{\tt{)}}{\tt{ }}{\tt{b-nor3}}{\tt{ }}{\tt{(}}{\tt{w-10}}{\tt{ }}{\tt{w-11}}{\tt{ }}{\tt{w-12}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-9}}{\tt{ }}{\tt{(}}{\tt{w-9}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{a3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-14}}{\tt{ }}{\tt{(}}{\tt{w-14}}{\tt{)}}{\tt{ }}{\tt{b-equv}}{\tt{ }}{\tt{(}}{\tt{w-9}}{\tt{ }}{\tt{w-13}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-7}}{\tt{ }}{\tt{(}}{\tt{w-7}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{w-10}}{\tt{ }}{\tt{w-11}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-8}}{\tt{ }}{\tt{(}}{\tt{w-8}}{\tt{)}}{\tt{ }}{\tt{b-equv}}{\tt{ }}{\tt{(}}{\tt{w-12}}{\tt{ }}{\tt{w-7}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-3}}{\tt{ }}{\tt{(}}{\tt{w-3}}{\tt{)}}{\tt{ }}{\tt{b-xor}}{\tt{ }}{\tt{(}}{\tt{w-11}}{\tt{ }}{\tt{w-10}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-inc4\&} \\  
\=\+{\rm{v-inc4\&}}\,({\it{netlist\/}})\index{v-inc4\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{v-inc4}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{v-inc4*}}\index{v-inc4*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-nor3\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{v-inc4}}, {\it{netlist\/}})\index{delete-module})\index{b-nor3\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{v-inc4}}, {\it{netlist\/}})\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nor\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{v-inc4}}, {\it{netlist\/}})\index{delete-module})\index{b-nor\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-equv\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{v-inc4}}, {\it{netlist\/}})\index{delete-module})\index{b-equv\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-xor\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{v-inc4}}, {\it{netlist\/}})\index{delete-module})\index{b-xor\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-inc4\&; name this event `v-inc4\&-off'.\index{v-inc4\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-inc4\$netlist} \\  
\=\+{\sc{v-inc4\$netlist}}\index{v-inc4\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{v-inc4*}}\index{v-inc4*}, \\ 
\=\+(\=\+(({\sc{b-nor3\$netlist}}\index{b-nor3\$netlist} $\cup$ {\sc{b-not\$netlist}}\index{b-not\$netlist}) $\cup$ {\sc{b-nor\$netlist}}\index{b-nor\$netlist}) \\ 
$\cup$$\;\;\;\;${\sc{b-equv\$netlist}}\index{b-equv\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-xor\$netlist}}\index{b-xor\$netlist}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-inc4\$value \\ \index{v-inc4\$value}
\=\+{\rm{v-inc4\&}}\,({\it{netlist\/}})\index{v-inc4\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{v-inc4}}, {\rm{list}}\,({\it{a0\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{a3\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$v-inc4}}\,({\it{a0\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{a3\/}})\index{f\$v-inc4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-inc4\$value; name this event `v-inc4\$value-off'.\index{v-inc4\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$v-inc4=v-inc4 \\ \index{f\$v-inc4=v-inc4}
\=\+({\rm{boolp}}\,({\it{a0\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{a1\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{a2\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{a3\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f\$v-inc4}}\,({\it{a0\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{a3\/}})\index{f\$v-inc4} $=$ {\rm{v-inc4}}\,({\it{a0\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{a3\/}})\index{v-inc4})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$v-inc4\$v} \\  
\=\+{\rm{f\$v-inc4\$v}}\,({\it{a\/}})\index{f\$v-inc4\$v} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{f-not}}\,({\rm{car}}\,({\it{a\/}}))\index{f-not}, \\ 
{\rm{f-xor}}\,({\rm{f-not}}\,({\rm{cadr}}\,({\it{a\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{car}}\,({\it{a\/}}))\index{f-not})\index{f-xor}, \\ 
{\rm{f-equv}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{a\/}}))\index{f-not}, {\rm{f-nor}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{a\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{cadr}}\,({\it{a\/}}))\index{f-not})\index{f-nor})\index{f-equv}, \\ 
{\rm{f-equv}}\,(\=\+{\rm{f-not}}\,({\rm{cadddr}}\,({\it{a\/}}))\index{f-not}, \\ 
{\rm{f-nor3}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{a\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{cadr}}\,({\it{a\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{caddr}}\,({\it{a\/}}))\index{f-not})\index{f-nor3})\-\index{f-equv})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$v-inc4\$v; name this event `f\$v-inc4\$v-off'.\index{f\$v-inc4\$v-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  properp-length-f\$v-inc4\$v \\ \index{properp-length-f\$v-inc4\$v}
{\rm{properp}}\,({\rm{f\$v-inc4\$v}}\,({\it{a\/}})\index{f\$v-inc4\$v})\index{properp} $\wedge$ ({\rm{length}}\,({\rm{f\$v-inc4\$v}}\,({\it{a\/}})\index{f\$v-inc4\$v})\index{length} $=$ {\tt{4}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-inc4\$value-as-v-inc \\ \index{v-inc4\$value-as-v-inc}
\=\+({\rm{v-inc4\&}}\,({\it{netlist\/}})\index{v-inc4\&} $\wedge$ {\rm{properp}}\,({\it{a\/}})\index{properp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\tt{4}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{v-inc4}}, {\it{a\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{f\$v-inc4\$v}}\,({\it{a\/}})\index{f\$v-inc4\$v})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f\$v-inc4\$v=v-inc \\ \index{f\$v-inc4\$v=v-inc}
({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\tt{4}})) $\rightarrow$ ({\rm{f\$v-inc4\$v}}\,({\it{a\/}})\index{f\$v-inc4\$v} $=$ {\rm{v-inc}}\,({\it{a\/}})\index{v-inc})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tv-dec-pass} \\  
\=\+{\rm{tv-dec-pass}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}})\index{tv-dec-pass} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{list}}\,({\rm{b-buf}}\,({\rm{car}}\,({\it{a\/}}))\index{b-buf}, {\rm{b-equv}}\,({\rm{car}}\,({\it{a\/}}), {\it{c\/}})\index{b-equv}) \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{b-or}}\,(\=\+{\rm{car}}\,({\rm{tv-dec-pass}}\,({\it{c\/}}, {\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, {\rm{car}}\,({\it{tree\/}}))\index{tv-dec-pass}), \\ 
{\rm{car}}\,({\rm{tv-dec-pass}}\,(\=\+{\rm{b-or}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{tv-dec-pass}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-dec-pass}))\-\index{b-or}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{cdr}}\,({\it{tree\/}}))\-\index{tv-dec-pass}))\-\index{b-or}, \\ 
{\rm{append}}\,(\=\+{\rm{cdr}}\,({\rm{tv-dec-pass}}\,({\it{c\/}}, {\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, {\rm{car}}\,({\it{tree\/}}))\index{tv-dec-pass}), \\ 
{\rm{cdr}}\,({\rm{tv-dec-pass}}\,(\=\+{\rm{b-or}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{tv-dec-pass}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-dec-pass}))\-\index{b-or}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{cdr}}\,({\it{tree\/}}))\-\index{tv-dec-pass}))\-)\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-dec-pass; name this event `tv-dec-pass-off'.\index{tv-dec-pass-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cdr-tv-dec-pass-length \\ \index{cdr-tv-dec-pass-length}
{\rm{length}}\,({\rm{cdr}}\,({\rm{tv-dec-pass}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}})\index{tv-dec-pass}))\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tv-dec-pass-length \\ \index{tv-dec-pass-length}
{\rm{length}}\,({\rm{tv-dec-pass}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}})\index{tv-dec-pass})\index{length} $=$ ($1\;+$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-cdr-tv-dec-pass \\ \index{bvp-cdr-tv-dec-pass}
{\rm{bvp}}\,({\rm{cdr}}\,({\rm{tv-dec-pass}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}})\index{tv-dec-pass}))\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-tv-dec-pass \\ \index{bvp-tv-dec-pass}
{\rm{bvp}}\,({\rm{tv-dec-pass}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}})\index{tv-dec-pass})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-length-tv-dec-pass \\ \index{bvp-length-tv-dec-pass}
\=\+{\rm{bvp-length}}\,({\rm{tv-dec-pass}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}})\index{tv-dec-pass}, {\it{n\/}})\index{bvp-length} \\ 
$=$$\;\;\;\;$\=\+{\bf if }($1\;+$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $<$ {\it{n\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tv-dec-pass-crock-1 \\ \index{tv-dec-pass-crock-1}
\=\+(({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{bvp}}\,({\it{a\/}})\index{bvp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tv-adder}}\,({\it{c\/}}, {\rm{v-not}}\,({\rm{nat-to-v}}\,({\tt{0}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{nat-to-v})\index{v-not}, {\it{a\/}}, {\it{tree\/}})\index{tv-adder} \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\bf{t}}, {\rm{tv-dec-pass}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}})\index{tv-dec-pass}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tv-dec-pass-crock-2 \\ \index{tv-dec-pass-crock-2}
\=\+(({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{bvp}}\,({\it{a\/}})\index{bvp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{cdr}}\,({\rm{tv-dec-pass}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}})\index{tv-dec-pass}) \\ 
$=$$\;\;\;\;${\rm{cddr}}\,({\rm{tv-adder}}\,({\it{c\/}}, {\rm{v-not}}\,({\rm{nat-to-v}}\,({\tt{0}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{nat-to-v})\index{v-not}, {\it{a\/}}, {\it{tree\/}})\index{tv-adder}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tv-dec-pass-works \\ \index{tv-dec-pass-works}
\=\+(({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{bvp}}\,({\it{a\/}})\index{bvp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{cdr}}\,({\rm{tv-dec-pass}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}})\index{tv-dec-pass}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{c\/}}$\;\;${\bf then }{\rm{v-buf}}\,({\it{a\/}})\index{v-buf} \\ 
{\bf else }{\rm{v-dec}}\,({\it{a\/}})\index{v-dec}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tv-dec-pass-ng} \\  
\=\+{\rm{tv-dec-pass-ng}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }\=\+{\bf if }{\it{make-g\/}}$\;\;${\bf then }{\rm{list}}\,({\rm{b-buf}}\,({\rm{car}}\,({\it{a\/}}))\index{b-buf}, {\rm{b-equv}}\,({\rm{car}}\,({\it{a\/}}), {\it{c\/}})\index{b-equv}) \\ 
{\bf else }{\rm{list}}\,({\rm{b-equv}}\,({\rm{car}}\,({\it{a\/}}), {\it{c\/}})\index{b-equv})$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{make-g\/}} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{b-or}}\,(\=\+{\rm{car}}\,({\rm{tv-dec-pass-ng}}\,({\it{c\/}}, {\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, {\rm{car}}\,({\it{tree\/}}), {\bf{t}})\index{tv-dec-pass-ng}), \\ 
{\rm{car}}\,({\rm{tv-dec-pass-ng}}\,(\=\+{\rm{b-or}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{tv-dec-pass-ng}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{car}}\,({\it{tree\/}}), \\ 
{\bf{t}})\-\index{tv-dec-pass-ng}))\-\index{b-or}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{cdr}}\,({\it{tree\/}}), \\ 
{\it{make-g\/}})\-\index{tv-dec-pass-ng}))\-\index{b-or}, \\ 
{\rm{append}}\,(\=\+{\rm{cdr}}\,({\rm{tv-dec-pass-ng}}\,({\it{c\/}}, {\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, {\rm{car}}\,({\it{tree\/}}), {\bf{t}})\index{tv-dec-pass-ng}), \\ 
{\rm{cdr}}\,({\rm{tv-dec-pass-ng}}\,(\=\+{\rm{b-or}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{tv-dec-pass-ng}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{car}}\,({\it{tree\/}}), \\ 
{\bf{t}})\-\index{tv-dec-pass-ng}))\-\index{b-or}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{cdr}}\,({\it{tree\/}}), \\ 
{\it{make-g\/}})\-\index{tv-dec-pass-ng}))\-)\- \\ 
{\bf else }{\rm{append}}\,(\=\+{\rm{cdr}}\,({\rm{tv-dec-pass-ng}}\,({\it{c\/}}, {\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, {\rm{car}}\,({\it{tree\/}}), {\bf{t}})\index{tv-dec-pass-ng}), \\ 
{\rm{tv-dec-pass-ng}}\,(\=\+{\rm{b-or}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{tv-dec-pass-ng}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{car}}\,({\it{tree\/}}), \\ 
{\bf{t}})\-\index{tv-dec-pass-ng}))\-\index{b-or}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{cdr}}\,({\it{tree\/}}), \\ 
{\it{make-g\/}})\-\index{tv-dec-pass-ng})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-dec-pass-ng; name this event `tv-dec-pass-ng-off'.\index{tv-dec-pass-ng-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tv-dec-pass-ng-length \\ \index{tv-dec-pass-ng-length}
\=\+{\rm{length}}\,({\rm{tv-dec-pass-ng}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng})\index{length} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{make-g\/}}$\;\;${\bf then }$1\;+$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size} \\ 
{\bf else }{\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tv-dec-pass-ng-length-1 \\ \index{tv-dec-pass-ng-length-1}
{\it{make-g\/}} $\rightarrow$ ({\rm{length}}\,({\rm{cdr}}\,({\rm{tv-dec-pass-ng}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng}))\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-tv-dec-pass-ng \\ \index{bvp-tv-dec-pass-ng}
{\rm{bvp}}\,({\rm{tv-dec-pass-ng}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-cdr-tv-dec-pass-ng \\ \index{bvp-cdr-tv-dec-pass-ng}
{\it{make-g\/}} $\rightarrow$ {\rm{bvp}}\,({\rm{cdr}}\,({\rm{tv-dec-pass-ng}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng}))\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-length-tv-dec-pass-ng \\ \index{bvp-length-tv-dec-pass-ng}
\=\+{\rm{bvp-length}}\,({\rm{tv-dec-pass-ng}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng}, {\it{n\/}})\index{bvp-length} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{make-g\/}} \\ 
{\bf then }\=\+{\bf if }($1\;+$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $<$ {\it{n\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{n\/}} $<$ ($1\;+$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tv-dec-pass-ng-is-cdr-tv-dec-pass \\ \index{tv-dec-pass-ng-is-cdr-tv-dec-pa!ss}
\=\+{\rm{tv-dec-pass-ng}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{make-g\/}}$\;\;${\bf then }{\rm{tv-dec-pass}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}})\index{tv-dec-pass} \\ 
{\bf else }{\rm{cdr}}\,({\rm{tv-dec-pass}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}})\index{tv-dec-pass})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  boolp-car-tv-dec-pass-ng \\ \index{boolp-car-tv-dec-pass-ng}
{\rm{boolp}}\,({\rm{car}}\,({\rm{tv-dec-pass-ng}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng}))\index{boolp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tv-dec-pass-ng-works-1 \\ \index{tv-dec-pass-ng-works-1}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\it{make-g\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{cdr}}\,({\rm{tv-dec-pass-ng}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{c\/}}$\;\;${\bf then }{\rm{v-buf}}\,({\it{a\/}})\index{v-buf} \\ 
{\bf else }{\rm{v-dec}}\,({\it{a\/}})\index{v-dec}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tv-dec-pass-ng-works-2 \\ \index{tv-dec-pass-ng-works-2}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ ($\neg$ {\it{make-g\/}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tv-dec-pass-ng}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{c\/}}$\;\;${\bf then }{\rm{v-buf}}\,({\it{a\/}})\index{v-buf} \\ 
{\bf else }{\rm{v-dec}}\,({\it{a\/}})\index{v-dec}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$tv-dec-pass-ng} \\  
\=\+{\rm{f\$tv-dec-pass-ng}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{f\$tv-dec-pass-ng} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }\=\+{\bf if }{\it{make-g\/}}$\;\;${\bf then }{\rm{list}}\,({\rm{car}}\,({\it{a\/}}), {\rm{f-equv}}\,({\rm{car}}\,({\it{a\/}}), {\it{c\/}})\index{f-equv}) \\ 
{\bf else }{\rm{list}}\,({\rm{f-equv}}\,({\rm{car}}\,({\it{a\/}}), {\it{c\/}})\index{f-equv})$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{make-g\/}} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{f-or}}\,(\=\+{\rm{car}}\,({\rm{f\$tv-dec-pass-ng}}\,({\it{c\/}}, {\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, {\rm{car}}\,({\it{tree\/}}), {\bf{t}})\index{f\$tv-dec-pass-ng}), \\ 
{\rm{car}}\,({\rm{f\$tv-dec-pass-ng}}\,(\=\+{\rm{f-or}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{f\$tv-dec-pass-ng}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{car}}\,({\it{tree\/}}), \\ 
{\bf{t}})\-\index{f\$tv-dec-pass-ng}))\-\index{f-or}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{cdr}}\,({\it{tree\/}}), \\ 
{\it{make-g\/}})\-\index{f\$tv-dec-pass-ng}))\-\index{f-or}, \\ 
{\rm{append}}\,(\=\+{\rm{cdr}}\,({\rm{f\$tv-dec-pass-ng}}\,({\it{c\/}}, {\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, {\rm{car}}\,({\it{tree\/}}), {\bf{t}})\index{f\$tv-dec-pass-ng}), \\ 
{\rm{cdr}}\,({\rm{f\$tv-dec-pass-ng}}\,(\=\+{\rm{f-or}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{f\$tv-dec-pass-ng}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{car}}\,({\it{tree\/}}), \\ 
{\bf{t}})\-\index{f\$tv-dec-pass-ng}))\-\index{f-or}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{cdr}}\,({\it{tree\/}}), \\ 
{\it{make-g\/}})\-\index{f\$tv-dec-pass-ng}))\-)\- \\ 
{\bf else }{\rm{append}}\,(\=\+{\rm{cdr}}\,({\rm{f\$tv-dec-pass-ng}}\,({\it{c\/}}, {\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, {\rm{car}}\,({\it{tree\/}}), {\bf{t}})\index{f\$tv-dec-pass-ng}), \\ 
{\rm{f\$tv-dec-pass-ng}}\,(\=\+{\rm{f-or}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{f\$tv-dec-pass-ng}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{car}}\,({\it{tree\/}}), \\ 
{\bf{t}})\-\index{f\$tv-dec-pass-ng}))\-\index{f-or}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{cdr}}\,({\it{tree\/}}), \\ 
{\it{make-g\/}})\-\index{f\$tv-dec-pass-ng})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$tv-dec-pass-ng; name this event `f\$tv-dec-pass-ng-off'.\index{f\$tv-dec-pass-ng-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$tv-dec-pass-ng-length \\ \index{f\$tv-dec-pass-ng-length}
\=\+{\rm{length}}\,({\rm{f\$tv-dec-pass-ng}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{f\$tv-dec-pass-ng})\index{length} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{make-g\/}}$\;\;${\bf then }$1\;+$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size} \\ 
{\bf else }{\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f\$tv-dec-pass-ng-length-1 \\ \index{f\$tv-dec-pass-ng-length-1}
{\it{make-g\/}} $\rightarrow$ (\=\+{\rm{length}}\,({\rm{cdr}}\,({\rm{f\$tv-dec-pass-ng}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{f\$tv-dec-pass-ng}))\index{length} \\ 
$=$$\;\;\;\;${\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-f\$tv-dec-pass-ng \\ \index{properp-f\$tv-dec-pass-ng}
{\rm{properp}}\,({\rm{f\$tv-dec-pass-ng}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{f\$tv-dec-pass-ng})\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-cdr-f\$tv-dec-pass-ng \\ \index{properp-cdr-f\$tv-dec-pass-ng}
{\it{make-g\/}} $\rightarrow$ {\rm{properp}}\,({\rm{cdr}}\,({\rm{f\$tv-dec-pass-ng}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{f\$tv-dec-pass-ng}))\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f\$tv-dec-pass-ng=tv-dec-pass-ng\$super-crock \\ \index{f\$tv-dec-pass-ng=tv-dec-pass-n!g\$super-crock}
\=\+({\rm{f\$tv-dec-pass-ng}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{f\$tv-dec-pass-ng} $=$ {\rm{tv-dec-pass-ng}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng}) \\ 
$\rightarrow$$\;\;\;\;${\rm{boolp}}\,({\rm{car}}\,({\rm{f\$tv-dec-pass-ng}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{f\$tv-dec-pass-ng}))\index{boolp}\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$tv-dec-pass-ng=tv-dec-pass-ng\$super-crock; name this event `f\$tv-dec-pass-ng=tv-dec-pass-ng\$super-crock-off'.\index{f\$tv-dec-pass-ng=tv-dec-pass-n!g\$super-crock-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$tv-dec-pass-ng=tv-dec-pass-ng \\ \index{f\$tv-dec-pass-ng=tv-dec-pass-n!g}
\=\+({\rm{boolp}}\,({\it{c\/}})\index{boolp} $\wedge$ {\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$tv-dec-pass-ng}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{f\$tv-dec-pass-ng} \\ 
$=$$\;\;\;\;${\rm{tv-dec-pass-ng}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{dec-pass-cell*} \\  
\=\+{\sc{dec-pass-cell*}}\index{dec-pass-cell*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{dec-pass-cell}} \\ 
{\tt{(}}{\tt{c}}{\tt{ }}{\tt{a}}{\tt{)}} \\ 
{\tt{(}}{\tt{g}}{\tt{ }}{\tt{z}}{\tt{)}} \\ 
{\tt{(}}{\tt{(}}{\tt{g0}}{\tt{ }}{\tt{(}}{\tt{g}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{a}}{\tt{)}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{g1}}{\tt{ }}{\tt{(}}{\tt{z}}{\tt{)}}{\tt{ }}{\tt{b-equv}}{\tt{ }}{\tt{(}}{\tt{a}}{\tt{ }}{\tt{c}}{\tt{)}}{\tt{)}}{\tt{)}} \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{dec-pass-cell\&} \\  
\=\+{\rm{dec-pass-cell\&}}\,({\it{netlist\/}})\index{dec-pass-cell\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{dec-pass-cell}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{dec-pass-cell*}}\index{dec-pass-cell*}) \\ 
$\wedge$$\;\;\;\;${\rm{id\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{dec-pass-cell}}, {\it{netlist\/}})\index{delete-module})\index{id\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-equv\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{dec-pass-cell}}, {\it{netlist\/}})\index{delete-module})\index{b-equv\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable dec-pass-cell\&; name this event `dec-pass-cell\&-off'.\index{dec-pass-cell\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{dec-pass-cell\$netlist} \\  
\=\+{\sc{dec-pass-cell\$netlist}}\index{dec-pass-cell\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\sc{dec-pass-cell*}}\index{dec-pass-cell*}, {\sc{id\$netlist}}\index{id\$netlist} $\cup$ {\sc{b-equv\$netlist}}\index{b-equv\$netlist})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dec-pass-cell\$value \\ \index{dec-pass-cell\$value}
\=\+{\rm{dec-pass-cell\&}}\,({\it{netlist\/}})\index{dec-pass-cell\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{dec-pass-cell}}, {\rm{list}}\,({\it{c\/}}, {\it{a\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\it{a\/}}, {\rm{f-equv}}\,({\it{a\/}}, {\it{c\/}})\index{f-equv}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tv-dec-pass-name} \\  
\=\+{\rm{tv-dec-pass-name}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-name} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{make-g\/}}$\;\;${\bf then }{\rm{index}}\,({\tt{'}}{\tt{tv-dec-pass-g}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index} \\ 
{\bf else }{\rm{index}}\,({\tt{'}}{\tt{tv-dec-pass-ng}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tv-dec-pass-ng-body} \\  
\=\+{\rm{tv-dec-pass-ng-body}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng-body} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }{\rm{list}}\,({\rm{list}}\,(\=\+{\tt{'}}{\tt{leaf}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{g}}, {\rm{index}}\,({\tt{'}}{\tt{z}}, {\tt{0}})\index{index}), \\ 
{\tt{'}}{\tt{dec-pass-cell}}, \\ 
{\rm{list}}\,({\tt{'}}{\tt{c}}, {\rm{index}}\,({\tt{'}}{\tt{a}}, {\tt{0}})\index{index}))\-) \\ 
{\bf elseif }{\it{make-g\/}} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{left}}, \\ 
{\rm{cons}}\,({\tt{'}}{\tt{gl}}, {\rm{tfirstn}}\,({\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, {\it{tree\/}})\index{tfirstn}), \\ 
{\rm{index}}\,({\tt{'}}{\tt{tv-dec-pass-g}}, {\rm{tree-number}}\,({\rm{car}}\,({\it{tree\/}}))\index{tree-number})\index{index}, \\ 
{\rm{cons}}\,({\tt{'}}{\tt{c}}, {\rm{tfirstn}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, {\it{tree\/}})\index{tfirstn}))\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{carry}}{\tt{ }}{\tt{(}}{\tt{cx}}{\tt{)}}{\tt{ }}{\tt{b-or}}{\tt{ }}{\tt{(}}{\tt{c}}{\tt{ }}{\tt{gl}}{\tt{)}}{\tt{)}}, \\ 
{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{right}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{gr}}, \\ 
{\rm{trestn}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\it{tree\/}})\-\index{trestn})\-, \\ 
{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-dec-pass-g}}, \\ 
{\rm{tree-number}}\,({\rm{cdr}}\,({\it{tree\/}}))\index{tree-number})\-\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{cx}}, \\ 
{\rm{trestn}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\it{tree\/}})\-\index{trestn})\-)\-, \\ 
{\tt{'}}{\tt{(}}{\tt{(}}{\tt{generate}}{\tt{ }}{\tt{(}}{\tt{g}}{\tt{)}}{\tt{ }}{\tt{b-or}}{\tt{ }}{\tt{(}}{\tt{gl}}{\tt{ }}{\tt{gr}}{\tt{)}}{\tt{)}}{\tt{)}})\-)\-)\- \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{left}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{gl}}, \\ 
{\rm{tfirstn}}\,({\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, {\it{tree\/}})\index{tfirstn})\-, \\ 
{\rm{index}}\,({\tt{'}}{\tt{tv-dec-pass-g}}, {\rm{tree-number}}\,({\rm{car}}\,({\it{tree\/}}))\index{tree-number})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{c}}, \\ 
{\rm{tfirstn}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, {\it{tree\/}})\index{tfirstn})\-)\-, \\ 
{\tt{'}}{\tt{(}}{\tt{carry}}{\tt{ }}{\tt{(}}{\tt{cx}}{\tt{)}}{\tt{ }}{\tt{b-or}}{\tt{ }}{\tt{(}}{\tt{c}}{\tt{ }}{\tt{gl}}{\tt{)}}{\tt{)}}, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{right}}, \\ 
{\rm{trestn}}\,({\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-dec-pass-ng}}, \\ 
{\rm{tree-number}}\,({\rm{cdr}}\,({\it{tree\/}}))\index{tree-number})\-\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{cx}}, \\ 
{\rm{trestn}}\,({\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, {\it{tree\/}})\index{trestn})\-)\-)\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-dec-pass-ng-body; name this event `tv-dec-pass-ng-body-off'.\index{tv-dec-pass-ng-body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tv-dec-pass-ng*} \\  
\=\+{\rm{tv-dec-pass-ng*}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{tv-dec-pass-name}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-name}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,({\tt{'}}{\tt{c}}, {\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}), \\ 
{\rm{cons}}\,(\=\+\=\+{\bf if }{\it{make-g\/}} \\ 
{\bf then }{\rm{cons}}\,({\tt{'}}{\tt{g}}, {\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}) \\ 
{\bf else }{\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}$\;${\bf  endif}\-, \\ 
{\rm{cons}}\,({\rm{tv-dec-pass-ng-body}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng-body}, {\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}}))\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tv-dec-pass-ng*\$destructure \\ \index{tv-dec-pass-ng*\$destructure}
\=\+({\rm{car}}\,({\rm{tv-dec-pass-ng*}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng*}) $=$ {\rm{tv-dec-pass-name}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-name}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadr}}\,({\rm{tv-dec-pass-ng*}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng*}) \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\tt{'}}{\tt{c}}, {\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{caddr}}\,({\rm{tv-dec-pass-ng*}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng*}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{make-g\/}}$\;\;${\bf then }{\rm{cons}}\,({\tt{'}}{\tt{g}}, {\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}) \\ 
{\bf else }{\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadddr}}\,({\rm{tv-dec-pass-ng*}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng*}) \\ 
$=$$\;\;\;\;${\rm{tv-dec-pass-ng-body}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng-body})\- \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{tv-dec-pass-ng*}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng*}) $=$ {\bf{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-dec-pass-ng*; name this event `tv-dec-pass-ng*-off'.\index{tv-dec-pass-ng*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable tv-dec-pass-ng*\$destructure; name this event `tv-dec-pass-ng*\$destructure-off'.\index{tv-dec-pass-ng*\$destructure-of!f}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tv-dec-pass-ng\&} \\  
\=\+{\rm{tv-dec-pass-ng\&}}\,({\it{netlist\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng\&} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }\=\+(\=\+{\rm{lookup-module}}\,({\rm{tv-dec-pass-name}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-name}, {\it{netlist\/}})\index{lookup-module} \\ 
$=$$\;\;\;\;${\rm{tv-dec-pass-ng*}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng*})\- \\ 
$\wedge$$\;\;\;\;${\rm{dec-pass-cell\&}}\,({\rm{delete-module}}\,(\=\+{\rm{tv-dec-pass-name}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-name}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{dec-pass-cell\&}\- \\ 
{\bf else }\=\+(\=\+{\rm{lookup-module}}\,({\rm{tv-dec-pass-name}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-name}, {\it{netlist\/}})\index{lookup-module} \\ 
$=$$\;\;\;\;${\rm{tv-dec-pass-ng*}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng*})\- \\ 
$\wedge$$\;\;\;\;${\rm{tv-dec-pass-ng\&}}\,(\=\+{\rm{delete-module}}\,(\=\+{\rm{tv-dec-pass-name}}\,(\=\+{\it{tree\/}}, \\ 
{\it{make-g\/}})\-\index{tv-dec-pass-name}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\rm{car}}\,({\it{tree\/}}), \\ 
{\bf{t}})\-\index{tv-dec-pass-ng\&} \\ 
$\wedge$$\;\;\;\;${\rm{tv-dec-pass-ng\&}}\,(\=\+{\rm{delete-module}}\,(\=\+{\rm{tv-dec-pass-name}}\,(\=\+{\it{tree\/}}, \\ 
{\it{make-g\/}})\-\index{tv-dec-pass-name}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\rm{cdr}}\,({\it{tree\/}}), \\ 
{\it{make-g\/}})\-\index{tv-dec-pass-ng\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-or\&}}\,({\rm{delete-module}}\,(\=\+{\rm{tv-dec-pass-name}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-name}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{b-or\&}\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-dec-pass-ng\&; name this event `tv-dec-pass-ng\&-off'.\index{tv-dec-pass-ng\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tv-dec-pass-ng-induction} \\  
\=\+{\rm{tv-dec-pass-ng-induction}}\,({\it{tree\/}}, {\it{c\/}}, {\it{a\/}}, {\it{make-g\/}}, {\it{name\/}}, {\it{state\/}}, {\it{netlist\/}})\index{tv-dec-pass-ng-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }\=\+{\rm{tv-dec-pass-ng-induction}}\,(\=\+{\rm{car}}\,({\it{tree\/}}), \\ 
{\it{c\/}}, \\ 
{\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\bf{t}}, \\ 
{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-dec-pass-g}}, \\ 
{\rm{tree-number}}\,({\rm{car}}\,({\it{tree\/}}))\index{tree-number})\-\index{index}, \\ 
{\tt{0}}, \\ 
{\rm{delete-module}}\,(\=\+{\rm{tv-dec-pass-name}}\,(\=\+{\it{tree\/}}, \\ 
{\it{make-g\/}})\-\index{tv-dec-pass-name}, \\ 
{\it{netlist\/}})\-\index{delete-module})\-\index{tv-dec-pass-ng-induction} \\ 
$\wedge$$\;\;\;\;${\rm{tv-dec-pass-ng-induction}}\,(\=\+{\rm{cdr}}\,({\it{tree\/}}), \\ 
{\rm{f-or}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{f\$tv-dec-pass-ng}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{car}}\,({\it{tree\/}}), \\ 
{\bf{t}})\-\index{f\$tv-dec-pass-ng}))\-\index{f-or}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\bf{t}}, \\ 
{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-dec-pass-g}}, \\ 
{\rm{tree-number}}\,({\rm{cdr}}\,({\it{tree\/}}))\index{tree-number})\-\index{index}, \\ 
{\tt{0}}, \\ 
{\rm{delete-module}}\,(\=\+{\rm{tv-dec-pass-name}}\,(\=\+{\it{tree\/}}, \\ 
{\it{make-g\/}})\-\index{tv-dec-pass-name}, \\ 
{\it{netlist\/}})\-\index{delete-module})\-\index{tv-dec-pass-ng-induction} \\ 
$\wedge$$\;\;\;\;${\rm{tv-dec-pass-ng-induction}}\,(\=\+{\rm{cdr}}\,({\it{tree\/}}), \\ 
{\rm{f-or}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{f\$tv-dec-pass-ng}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{car}}\,({\it{tree\/}}), \\ 
{\bf{t}})\-\index{f\$tv-dec-pass-ng}))\-\index{f-or}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\bf{f}}, \\ 
{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-dec-pass-ng}}, \\ 
{\rm{tree-number}}\,({\rm{cdr}}\,({\it{tree\/}}))\index{tree-number})\-\index{index}, \\ 
{\tt{0}}, \\ 
{\rm{delete-module}}\,(\=\+{\rm{tv-dec-pass-name}}\,(\=\+{\it{tree\/}}, \\ 
{\it{make-g\/}})\-\index{tv-dec-pass-name}, \\ 
{\it{netlist\/}})\-\index{delete-module})\-\index{tv-dec-pass-ng-induction}\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tv-dec-pass-ng-lemma-crock \\ \index{tv-dec-pass-ng-lemma-crock}
\=\+(\=\+{\rm{tv-dec-pass-ng\&}}\,(\=\+{\rm{delete-module}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{tv-dec-pass-g}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\rm{car}}\,({\it{tree\/}}), \\ 
{\it{make-g\/}})\-\index{tv-dec-pass-ng\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{append}}\,(\=\+{\rm{collect-value}}\,(\=\+{\rm{firstn}}\,(\=\+{\rm{tree-size}}\,({\rm{car}}\,({\it{tree\/}}))\index{tree-size}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\it{n\/}})\index{indices})\-\index{firstn}, \\ 
{\it{bindings\/}})\-\index{collect-value}, \\ 
{\rm{collect-value}}\,(\=\+{\rm{restn}}\,(\=\+{\rm{tree-size}}\,({\rm{car}}\,({\it{tree\/}}))\index{tree-size}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\it{n\/}})\index{indices})\-\index{restn}, \\ 
{\it{bindings\/}})\-\index{collect-value})\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tv-dec-pass-ng\&}}\,(\=\+{\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-dec-pass-ng}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\rm{car}}\,({\it{tree\/}}), \\ 
{\it{make-g\/}})\-\index{tv-dec-pass-ng\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{append}}\,(\=\+{\rm{collect-value}}\,(\=\+{\rm{firstn}}\,(\=\+{\rm{tree-size}}\,({\rm{car}}\,({\it{tree\/}}))\index{tree-size}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\it{n\/}})\index{indices})\-\index{firstn}, \\ 
{\it{bindings\/}})\-\index{collect-value}, \\ 
{\rm{collect-value}}\,(\=\+{\rm{restn}}\,(\=\+{\rm{tree-size}}\,({\rm{car}}\,({\it{tree\/}}))\index{tree-size}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\it{n\/}})\index{indices})\-\index{restn}, \\ 
{\it{bindings\/}})\-\index{collect-value})\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-dec-pass-ng-lemma-crock; name this event `tv-dec-pass-ng-lemma-crock-off'.\index{tv-dec-pass-ng-lemma-crock-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tv-dec-pass-ng\$value \\ \index{tv-dec-pass-ng\$value}
\=\+(\=\+{\rm{tv-dec-pass-ng\&}}\,({\it{netlist\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng\&} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{a\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{make-g\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{name\/}} $=$ {\rm{tv-dec-pass-name}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-name}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\it{name\/}}, {\rm{cons}}\,({\it{c\/}}, {\it{a\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$tv-dec-pass-ng}}\,({\it{c\/}}, {\it{a\/}}, {\it{tree\/}}, {\it{make-g\/}})\index{f\$tv-dec-pass-ng})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-dec-pass-ng\$value; name this event `tv-dec-pass-ng\$value-off'.\index{tv-dec-pass-ng\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tv-dec-pass-ng\$netlist} \\  
\=\+{\rm{tv-dec-pass-ng\$netlist}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng\$netlist} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{list}}\,({\rm{tv-dec-pass-ng*}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng*}, {\sc{dec-pass-cell*}}\index{dec-pass-cell*}) \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{tv-dec-pass-ng*}}\,({\it{tree\/}}, {\it{make-g\/}})\index{tv-dec-pass-ng*}, \\ 
\=\+{\rm{tv-dec-pass-ng\$netlist}}\,({\rm{car}}\,({\it{tree\/}}), {\bf{t}})\index{tv-dec-pass-ng\$netlist} \\ 
$\cup$$\;\;\;\;${\rm{tv-dec-pass-ng\$netlist}}\,({\rm{cdr}}\,({\it{tree\/}}), {\it{make-g\/}})\index{tv-dec-pass-ng\$netlist}\-)\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  check-tv-dec-pass-ng\$netlist \\ \index{check-tv-dec-pass-ng\$netlist}
\=\+{\rm{boolp}}\,({\it{make-g\/}})\index{boolp} \\ 
$\rightarrow$$\;\;\;\;${\rm{tv-dec-pass-ng\&}}\,(\=\+{\rm{tv-dec-pass-ng\$netlist}}\,({\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{ .\ }}{\tt{0}}{\tt{)}}, {\it{make-g\/}})\index{tv-dec-pass-ng\$netlist}, \\ 
{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{ .\ }}{\tt{0}}{\tt{)}}, \\ 
{\it{make-g\/}})\-\index{tv-dec-pass-ng\&}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{dec-pass*} \\  
\=\+{\rm{dec-pass*}}\,({\it{n\/}})\index{dec-pass*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{dec-pass}}, {\it{n\/}})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,({\tt{'}}{\tt{c}}, {\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}), \\ 
{\rm{cons}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\it{n\/}})\index{indices}, \\ 
{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{m0}}{\tt{ }}{\tt{(}}{\tt{cn}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{c}}{\tt{)}}{\tt{)}}, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{m1}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\it{n\/}})\index{indices}, \\ 
{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-dec-pass-ng}}, \\ 
{\rm{tree-number}}\,({\rm{make-tree}}\,({\it{n\/}})\index{make-tree})\index{tree-number})\-\index{index}, \\ 
{\rm{cons}}\,({\tt{'}}{\tt{cn}}, {\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}))\-)\-, \\ 
{\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}})\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dec-pass*\$destructure \\ \index{dec-pass*\$destructure}
\=\+({\rm{car}}\,({\rm{dec-pass*}}\,({\it{n\/}})\index{dec-pass*}) $=$ {\rm{index}}\,({\tt{'}}{\tt{dec-pass}}, {\it{n\/}})\index{index}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadr}}\,({\rm{dec-pass*}}\,({\it{n\/}})\index{dec-pass*}) $=$ {\rm{cons}}\,({\tt{'}}{\tt{c}}, {\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices})) \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\rm{dec-pass*}}\,({\it{n\/}})\index{dec-pass*}) $=$ {\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\it{n\/}})\index{indices}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadddr}}\,({\rm{dec-pass*}}\,({\it{n\/}})\index{dec-pass*}) \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{m0}}{\tt{ }}{\tt{(}}{\tt{cn}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{c}}{\tt{)}}{\tt{)}}, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{m1}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\it{n\/}})\index{indices}, \\ 
{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-dec-pass-ng}}, \\ 
{\rm{tree-number}}\,({\rm{make-tree}}\,({\it{n\/}})\index{make-tree})\index{tree-number})\-\index{index}, \\ 
{\rm{cons}}\,({\tt{'}}{\tt{cn}}, {\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\it{n\/}})\index{indices}))\-)\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{dec-pass*}}\,({\it{n\/}})\index{dec-pass*}) $=$ {\bf{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable dec-pass*; name this event `dec-pass*-off'.\index{dec-pass*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dec-pass*\$destructure; name this event `dec-pass*\$destructure-off'.\index{dec-pass*\$destructure-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{dec-pass\&} \\  
\=\+{\rm{dec-pass\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{dec-pass\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\rm{index}}\,({\tt{'}}{\tt{dec-pass}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{lookup-module} $=$ {\rm{dec-pass*}}\,({\it{n\/}})\index{dec-pass*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{dec-pass}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{tv-dec-pass-ng\&}}\,(\=\+{\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{dec-pass}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{delete-module}, \\ 
{\rm{make-tree}}\,({\it{n\/}})\index{make-tree}, \\ 
{\bf{f}})\-\index{tv-dec-pass-ng\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable dec-pass\&; name this event `dec-pass\&-off'.\index{dec-pass\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{f\$dec-pass} \\  
{\rm{f\$dec-pass}}\,({\it{c\/}}, {\it{a\/}})\index{f\$dec-pass} $=$ {\rm{f\$tv-dec-pass-ng}}\,({\rm{f-not}}\,({\it{c\/}})\index{f-not}, {\it{a\/}}, {\rm{make-tree}}\,({\rm{length}}\,({\it{a\/}})\index{length})\index{make-tree}, {\bf{f}})\index{f\$tv-dec-pass-ng}
\end{tabbing}


\noindent{\sc Event}:   Enable f\$dec-pass; name this event `f\$dec-pass-off'.\index{f\$dec-pass-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  properp-length-f\$dec-pass \\ \index{properp-length-f\$dec-pass}
\=\+{\rm{properp}}\,({\rm{f\$dec-pass}}\,({\it{c\/}}, {\it{v\/}})\index{f\$dec-pass})\index{properp} \\ 
$\wedge$$\;\;\;\;$(({\rm{length}}\,({\it{v\/}})\index{length} $\not=$ {\tt{0}}) $\rightarrow$ ({\rm{length}}\,({\rm{f\$dec-pass}}\,({\it{c\/}}, {\it{v\/}})\index{f\$dec-pass})\index{length} $=$ {\rm{length}}\,({\it{v\/}})\index{length}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f\$dec-pass=dec-or-pass \\ \index{f\$dec-pass=dec-or-pass}
\=\+({\rm{bvp}}\,({\it{v\/}})\index{bvp} $\wedge$ {\rm{boolp}}\,({\it{dec\/}})\index{boolp} $\wedge$ ({\rm{length}}\,({\it{v\/}})\index{length} $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f\$dec-pass}}\,({\it{dec\/}}, {\it{v\/}})\index{f\$dec-pass} $=$ {\rm{if*}}\,({\it{dec\/}}, {\rm{v-dec}}\,({\it{v\/}})\index{v-dec}, {\it{v\/}})\index{if*})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dec-pass\$value \\ \index{dec-pass\$value}
\=\+({\rm{dec-pass\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{dec-pass\&} $\wedge$ ({\it{n\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\it{n\/}}) $\wedge$ {\rm{properp}}\,({\it{a\/}})\index{properp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\rm{index}}\,({\tt{'}}{\tt{dec-pass}}, {\it{n\/}})\index{index}, {\rm{cons}}\,({\it{c\/}}, {\it{a\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$dec-pass}}\,({\it{c\/}}, {\it{a\/}})\index{f\$dec-pass})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable dec-pass\$value; name this event `dec-pass\$value-off'.\index{dec-pass\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{dec-pass\$netlist} \\  
\=\+{\rm{dec-pass\$netlist}}\,({\it{n\/}})\index{dec-pass\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{dec-pass*}}\,({\it{n\/}})\index{dec-pass*}, \\ 
{\sc{b-not\$netlist}}\index{b-not\$netlist} $\cup$ {\rm{tv-dec-pass-ng\$netlist}}\,({\rm{make-tree}}\,({\it{n\/}})\index{make-tree}, {\bf{f}})\index{tv-dec-pass-ng\$netlist})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  check-dec-pass\$netlist \\ \index{check-dec-pass\$netlist}
{\rm{dec-pass\&}}\,({\rm{dec-pass\$netlist}}\,({\tt{7}})\index{dec-pass\$netlist}, {\tt{7}})\index{dec-pass\&}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{reg-body} \\  
\=\+{\rm{reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}}, {\it{te\/}})\index{reg-body} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{g}}, {\it{m\/}})\index{index}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{q}}, {\it{m\/}})\index{index}, {\rm{index}}\,({\tt{'}}{\tt{qb}}, {\it{m\/}})\index{index}), \\ 
{\tt{'}}{\tt{fd1s}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{d}}, {\it{m\/}})\index{index}, {\tt{'}}{\tt{clk}}, {\it{ti\/}}, {\it{te\/}}))\-, \\ 
{\rm{reg-body}}\,($1\;+$ {\it{m\/}}, {\it{n\/}} $-\;1$, {\rm{index}}\,({\tt{'}}{\tt{q}}, {\it{m\/}})\index{index}, {\it{te\/}})\index{reg-body})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable reg-body; name this event `reg-body-off'.\index{reg-body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{reg*} \\  
\=\+{\rm{reg*}}\,({\it{n\/}})\index{reg*} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{reg}}, {\it{n\/}})\index{index}, \\ 
{\rm{cons}}\,({\tt{'}}{\tt{clk}}, {\rm{cons}}\,({\tt{'}}{\tt{te}}, {\rm{cons}}\,({\tt{'}}{\tt{ti}}, {\rm{indices}}\,({\tt{'}}{\tt{d}}, {\tt{0}}, {\it{n\/}})\index{indices}))), \\ 
{\rm{indices}}\,({\tt{'}}{\tt{q}}, {\tt{0}}, {\it{n\/}})\index{indices}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{te-buffer}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{te-buf}}{\tt{)}}, \\ 
{\rm{cons}}\,(\=\+\=\+{\bf if }{\it{n\/}} $<$ {\tt{8}}$\;\;${\bf then }{\tt{'}}{\tt{b-buf}} \\ 
{\bf else }{\tt{'}}{\tt{b-buf-pwr}}$\;${\bf  endif}\-, \\ 
{\tt{'}}{\tt{(}}{\tt{(}}{\tt{te}}{\tt{)}}{\tt{)}})\-)\-)\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{ti-del}}{\tt{ }}{\tt{(}}{\tt{ti-buf}}{\tt{)}}{\tt{ }}{\tt{del4}}{\tt{ }}{\tt{(}}{\tt{ti}}{\tt{)}}{\tt{)}}, \\ 
{\rm{reg-body}}\,({\tt{0}}, {\it{n\/}}, {\tt{'}}{\tt{ti-buf}}, {\tt{'}}{\tt{te-buf}})\index{reg-body})\-)\-, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{g}}, {\tt{0}}, {\it{n\/}})\index{indices})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  reg*\$destructure \\ \index{reg*\$destructure}
\=\+({\rm{car}}\,({\rm{reg*}}\,({\it{n\/}})\index{reg*}) $=$ {\rm{index}}\,({\tt{'}}{\tt{reg}}, {\it{n\/}})\index{index}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadr}}\,({\rm{reg*}}\,({\it{n\/}})\index{reg*}) $=$ {\rm{cons}}\,({\tt{'}}{\tt{clk}}, {\rm{cons}}\,({\tt{'}}{\tt{te}}, {\rm{cons}}\,({\tt{'}}{\tt{ti}}, {\rm{indices}}\,({\tt{'}}{\tt{d}}, {\tt{0}}, {\it{n\/}})\index{indices})))) \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\rm{reg*}}\,({\it{n\/}})\index{reg*}) $=$ {\rm{indices}}\,({\tt{'}}{\tt{q}}, {\tt{0}}, {\it{n\/}})\index{indices}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadddr}}\,({\rm{reg*}}\,({\it{n\/}})\index{reg*}) \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{te-buffer}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{te-buf}}{\tt{)}}, \\ 
{\rm{cons}}\,(\=\+\=\+{\bf if }{\it{n\/}} $<$ {\tt{8}}$\;\;${\bf then }{\tt{'}}{\tt{b-buf}} \\ 
{\bf else }{\tt{'}}{\tt{b-buf-pwr}}$\;${\bf  endif}\-, \\ 
{\tt{'}}{\tt{(}}{\tt{(}}{\tt{te}}{\tt{)}}{\tt{)}})\-)\-)\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{ti-del}}{\tt{ }}{\tt{(}}{\tt{ti-buf}}{\tt{)}}{\tt{ }}{\tt{del4}}{\tt{ }}{\tt{(}}{\tt{ti}}{\tt{)}}{\tt{)}}, \\ 
{\rm{reg-body}}\,({\tt{0}}, {\it{n\/}}, {\tt{'}}{\tt{ti-buf}}, {\tt{'}}{\tt{te-buf}})\index{reg-body})\-)\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{reg*}}\,({\it{n\/}})\index{reg*}) $=$ {\rm{indices}}\,({\tt{'}}{\tt{g}}, {\tt{0}}, {\it{n\/}})\index{indices})\-
\end{tabbing}


\noindent{\sc Event}:   Enable reg*; name this event `reg*-off'.\index{reg*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable reg*\$destructure; name this event `reg*\$destructure-off'.\index{reg*\$destructure-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{reg\&} \\  
\=\+{\rm{reg\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{reg\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\rm{index}}\,({\tt{'}}{\tt{reg}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{lookup-module} $=$ {\rm{reg*}}\,({\it{n\/}})\index{reg*}) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $<$ {\tt{8}} \\ 
{\bf then }{\rm{b-buf\&}}\,({\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{reg}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{delete-module})\index{b-buf\&} \\ 
{\bf else }{\rm{b-buf-pwr\&}}\,({\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{reg}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{delete-module})\index{b-buf-pwr\&}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;${\rm{del4\&}}\,({\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{reg}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{delete-module})\index{del4\&} \\ 
$\wedge$$\;\;\;\;${\rm{fd1s\&}}\,({\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{reg}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{delete-module})\index{fd1s\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable reg\&; name this event `reg\&-off'.\index{reg\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{reg\$netlist} \\  
\=\+{\rm{reg\$netlist}}\,({\it{n\/}})\index{reg\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{reg*}}\,({\it{n\/}})\index{reg*}, \\ 
\=\+\=\+{\bf if }{\it{n\/}} $<$ {\tt{8}}$\;\;${\bf then }{\sc{b-buf\$netlist}}\index{b-buf\$netlist} \\ 
{\bf else }{\sc{b-buf-pwr\$netlist}}\index{b-buf-pwr\$netlist}$\;${\bf  endif}\- \\ 
$\cup$$\;\;\;\;$({\sc{del4\$netlist}}\index{del4\$netlist} $\cup$ {\sc{fd1s\$netlist}}\index{fd1s\$netlist})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  reg-body\$unbound-in-body \\ \index{reg-body\$unbound-in-body}
\=\+{\rm{unbound-in-body}}\,({\tt{'}}{\tt{clk}}, {\rm{reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}}, {\it{te\/}})\index{reg-body})\index{unbound-in-body} \\ 
$\wedge$$\;\;\;\;${\rm{unbound-in-body}}\,({\tt{'}}{\tt{ti}}, {\rm{reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}}, {\it{te\/}})\index{reg-body})\index{unbound-in-body} \\ 
$\wedge$$\;\;\;\;${\rm{unbound-in-body}}\,({\tt{'}}{\tt{ti-del}}, {\rm{reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}}, {\it{te\/}})\index{reg-body})\index{unbound-in-body} \\ 
$\wedge$$\;\;\;\;${\rm{unbound-in-body}}\,({\tt{'}}{\tt{te}}, {\rm{reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}}, {\it{te\/}})\index{reg-body})\index{unbound-in-body} \\ 
$\wedge$$\;\;\;\;${\rm{unbound-in-body}}\,({\tt{'}}{\tt{te-buf}}, {\rm{reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}}, {\it{te\/}})\index{reg-body})\index{unbound-in-body} \\ 
$\wedge$$\;\;\;\;${\rm{unbound-in-body}}\,({\rm{index}}\,({\tt{'}}{\tt{d}}, {\it{l\/}})\index{index}, {\rm{reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}}, {\it{te\/}})\index{reg-body})\index{unbound-in-body} \\ 
$\wedge$$\;\;\;\;$(({\it{l\/}} $<$ {\it{m\/}}) $\rightarrow$ {\rm{unbound-in-body}}\,({\rm{index}}\,({\tt{'}}{\tt{q}}, {\it{l\/}})\index{index}, {\rm{reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}}, {\it{te\/}})\index{reg-body})\index{unbound-in-body})\-
\end{tabbing}


\noindent{\sc Event}:   Enable reg-body\$unbound-in-body; name this event `reg-body\$unbound-in-body-off'.\index{reg-body\$unbound-in-body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  reg-body\$all-unbound-in-body \\ \index{reg-body\$all-unbound-in-body}
{\rm{all-unbound-in-body}}\,({\rm{indices}}\,({\tt{'}}{\tt{d}}, {\it{x\/}}, {\it{y\/}})\index{indices}, {\rm{reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}}, {\it{te\/}})\index{reg-body})\index{all-unbound-in-body}
\end{tabbing}


\noindent{\sc Event}:   Enable reg-body\$all-unbound-in-body; name this event `reg-body\$all-unbound-in-body-off'.\index{reg-body\$all-unbound-in-body-o!ff}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{reg-body-induction} \\  
\=\+{\rm{reg-body-induction}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}}, {\it{te\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{reg-body-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{reg-body-induction}}\,(\=\+$1\;+$ {\it{m\/}}, \\ 
{\it{n\/}} $-\;1$, \\ 
{\rm{index}}\,({\tt{'}}{\tt{q}}, {\it{m\/}})\index{index}, \\ 
{\it{te\/}}, \\ 
{\rm{dual-eval-body-bindings}}\,(\=\+{\tt{1}}, \\ 
{\rm{reg-body}}\,(\=\+{\it{m\/}}, \\ 
{\it{n\/}}, \\ 
{\it{ti\/}}, \\ 
{\it{te\/}})\-\index{reg-body}, \\ 
{\it{bindings\/}}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval-body-bindings}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{reg-body-induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  reg-body\$value \\ \index{reg-body\$value}
\=\+{\rm{fd1s\&}}\,({\it{netlist\/}})\index{fd1s\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{q}}, {\it{m\/}}, {\it{n\/}})\index{indices}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{1}}, \\ 
{\rm{reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}}, {\it{te\/}})\index{reg-body}, \\ 
{\it{bindings\/}}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{v-threefix}}\,({\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{g}}, {\it{m\/}}, {\it{n\/}})\index{indices}, {\it{state-bindings\/}})\index{collect-value})\index{v-threefix})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  reg\$value \\ \index{reg\$value}
\=\+({\rm{reg\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{reg\&} $\wedge$ ({\rm{length}}\,({\it{state\/}})\index{length} $=$ {\it{n\/}}) $\wedge$ {\rm{properp}}\,({\it{state\/}})\index{properp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\rm{index}}\,({\tt{'}}{\tt{reg}}, {\it{n\/}})\index{index}, {\it{inputs\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{v-threefix}}\,({\it{state\/}})\index{v-threefix})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable reg\$value; name this event `reg\$value-off'.\index{reg\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  reg-body\$state \\ \index{reg-body\$state}
\=\+({\rm{fd1s\&}}\,({\it{netlist\/}})\index{fd1s\&} $\wedge$ ($\neg$ {\rm{value}}\,({\it{te\/}}, {\it{bindings\/}})\index{value})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{g}}, {\it{m\/}}, {\it{n\/}})\index{indices}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{3}}, \\ 
{\rm{reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}}, {\it{te\/}})\index{reg-body}, \\ 
{\it{bindings\/}}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{v-threefix}}\,({\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{d}}, {\it{m\/}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value})\index{v-threefix})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  reg\$state \\ \index{reg\$state}
\=\+({\rm{reg\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{reg\&} $\wedge$ ({\rm{length}}\,({\it{d\/}})\index{length} $=$ {\it{n\/}}) $\wedge$ {\rm{properp}}\,({\it{d\/}})\index{properp} $\wedge$ ($\neg$ {\it{te\/}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{reg}}, {\it{n\/}})\index{index}, \\ 
{\rm{cons}}\,({\it{clk\/}}, {\rm{cons}}\,({\it{te\/}}, {\rm{cons}}\,({\it{ti\/}}, {\it{d\/}}))), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{v-threefix}}\,({\it{d\/}})\index{v-threefix})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable reg\$state; name this event `reg\$state-off'.\index{reg\$state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{we-reg-body} \\  
\=\+{\rm{we-reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}})\index{we-reg-body} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{g}}, {\it{m\/}})\index{index}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{q}}, {\it{m\/}})\index{index}, {\rm{index}}\,({\tt{'}}{\tt{qb}}, {\it{m\/}})\index{index}), \\ 
{\tt{'}}{\tt{fd1slp}}, \\ 
{\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{d}}, {\it{m\/}})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{clk}}, \\ 
{\rm{cons}}\,({\tt{'}}{\tt{we-buf}}, {\rm{cons}}\,({\it{ti\/}}, {\tt{'}}{\tt{(}}{\tt{te-buf}}{\tt{)}})))\-)\-)\-, \\ 
{\rm{we-reg-body}}\,($1\;+$ {\it{m\/}}, {\it{n\/}} $-\;1$, {\rm{index}}\,({\tt{'}}{\tt{q}}, {\it{m\/}})\index{index})\index{we-reg-body})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable we-reg-body; name this event `we-reg-body-off'.\index{we-reg-body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{we-reg*} \\  
\=\+{\rm{we-reg*}}\,({\it{n\/}})\index{we-reg*} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{we-reg}}, {\it{n\/}})\index{index}, \\ 
{\rm{cons}}\,({\tt{'}}{\tt{clk}}, {\rm{cons}}\,({\tt{'}}{\tt{we}}, {\rm{cons}}\,({\tt{'}}{\tt{te}}, {\rm{cons}}\,({\tt{'}}{\tt{ti}}, {\rm{indices}}\,({\tt{'}}{\tt{d}}, {\tt{0}}, {\it{n\/}})\index{indices})))), \\ 
{\rm{indices}}\,({\tt{'}}{\tt{q}}, {\tt{0}}, {\it{n\/}})\index{indices}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{we-buffer}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{we-buf}}{\tt{)}}, \\ 
{\rm{cons}}\,(\=\+\=\+{\bf if }{\it{n\/}} $<$ {\tt{8}}$\;\;${\bf then }{\tt{'}}{\tt{b-buf}} \\ 
{\bf else }{\tt{'}}{\tt{b-buf-pwr}}$\;${\bf  endif}\-, \\ 
{\tt{'}}{\tt{(}}{\tt{(}}{\tt{we}}{\tt{)}}{\tt{)}})\-)\-)\-, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{te-buffer}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{te-buf}}{\tt{)}}, \\ 
{\rm{cons}}\,(\=\+\=\+{\bf if }{\it{n\/}} $<$ {\tt{8}}$\;\;${\bf then }{\tt{'}}{\tt{b-buf}} \\ 
{\bf else }{\tt{'}}{\tt{b-buf-pwr}}$\;${\bf  endif}\-, \\ 
{\tt{'}}{\tt{(}}{\tt{(}}{\tt{te}}{\tt{)}}{\tt{)}})\-)\-)\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{ti-del}}{\tt{ }}{\tt{(}}{\tt{ti-buf}}{\tt{)}}{\tt{ }}{\tt{del4}}{\tt{ }}{\tt{(}}{\tt{ti}}{\tt{)}}{\tt{)}}, \\ 
{\rm{we-reg-body}}\,({\tt{0}}, {\it{n\/}}, {\tt{'}}{\tt{ti-buf}})\index{we-reg-body})\-)\-)\-, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{g}}, {\tt{0}}, {\it{n\/}})\index{indices})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  we-reg*\$destructure \\ \index{we-reg*\$destructure}
\=\+({\rm{car}}\,({\rm{we-reg*}}\,({\it{n\/}})\index{we-reg*}) $=$ {\rm{index}}\,({\tt{'}}{\tt{we-reg}}, {\it{n\/}})\index{index}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadr}}\,({\rm{we-reg*}}\,({\it{n\/}})\index{we-reg*}) \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\tt{'}}{\tt{clk}}, {\rm{cons}}\,({\tt{'}}{\tt{we}}, {\rm{cons}}\,({\tt{'}}{\tt{te}}, {\rm{cons}}\,({\tt{'}}{\tt{ti}}, {\rm{indices}}\,({\tt{'}}{\tt{d}}, {\tt{0}}, {\it{n\/}})\index{indices})))))\- \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\rm{we-reg*}}\,({\it{n\/}})\index{we-reg*}) $=$ {\rm{indices}}\,({\tt{'}}{\tt{q}}, {\tt{0}}, {\it{n\/}})\index{indices}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadddr}}\,({\rm{we-reg*}}\,({\it{n\/}})\index{we-reg*}) \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{we-buffer}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{we-buf}}{\tt{)}}, \\ 
{\rm{cons}}\,(\=\+\=\+{\bf if }{\it{n\/}} $<$ {\tt{8}}$\;\;${\bf then }{\tt{'}}{\tt{b-buf}} \\ 
{\bf else }{\tt{'}}{\tt{b-buf-pwr}}$\;${\bf  endif}\-, \\ 
{\tt{'}}{\tt{(}}{\tt{(}}{\tt{we}}{\tt{)}}{\tt{)}})\-)\-)\-, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{te-buffer}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{te-buf}}{\tt{)}}, \\ 
{\rm{cons}}\,(\=\+\=\+{\bf if }{\it{n\/}} $<$ {\tt{8}}$\;\;${\bf then }{\tt{'}}{\tt{b-buf}} \\ 
{\bf else }{\tt{'}}{\tt{b-buf-pwr}}$\;${\bf  endif}\-, \\ 
{\tt{'}}{\tt{(}}{\tt{(}}{\tt{te}}{\tt{)}}{\tt{)}})\-)\-)\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{ti-del}}{\tt{ }}{\tt{(}}{\tt{ti-buf}}{\tt{)}}{\tt{ }}{\tt{del4}}{\tt{ }}{\tt{(}}{\tt{ti}}{\tt{)}}{\tt{)}}, \\ 
{\rm{we-reg-body}}\,({\tt{0}}, {\it{n\/}}, {\tt{'}}{\tt{ti-buf}})\index{we-reg-body})\-)\-)\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{we-reg*}}\,({\it{n\/}})\index{we-reg*}) $=$ {\rm{indices}}\,({\tt{'}}{\tt{g}}, {\tt{0}}, {\it{n\/}})\index{indices})\-
\end{tabbing}


\noindent{\sc Event}:   Enable we-reg*; name this event `we-reg*-off'.\index{we-reg*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable we-reg*\$destructure; name this event `we-reg*\$destructure-off'.\index{we-reg*\$destructure-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{we-reg\&} \\  
\=\+{\rm{we-reg\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{we-reg\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\rm{index}}\,({\tt{'}}{\tt{we-reg}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{lookup-module} $=$ {\rm{we-reg*}}\,({\it{n\/}})\index{we-reg*}) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $<$ {\tt{8}} \\ 
{\bf then }{\rm{b-buf\&}}\,({\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{we-reg}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{delete-module})\index{b-buf\&} \\ 
{\bf else }{\rm{b-buf-pwr\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{we-reg}}, {\it{n\/}})\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{b-buf-pwr\&}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;${\rm{del4\&}}\,({\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{we-reg}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{delete-module})\index{del4\&} \\ 
$\wedge$$\;\;\;\;${\rm{fd1slp\&}}\,({\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{we-reg}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{delete-module})\index{fd1slp\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable we-reg\&; name this event `we-reg\&-off'.\index{we-reg\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{we-reg\$netlist} \\  
\=\+{\rm{we-reg\$netlist}}\,({\it{n\/}})\index{we-reg\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{we-reg*}}\,({\it{n\/}})\index{we-reg*}, \\ 
\=\+\=\+{\bf if }{\it{n\/}} $<$ {\tt{8}}$\;\;${\bf then }{\sc{b-buf\$netlist}}\index{b-buf\$netlist} \\ 
{\bf else }{\sc{b-buf-pwr\$netlist}}\index{b-buf-pwr\$netlist}$\;${\bf  endif}\- \\ 
$\cup$$\;\;\;\;$({\sc{del4\$netlist}}\index{del4\$netlist} $\cup$ {\sc{fd1slp\$netlist}}\index{fd1slp\$netlist})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  we-reg-body\$unbound-in-body \\ \index{we-reg-body\$unbound-in-body}
\=\+{\rm{unbound-in-body}}\,({\tt{'}}{\tt{clk}}, {\rm{we-reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}})\index{we-reg-body})\index{unbound-in-body} \\ 
$\wedge$$\;\;\;\;${\rm{unbound-in-body}}\,({\tt{'}}{\tt{we}}, {\rm{we-reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}})\index{we-reg-body})\index{unbound-in-body} \\ 
$\wedge$$\;\;\;\;${\rm{unbound-in-body}}\,({\tt{'}}{\tt{we-buf}}, {\rm{we-reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}})\index{we-reg-body})\index{unbound-in-body} \\ 
$\wedge$$\;\;\;\;${\rm{unbound-in-body}}\,({\tt{'}}{\tt{ti}}, {\rm{we-reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}})\index{we-reg-body})\index{unbound-in-body} \\ 
$\wedge$$\;\;\;\;${\rm{unbound-in-body}}\,({\tt{'}}{\tt{ti-buf}}, {\rm{we-reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}})\index{we-reg-body})\index{unbound-in-body} \\ 
$\wedge$$\;\;\;\;${\rm{unbound-in-body}}\,({\tt{'}}{\tt{te}}, {\rm{we-reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}})\index{we-reg-body})\index{unbound-in-body} \\ 
$\wedge$$\;\;\;\;${\rm{unbound-in-body}}\,({\tt{'}}{\tt{te-buf}}, {\rm{we-reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}})\index{we-reg-body})\index{unbound-in-body} \\ 
$\wedge$$\;\;\;\;${\rm{unbound-in-body}}\,({\rm{index}}\,({\tt{'}}{\tt{d}}, {\it{l\/}})\index{index}, {\rm{we-reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}})\index{we-reg-body})\index{unbound-in-body} \\ 
$\wedge$$\;\;\;\;$(({\it{l\/}} $<$ {\it{m\/}}) $\rightarrow$ {\rm{unbound-in-body}}\,({\rm{index}}\,({\tt{'}}{\tt{q}}, {\it{l\/}})\index{index}, {\rm{we-reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}})\index{we-reg-body})\index{unbound-in-body})\-
\end{tabbing}


\noindent{\sc Event}:   Enable we-reg-body\$unbound-in-body; name this event `we-reg-body\$unbound-in-body-off'.\index{we-reg-body\$unbound-in-body-of!f}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  we-reg-body\$all-unbound-in-body \\ \index{we-reg-body\$all-unbound-in-bod!y}
{\rm{all-unbound-in-body}}\,({\rm{indices}}\,({\tt{'}}{\tt{d}}, {\it{x\/}}, {\it{y\/}})\index{indices}, {\rm{we-reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}})\index{we-reg-body})\index{all-unbound-in-body}
\end{tabbing}


\noindent{\sc Event}:   Enable we-reg-body\$all-unbound-in-body; name this event `we-reg-body\$all-unbound-in-body-off'.\index{we-reg-body\$all-unbound-in-bod!y-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{we-reg-body-induction} \\  
\=\+{\rm{we-reg-body-induction}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{we-reg-body-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{we-reg-body-induction}}\,(\=\+$1\;+$ {\it{m\/}}, \\ 
{\it{n\/}} $-\;1$, \\ 
{\rm{index}}\,({\tt{'}}{\tt{q}}, {\it{m\/}})\index{index}, \\ 
{\rm{dual-eval-body-bindings}}\,(\=\+{\tt{1}}, \\ 
{\rm{we-reg-body}}\,(\=\+{\it{m\/}}, \\ 
{\it{n\/}}, \\ 
{\it{ti\/}})\-\index{we-reg-body}, \\ 
{\it{bindings\/}}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval-body-bindings}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{we-reg-body-induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  we-reg-body\$value \\ \index{we-reg-body\$value}
\=\+{\rm{fd1slp\&}}\,({\it{netlist\/}})\index{fd1slp\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{q}}, {\it{m\/}}, {\it{n\/}})\index{indices}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{1}}, \\ 
{\rm{we-reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}})\index{we-reg-body}, \\ 
{\it{bindings\/}}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{v-threefix}}\,({\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{g}}, {\it{m\/}}, {\it{n\/}})\index{indices}, {\it{state-bindings\/}})\index{collect-value})\index{v-threefix})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable we-reg-body\$value; name this event `we-reg-body\$value-off'.\index{we-reg-body\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  we-reg\$value \\ \index{we-reg\$value}
\=\+({\rm{we-reg\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{we-reg\&} $\wedge$ ({\rm{length}}\,({\it{state\/}})\index{length} $=$ {\it{n\/}}) $\wedge$ {\rm{properp}}\,({\it{state\/}})\index{properp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\rm{index}}\,({\tt{'}}{\tt{we-reg}}, {\it{n\/}})\index{index}, {\it{inputs\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{v-threefix}}\,({\it{state\/}})\index{v-threefix})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable we-reg\$value; name this event `we-reg\$value-off'.\index{we-reg\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  we-reg-body\$state \\ \index{we-reg-body\$state}
\=\+({\rm{fd1slp\&}}\,({\it{netlist\/}})\index{fd1slp\&} $\wedge$ ($\neg$ {\rm{value}}\,({\tt{'}}{\tt{te-buf}}, {\it{bindings\/}})\index{value})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{g}}, {\it{m\/}}, {\it{n\/}})\index{indices}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{3}}, \\ 
{\rm{we-reg-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{ti\/}})\index{we-reg-body}, \\ 
{\it{bindings\/}}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{fv-if}}\,(\=\+{\rm{value}}\,({\tt{'}}{\tt{we-buf}}, {\it{bindings\/}})\index{value}, \\ 
{\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{d}}, {\it{m\/}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value}, \\ 
{\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{g}}, {\it{m\/}}, {\it{n\/}})\index{indices}, {\it{state-bindings\/}})\index{collect-value})\-\index{fv-if})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable we-reg-body\$state; name this event `we-reg-body\$state-off'.\index{we-reg-body\$state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  we-reg\$state \\ \index{we-reg\$state}
\=\+(\=\+{\rm{we-reg\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{we-reg\&} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{d\/}})\index{length} $=$ {\it{n\/}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{d\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{state\/}})\index{length} $=$ {\it{n\/}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{state\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\it{te\/}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{we-reg}}, {\it{n\/}})\index{index}, \\ 
{\rm{cons}}\,({\it{clk\/}}, {\rm{cons}}\,({\it{we\/}}, {\rm{cons}}\,({\it{te\/}}, {\rm{cons}}\,({\it{ti\/}}, {\it{d\/}})))), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{fv-if}}\,({\it{we\/}}, {\it{d\/}}, {\it{state\/}})\index{fv-if})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable we-reg\$state; name this event `we-reg\$state-off'.\index{we-reg\$state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{cvzbv} \\  
\=\+{\rm{cvzbv}}\,({\it{carry\/}}, {\it{overflow\/}}, {\it{vector\/}})\index{cvzbv} \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\it{carry\/}}, {\rm{cons}}\,({\it{overflow\/}}, {\rm{cons}}\,({\rm{v-zerop}}\,({\it{vector\/}})\index{v-zerop}, {\it{vector\/}})))\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{c}$\;\;$
{\rm{c}}\,({\it{cvzbv\/}})\index{c} $=$ {\rm{car}}\,({\it{cvzbv\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v}$\;\;$
{\rm{v}}\,({\it{cvzbv\/}})\index{v} $=$ {\rm{cadr}}\,({\it{cvzbv\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{bv}$\;\;$
{\rm{bv}}\,({\it{cvzbv\/}})\index{bv} $=$ {\rm{cdddr}}\,({\it{cvzbv\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{n}$\;\;$
{\rm{n}}\,({\it{cvzbv\/}})\index{n} $=$ {\rm{v-negp}}\,({\rm{bv}}\,({\it{cvzbv\/}})\index{bv})\index{v-negp}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{zb}$\;\;$
{\rm{zb}}\,({\it{cvzbv\/}})\index{zb} $=$ {\rm{caddr}}\,({\it{cvzbv\/}})
\end{tabbing}


\noindent{\sc Event}:   Enable c; name this event `c-off'.\index{c-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v; name this event `v-off'.\index{v-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable n; name this event `n-off'.\index{n-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable zb; name this event `zb-off'.\index{zb-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable bv; name this event `bv-off'.\index{bv-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  boolp-n \\ \index{boolp-n}
{\rm{bvp}}\,({\rm{bv}}\,({\it{v\/}})\index{bv})\index{bvp} $\rightarrow$ {\rm{boolp}}\,({\rm{n}}\,({\it{v\/}})\index{n})\index{boolp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  boolp-bvp-cvzbv \\ \index{boolp-bvp-cvzbv}
\=\+({\rm{boolp}}\,({\rm{c}}\,({\rm{cvzbv}}\,({\it{c\/}}, {\it{v\/}}, {\it{bv\/}})\index{cvzbv})\index{c})\index{boolp} $=$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\wedge$$\;\;\;\;$({\rm{boolp}}\,({\rm{v}}\,({\rm{cvzbv}}\,({\it{c\/}}, {\it{v\/}}, {\it{bv\/}})\index{cvzbv})\index{v})\index{boolp} $=$ {\rm{boolp}}\,({\it{v\/}})\index{boolp}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{zb}}\,({\rm{cvzbv}}\,({\it{c\/}}, {\it{v\/}}, {\it{bv\/}})\index{cvzbv})\index{zb})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\rm{bvp}}\,({\rm{bv}}\,({\rm{cvzbv}}\,({\it{c\/}}, {\it{v\/}}, {\it{bv\/}})\index{cvzbv})\index{bv})\index{bvp} $=$ {\rm{bvp}}\,({\it{bv\/}})\index{bvp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-cvzbv \\ \index{bvp-cvzbv}
\=\+({\rm{boolp}}\,({\rm{c}}\,({\it{cvzbv\/}})\index{c})\index{boolp} $\wedge$ {\rm{boolp}}\,({\rm{v}}\,({\it{cvzbv\/}})\index{v})\index{boolp} $\wedge$ {\rm{boolp}}\,({\rm{zb}}\,({\it{cvzbv\/}})\index{zb})\index{boolp} $\wedge$ {\rm{bvp}}\,({\rm{bv}}\,({\it{cvzbv\/}})\index{bv})\index{bvp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{bvp}}\,({\it{cvzbv\/}})\index{bvp}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cvzbv-v-ror} \\  
\=\+{\rm{cvzbv-v-ror}}\,({\it{c\/}}, {\it{a\/}})\index{cvzbv-v-ror} \\ 
$=$$\;\;\;\;${\rm{cvzbv}}\,(\=\+\=\+{\bf if }{\it{a\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{c\/}} \\ 
{\bf else }{\rm{nth}}\,({\tt{0}}, {\it{a\/}})\index{nth}$\;${\bf  endif}\-, \\ 
{\bf{f}}, \\ 
{\rm{v-ror}}\,({\it{a\/}}, {\it{c\/}})\index{v-ror})\-\index{cvzbv}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cvzbv-v-adder} \\  
\=\+{\rm{cvzbv-v-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{cvzbv-v-adder} \\ 
$=$$\;\;\;\;${\rm{cvzbv}}\,(\=\+{\rm{v-adder-carry-out}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder-carry-out}, \\ 
{\rm{v-adder-overflowp}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder-overflowp}, \\ 
{\rm{v-adder-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder-output})\-\index{cvzbv}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cvzbv-v-lsl}$\;\;$
{\rm{cvzbv-v-lsl}}\,({\it{a\/}})\index{cvzbv-v-lsl} $=$ {\rm{cvzbv-v-adder}}\,({\bf{f}}, {\it{a\/}}, {\it{a\/}})\index{cvzbv-v-adder}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cvzbv-v-subtracter} \\  
\=\+{\rm{cvzbv-v-subtracter}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{cvzbv-v-subtracter} \\ 
$=$$\;\;\;\;${\rm{cvzbv}}\,(\=\+{\rm{v-subtracter-carry-out}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-subtracter-carry-out}, \\ 
{\rm{v-subtracter-overflowp}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-subtracter-overflowp}, \\ 
{\rm{v-subtracter-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-subtracter-output})\-\index{cvzbv}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cvzbv-inc} \\  
{\rm{cvzbv-inc}}\,({\it{a\/}})\index{cvzbv-inc} $=$ {\rm{cvzbv-v-adder}}\,({\bf{t}}, {\it{a\/}}, {\rm{nat-to-v}}\,({\tt{0}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{nat-to-v})\index{cvzbv-v-adder}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cvzbv-neg} \\  
{\rm{cvzbv-neg}}\,({\it{a\/}})\index{cvzbv-neg} $=$ {\rm{cvzbv-v-subtracter}}\,({\bf{f}}, {\it{a\/}}, {\rm{nat-to-v}}\,({\tt{0}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{nat-to-v})\index{cvzbv-v-subtracter}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cvzbv-dec} \\  
{\rm{cvzbv-dec}}\,({\it{a\/}})\index{cvzbv-dec} $=$ {\rm{cvzbv-v-subtracter}}\,({\bf{t}}, {\rm{nat-to-v}}\,({\tt{0}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{nat-to-v}, {\it{a\/}})\index{cvzbv-v-subtracter}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cvzbv-v-not}$\;\;$
{\rm{cvzbv-v-not}}\,({\it{a\/}})\index{cvzbv-v-not} $=$ {\rm{cvzbv}}\,({\bf{f}}, {\bf{f}}, {\rm{v-not}}\,({\it{a\/}})\index{v-not})\index{cvzbv}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cvzbv-v-asr} \\  
\=\+{\rm{cvzbv-v-asr}}\,({\it{a\/}})\index{cvzbv-v-asr} \\ 
$=$$\;\;\;\;${\rm{cvzbv}}\,(\=\+\=\+{\bf if }{\rm{listp}}\,({\it{a\/}})$\;\;${\bf then }{\rm{nth}}\,({\tt{0}}, {\it{a\/}})\index{nth} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-, \\ 
{\bf{f}}, \\ 
{\rm{v-asr}}\,({\it{a\/}})\index{v-asr})\-\index{cvzbv}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cvzbv-v-lsr} \\  
\=\+{\rm{cvzbv-v-lsr}}\,({\it{a\/}})\index{cvzbv-v-lsr} \\ 
$=$$\;\;\;\;${\rm{cvzbv}}\,(\=\+\=\+{\bf if }{\rm{listp}}\,({\it{a\/}})$\;\;${\bf then }{\rm{nth}}\,({\tt{0}}, {\it{a\/}})\index{nth} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-, \\ 
{\bf{f}}, \\ 
{\rm{v-lsr}}\,({\it{a\/}})\index{v-lsr})\-\index{cvzbv}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu} \\  
\=\+{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\rm{cvzbv}}\,({\bf{f}}, {\bf{f}}, {\rm{v-buf}}\,({\it{a\/}})\index{v-buf})\index{cvzbv} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\rm{cvzbv-inc}}\,({\it{a\/}})\index{cvzbv-inc} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\rm{cvzbv-v-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{cvzbv-v-adder} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\rm{cvzbv-v-adder}}\,({\bf{f}}, {\it{a\/}}, {\it{b\/}})\index{cvzbv-v-adder} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }{\rm{cvzbv-neg}}\,({\it{a\/}})\index{cvzbv-neg} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }{\rm{cvzbv-dec}}\,({\it{a\/}})\index{cvzbv-dec} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }{\rm{cvzbv-v-subtracter}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{cvzbv-v-subtracter} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }{\rm{cvzbv-v-subtracter}}\,({\bf{f}}, {\it{a\/}}, {\it{b\/}})\index{cvzbv-v-subtracter} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}})$\;\;${\bf then }{\rm{cvzbv-v-ror}}\,({\it{c\/}}, {\it{a\/}})\index{cvzbv-v-ror} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}})$\;\;${\bf then }{\rm{cvzbv-v-asr}}\,({\it{a\/}})\index{cvzbv-v-asr} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}})$\;\;${\bf then }{\rm{cvzbv-v-lsr}}\,({\it{a\/}})\index{cvzbv-v-lsr} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}})$\;\;${\bf then }{\rm{cvzbv}}\,({\bf{f}}, {\bf{f}}, {\rm{v-xor}}\,({\it{a\/}}, {\it{b\/}})\index{v-xor})\index{cvzbv} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}})$\;\;${\bf then }{\rm{cvzbv}}\,({\bf{f}}, {\bf{f}}, {\rm{v-or}}\,({\it{a\/}}, {\it{b\/}})\index{v-or})\index{cvzbv} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}})$\;\;${\bf then }{\rm{cvzbv}}\,({\bf{f}}, {\bf{f}}, {\rm{v-and}}\,({\it{a\/}}, {\it{b\/}})\index{v-and})\index{cvzbv} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}})$\;\;${\bf then }{\rm{cvzbv-v-not}}\,({\it{a\/}})\index{cvzbv-v-not} \\ 
{\bf else }{\rm{cvzbv}}\,({\bf{f}}, {\bf{f}}, {\rm{v-buf}}\,({\it{a\/}})\index{v-buf})\index{cvzbv}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-alu; name this event `v-alu-off'.\index{v-alu-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  boolp-c-v-alu \\ \index{boolp-c-v-alu}
({\rm{boolp}}\,({\it{c\/}})\index{boolp} $\wedge$ {\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}})) $\rightarrow$ {\rm{boolp}}\,({\rm{c}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu})\index{c})\index{boolp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  boolp-v-v-alu \\ \index{boolp-v-v-alu}
({\rm{boolp}}\,({\it{c\/}})\index{boolp} $\wedge$ {\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}})) $\rightarrow$ {\rm{boolp}}\,({\rm{v}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu})\index{v})\index{boolp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  boolp-zb-v-alu \\ \index{boolp-zb-v-alu}
{\rm{boolp}}\,({\rm{zb}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu})\index{zb})\index{boolp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-bv-v-alu \\ \index{bvp-bv-v-alu}
{\rm{bvp}}\,({\it{a\/}})\index{bvp} $\rightarrow$ {\rm{bvp}}\,({\rm{bv}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu})\index{bv})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-v-alu \\ \index{bvp-v-alu}
({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}})) $\rightarrow$ {\rm{bvp}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-cvzbv-subtracter \\ \index{length-cvzbv-subtracter}
{\rm{length}}\,({\rm{cvzbv-v-subtracter}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{cvzbv-v-subtracter})\index{length} $=$ ($1\;+$ ($1\;+$ ($1\;+$ {\rm{length}}\,({\it{a\/}})\index{length})))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-cvzbv-adder \\ \index{length-cvzbv-adder}
{\rm{length}}\,({\rm{cvzbv-v-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{cvzbv-v-adder})\index{length} $=$ ($1\;+$ ($1\;+$ ($1\;+$ {\rm{length}}\,({\it{a\/}})\index{length})))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-v-alu \\ \index{length-v-alu}
{\rm{length}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu})\index{length} $=$ ($1\;+$ ($1\;+$ ($1\;+$ {\rm{length}}\,({\it{a\/}})\index{length})))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-length-bv \\ \index{bvp-length-bv}
\=\+({\rm{length}}\,({\rm{bv}}\,({\it{x\/}})\index{bv})\index{length} $=$ ({\rm{length}}\,({\it{x\/}})\index{length} $-$ {\tt{3}})) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{bvp}}\,({\it{x\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{x\/}})\index{length} $<$ {\tt{3}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{bvp}}\,({\rm{bv}}\,({\it{x\/}})\index{bv})\index{bvp})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{unary-op-code-p} \\  
\=\+{\rm{unary-op-code-p}}\,({\it{op-code\/}})\index{unary-op-code-p} \\ 
$=$$\;\;\;\;$(\=\+({\it{op-code\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}})) \\ 
$\vee$$\;\;\;\;$({\it{op-code\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}})) \\ 
$\vee$$\;\;\;\;$({\it{op-code\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}})) \\ 
$\vee$$\;\;\;\;$({\it{op-code\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}})) \\ 
$\vee$$\;\;\;\;$({\it{op-code\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}})) \\ 
$\vee$$\;\;\;\;$({\it{op-code\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}})) \\ 
$\vee$$\;\;\;\;$({\it{op-code\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}})) \\ 
$\vee$$\;\;\;\;$({\it{op-code\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}})) \\ 
$\vee$$\;\;\;\;$({\it{op-code\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}})))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable unary-op-code-p; name this event `unary-op-code-p-off'.\index{unary-op-code-p-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-alu-1}$\;\;$
{\rm{v-alu-1}}\,({\it{c\/}}, {\it{a\/}}, {\it{op-code\/}})\index{v-alu-1} $=$ {\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{a\/}}, {\it{op-code\/}})\index{v-alu}
\end{tabbing}


\noindent{\sc Event}:   Enable v-alu-1; name this event `v-alu-1-off'.\index{v-alu-1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  bvp-v-alu-1 \\ \index{bvp-v-alu-1}
({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}})) $\rightarrow$ {\rm{bvp}}\,({\rm{v-alu-1}}\,({\it{c\/}}, {\it{a\/}}, {\it{op\/}})\index{v-alu-1})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-v-alu-1 \\ \index{length-v-alu-1}
{\rm{length}}\,({\rm{v-alu-1}}\,({\it{c\/}}, {\it{a\/}}, {\it{op\/}})\index{v-alu-1})\index{length} $=$ ($1\;+$ ($1\;+$ ($1\;+$ {\rm{length}}\,({\it{a\/}})\index{length})))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  unary-op-code-p-$>$v-alu=v-alu-1 \\ \index{unary-op-code-p-$>$v-alu=v-alu-!1}
\=\+{\rm{unary-op-code-p}}\,({\it{op-code\/}})\index{unary-op-code-p} \\ 
$\rightarrow$$\;\;\;\;$({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op-code\/}})\index{v-alu} $=$ {\rm{v-alu-1}}\,({\it{c\/}}, {\it{a\/}}, {\it{op-code\/}})\index{v-alu-1})\-
\end{tabbing}


\noindent{\sc Event}:   Enable unary-op-code-p-$>$v-alu=v-alu-1; name this event `unary-op-code-p-$>$v-alu=v-alu-1-off'.\index{unary-op-code-p-$>$v-alu=v-alu-!1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{alu-inc-op}$\;\;$
{\sc{alu-inc-op}}\index{alu-inc-op} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}})
\end{tabbing}


\noindent{\sc Event}:   Enable alu-inc-op; name this event `alu-inc-op-off'.\index{alu-inc-op-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*alu-inc-op; name this event `g*1*alu-inc-op-off'.\index{g*1*alu-inc-op-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  bvp-length-alu-inc-op \\ \index{bvp-length-alu-inc-op}
({\rm{length}}\,({\sc{alu-inc-op}}\index{alu-inc-op})\index{length} $=$ {\tt{4}}) $\wedge$ {\rm{bvp}}\,({\sc{alu-inc-op}}\index{alu-inc-op})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{alu-dec-op}$\;\;$
{\sc{alu-dec-op}}\index{alu-dec-op} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}})
\end{tabbing}


\noindent{\sc Event}:   Enable alu-dec-op; name this event `alu-dec-op-off'.\index{alu-dec-op-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*alu-dec-op; name this event `g*1*alu-dec-op-off'.\index{g*1*alu-dec-op-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  bvp-length-alu-dec-op \\ \index{bvp-length-alu-dec-op}
({\rm{length}}\,({\sc{alu-dec-op}}\index{alu-dec-op})\index{length} $=$ {\tt{4}}) $\wedge$ {\rm{bvp}}\,({\sc{alu-dec-op}}\index{alu-dec-op})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bv-v-alu-alu-inc-alu-dec \\ \index{bv-v-alu-alu-inc-alu-dec}
\=\+({\rm{bv}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\sc{alu-inc-op}}\index{alu-inc-op})\index{v-alu})\index{bv} $=$ {\rm{v-inc}}\,({\it{a\/}})\index{v-inc}) \\ 
$\wedge$$\;\;\;\;$({\rm{bv}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\sc{alu-dec-op}}\index{alu-dec-op})\index{v-alu})\index{bv} $=$ {\rm{v-dec}}\,({\it{a\/}})\index{v-dec})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{decode-mode} \\  
{\rm{decode-mode}}\,({\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{decode-mode} $=$ {\rm{b-nor}}\,({\rm{b-nor3}}\,({\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}})\index{b-nor3}, {\it{op3\/}})\index{b-nor}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$decode-mode} \\  
{\rm{f\$decode-mode}}\,({\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$decode-mode} $=$ {\rm{f-nor}}\,({\rm{f-nor3}}\,({\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}})\index{f-nor3}, {\it{op3\/}})\index{f-nor}
\end{tabbing}


\noindent{\sc Event}:   Enable f\$decode-mode; name this event `f\$decode-mode-off'.\index{f\$decode-mode-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{decode-mode*} \\  
\=\+{\sc{decode-mode*}}\index{decode-mode*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{decode-mode}} \\ 
{\tt{(}}{\tt{op0}}{\tt{ }}{\tt{op1}}{\tt{ }}{\tt{op2}}{\tt{ }}{\tt{op3}}{\tt{)}} \\ 
{\tt{(}}{\tt{w-1}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{g-0}}{\tt{ }}{\tt{(}}{\tt{w-0}}{\tt{)}}{\tt{ }}{\tt{b-nor3}}{\tt{ }}{\tt{(}}{\tt{op0}}{\tt{ }}{\tt{op1}}{\tt{ }}{\tt{op2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-1}}{\tt{ }}{\tt{(}}{\tt{w-1}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{w-0}}{\tt{ }}{\tt{op3}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{decode-mode\&} \\  
\=\+{\rm{decode-mode\&}}\,({\it{netlist\/}})\index{decode-mode\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{decode-mode}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{decode-mode*}}\index{decode-mode*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-nor3\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-mode}}, {\it{netlist\/}})\index{delete-module})\index{b-nor3\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nor\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-mode}}, {\it{netlist\/}})\index{delete-module})\index{b-nor\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable decode-mode\&; name this event `decode-mode\&-off'.\index{decode-mode\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{decode-mode\$netlist} \\  
{\sc{decode-mode\$netlist}}\index{decode-mode\$netlist} $=$ {\rm{cons}}\,({\sc{decode-mode*}}\index{decode-mode*}, {\sc{b-nor3\$netlist}}\index{b-nor3\$netlist} $\cup$ {\sc{b-nor\$netlist}}\index{b-nor\$netlist})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  decode-mode\$value \\ \index{decode-mode\$value}
\=\+{\rm{decode-mode\&}}\,({\it{netlist\/}})\index{decode-mode\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{decode-mode}}, {\rm{list}}\,({\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f\$decode-mode}}\,({\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$decode-mode}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable decode-mode\$value; name this event `decode-mode\$value-off'.\index{decode-mode\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$decode-mode=decode-mode \\ \index{f\$decode-mode=decode-mode}
\=\+({\rm{boolp}}\,({\it{op0\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{op1\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{op2\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{op3\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f\$decode-mode}}\,({\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$decode-mode} $=$ {\rm{decode-mode}}\,({\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{decode-mode})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  decode-mode\$value-zero \\ \index{decode-mode\$value-zero}
\=\+{\rm{decode-mode\&}}\,({\it{netlist\/}})\index{decode-mode\&} \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{decode-mode}}, {\sc{alu-inc-op}}\index{alu-inc-op}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\bf{t}}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable decode-mode\$value-zero; name this event `decode-mode\$value-zero-off'.\index{decode-mode\$value-zero-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{decode-prop} \\  
\=\+{\rm{decode-prop}}\,({\it{zero\/}}, {\it{swap\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{decode-prop} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{b-nand3}}\,(\=\+{\rm{b-nand4}}\,(\=\+{\rm{b-not}}\,({\it{op0\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\it{op1\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\it{op2\/}})\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\it{op3\/}})\index{b-not})\index{b-not})\-\index{b-nand4}, \\ 
{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\it{op1\/}})\index{b-not})\index{b-not}, {\rm{b-not}}\,({\it{op3\/}})\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,({\rm{b-not}}\,({\it{op2\/}})\index{b-not}, {\rm{b-not}}\,({\it{op3\/}})\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\it{swap\/}})\index{b-not})\index{b-not})\index{b-nand3})\-\index{b-nand3}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-not}}\,({\it{op2\/}})\index{b-not}, \\ 
{\rm{b-nor}}\,({\rm{b-not}}\,({\it{op3\/}})\index{b-not}, {\rm{b-nor}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\it{op0\/}})\index{b-not})\index{b-not}, {\rm{b-not}}\,({\it{op1\/}})\index{b-not})\index{b-nor})\index{b-nor})\-\index{b-nor}, \\ 
{\rm{b-and}}\,(\=\+{\rm{b-nand3}}\,(\=\+{\rm{b-nand}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\it{op3\/}})\index{b-not})\index{b-not}, \\ 
{\rm{b-equv}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\it{op0\/}})\index{b-not})\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\it{op1\/}})\index{b-not})\index{b-not})\index{b-equv})\-\index{b-nand}, \\ 
{\rm{b-nand}}\,(\=\+{\rm{b-not}}\,({\it{op2\/}})\index{b-not}, \\ 
{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\it{swap\/}})\index{b-not})\index{b-not}, {\rm{b-not}}\,({\it{op3\/}})\index{b-not})\index{b-nand})\-\index{b-nand}, \\ 
{\rm{b-nand4}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\it{op0\/}})\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\it{op1\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\it{op2\/}})\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\it{op3\/}})\index{b-not})\-\index{b-nand4})\-\index{b-nand3}, \\ 
{\rm{b-not}}\,({\it{zero\/}})\index{b-not})\-\index{b-and})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$decode-prop} \\  
\=\+{\rm{f\$decode-prop}}\,({\it{zero\/}}, {\it{swap\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$decode-prop} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{f-nand3}}\,(\=\+{\rm{f-nand4}}\,(\=\+{\rm{f-not}}\,({\it{op0\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{op1\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\it{op2\/}})\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\it{op3\/}})\index{f-not})\index{f-not})\-\index{f-nand4}, \\ 
{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\it{op1\/}})\index{f-not})\index{f-not}, {\rm{f-not}}\,({\it{op3\/}})\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,({\rm{f-not}}\,({\it{op2\/}})\index{f-not}, {\rm{f-not}}\,({\it{op3\/}})\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\it{swap\/}})\index{f-not})\index{f-not})\index{f-nand3})\-\index{f-nand3}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-not}}\,({\it{op2\/}})\index{f-not}, \\ 
{\rm{f-nor}}\,({\rm{f-not}}\,({\it{op3\/}})\index{f-not}, {\rm{f-nor}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\it{op0\/}})\index{f-not})\index{f-not}, {\rm{f-not}}\,({\it{op1\/}})\index{f-not})\index{f-nor})\index{f-nor})\-\index{f-nor}, \\ 
{\rm{f-and}}\,(\=\+{\rm{f-nand3}}\,(\=\+{\rm{f-nand}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\it{op3\/}})\index{f-not})\index{f-not}, \\ 
{\rm{f-equv}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\it{op0\/}})\index{f-not})\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\it{op1\/}})\index{f-not})\index{f-not})\index{f-equv})\-\index{f-nand}, \\ 
{\rm{f-nand}}\,(\=\+{\rm{f-not}}\,({\it{op2\/}})\index{f-not}, \\ 
{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\it{swap\/}})\index{f-not})\index{f-not}, {\rm{f-not}}\,({\it{op3\/}})\index{f-not})\index{f-nand})\-\index{f-nand}, \\ 
{\rm{f-nand4}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\it{op0\/}})\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{op1\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\it{op2\/}})\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{op3\/}})\index{f-not})\-\index{f-nand4})\-\index{f-nand3}, \\ 
{\rm{f-not}}\,({\it{zero\/}})\index{f-not})\-\index{f-and})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$decode-prop; name this event `f\$decode-prop-off'.\index{f\$decode-prop-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{decode-prop*} \\  
\=\+{\sc{decode-prop*}}\index{decode-prop*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{decode-prop}} \\ 
{\tt{(}}{\tt{zero}}{\tt{ }}{\tt{swap}}{\tt{ }}{\tt{op0}}{\tt{ }}{\tt{op1}}{\tt{ }}{\tt{op2}}{\tt{ }}{\tt{op3}}{\tt{)}} \\ 
{\tt{(}}{\tt{w-16}}{\tt{ }}{\tt{w-24}}{\tt{ }}{\tt{w-48}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{g-47}}{\tt{ }}{\tt{(}}{\tt{w-47}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{zero}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-44}}{\tt{ }}{\tt{(}}{\tt{w-44}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-42}}{\tt{ }}{\tt{(}}{\tt{w-42}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-43}}{\tt{ }}{\tt{(}}{\tt{w-43}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{w-42}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-41}}{\tt{ }}{\tt{(}}{\tt{w-41}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-39}}{\tt{ }}{\tt{(}}{\tt{w-39}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-40}}{\tt{ }}{\tt{(}}{\tt{w-40}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{w-39}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-45}}{\tt{ }}{\tt{(}}{\tt{w-45}}{\tt{)}}{\tt{ }}{\tt{b-nand4}}{\tt{ }}{\tt{(}}{\tt{w-40}}{\tt{ }}{\tt{w-41}}{\tt{ }}{\tt{w-43}}{\tt{ }}{\tt{w-44}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-34}}{\tt{ }}{\tt{(}}{\tt{w-34}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{swap}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-35}}{\tt{ }}{\tt{(}}{\tt{w-35}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{w-34}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-37}}{\tt{ }}{\tt{(}}{\tt{w-37}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{w-35}}{\tt{ }}{\tt{w-44}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-38}}{\tt{ }}{\tt{(}}{\tt{w-38}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{w-42}}{\tt{ }}{\tt{w-37}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-30}}{\tt{ }}{\tt{(}}{\tt{w-30}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{w-41}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-31}}{\tt{ }}{\tt{(}}{\tt{w-31}}{\tt{)}}{\tt{ }}{\tt{b-equv}}{\tt{ }}{\tt{(}}{\tt{w-40}}{\tt{ }}{\tt{w-30}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-26}}{\tt{ }}{\tt{(}}{\tt{w-26}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{w-44}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-32}}{\tt{ }}{\tt{(}}{\tt{w-32}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{w-26}}{\tt{ }}{\tt{w-31}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-46}}{\tt{ }}{\tt{(}}{\tt{w-46}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{w-32}}{\tt{ }}{\tt{w-38}}{\tt{ }}{\tt{w-45}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-48}}{\tt{ }}{\tt{(}}{\tt{w-48}}{\tt{)}}{\tt{ }}{\tt{b-and}}{\tt{ }}{\tt{(}}{\tt{w-46}}{\tt{ }}{\tt{w-47}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-22}}{\tt{ }}{\tt{(}}{\tt{w-22}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{w-40}}{\tt{ }}{\tt{w-41}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-23}}{\tt{ }}{\tt{(}}{\tt{w-23}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{w-44}}{\tt{ }}{\tt{w-22}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-24}}{\tt{ }}{\tt{(}}{\tt{w-24}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{w-42}}{\tt{ }}{\tt{w-23}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-15}}{\tt{ }}{\tt{(}}{\tt{w-15}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{w-42}}{\tt{ }}{\tt{w-44}}{\tt{ }}{\tt{w-35}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-10}}{\tt{ }}{\tt{(}}{\tt{w-10}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{w-30}}{\tt{ }}{\tt{w-44}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-6}}{\tt{ }}{\tt{(}}{\tt{w-6}}{\tt{)}}{\tt{ }}{\tt{b-nand4}}{\tt{ }}{\tt{(}}{\tt{w-39}}{\tt{ }}{\tt{w-41}}{\tt{ }}{\tt{w-43}}{\tt{ }}{\tt{w-26}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-16}}{\tt{ }}{\tt{(}}{\tt{w-16}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{w-6}}{\tt{ }}{\tt{w-10}}{\tt{ }}{\tt{w-15}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{decode-prop\&} \\  
\=\+{\rm{decode-prop\&}}\,({\it{netlist\/}})\index{decode-prop\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{decode-prop}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{decode-prop*}}\index{decode-prop*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-equv\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-prop}}, {\it{netlist\/}})\index{delete-module})\index{b-equv\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-prop}}, {\it{netlist\/}})\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-and\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-prop}}, {\it{netlist\/}})\index{delete-module})\index{b-and\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nor\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-prop}}, {\it{netlist\/}})\index{delete-module})\index{b-nor\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-prop}}, {\it{netlist\/}})\index{delete-module})\index{b-nand\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand4\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-prop}}, {\it{netlist\/}})\index{delete-module})\index{b-nand4\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand3\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-prop}}, {\it{netlist\/}})\index{delete-module})\index{b-nand3\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable decode-prop\&; name this event `decode-prop\&-off'.\index{decode-prop\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{decode-prop\$netlist} \\  
\=\+{\sc{decode-prop\$netlist}}\index{decode-prop\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{decode-prop*}}\index{decode-prop*}, \\ 
\=\+(\=\+(\=\+(\=\+(({\sc{b-equv\$netlist}}\index{b-equv\$netlist} $\cup$ {\sc{b-not\$netlist}}\index{b-not\$netlist}) $\cup$ {\sc{b-and\$netlist}}\index{b-and\$netlist}) \\ 
$\cup$$\;\;\;\;${\sc{b-nor\$netlist}}\index{b-nor\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-nand\$netlist}}\index{b-nand\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-nand4\$netlist}}\index{b-nand4\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-nand3\$netlist}}\index{b-nand3\$netlist}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  decode-prop\$value \\ \index{decode-prop\$value}
\=\+{\rm{decode-prop\&}}\,({\it{netlist\/}})\index{decode-prop\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{decode-prop}}, \\ 
{\rm{list}}\,({\it{zero\/}}, {\it{swap\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}}), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$decode-prop}}\,({\it{zero\/}}, {\it{swap\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$decode-prop})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable decode-prop\$value; name this event `decode-prop\$value-off'.\index{decode-prop\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$decode-prop=decode-prop \\ \index{f\$decode-prop=decode-prop}
\=\+(\=\+{\rm{boolp}}\,({\it{zero\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{swap\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op0\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op1\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op2\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op3\/}})\index{boolp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$decode-prop}}\,({\it{zero\/}}, {\it{swap\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$decode-prop} \\ 
$=$$\;\;\;\;${\rm{decode-prop}}\,({\it{zero\/}}, {\it{swap\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{decode-prop})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  decode-prop\$value-zero \\ \index{decode-prop\$value-zero}
\=\+{\rm{decode-prop\&}}\,({\it{netlist\/}})\index{decode-prop\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{decode-prop}}, \\ 
{\rm{cons}}\,({\bf{t}}, {\rm{cons}}\,({\bf{f}}, {\sc{alu-inc-op}}\index{alu-inc-op})), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable decode-prop\$value-zero; name this event `decode-prop\$value-zero-off'.\index{decode-prop\$value-zero-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{decode-gen} \\  
\=\+{\rm{decode-gen}}\,({\it{zero\/}}, {\it{swap\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{decode-gen} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{b-nand3}}\,(\=\+{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\it{op0\/}})\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\it{op3\/}})\index{b-not})\index{b-not}, \\ 
{\rm{b-xor}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\it{op1\/}})\index{b-not})\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\it{op2\/}})\index{b-not})\index{b-not})\index{b-xor})\-\index{b-nand3}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\it{op2\/}})\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\it{op3\/}})\index{b-not}, \\ 
{\rm{b-nand}}\,({\rm{b-not}}\,({\it{op1\/}})\index{b-not}, {\rm{b-not}}\,({\it{swap\/}})\index{b-not})\index{b-nand})\-\index{b-nand3}, \\ 
{\rm{b-nand3}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\it{op1\/}})\index{b-not})\index{b-not}, {\rm{b-not}}\,({\it{op2\/}})\index{b-not}, {\rm{b-not}}\,({\it{op3\/}})\index{b-not})\index{b-nand3})\-\index{b-nand3}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,(\=\+{\rm{b-nand4}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\it{op0\/}})\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\it{op1\/}})\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\it{op2\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\it{op3\/}})\index{b-not})\index{b-not})\-\index{b-nand4}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\it{op2\/}})\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\it{op3\/}})\index{b-not}, \\ 
{\rm{b-nand}}\,({\rm{b-not}}\,({\it{op1\/}})\index{b-not}, {\rm{b-not}}\,({\it{swap\/}})\index{b-not})\index{b-nand})\-\index{b-nand3})\-\index{b-nand}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\it{zero\/}})\index{b-not})\index{b-not})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand3}}\,(\=\+{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\it{op0\/}})\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\it{op3\/}})\index{b-not})\index{b-not}, \\ 
{\rm{b-xor}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\it{op1\/}})\index{b-not})\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\it{op2\/}})\index{b-not})\index{b-not})\index{b-xor})\-\index{b-nand3}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\it{op0\/}})\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\it{op1\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\it{op2\/}})\index{b-not})\index{b-not})\-\index{b-nand3}, \\ 
{\rm{b-nand3}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\it{op1\/}})\index{b-not})\index{b-not}, {\rm{b-not}}\,({\it{op2\/}})\index{b-not}, {\rm{b-not}}\,({\it{op3\/}})\index{b-not})\index{b-nand3})\-\index{b-nand3}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\it{zero\/}})\index{b-not})\index{b-not})\-\index{b-nor})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$decode-gen} \\  
\=\+{\rm{f\$decode-gen}}\,({\it{zero\/}}, {\it{swap\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$decode-gen} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{f-nand3}}\,(\=\+{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\it{op0\/}})\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\it{op3\/}})\index{f-not})\index{f-not}, \\ 
{\rm{f-xor}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\it{op1\/}})\index{f-not})\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\it{op2\/}})\index{f-not})\index{f-not})\index{f-xor})\-\index{f-nand3}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\it{op2\/}})\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{op3\/}})\index{f-not}, \\ 
{\rm{f-nand}}\,({\rm{f-not}}\,({\it{op1\/}})\index{f-not}, {\rm{f-not}}\,({\it{swap\/}})\index{f-not})\index{f-nand})\-\index{f-nand3}, \\ 
{\rm{f-nand3}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\it{op1\/}})\index{f-not})\index{f-not}, {\rm{f-not}}\,({\it{op2\/}})\index{f-not}, {\rm{f-not}}\,({\it{op3\/}})\index{f-not})\index{f-nand3})\-\index{f-nand3}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,(\=\+{\rm{f-nand4}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\it{op0\/}})\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\it{op1\/}})\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{op2\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\it{op3\/}})\index{f-not})\index{f-not})\-\index{f-nand4}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\it{op2\/}})\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{op3\/}})\index{f-not}, \\ 
{\rm{f-nand}}\,({\rm{f-not}}\,({\it{op1\/}})\index{f-not}, {\rm{f-not}}\,({\it{swap\/}})\index{f-not})\index{f-nand})\-\index{f-nand3})\-\index{f-nand}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\it{zero\/}})\index{f-not})\index{f-not})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand3}}\,(\=\+{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\it{op0\/}})\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\it{op3\/}})\index{f-not})\index{f-not}, \\ 
{\rm{f-xor}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\it{op1\/}})\index{f-not})\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\it{op2\/}})\index{f-not})\index{f-not})\index{f-xor})\-\index{f-nand3}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\it{op0\/}})\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{op1\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\it{op2\/}})\index{f-not})\index{f-not})\-\index{f-nand3}, \\ 
{\rm{f-nand3}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\it{op1\/}})\index{f-not})\index{f-not}, {\rm{f-not}}\,({\it{op2\/}})\index{f-not}, {\rm{f-not}}\,({\it{op3\/}})\index{f-not})\index{f-nand3})\-\index{f-nand3}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\it{zero\/}})\index{f-not})\index{f-not})\-\index{f-nor})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$decode-gen; name this event `f\$decode-gen-off'.\index{f\$decode-gen-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{decode-gen*} \\  
\=\+{\sc{decode-gen*}}\index{decode-gen*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{decode-gen}} \\ 
{\tt{(}}{\tt{zero}}{\tt{ }}{\tt{swap}}{\tt{ }}{\tt{op0}}{\tt{ }}{\tt{op1}}{\tt{ }}{\tt{op2}}{\tt{ }}{\tt{op3}}{\tt{)}} \\ 
{\tt{(}}{\tt{w-22}}{\tt{ }}{\tt{w-41}}{\tt{ }}{\tt{w-66}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{g-64}}{\tt{ }}{\tt{(}}{\tt{w-64}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{zero}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-65}}{\tt{ }}{\tt{(}}{\tt{w-65}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{w-64}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-61}}{\tt{ }}{\tt{(}}{\tt{w-61}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-60}}{\tt{ }}{\tt{(}}{\tt{w-60}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-58}}{\tt{ }}{\tt{(}}{\tt{w-58}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-59}}{\tt{ }}{\tt{(}}{\tt{w-59}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{w-58}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-62}}{\tt{ }}{\tt{(}}{\tt{w-62}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{w-59}}{\tt{ }}{\tt{w-60}}{\tt{ }}{\tt{w-61}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-56}}{\tt{ }}{\tt{(}}{\tt{w-56}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{w-60}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-52}}{\tt{ }}{\tt{(}}{\tt{w-52}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-53}}{\tt{ }}{\tt{(}}{\tt{w-53}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{w-52}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-57}}{\tt{ }}{\tt{(}}{\tt{w-57}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{w-53}}{\tt{ }}{\tt{w-58}}{\tt{ }}{\tt{w-56}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-50}}{\tt{ }}{\tt{(}}{\tt{w-50}}{\tt{)}}{\tt{ }}{\tt{b-xor}}{\tt{ }}{\tt{(}}{\tt{w-59}}{\tt{ }}{\tt{w-56}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-45}}{\tt{ }}{\tt{(}}{\tt{w-45}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{w-61}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-51}}{\tt{ }}{\tt{(}}{\tt{w-51}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{w-53}}{\tt{ }}{\tt{w-45}}{\tt{ }}{\tt{w-50}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-63}}{\tt{ }}{\tt{(}}{\tt{w-63}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{w-51}}{\tt{ }}{\tt{w-57}}{\tt{ }}{\tt{w-62}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-66}}{\tt{ }}{\tt{(}}{\tt{w-66}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{w-63}}{\tt{ }}{\tt{w-65}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-35}}{\tt{ }}{\tt{(}}{\tt{w-35}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{swap}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-36}}{\tt{ }}{\tt{(}}{\tt{w-36}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{w-58}}{\tt{ }}{\tt{w-35}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-37}}{\tt{ }}{\tt{(}}{\tt{w-37}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{w-56}}{\tt{ }}{\tt{w-61}}{\tt{ }}{\tt{w-36}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-30}}{\tt{ }}{\tt{(}}{\tt{w-30}}{\tt{)}}{\tt{ }}{\tt{b-nand4}}{\tt{ }}{\tt{(}}{\tt{w-53}}{\tt{ }}{\tt{w-59}}{\tt{ }}{\tt{w-60}}{\tt{ }}{\tt{w-45}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-38}}{\tt{ }}{\tt{(}}{\tt{w-38}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{w-30}}{\tt{ }}{\tt{w-37}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-41}}{\tt{ }}{\tt{(}}{\tt{w-41}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{w-38}}{\tt{ }}{\tt{w-65}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-22}}{\tt{ }}{\tt{(}}{\tt{w-22}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{w-51}}{\tt{ }}{\tt{w-37}}{\tt{ }}{\tt{w-62}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{decode-gen\&} \\  
\=\+{\rm{decode-gen\&}}\,({\it{netlist\/}})\index{decode-gen\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{decode-gen}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{decode-gen*}}\index{decode-gen*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-xor\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-gen}}, {\it{netlist\/}})\index{delete-module})\index{b-xor\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-gen}}, {\it{netlist\/}})\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand4\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-gen}}, {\it{netlist\/}})\index{delete-module})\index{b-nand4\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-gen}}, {\it{netlist\/}})\index{delete-module})\index{b-nand\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nor\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-gen}}, {\it{netlist\/}})\index{delete-module})\index{b-nor\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand3\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-gen}}, {\it{netlist\/}})\index{delete-module})\index{b-nand3\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable decode-gen\&; name this event `decode-gen\&-off'.\index{decode-gen\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{decode-gen\$netlist} \\  
\=\+{\sc{decode-gen\$netlist}}\index{decode-gen\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{decode-gen*}}\index{decode-gen*}, \\ 
\=\+(\=\+(\=\+(({\sc{b-xor\$netlist}}\index{b-xor\$netlist} $\cup$ {\sc{b-not\$netlist}}\index{b-not\$netlist}) $\cup$ {\sc{b-nand4\$netlist}}\index{b-nand4\$netlist}) \\ 
$\cup$$\;\;\;\;${\sc{b-nand\$netlist}}\index{b-nand\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-nor\$netlist}}\index{b-nor\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-nand3\$netlist}}\index{b-nand3\$netlist}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  decode-gen\$value \\ \index{decode-gen\$value}
\=\+{\rm{decode-gen\&}}\,({\it{netlist\/}})\index{decode-gen\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{decode-gen}}, \\ 
{\rm{list}}\,({\it{zero\/}}, {\it{swap\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}}), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$decode-gen}}\,({\it{zero\/}}, {\it{swap\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$decode-gen})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable decode-gen\$value; name this event `decode-gen\$value-off'.\index{decode-gen\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$decode-gen=decode-gen \\ \index{f\$decode-gen=decode-gen}
\=\+(\=\+{\rm{boolp}}\,({\it{zero\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{swap\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op0\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op1\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op2\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op3\/}})\index{boolp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$decode-gen}}\,({\it{zero\/}}, {\it{swap\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$decode-gen} \\ 
$=$$\;\;\;\;${\rm{decode-gen}}\,({\it{zero\/}}, {\it{swap\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{decode-gen})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  decode-gen\$value-zero \\ \index{decode-gen\$value-zero}
\=\+{\rm{decode-gen\&}}\,({\it{netlist\/}})\index{decode-gen\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{decode-gen}}, {\rm{cons}}\,({\bf{t}}, {\rm{cons}}\,({\bf{f}}, {\sc{alu-inc-op}}\index{alu-inc-op})), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable decode-gen\$value-zero; name this event `decode-gen\$value-zero-off'.\index{decode-gen\$value-zero-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{f\$mpg} \\  
\=\+{\rm{f\$mpg}}\,({\it{zsop\/}})\index{f\$mpg} \\ 
$=$$\;\;\;\;${\rm{append}}\,(\=\+{\rm{f\$decode-gen}}\,(\=\+{\rm{car}}\,({\it{zsop\/}}), \\ 
{\rm{cadr}}\,({\it{zsop\/}}), \\ 
{\rm{caddr}}\,({\it{zsop\/}}), \\ 
{\rm{cadddr}}\,({\it{zsop\/}}), \\ 
{\rm{caddddr}}\,({\it{zsop\/}}), \\ 
{\rm{cadddddr}}\,({\it{zsop\/}}))\-\index{f\$decode-gen}, \\ 
{\rm{append}}\,(\=\+{\rm{f\$decode-prop}}\,(\=\+{\rm{car}}\,({\it{zsop\/}}), \\ 
{\rm{cadr}}\,({\it{zsop\/}}), \\ 
{\rm{caddr}}\,({\it{zsop\/}}), \\ 
{\rm{cadddr}}\,({\it{zsop\/}}), \\ 
{\rm{caddddr}}\,({\it{zsop\/}}), \\ 
{\rm{cadddddr}}\,({\it{zsop\/}}))\-\index{f\$decode-prop}, \\ 
{\rm{list}}\,({\rm{f\$decode-mode}}\,(\=\+{\rm{caddr}}\,({\it{zsop\/}}), \\ 
{\rm{cadddr}}\,({\it{zsop\/}}), \\ 
{\rm{caddddr}}\,({\it{zsop\/}}), \\ 
{\rm{cadddddr}}\,({\it{zsop\/}}))\-\index{f\$decode-mode}))\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$mpg; name this event `f\$mpg-off'.\index{f\$mpg-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{mpg} \\  
\=\+{\rm{mpg}}\,({\it{zsop\/}})\index{mpg} \\ 
$=$$\;\;\;\;${\rm{append}}\,(\=\+{\rm{decode-gen}}\,(\=\+{\rm{car}}\,({\it{zsop\/}}), \\ 
{\rm{cadr}}\,({\it{zsop\/}}), \\ 
{\rm{caddr}}\,({\it{zsop\/}}), \\ 
{\rm{cadddr}}\,({\it{zsop\/}}), \\ 
{\rm{caddddr}}\,({\it{zsop\/}}), \\ 
{\rm{cadddddr}}\,({\it{zsop\/}}))\-\index{decode-gen}, \\ 
{\rm{append}}\,(\=\+{\rm{decode-prop}}\,(\=\+{\rm{car}}\,({\it{zsop\/}}), \\ 
{\rm{cadr}}\,({\it{zsop\/}}), \\ 
{\rm{caddr}}\,({\it{zsop\/}}), \\ 
{\rm{cadddr}}\,({\it{zsop\/}}), \\ 
{\rm{caddddr}}\,({\it{zsop\/}}), \\ 
{\rm{cadddddr}}\,({\it{zsop\/}}))\-\index{decode-prop}, \\ 
{\rm{list}}\,({\rm{decode-mode}}\,(\=\+{\rm{caddr}}\,({\it{zsop\/}}), \\ 
{\rm{cadddr}}\,({\it{zsop\/}}), \\ 
{\rm{caddddr}}\,({\it{zsop\/}}), \\ 
{\rm{cadddddr}}\,({\it{zsop\/}}))\-\index{decode-mode}))\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable mpg; name this event `mpg-off'.\index{mpg-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$mpg=mpg \\ \index{f\$mpg=mpg}
({\rm{bvp}}\,({\it{zsop\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{zsop\/}})\index{length} $=$ {\tt{6}})) $\rightarrow$ ({\rm{f\$mpg}}\,({\it{zsop\/}})\index{f\$mpg} $=$ {\rm{mpg}}\,({\it{zsop\/}})\index{mpg})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-length-f\$mpg \\ \index{properp-length-f\$mpg}
{\rm{properp}}\,({\rm{f\$mpg}}\,({\it{zsop\/}})\index{f\$mpg})\index{properp} $\wedge$ ({\rm{length}}\,({\rm{f\$mpg}}\,({\it{zsop\/}})\index{f\$mpg})\index{length} $=$ {\tt{7}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-mpg \\ \index{length-mpg}
{\rm{length}}\,({\rm{mpg}}\,({\it{zsop\/}})\index{mpg})\index{length} $=$ {\tt{7}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-mpg \\ \index{bvp-mpg}
{\rm{bvp}}\,({\rm{mpg}}\,({\it{zsop\/}})\index{mpg})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-mpg \\ \index{properp-mpg}
{\rm{properp}}\,({\rm{mpg}}\,({\it{zsop\/}})\index{mpg})\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  mpg-if-op-code \\ \index{mpg-if-op-code}
\=\+{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\it{a\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{b\/}}, \\ 
\=\+{\bf if }{\it{c\/}}$\;\;${\bf then }{\it{d\/}} \\ 
{\bf else }{\it{e\/}}$\;${\bf  endif}\-)\-)\-)\index{mpg} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{c\/}}$\;\;${\bf then }{\rm{mpg}}\,({\rm{cons}}\,({\it{a\/}}, {\rm{cons}}\,({\it{b\/}}, {\it{d\/}})))\index{mpg} \\ 
{\bf else }{\rm{mpg}}\,({\rm{cons}}\,({\it{a\/}}, {\rm{cons}}\,({\it{b\/}}, {\it{e\/}})))\index{mpg}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  mpg-zero \\ \index{mpg-zero}
{\rm{mpg}}\,({\rm{cons}}\,({\bf{t}}, {\rm{cons}}\,({\bf{f}}, {\sc{alu-inc-op}}\index{alu-inc-op})))\index{mpg} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}})
\end{tabbing}


\noindent{\sc Event}:   Enable mpg-zero; name this event `mpg-zero-off'.\index{mpg-zero-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{mpg*} \\  
\=\+{\sc{mpg*}}\index{mpg*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{mpg}} \\ 
{\tt{(}}{\tt{zero}}{\tt{ }}{\tt{swap}}{\tt{ }}{\tt{op0}}{\tt{ }}{\tt{op1}}{\tt{ }}{\tt{op2}}{\tt{ }}{\tt{op3}}{\tt{)}} \\ 
{\tt{(}}{\tt{gbn}}{\tt{ }}{\tt{gan}}{\tt{ }}{\tt{ga}}{\tt{ }}{\tt{pb}}{\tt{ }}{\tt{pan}}{\tt{ }}{\tt{pa}}{\tt{ }}{\tt{mode}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{m}}{\tt{ }}{\tt{(}}{\tt{mode}}{\tt{)}}{\tt{ }}{\tt{decode-mode}}{\tt{ }}{\tt{(}}{\tt{op0}}{\tt{ }}{\tt{op1}}{\tt{ }}{\tt{op2}}{\tt{ }}{\tt{op3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{p}} \\ 
{\tt{(}}{\tt{pb}}{\tt{ }}{\tt{pan}}{\tt{ }}{\tt{pa}}{\tt{)}} \\ 
{\tt{decode-prop}} \\ 
{\tt{(}}{\tt{zero}}{\tt{ }}{\tt{swap}}{\tt{ }}{\tt{op0}}{\tt{ }}{\tt{op1}}{\tt{ }}{\tt{op2}}{\tt{ }}{\tt{op3}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g}} \\ 
{\tt{(}}{\tt{gbn}}{\tt{ }}{\tt{gan}}{\tt{ }}{\tt{ga}}{\tt{)}} \\ 
{\tt{decode-gen}} \\ 
{\tt{(}}{\tt{zero}}{\tt{ }}{\tt{swap}}{\tt{ }}{\tt{op0}}{\tt{ }}{\tt{op1}}{\tt{ }}{\tt{op2}}{\tt{ }}{\tt{op3}}{\tt{)}}{\tt{)}}\-{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{mpg\&} \\  
\=\+{\rm{mpg\&}}\,({\it{netlist\/}})\index{mpg\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{mpg}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{mpg*}}\index{mpg*}) \\ 
$\wedge$$\;\;\;\;${\rm{decode-mode\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{mpg}}, {\it{netlist\/}})\index{delete-module})\index{decode-mode\&} \\ 
$\wedge$$\;\;\;\;${\rm{decode-prop\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{mpg}}, {\it{netlist\/}})\index{delete-module})\index{decode-prop\&} \\ 
$\wedge$$\;\;\;\;${\rm{decode-gen\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{mpg}}, {\it{netlist\/}})\index{delete-module})\index{decode-gen\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable mpg\&; name this event `mpg\&-off'.\index{mpg\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{mpg\$netlist} \\  
\=\+{\sc{mpg\$netlist}}\index{mpg\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{mpg*}}\index{mpg*}, \\ 
\=\+({\sc{decode-mode\$netlist}}\index{decode-mode\$netlist} $\cup$ {\sc{decode-prop\$netlist}}\index{decode-prop\$netlist}) \\ 
$\cup$$\;\;\;\;${\sc{decode-gen\$netlist}}\index{decode-gen\$netlist}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  mpg\$value \\ \index{mpg\$value}
\=\+({\rm{mpg\&}}\,({\it{netlist\/}})\index{mpg\&} $\wedge$ {\rm{properp}}\,({\it{zsop\/}})\index{properp} $\wedge$ ({\rm{length}}\,({\it{zsop\/}})\index{length} $=$ {\tt{6}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{mpg}}, {\it{zsop\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{f\$mpg}}\,({\it{zsop\/}})\index{f\$mpg})\-
\end{tabbing}


\noindent{\sc Event}:   Enable mpg\$value; name this event `mpg\$value-off'.\index{mpg\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mpg\$value-zero \\ \index{mpg\$value-zero}
\=\+({\rm{mpg\&}}\,({\it{netlist\/}})\index{mpg\&} $\wedge$ ({\it{zsop\/}} $=$ {\rm{cons}}\,({\bf{t}}, {\rm{cons}}\,({\bf{f}}, {\sc{alu-inc-op}}\index{alu-inc-op})))) \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{mpg}}, {\it{zsop\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable mpg\$value-zero; name this event `mpg\$value-zero-off'.\index{mpg\$value-zero-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{carry-in-help} \\  
\=\+{\rm{carry-in-help}}\,({\it{czop\/}})\index{carry-in-help} \\ 
$=$$\;\;\;\;${\rm{b-or}}\,(\=\+{\rm{b-nand3}}\,(\=\+{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{cadddr}}\,({\it{czop\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{caddddr}}\,({\it{czop\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{cadddddr}}\,({\it{czop\/}}))\index{b-not})\-\index{b-nand3}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{caddr}}\,({\it{czop\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{cadddr}}\,({\it{czop\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddddr}}\,({\it{czop\/}}))\index{b-not})\index{b-not})\-\index{b-nand3}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddr}}\,({\it{czop\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadddr}}\,({\it{czop\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddddr}}\,({\it{czop\/}}))\index{b-not})\index{b-not})\-\index{b-nand3})\-\index{b-nand3}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-nand}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadddddr}}\,({\it{czop\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{czop\/}}))\index{b-not})\index{b-not})\-\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{caddr}}\,({\it{czop\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{caddddr}}\,({\it{czop\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{czop\/}}))\index{b-not})\index{b-not})\-\index{b-nand3}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{caddr}}\,({\it{czop\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddddr}}\,({\it{czop\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{car}}\,({\it{czop\/}}))\index{b-not})\-\index{b-nand3})\-\index{b-nand3})\-\index{b-or}\-
\end{tabbing}


\noindent{\sc Event}:   Enable carry-in-help; name this event `carry-in-help-off'.\index{carry-in-help-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{f\$carry-in-help} \\  
\=\+{\rm{f\$carry-in-help}}\,({\it{czop\/}})\index{f\$carry-in-help} \\ 
$=$$\;\;\;\;${\rm{f-or}}\,(\=\+{\rm{f-nand3}}\,(\=\+{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{cadddr}}\,({\it{czop\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{caddddr}}\,({\it{czop\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{cadddddr}}\,({\it{czop\/}}))\index{f-not})\-\index{f-nand3}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{caddr}}\,({\it{czop\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{cadddr}}\,({\it{czop\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddddr}}\,({\it{czop\/}}))\index{f-not})\index{f-not})\-\index{f-nand3}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{czop\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadddr}}\,({\it{czop\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddddr}}\,({\it{czop\/}}))\index{f-not})\index{f-not})\-\index{f-nand3})\-\index{f-nand3}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-nand}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadddddr}}\,({\it{czop\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{czop\/}}))\index{f-not})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{caddr}}\,({\it{czop\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{caddddr}}\,({\it{czop\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{czop\/}}))\index{f-not})\index{f-not})\-\index{f-nand3}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{caddr}}\,({\it{czop\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddddr}}\,({\it{czop\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{car}}\,({\it{czop\/}}))\index{f-not})\-\index{f-nand3})\-\index{f-nand3})\-\index{f-or}\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$carry-in-help; name this event `f\$carry-in-help-off'.\index{f\$carry-in-help-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$carry-in-help=carry-in-help \\ \index{f\$carry-in-help=carry-in-help}
\=\+({\rm{bvp}}\,({\it{czop\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{czop\/}})\index{length} $=$ {\tt{6}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f\$carry-in-help}}\,({\it{czop\/}})\index{f\$carry-in-help} $=$ {\rm{carry-in-help}}\,({\it{czop\/}})\index{carry-in-help})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{carry-in-help*} \\  
\=\+{\sc{carry-in-help*}}\index{carry-in-help*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{carry-in-help}} \\ 
{\tt{(}}{\tt{cin}}{\tt{ }}{\tt{z}}{\tt{ }}{\tt{op0in}}{\tt{ }}{\tt{op1in}}{\tt{ }}{\tt{op2in}}{\tt{ }}{\tt{op3in}}{\tt{)}} \\ 
{\tt{(}}{\tt{cout}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{g0}}{\tt{ }}{\tt{(}}{\tt{c-}}{\tt{ }}{\tt{c}}{\tt{)}}{\tt{ }}{\tt{b-nbuf}}{\tt{ }}{\tt{(}}{\tt{cin}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g1}}{\tt{ }}{\tt{(}}{\tt{op0-}}{\tt{ }}{\tt{op0}}{\tt{)}}{\tt{ }}{\tt{b-nbuf}}{\tt{ }}{\tt{(}}{\tt{op0in}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g2}}{\tt{ }}{\tt{(}}{\tt{op1-}}{\tt{ }}{\tt{op1}}{\tt{)}}{\tt{ }}{\tt{b-nbuf}}{\tt{ }}{\tt{(}}{\tt{op1in}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g3}}{\tt{ }}{\tt{(}}{\tt{op2-}}{\tt{ }}{\tt{op2}}{\tt{)}}{\tt{ }}{\tt{b-nbuf}}{\tt{ }}{\tt{(}}{\tt{op2in}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g4}}{\tt{ }}{\tt{(}}{\tt{op3-}}{\tt{ }}{\tt{op3}}{\tt{)}}{\tt{ }}{\tt{b-nbuf}}{\tt{ }}{\tt{(}}{\tt{op3in}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g5}}{\tt{ }}{\tt{(}}{\tt{s5}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{op1-}}{\tt{ }}{\tt{op2-}}{\tt{ }}{\tt{op3-}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g6}}{\tt{ }}{\tt{(}}{\tt{s6}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{op0-}}{\tt{ }}{\tt{op1-}}{\tt{ }}{\tt{op2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g7}}{\tt{ }}{\tt{(}}{\tt{s7}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{op0}}{\tt{ }}{\tt{op1}}{\tt{ }}{\tt{op2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g8}}{\tt{ }}{\tt{(}}{\tt{s8}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{s5}}{\tt{ }}{\tt{s6}}{\tt{ }}{\tt{s7}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g9}}{\tt{ }}{\tt{(}}{\tt{s9}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{op3}}{\tt{ }}{\tt{c}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g10}}{\tt{ }}{\tt{(}}{\tt{s10}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{op0-}}{\tt{ }}{\tt{op2-}}{\tt{ }}{\tt{c}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g11}}{\tt{ }}{\tt{(}}{\tt{s11}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{op0-}}{\tt{ }}{\tt{op2}}{\tt{ }}{\tt{c-}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g12}}{\tt{ }}{\tt{(}}{\tt{s12}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{s9}}{\tt{ }}{\tt{s10}}{\tt{ }}{\tt{s11}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g13}}{\tt{ }}{\tt{(}}{\tt{cout}}{\tt{)}}{\tt{ }}{\tt{b-or}}{\tt{ }}{\tt{(}}{\tt{s8}}{\tt{ }}{\tt{s12}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{carry-in-help\&} \\  
\=\+{\rm{carry-in-help\&}}\,({\it{netlist\/}})\index{carry-in-help\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{carry-in-help}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{carry-in-help*}}\index{carry-in-help*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-nbuf\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{carry-in-help}}, {\it{netlist\/}})\index{delete-module})\index{b-nbuf\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{carry-in-help}}, {\it{netlist\/}})\index{delete-module})\index{b-nand\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand3\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{carry-in-help}}, {\it{netlist\/}})\index{delete-module})\index{b-nand3\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-or\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{carry-in-help}}, {\it{netlist\/}})\index{delete-module})\index{b-or\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable carry-in-help\&; name this event `carry-in-help\&-off'.\index{carry-in-help\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{carry-in-help\$netlist} \\  
\=\+{\sc{carry-in-help\$netlist}}\index{carry-in-help\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{carry-in-help*}}\index{carry-in-help*}, \\ 
\=\+(({\sc{b-nbuf\$netlist}}\index{b-nbuf\$netlist} $\cup$ {\sc{b-nand\$netlist}}\index{b-nand\$netlist}) $\cup$ {\sc{b-nand3\$netlist}}\index{b-nand3\$netlist}) \\ 
$\cup$$\;\;\;\;${\sc{b-or\$netlist}}\index{b-or\$netlist}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  carry-in-help-zero \\ \index{carry-in-help-zero}
{\rm{carry-in-help}}\,({\rm{cons}}\,({\it{c\/}}, {\rm{cons}}\,({\bf{t}}, {\sc{alu-inc-op}}\index{alu-inc-op})))\index{carry-in-help} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Enable carry-in-help-zero; name this event `carry-in-help-zero-off'.\index{carry-in-help-zero-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  carry-in-help-if-op-code \\ \index{carry-in-help-if-op-code}
\=\+{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\it{a\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{b\/}}, \\ 
\=\+{\bf if }{\it{c\/}}$\;\;${\bf then }{\it{d\/}} \\ 
{\bf else }{\it{e\/}}$\;${\bf  endif}\-)\-)\-)\index{carry-in-help} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{c\/}}$\;\;${\bf then }{\rm{carry-in-help}}\,({\rm{cons}}\,({\it{a\/}}, {\rm{cons}}\,({\it{b\/}}, {\it{d\/}})))\index{carry-in-help} \\ 
{\bf else }{\rm{carry-in-help}}\,({\rm{cons}}\,({\it{a\/}}, {\rm{cons}}\,({\it{b\/}}, {\it{e\/}})))\index{carry-in-help}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  carry-in-help\$value \\ \index{carry-in-help\$value}
\=\+{\rm{carry-in-help\&}}\,({\it{netlist\/}})\index{carry-in-help\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{carry-in-help}}, {\it{czop\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f\$carry-in-help}}\,({\it{czop\/}})\index{f\$carry-in-help}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable carry-in-help\$value; name this event `carry-in-help\$value-off'.\index{carry-in-help\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  carry-in-help\$value-zero \\ \index{carry-in-help\$value-zero}
\=\+({\rm{carry-in-help\&}}\,({\it{netlist\/}})\index{carry-in-help\&} $\wedge$ ({\it{czop\/}} $=$ {\rm{cons}}\,({\it{c\/}}, {\rm{cons}}\,({\bf{t}}, {\sc{alu-inc-op}}\index{alu-inc-op})))) \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{carry-in-help}}, {\it{czop\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\bf{t}}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable carry-in-help\$value-zero; name this event `carry-in-help\$value-zero-off'.\index{carry-in-help\$value-zero-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{p-cell} \\  
\=\+{\rm{p-cell}}\,({\it{a\/}}, {\it{an\/}}, {\it{b\/}}, {\it{pa\/}}, {\it{pan\/}}, {\it{pb\/}})\index{p-cell} \\ 
$=$$\;\;\;\;${\rm{b-nand3}}\,({\rm{b-nand}}\,({\it{a\/}}, {\it{pa\/}})\index{b-nand}, {\rm{b-nand}}\,({\it{an\/}}, {\it{pan\/}})\index{b-nand}, {\rm{b-nand}}\,({\it{b\/}}, {\it{pb\/}})\index{b-nand})\index{b-nand3}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$p-cell} \\  
\=\+{\rm{f\$p-cell}}\,({\it{a\/}}, {\it{an\/}}, {\it{b\/}}, {\it{pa\/}}, {\it{pan\/}}, {\it{pb\/}})\index{f\$p-cell} \\ 
$=$$\;\;\;\;${\rm{f-nand3}}\,({\rm{f-nand}}\,({\it{a\/}}, {\it{pa\/}})\index{f-nand}, {\rm{f-nand}}\,({\it{an\/}}, {\it{pan\/}})\index{f-nand}, {\rm{f-nand}}\,({\it{b\/}}, {\it{pb\/}})\index{f-nand})\index{f-nand3}\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$p-cell; name this event `f\$p-cell-off'.\index{f\$p-cell-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{p-cell*} \\  
\=\+{\sc{p-cell*}}\index{p-cell*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{p-cell}} \\ 
{\tt{(}}{\tt{a}}{\tt{ }}{\tt{an}}{\tt{ }}{\tt{b}}{\tt{ }}{\tt{pa}}{\tt{ }}{\tt{pan}}{\tt{ }}{\tt{pb}}{\tt{)}} \\ 
{\tt{(}}{\tt{w-3}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{g-2}}{\tt{ }}{\tt{(}}{\tt{w-2}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{b}}{\tt{ }}{\tt{pb}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-1}}{\tt{ }}{\tt{(}}{\tt{w-1}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{an}}{\tt{ }}{\tt{pan}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-0}}{\tt{ }}{\tt{(}}{\tt{w-0}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{a}}{\tt{ }}{\tt{pa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-3}}{\tt{ }}{\tt{(}}{\tt{w-3}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{w-0}}{\tt{ }}{\tt{w-1}}{\tt{ }}{\tt{w-2}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{p-cell\&} \\  
\=\+{\rm{p-cell\&}}\,({\it{netlist\/}})\index{p-cell\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{p-cell}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{p-cell*}}\index{p-cell*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-nand\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{p-cell}}, {\it{netlist\/}})\index{delete-module})\index{b-nand\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand3\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{p-cell}}, {\it{netlist\/}})\index{delete-module})\index{b-nand3\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable p-cell\&; name this event `p-cell\&-off'.\index{p-cell\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{p-cell\$netlist} \\  
{\sc{p-cell\$netlist}}\index{p-cell\$netlist} $=$ {\rm{cons}}\,({\sc{p-cell*}}\index{p-cell*}, {\sc{b-nand\$netlist}}\index{b-nand\$netlist} $\cup$ {\sc{b-nand3\$netlist}}\index{b-nand3\$netlist})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  p-cell\$value \\ \index{p-cell\$value}
\=\+{\rm{p-cell\&}}\,({\it{netlist\/}})\index{p-cell\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{p-cell}}, {\rm{list}}\,({\it{a\/}}, {\it{an\/}}, {\it{b\/}}, {\it{pa\/}}, {\it{pan\/}}, {\it{pb\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f\$p-cell}}\,({\it{a\/}}, {\it{an\/}}, {\it{b\/}}, {\it{pa\/}}, {\it{pan\/}}, {\it{pb\/}})\index{f\$p-cell}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable p-cell\$value; name this event `p-cell\$value-off'.\index{p-cell\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$p-cell=p-cell \\ \index{f\$p-cell=p-cell}
\=\+(\=\+{\rm{boolp}}\,({\it{a\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{an\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{b\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{pa\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{pan\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{pb\/}})\index{boolp})\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{f\$p-cell}}\,({\it{a\/}}, {\it{an\/}}, {\it{b\/}}, {\it{pa\/}}, {\it{pan\/}}, {\it{pb\/}})\index{f\$p-cell} $=$ {\rm{p-cell}}\,({\it{a\/}}, {\it{an\/}}, {\it{b\/}}, {\it{pa\/}}, {\it{pan\/}}, {\it{pb\/}})\index{p-cell})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  p-cell\$value-zero \\ \index{p-cell\$value-zero}
\=\+{\rm{p-cell\&}}\,({\it{netlist\/}})\index{p-cell\&} \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{p-cell}}, {\rm{list}}\,({\it{a\/}}, {\it{an\/}}, {\it{b\/}}, {\bf{f}}, {\bf{f}}, {\bf{f}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\bf{f}}))\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{g-cell} \\  
\=\+{\rm{g-cell}}\,({\it{a\/}}, {\it{an\/}}, {\it{bn\/}}, {\it{ga\/}}, {\it{gan\/}}, {\it{gbn\/}})\index{g-cell} \\ 
$=$$\;\;\;\;${\rm{b-and3}}\,({\rm{b-nand}}\,({\it{a\/}}, {\it{ga\/}})\index{b-nand}, {\rm{b-nand}}\,({\it{an\/}}, {\it{gan\/}})\index{b-nand}, {\rm{b-nand}}\,({\it{bn\/}}, {\it{gbn\/}})\index{b-nand})\index{b-and3}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$g-cell} \\  
\=\+{\rm{f\$g-cell}}\,({\it{a\/}}, {\it{an\/}}, {\it{bn\/}}, {\it{ga\/}}, {\it{gan\/}}, {\it{gbn\/}})\index{f\$g-cell} \\ 
$=$$\;\;\;\;${\rm{f-and3}}\,({\rm{f-nand}}\,({\it{a\/}}, {\it{ga\/}})\index{f-nand}, {\rm{f-nand}}\,({\it{an\/}}, {\it{gan\/}})\index{f-nand}, {\rm{f-nand}}\,({\it{bn\/}}, {\it{gbn\/}})\index{f-nand})\index{f-and3}\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$g-cell; name this event `f\$g-cell-off'.\index{f\$g-cell-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{g-cell*} \\  
\=\+{\sc{g-cell*}}\index{g-cell*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{g-cell}} \\ 
{\tt{(}}{\tt{a}}{\tt{ }}{\tt{an}}{\tt{ }}{\tt{bn}}{\tt{ }}{\tt{ga}}{\tt{ }}{\tt{gan}}{\tt{ }}{\tt{gbn}}{\tt{)}} \\ 
{\tt{(}}{\tt{w-3}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{g-2}}{\tt{ }}{\tt{(}}{\tt{w-2}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{bn}}{\tt{ }}{\tt{gbn}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-1}}{\tt{ }}{\tt{(}}{\tt{w-1}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{an}}{\tt{ }}{\tt{gan}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-0}}{\tt{ }}{\tt{(}}{\tt{w-0}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{a}}{\tt{ }}{\tt{ga}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-3}}{\tt{ }}{\tt{(}}{\tt{w-3}}{\tt{)}}{\tt{ }}{\tt{b-and3}}{\tt{ }}{\tt{(}}{\tt{w-0}}{\tt{ }}{\tt{w-1}}{\tt{ }}{\tt{w-2}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{g-cell\&} \\  
\=\+{\rm{g-cell\&}}\,({\it{netlist\/}})\index{g-cell\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{g-cell}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{g-cell*}}\index{g-cell*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-nand\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{g-cell}}, {\it{netlist\/}})\index{delete-module})\index{b-nand\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-and3\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{g-cell}}, {\it{netlist\/}})\index{delete-module})\index{b-and3\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable g-cell\&; name this event `g-cell\&-off'.\index{g-cell\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{g-cell\$netlist} \\  
{\sc{g-cell\$netlist}}\index{g-cell\$netlist} $=$ {\rm{cons}}\,({\sc{g-cell*}}\index{g-cell*}, {\sc{b-nand\$netlist}}\index{b-nand\$netlist} $\cup$ {\sc{b-and3\$netlist}}\index{b-and3\$netlist})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  g-cell\$value \\ \index{g-cell\$value}
\=\+{\rm{g-cell\&}}\,({\it{netlist\/}})\index{g-cell\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{g-cell}}, {\rm{list}}\,({\it{a\/}}, {\it{an\/}}, {\it{bn\/}}, {\it{ga\/}}, {\it{gan\/}}, {\it{gbn\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f\$g-cell}}\,({\it{a\/}}, {\it{an\/}}, {\it{bn\/}}, {\it{ga\/}}, {\it{gan\/}}, {\it{gbn\/}})\index{f\$g-cell}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable g-cell\$value; name this event `g-cell\$value-off'.\index{g-cell\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$g-cell=g-cell \\ \index{f\$g-cell=g-cell}
\=\+(\=\+{\rm{boolp}}\,({\it{a\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{an\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{bn\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{ga\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{gan\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{gbn\/}})\index{boolp})\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{f\$g-cell}}\,({\it{a\/}}, {\it{an\/}}, {\it{bn\/}}, {\it{ga\/}}, {\it{gan\/}}, {\it{gbn\/}})\index{f\$g-cell} $=$ {\rm{g-cell}}\,({\it{a\/}}, {\it{an\/}}, {\it{bn\/}}, {\it{ga\/}}, {\it{gan\/}}, {\it{gbn\/}})\index{g-cell})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  g-cell\$value-zero \\ \index{g-cell\$value-zero}
\=\+{\rm{g-cell\&}}\,({\it{netlist\/}})\index{g-cell\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{g-cell}}, {\rm{list}}\,({\it{a\/}}, {\it{an\/}}, {\it{bn\/}}, {\bf{f}}, {\bf{f}}, {\bf{f}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\bf{t}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{alu-cell} \\  
\=\+{\rm{alu-cell}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}})\index{alu-cell} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{p-cell}}\,({\it{a\/}}, {\rm{b-not}}\,({\it{a\/}})\index{b-not}, {\it{b\/}}, {\rm{cadddddr}}\,({\it{mpg\/}}), {\rm{caddddr}}\,({\it{mpg\/}}), {\rm{cadddr}}\,({\it{mpg\/}}))\index{p-cell}, \\ 
{\rm{g-cell}}\,({\it{a\/}}, {\rm{b-not}}\,({\it{a\/}})\index{b-not}, {\rm{b-not}}\,({\it{b\/}})\index{b-not}, {\rm{caddr}}\,({\it{mpg\/}}), {\rm{cadr}}\,({\it{mpg\/}}), {\rm{car}}\,({\it{mpg\/}}))\index{g-cell}, \\ 
{\rm{b-equv3}}\,(\=\+{\rm{b-nand}}\,({\it{c\/}}, {\rm{caddddddr}}\,({\it{mpg\/}}))\index{b-nand}, \\ 
{\rm{p-cell}}\,(\=\+{\it{a\/}}, \\ 
{\rm{b-not}}\,({\it{a\/}})\index{b-not}, \\ 
{\it{b\/}}, \\ 
{\rm{cadddddr}}\,({\it{mpg\/}}), \\ 
{\rm{caddddr}}\,({\it{mpg\/}}), \\ 
{\rm{cadddr}}\,({\it{mpg\/}}))\-\index{p-cell}, \\ 
{\rm{g-cell}}\,({\it{a\/}}, {\rm{b-not}}\,({\it{a\/}})\index{b-not}, {\rm{b-not}}\,({\it{b\/}})\index{b-not}, {\rm{caddr}}\,({\it{mpg\/}}), {\rm{cadr}}\,({\it{mpg\/}}), {\rm{car}}\,({\it{mpg\/}}))\index{g-cell})\-\index{b-equv3})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$alu-cell} \\  
\=\+{\rm{f\$alu-cell}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}})\index{f\$alu-cell} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{f\$p-cell}}\,({\it{a\/}}, {\rm{f-not}}\,({\it{a\/}})\index{f-not}, {\it{b\/}}, {\rm{cadddddr}}\,({\it{mpg\/}}), {\rm{caddddr}}\,({\it{mpg\/}}), {\rm{cadddr}}\,({\it{mpg\/}}))\index{f\$p-cell}, \\ 
{\rm{f\$g-cell}}\,({\it{a\/}}, {\rm{f-not}}\,({\it{a\/}})\index{f-not}, {\rm{f-not}}\,({\it{b\/}})\index{f-not}, {\rm{caddr}}\,({\it{mpg\/}}), {\rm{cadr}}\,({\it{mpg\/}}), {\rm{car}}\,({\it{mpg\/}}))\index{f\$g-cell}, \\ 
{\rm{f-equv3}}\,(\=\+{\rm{f-nand}}\,({\it{c\/}}, {\rm{caddddddr}}\,({\it{mpg\/}}))\index{f-nand}, \\ 
{\rm{f\$p-cell}}\,(\=\+{\it{a\/}}, \\ 
{\rm{f-not}}\,({\it{a\/}})\index{f-not}, \\ 
{\it{b\/}}, \\ 
{\rm{cadddddr}}\,({\it{mpg\/}}), \\ 
{\rm{caddddr}}\,({\it{mpg\/}}), \\ 
{\rm{cadddr}}\,({\it{mpg\/}}))\-\index{f\$p-cell}, \\ 
{\rm{f\$g-cell}}\,(\=\+{\it{a\/}}, \\ 
{\rm{f-not}}\,({\it{a\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{b\/}})\index{f-not}, \\ 
{\rm{caddr}}\,({\it{mpg\/}}), \\ 
{\rm{cadr}}\,({\it{mpg\/}}), \\ 
{\rm{car}}\,({\it{mpg\/}}))\-\index{f\$g-cell})\-\index{f-equv3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$alu-cell; name this event `f\$alu-cell-off'.\index{f\$alu-cell-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$alu-cell=alu-cell \\ \index{f\$alu-cell=alu-cell}
\=\+({\rm{boolp}}\,({\it{c\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{a\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{b\/}})\index{boolp} $\wedge$ {\rm{bvp}}\,({\it{mpg\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{mpg\/}})\index{length} $=$ {\tt{7}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f\$alu-cell}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}})\index{f\$alu-cell} $=$ {\rm{alu-cell}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}})\index{alu-cell})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{alu-cell*} \\  
\=\+{\sc{alu-cell*}}\index{alu-cell*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{alu-cell}} \\ 
{\tt{(}}{\tt{c}}{\tt{ }}{\tt{a}}{\tt{ }}{\tt{b}}{\tt{ }}{\tt{gbn}}{\tt{ }}{\tt{gan}}{\tt{ }}{\tt{ga}}{\tt{ }}{\tt{pb}}{\tt{ }}{\tt{pan}}{\tt{ }}{\tt{pa}}{\tt{ }}{\tt{m}}{\tt{)}} \\ 
{\tt{(}}{\tt{p}}{\tt{ }}{\tt{g}}{\tt{ }}{\tt{z}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{n0}}{\tt{ }}{\tt{(}}{\tt{an}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{a}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{n1}}{\tt{ }}{\tt{(}}{\tt{bn}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{b}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{p0}}{\tt{ }}{\tt{(}}{\tt{p}}{\tt{)}}{\tt{ }}{\tt{p-cell}}{\tt{ }}{\tt{(}}{\tt{a}}{\tt{ }}{\tt{an}}{\tt{ }}{\tt{b}}{\tt{ }}{\tt{pa}}{\tt{ }}{\tt{pan}}{\tt{ }}{\tt{pb}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g0}}{\tt{ }}{\tt{(}}{\tt{g}}{\tt{)}}{\tt{ }}{\tt{g-cell}}{\tt{ }}{\tt{(}}{\tt{a}}{\tt{ }}{\tt{an}}{\tt{ }}{\tt{bn}}{\tt{ }}{\tt{ga}}{\tt{ }}{\tt{gan}}{\tt{ }}{\tt{gbn}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{m0}}{\tt{ }}{\tt{(}}{\tt{mc}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{c}}{\tt{ }}{\tt{m}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{z0}}{\tt{ }}{\tt{(}}{\tt{z}}{\tt{)}}{\tt{ }}{\tt{b-equv3}}{\tt{ }}{\tt{(}}{\tt{mc}}{\tt{ }}{\tt{p}}{\tt{ }}{\tt{g}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{alu-cell\&} \\  
\=\+{\rm{alu-cell\&}}\,({\it{netlist\/}})\index{alu-cell\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{alu-cell}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{alu-cell*}}\index{alu-cell*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{alu-cell}}, {\it{netlist\/}})\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{p-cell\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{alu-cell}}, {\it{netlist\/}})\index{delete-module})\index{p-cell\&} \\ 
$\wedge$$\;\;\;\;${\rm{g-cell\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{alu-cell}}, {\it{netlist\/}})\index{delete-module})\index{g-cell\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{alu-cell}}, {\it{netlist\/}})\index{delete-module})\index{b-nand\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-equv3\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{alu-cell}}, {\it{netlist\/}})\index{delete-module})\index{b-equv3\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable alu-cell\&; name this event `alu-cell\&-off'.\index{alu-cell\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{alu-cell\$netlist} \\  
\=\+{\sc{alu-cell\$netlist}}\index{alu-cell\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{alu-cell*}}\index{alu-cell*}, \\ 
\=\+(\=\+(({\sc{b-not\$netlist}}\index{b-not\$netlist} $\cup$ {\sc{p-cell\$netlist}}\index{p-cell\$netlist}) $\cup$ {\sc{g-cell\$netlist}}\index{g-cell\$netlist}) \\ 
$\cup$$\;\;\;\;${\sc{b-nand\$netlist}}\index{b-nand\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-equv3\$netlist}}\index{b-equv3\$netlist}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  alu-cell\$value \\ \index{alu-cell\$value}
\=\+{\rm{alu-cell\&}}\,({\it{netlist\/}})\index{alu-cell\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{alu-cell}}, {\rm{cons}}\,({\it{c\/}}, {\rm{cons}}\,({\it{a\/}}, {\rm{cons}}\,({\it{b\/}}, {\it{mpg\/}}))), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$alu-cell}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}})\index{f\$alu-cell})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable alu-cell\$value; name this event `alu-cell\$value-off'.\index{alu-cell\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  alu-cell\$value-zero \\ \index{alu-cell\$value-zero}
\=\+({\rm{alu-cell\&}}\,({\it{netlist\/}})\index{alu-cell\&} $\wedge$ ({\it{mpg\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{alu-cell}}, {\rm{cons}}\,({\bf{t}}, {\rm{cons}}\,({\it{a\/}}, {\rm{cons}}\,({\it{b\/}}, {\it{mpg\/}}))), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable alu-cell\$value-zero; name this event `alu-cell\$value-zero-off'.\index{alu-cell\$value-zero-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$alu-cell-v-threefix-mpg \\ \index{f\$alu-cell-v-threefix-mpg}
\=\+({\rm{length}}\,({\it{mpg\/}})\index{length} $=$ {\tt{7}}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f\$alu-cell}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\rm{v-threefix}}\,({\it{mpg\/}})\index{v-threefix})\index{f\$alu-cell} $=$ {\rm{f\$alu-cell}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}})\index{f\$alu-cell})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tv-alu-help} \\  
\=\+{\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{alu-cell}}\,({\it{c\/}}, {\rm{car}}\,({\it{a\/}}), {\rm{car}}\,({\it{b\/}}), {\it{mpg\/}})\index{alu-cell} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{b-and}}\,(\=\+{\rm{car}}\,({\rm{tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\rm{tfirstn}}\,({\it{b\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-alu-help}), \\ 
{\rm{car}}\,({\rm{tv-alu-help}}\,(\=\+{\rm{t-carry}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-alu-help}), \\ 
{\rm{cadr}}\,({\rm{tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-alu-help}))\-\index{t-carry}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{trestn}}\,({\it{b\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{cdr}}\,({\it{tree\/}}))\-\index{tv-alu-help}))\-\index{b-and}, \\ 
{\rm{cons}}\,(\=\+{\rm{t-carry}}\,(\=\+{\rm{cadr}}\,({\rm{tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\rm{tfirstn}}\,({\it{b\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-alu-help}), \\ 
{\rm{car}}\,({\rm{tv-alu-help}}\,(\=\+{\rm{t-carry}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-alu-help}), \\ 
{\rm{cadr}}\,({\rm{tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-alu-help}))\-\index{t-carry}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{trestn}}\,({\it{b\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{cdr}}\,({\it{tree\/}}))\-\index{tv-alu-help}), \\ 
{\rm{cadr}}\,({\rm{tv-alu-help}}\,(\=\+{\rm{t-carry}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-alu-help}), \\ 
{\rm{cadr}}\,({\rm{tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-alu-help}))\-\index{t-carry}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{trestn}}\,({\it{b\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{cdr}}\,({\it{tree\/}}))\-\index{tv-alu-help}))\-\index{t-carry}, \\ 
{\rm{append}}\,(\=\+{\rm{cddr}}\,({\rm{tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\rm{tfirstn}}\,({\it{b\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-alu-help}), \\ 
{\rm{cddr}}\,({\rm{tv-alu-help}}\,(\=\+{\rm{t-carry}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-alu-help}), \\ 
{\rm{cadr}}\,({\rm{tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-alu-help}))\-\index{t-carry}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{trestn}}\,({\it{b\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{cdr}}\,({\it{tree\/}}))\-\index{tv-alu-help}))\-)\-)\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-alu-help; name this event `tv-alu-help-off'.\index{tv-alu-help-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cddr-tv-alu-help-length \\ \index{cddr-tv-alu-help-length}
{\rm{length}}\,({\rm{cddr}}\,({\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help}))\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tv-alu-help-length \\ \index{tv-alu-help-length}
{\rm{length}}\,({\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help})\index{length} $=$ ($1\;+$ ($1\;+$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-cddr-tv-alu-help \\ \index{bvp-cddr-tv-alu-help}
{\rm{bvp}}\,({\rm{cddr}}\,({\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help}))\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-tv-alu-help \\ \index{bvp-tv-alu-help}
{\rm{bvp}}\,({\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-length-tv-alu-help \\ \index{bvp-length-tv-alu-help}
\=\+{\rm{bvp-length}}\,({\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help}, {\it{n\/}})\index{bvp-length} \\ 
$=$$\;\;\;\;$\=\+{\bf if }($1\;+$ ($1\;+$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})) $<$ {\it{n\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tv-alu-help-zero \\ \index{tv-alu-help-zero}
\=\+(\=\+({\it{mpg\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}})) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\wedge$$\;\;\;\;$({\it{c\/}} $=$ {\bf{t}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help} \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{t}}, {\rm{make-list}}\,({\rm{length}}\,({\it{a\/}})\index{length}, {\bf{f}})\index{make-list})))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-alu-help-zero; name this event `tv-alu-help-zero-off'.\index{tv-alu-help-zero-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tv-alu-help-v-and-works \\ \index{tv-alu-help-v-and-works}
\=\+(\=\+{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\wedge$$\;\;\;\;$({\it{mpg\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}})))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{cddr}}\,({\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help}) $=$ {\rm{v-and}}\,({\it{a\/}}, {\it{b\/}})\index{v-and})\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-alu-help-v-and-works; name this event `tv-alu-help-v-and-works-off'.\index{tv-alu-help-v-and-works-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tv-alu-help-v-or-works \\ \index{tv-alu-help-v-or-works}
\=\+(\=\+({\it{mpg\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}})) \\ 
$\wedge$$\;\;\;\;${\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{cddr}}\,({\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help}) $=$ {\rm{v-or}}\,({\it{a\/}}, {\it{b\/}})\index{v-or})\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-alu-help-v-or-works; name this event `tv-alu-help-v-or-works-off'.\index{tv-alu-help-v-or-works-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tv-alu-help-v-xor-works \\ \index{tv-alu-help-v-xor-works}
\=\+(\=\+({\it{mpg\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}})) \\ 
$\wedge$$\;\;\;\;${\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{cddr}}\,({\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help}) $=$ {\rm{v-xor}}\,({\it{a\/}}, {\it{b\/}})\index{v-xor})\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-alu-help-v-xor-works; name this event `tv-alu-help-v-xor-works-off'.\index{tv-alu-help-v-xor-works-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tv-alu-help-v-not-works \\ \index{tv-alu-help-v-not-works}
\=\+(\=\+({\it{mpg\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}})) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{cddr}}\,({\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help}) $=$ {\rm{v-not}}\,({\it{a\/}})\index{v-not})\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-alu-help-v-not-works; name this event `tv-alu-help-v-not-works-off'.\index{tv-alu-help-v-not-works-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tv-alu-help-v-buf-works \\ \index{tv-alu-help-v-buf-works}
\=\+(\=\+({\it{mpg\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}})) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{cddr}}\,({\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help}) $=$ {\rm{v-buf}}\,({\it{a\/}})\index{v-buf})\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-alu-help-v-buf-works; name this event `tv-alu-help-v-buf-works-off'.\index{tv-alu-help-v-buf-works-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tv-alu-help-tv-adder-works \\ \index{tv-alu-help-tv-adder-works}
\=\+(\=\+({\it{mpg\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}})) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help} $=$ {\rm{tv-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{tree\/}})\index{tv-adder})\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-alu-help-tv-adder-works; name this event `tv-alu-help-tv-adder-works-off'.\index{tv-alu-help-tv-adder-works-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tv-alu-help-tv-subtracter-works \\ \index{tv-alu-help-tv-subtracter-works}
\=\+(\=\+({\it{mpg\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}})) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help} $=$ {\rm{tv-adder}}\,({\it{c\/}}, {\rm{v-not}}\,({\it{a\/}})\index{v-not}, {\it{b\/}}, {\it{tree\/}})\index{tv-adder})\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-alu-help-tv-subtracter-works; name this event `tv-alu-help-tv-subtracter-works-off'.\index{tv-alu-help-tv-subtracter-works!-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tv-alu-help-tv-inc-a-works \\ \index{tv-alu-help-tv-inc-a-works}
\=\+(\=\+({\it{mpg\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}})) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help} \\ 
$=$$\;\;\;\;${\rm{tv-adder}}\,({\it{c\/}}, {\it{a\/}}, {\rm{nat-to-v}}\,({\tt{0}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{nat-to-v}, {\it{tree\/}})\index{tv-adder})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-alu-help-tv-inc-a-works; name this event `tv-alu-help-tv-inc-a-works-off'.\index{tv-alu-help-tv-inc-a-works-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tv-alu-help-tv-inc-b-works \\ \index{tv-alu-help-tv-inc-b-works}
\=\+(\=\+({\it{mpg\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}})) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help} \\ 
$=$$\;\;\;\;${\rm{tv-adder}}\,({\it{c\/}}, {\it{b\/}}, {\rm{nat-to-v}}\,({\tt{0}}, {\rm{length}}\,({\it{b\/}})\index{length})\index{nat-to-v}, {\it{tree\/}})\index{tv-adder})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-alu-help-tv-inc-b-works; name this event `tv-alu-help-tv-inc-b-works-off'.\index{tv-alu-help-tv-inc-b-works-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tv-alu-help-tv-dec-a-works \\ \index{tv-alu-help-tv-dec-a-works}
\=\+(\=\+({\it{mpg\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}})) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help} \\ 
$=$$\;\;\;\;${\rm{tv-adder}}\,({\it{c\/}}, {\rm{v-not}}\,({\rm{nat-to-v}}\,({\tt{0}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{nat-to-v})\index{v-not}, {\it{a\/}}, {\it{tree\/}})\index{tv-adder})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-alu-help-tv-dec-a-works; name this event `tv-alu-help-tv-dec-a-works-off'.\index{tv-alu-help-tv-dec-a-works-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tv-alu-help-tv-dec-b-works \\ \index{tv-alu-help-tv-dec-b-works}
\=\+(\=\+({\it{mpg\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}})) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help} \\ 
$=$$\;\;\;\;${\rm{tv-adder}}\,({\it{c\/}}, {\rm{v-not}}\,({\rm{nat-to-v}}\,({\tt{0}}, {\rm{length}}\,({\it{b\/}})\index{length})\index{nat-to-v})\index{v-not}, {\it{b\/}}, {\it{tree\/}})\index{tv-adder})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-alu-help-tv-dec-b-works; name this event `tv-alu-help-tv-dec-b-works-off'.\index{tv-alu-help-tv-dec-b-works-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tv-alu-help-tv-neg-works \\ \index{tv-alu-help-tv-neg-works}
\=\+(\=\+({\it{mpg\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}})) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help} \\ 
$=$$\;\;\;\;${\rm{tv-adder}}\,({\it{c\/}}, {\rm{v-not}}\,({\it{a\/}})\index{v-not}, {\rm{nat-to-v}}\,({\tt{0}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{nat-to-v}, {\it{tree\/}})\index{tv-adder})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-alu-help-tv-neg-works; name this event `tv-alu-help-tv-neg-works-off'.\index{tv-alu-help-tv-neg-works-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{f\$tv-alu-help} \\  
\=\+{\rm{f\$tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{f\$tv-alu-help} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{f\$alu-cell}}\,({\it{c\/}}, {\rm{car}}\,({\it{a\/}}), {\rm{car}}\,({\it{b\/}}), {\it{mpg\/}})\index{f\$alu-cell} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{f-and}}\,(\=\+{\rm{car}}\,({\rm{f\$tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\rm{tfirstn}}\,({\it{b\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{f\$tv-alu-help}), \\ 
{\rm{car}}\,({\rm{f\$tv-alu-help}}\,(\=\+{\rm{f\$t-carry}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{f\$tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{f\$tv-alu-help}), \\ 
{\rm{cadr}}\,({\rm{f\$tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{f\$tv-alu-help}))\-\index{f\$t-carry}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{trestn}}\,({\it{b\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{cdr}}\,({\it{tree\/}}))\-\index{f\$tv-alu-help}))\-\index{f-and}, \\ 
{\rm{cons}}\,(\=\+{\rm{f\$t-carry}}\,(\=\+{\rm{cadr}}\,({\rm{f\$tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\rm{tfirstn}}\,({\it{b\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{f\$tv-alu-help}), \\ 
{\rm{car}}\,({\rm{f\$tv-alu-help}}\,(\=\+{\rm{f\$t-carry}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{f\$tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{f\$tv-alu-help}), \\ 
{\rm{cadr}}\,({\rm{f\$tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{f\$tv-alu-help}))\-\index{f\$t-carry}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{trestn}}\,({\it{b\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{cdr}}\,({\it{tree\/}}))\-\index{f\$tv-alu-help}), \\ 
{\rm{cadr}}\,({\rm{f\$tv-alu-help}}\,(\=\+{\rm{f\$t-carry}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{f\$tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{f\$tv-alu-help}), \\ 
{\rm{cadr}}\,({\rm{f\$tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{f\$tv-alu-help}))\-\index{f\$t-carry}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{trestn}}\,({\it{b\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{cdr}}\,({\it{tree\/}}))\-\index{f\$tv-alu-help}))\-\index{f\$t-carry}, \\ 
{\rm{append}}\,(\=\+{\rm{cddr}}\,({\rm{f\$tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\rm{tfirstn}}\,({\it{b\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{f\$tv-alu-help}), \\ 
{\rm{cddr}}\,({\rm{f\$tv-alu-help}}\,(\=\+{\rm{f\$t-carry}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{f\$tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{f\$tv-alu-help}), \\ 
{\rm{cadr}}\,({\rm{f\$tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{f\$tv-alu-help}))\-\index{f\$t-carry}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{trestn}}\,({\it{b\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\it{mpg\/}}, \\ 
{\rm{cdr}}\,({\it{tree\/}}))\-\index{f\$tv-alu-help}))\-)\-)\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$tv-alu-help; name this event `f\$tv-alu-help-off'.\index{f\$tv-alu-help-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cddr-f\$tv-alu-help-length \\ \index{cddr-f\$tv-alu-help-length}
{\rm{length}}\,({\rm{cddr}}\,({\rm{f\$tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{f\$tv-alu-help}))\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f\$tv-alu-help-length \\ \index{f\$tv-alu-help-length}
{\rm{length}}\,({\rm{f\$tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{f\$tv-alu-help})\index{length} $=$ ($1\;+$ ($1\;+$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-cddr-f\$tv-alu-help \\ \index{properp-cddr-f\$tv-alu-help}
{\rm{properp}}\,({\rm{cddr}}\,({\rm{f\$tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{f\$tv-alu-help}))\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-f\$tv-alu-help \\ \index{properp-f\$tv-alu-help}
{\rm{properp}}\,({\rm{f\$tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{f\$tv-alu-help})\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  boolp-car-f\$tv-alu-help \\ \index{boolp-car-f\$tv-alu-help}
\=\+(\=\+{\rm{boolp}}\,({\it{c\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{mpg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{mpg\/}})\index{length} $=$ {\tt{7}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{boolp}}\,({\rm{car}}\,({\rm{f\$tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{f\$tv-alu-help}))\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{cadr}}\,({\rm{f\$tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{f\$tv-alu-help}))\index{boolp})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-cddr-f\$tv-alu-help \\ \index{bvp-cddr-f\$tv-alu-help}
\=\+(\=\+{\rm{boolp}}\,({\it{c\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{mpg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{mpg\/}})\index{length} $=$ {\tt{7}}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{bvp}}\,({\rm{cddr}}\,({\rm{f\$tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{f\$tv-alu-help}))\index{bvp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-f\$tv-alu-help \\ \index{bvp-f\$tv-alu-help}
\=\+(\=\+{\rm{boolp}}\,({\it{c\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{mpg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{mpg\/}})\index{length} $=$ {\tt{7}}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{bvp}}\,({\rm{f\$tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{f\$tv-alu-help})\index{bvp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f\$tv-alu-help=tv-alu-help \\ \index{f\$tv-alu-help=tv-alu-help}
\=\+(\=\+{\rm{boolp}}\,({\it{c\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{mpg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{mpg\/}})\index{length} $=$ {\tt{7}}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{f\$tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{f\$tv-alu-help} $=$ {\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help})\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN TV-ALU-HELP-BODY
 (TREE)
 (IF
  (NLISTP TREE)
  (LIST (LIST 'LEAF
              (LIST 'P 'G (INDEX 'OUT 0))
              'ALU-CELL
              (CONS 'C
                    (CONS (INDEX 'A 0)
                          (CONS (INDEX 'B 0)
                                (INDICES 'MPG 0 7))))))
  (APPEND
   (IF (EQUAL (REMAINDER (SUB1 (TREE-HEIGHT TREE))
                         3)
              0)
       (LIST (LIST 'BUFFERMPG
                   (INDICES 'MPG- 0 7)
                   (INDEX 'V-BUF 7)
                   (INDICES 'MPG 0 7)))
       NIL)
   (CONS
    (LIST 'LHS
          (CONS 'PL
                (CONS 'GL
                      (TFIRSTN (INDICES 'OUT 0 (TREE-SIZE TREE))
                               TREE)))
          (INDEX 'TV-ALU-HELP
                 (TREE-NUMBER (CAR TREE)))
          (CONS 'C
                (APPEND (TFIRSTN (INDICES 'A 0 (TREE-SIZE TREE))
                                 TREE)
                        (APPEND (TFIRSTN (INDICES 'B 0 (TREE-SIZE TREE))
                                         TREE)
                                (IF (EQUAL (REMAINDER (SUB1 (TREE-HEIGHT TREE))
                                                      3)
                                           0)
                                    (INDICES 'MPG- 0 7)
                                    (INDICES 'MPG 0 7))))))
    (CONS
     '(LHS-CARRY (CL) T-CARRY (C PL GL))
     (CONS
      (LIST 'RHS
          (CONS 'PR
                (CONS 'GR
                      (TRESTN (INDICES 'OUT 0 (TREE-SIZE TREE))
                              TREE)))
          (INDEX 'TV-ALU-HELP
                 (TREE-NUMBER (CDR TREE)))
          (CONS 'CL
                (APPEND (TRESTN (INDICES 'A 0 (TREE-SIZE TREE))
                                TREE)
                        (APPEND (TRESTN (INDICES 'B 0 (TREE-SIZE TREE))
                                        TREE)
                                (IF (EQUAL (REMAINDER (SUB1 (TREE-HEIGHT TREE))
                                                      3)
                                           0)
                                    (INDICES 'MPG- 0 7)
                                    (INDICES 'MPG 0 7))))))
      '((P (P) B-AND (PL PR))
        (G (G) T-CARRY (GL PR GR)))))))))
\end{verbatim}


\begin{tabbing}{\sc Definition}:\index{tv-alu-help*} \\  
\=\+{\rm{tv-alu-help*}}\,({\it{tree\/}})\index{tv-alu-help*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{tv-alu-help}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{c}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{b}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{mpg}}, {\tt{0}}, {\tt{7}})\index{indices})\-)\-)\-, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,({\tt{'}}{\tt{p}}, {\rm{cons}}\,({\tt{'}}{\tt{g}}, {\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices})), \\ 
{\rm{cons}}\,({\rm{tv-alu-help-body}}\,({\it{tree\/}})\index{tv-alu-help-body}, {\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}}))\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tv-alu-help*\$destructure \\ \index{tv-alu-help*\$destructure}
\=\+({\rm{car}}\,({\rm{tv-alu-help*}}\,({\it{tree\/}})\index{tv-alu-help*}) $=$ {\rm{index}}\,({\tt{'}}{\tt{tv-alu-help}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadr}}\,({\rm{tv-alu-help*}}\,({\it{tree\/}})\index{tv-alu-help*}) \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\tt{'}}{\tt{c}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{b}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{mpg}}, {\tt{0}}, {\tt{7}})\index{indices})\-)\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{caddr}}\,({\rm{tv-alu-help*}}\,({\it{tree\/}})\index{tv-alu-help*}) \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\tt{'}}{\tt{p}}, {\rm{cons}}\,({\tt{'}}{\tt{g}}, {\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices})))\- \\ 
$\wedge$$\;\;\;\;$({\rm{cadddr}}\,({\rm{tv-alu-help*}}\,({\it{tree\/}})\index{tv-alu-help*}) $=$ {\rm{tv-alu-help-body}}\,({\it{tree\/}})\index{tv-alu-help-body}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{tv-alu-help*}}\,({\it{tree\/}})\index{tv-alu-help*}) $=$ {\bf{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-alu-help*; name this event `tv-alu-help*-off'.\index{tv-alu-help*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable tv-alu-help*\$destructure; name this event `tv-alu-help*\$destructure-off'.\index{tv-alu-help*\$destructure-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tv-alu-help\&} \\  
\=\+{\rm{tv-alu-help\&}}\,({\it{netlist\/}}, {\it{tree\/}})\index{tv-alu-help\&} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$ \\ 
{\bf then }\=\+(\=\+{\rm{lookup-module}}\,({\rm{index}}\,({\tt{'}}{\tt{tv-alu-help}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, {\it{netlist\/}})\index{lookup-module} \\ 
$=$$\;\;\;\;${\rm{tv-alu-help*}}\,({\it{tree\/}})\index{tv-alu-help*})\- \\ 
$\wedge$$\;\;\;\;${\rm{alu-cell\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-alu-help}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{alu-cell\&}\- \\ 
{\bf else }\=\+(\=\+{\rm{lookup-module}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{tv-alu-help}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\it{netlist\/}})\-\index{lookup-module} \\ 
$=$$\;\;\;\;${\rm{tv-alu-help*}}\,({\it{tree\/}})\index{tv-alu-help*})\- \\ 
$\wedge$$\;\;\;\;${\rm{t-carry\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-alu-help}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{t-carry\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-and\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-alu-help}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{b-and\&} \\ 
$\wedge$$\;\;\;\;${\rm{v-buf\&}}\,(\=\+{\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-alu-help}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\tt{7}})\-\index{v-buf\&} \\ 
$\wedge$$\;\;\;\;${\rm{tv-alu-help\&}}\,(\=\+{\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-alu-help}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-alu-help\&} \\ 
$\wedge$$\;\;\;\;${\rm{tv-alu-help\&}}\,(\=\+{\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-alu-help}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\rm{cdr}}\,({\it{tree\/}}))\-\index{tv-alu-help\&}\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-alu-help\&; name this event `tv-alu-help\&-off'.\index{tv-alu-help\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tv-alu-help\$netlist} \\  
\=\+{\rm{tv-alu-help\$netlist}}\,({\it{tree\/}})\index{tv-alu-help\$netlist} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\rm{cons}}\,({\rm{tv-alu-help*}}\,({\it{tree\/}})\index{tv-alu-help*}, {\sc{alu-cell\$netlist}}\index{alu-cell\$netlist}) \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{tv-alu-help*}}\,({\it{tree\/}})\index{tv-alu-help*}, \\ 
\=\+{\rm{tv-alu-help\$netlist}}\,({\rm{car}}\,({\it{tree\/}}))\index{tv-alu-help\$netlist} \\ 
$\cup$$\;\;\;\;$(\=\+{\rm{tv-alu-help\$netlist}}\,({\rm{cdr}}\,({\it{tree\/}}))\index{tv-alu-help\$netlist} \\ 
$\cup$$\;\;\;\;$(\=\+{\sc{t-carry\$netlist}}\index{t-carry\$netlist} \\ 
$\cup$$\;\;\;\;$(\=\+{\sc{b-and\$netlist}}\index{b-and\$netlist} \\ 
$\cup$$\;\;\;\;${\rm{v-buf\$netlist}}\,({\tt{7}})\index{v-buf\$netlist})\-)\-)\-\-)\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tv-alu-help-induction} \\  
\=\+{\rm{tv-alu-help-induction}}\,({\it{tree\/}}, {\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{state\/}}, {\it{netlist\/}})\index{tv-alu-help-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }\=\+{\rm{tv-alu-help-induction}}\,(\=\+{\rm{car}}\,({\it{tree\/}}), \\ 
{\it{c\/}}, \\ 
{\rm{tfirstn}}\,({\it{a\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
{\rm{tfirstn}}\,({\it{b\/}}, {\it{tree\/}})\index{tfirstn}, \\ 
\=\+{\bf if }\=\+(({\rm{tree-height}}\,({\it{tree\/}})\index{tree-height} $-\;1$) ${}${\bf{mod}}${}$ {\tt{3}}) \\ 
$=$$\;\;\;\;${\tt{0}}\-$\;\;${\bf then }{\rm{v-threefix}}\,({\it{mpg\/}})\index{v-threefix} \\ 
{\bf else }{\it{mpg\/}}$\;${\bf  endif}\-, \\ 
{\tt{0}}, \\ 
{\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-alu-help}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\-\index{tv-alu-help-induction} \\ 
$\wedge$$\;\;\;\;${\rm{tv-alu-help-induction}}\,(\=\+{\rm{cdr}}\,({\it{tree\/}}), \\ 
{\rm{f\$t-carry}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{f\$tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
\=\+{\bf if }\=\+(\=\+({\rm{tree-height}}\,({\it{tree\/}})\index{tree-height} $-\;1$) \\ 
${}${\bf{mod}}${}$$\;\;\;\;${\tt{3}})\- \\ 
$=$$\;\;\;\;${\tt{0}}\- \\ 
{\bf then }{\rm{v-threefix}}\,({\it{mpg\/}})\index{v-threefix} \\ 
{\bf else }{\it{mpg\/}}$\;${\bf  endif}\-, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{f\$tv-alu-help}), \\ 
{\rm{cadr}}\,({\rm{f\$tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{a\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
{\rm{tfirstn}}\,(\=\+{\it{b\/}}, \\ 
{\it{tree\/}})\-\index{tfirstn}, \\ 
\=\+{\bf if }\=\+(\=\+({\rm{tree-height}}\,({\it{tree\/}})\index{tree-height} $-\;1$) \\ 
${}${\bf{mod}}${}$$\;\;\;\;${\tt{3}})\- \\ 
$=$$\;\;\;\;${\tt{0}}\- \\ 
{\bf then }{\rm{v-threefix}}\,({\it{mpg\/}})\index{v-threefix} \\ 
{\bf else }{\it{mpg\/}}$\;${\bf  endif}\-, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{f\$tv-alu-help}))\-\index{f\$t-carry}, \\ 
{\rm{trestn}}\,({\it{a\/}}, {\it{tree\/}})\index{trestn}, \\ 
{\rm{trestn}}\,({\it{b\/}}, {\it{tree\/}})\index{trestn}, \\ 
\=\+{\bf if }\=\+(\=\+({\rm{tree-height}}\,({\it{tree\/}})\index{tree-height} $-\;1$) \\ 
${}${\bf{mod}}${}$$\;\;\;\;${\tt{3}})\- \\ 
$=$$\;\;\;\;${\tt{0}}\- \\ 
{\bf then }{\rm{v-threefix}}\,({\it{mpg\/}})\index{v-threefix} \\ 
{\bf else }{\it{mpg\/}}$\;${\bf  endif}\-, \\ 
{\tt{0}}, \\ 
{\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-alu-help}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\-\index{tv-alu-help-induction}\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tv-alu-help-lemma-crock \\ \index{tv-alu-help-lemma-crock}
\=\+{\rm{tv-alu-help\&}}\,(\=\+{\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{tv-alu-help}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, {\it{netlist\/}})\index{delete-module}, \\ 
{\rm{car}}\,({\it{tree\/}}))\-\index{tv-alu-help\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{append}}\,(\=\+{\rm{collect-value}}\,(\=\+{\rm{firstn}}\,(\=\+{\rm{tree-size}}\,({\rm{car}}\,({\it{tree\/}}))\index{tree-size}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\it{n\/}})\index{indices})\-\index{firstn}, \\ 
{\it{bindings\/}})\-\index{collect-value}, \\ 
{\rm{collect-value}}\,(\=\+{\rm{restn}}\,(\=\+{\rm{tree-size}}\,({\rm{car}}\,({\it{tree\/}}))\index{tree-size}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\it{n\/}})\index{indices})\-\index{restn}, \\ 
{\it{bindings\/}})\-\index{collect-value})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-alu-help-lemma-crock; name this event `tv-alu-help-lemma-crock-off'.\index{tv-alu-help-lemma-crock-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tv-alu-help\$value-base-case \\ \index{tv-alu-help\$value-base-case}
\=\+(\=\+({\it{tree\/}} $\simeq\;${{\bf{nil}}}${}$) \\ 
$\wedge$$\;\;\;\;${\rm{tv-alu-help\&}}\,({\it{netlist\/}}, {\it{tree\/}})\index{tv-alu-help\&} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\tt{1}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{a\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\tt{1}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{b\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{mpg\/}})\index{length} $=$ {\tt{7}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{mpg\/}})\index{properp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{tv-alu-help}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\rm{cons}}\,({\it{c\/}}, {\rm{append}}\,({\it{a\/}}, {\rm{append}}\,({\it{b\/}}, {\it{mpg\/}}))), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{f\$tv-alu-help})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-alu-help\$value-base-case; name this event `tv-alu-help\$value-base-case-off'.\index{tv-alu-help\$value-base-case-of!f}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$tv-alu-help-v-threefix-mpg \\ \index{f\$tv-alu-help-v-threefix-mpg}
\=\+({\rm{length}}\,({\it{mpg\/}})\index{length} $=$ {\tt{7}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\rm{v-threefix}}\,({\it{mpg\/}})\index{v-threefix}, {\it{tree\/}})\index{f\$tv-alu-help} \\ 
$=$$\;\;\;\;${\rm{f\$tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{f\$tv-alu-help})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tv-alu-help\$value \\ \index{tv-alu-help\$value}
\=\+(\=\+{\rm{tv-alu-help\&}}\,({\it{netlist\/}}, {\it{tree\/}})\index{tv-alu-help\&} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{a\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{b\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{mpg\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{mpg\/}})\index{length} $=$ {\tt{7}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{tv-alu-help}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\rm{cons}}\,({\it{c\/}}, {\rm{append}}\,({\it{a\/}}, {\rm{append}}\,({\it{b\/}}, {\it{mpg\/}}))), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{f\$tv-alu-help})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-alu-help\$value; name this event `tv-alu-help\$value-off'.\index{tv-alu-help\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{carry-out-help} \\  
\=\+{\rm{carry-out-help}}\,({\it{a0\/}}, {\it{result\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{carry-out-help} \\ 
$=$$\;\;\;\;${\rm{b-and}}\,(\=\+{\rm{b-nand3}}\,(\=\+{\rm{b-nand4}}\,(\=\+{\rm{b-not}}\,({\it{op3\/}})\index{b-not}, \\ 
{\rm{b-nand}}\,({\rm{b-not}}\,({\it{op0\/}})\index{b-not}, {\rm{b-not}}\,({\it{op1\/}})\index{b-not})\index{b-nand}, \\ 
{\rm{b-not}}\,({\it{op2\/}})\index{b-not}, \\ 
{\it{result\/}})\-\index{b-nand4}, \\ 
{\rm{b-nand3}}\,({\rm{b-not}}\,({\it{op3\/}})\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\it{op2\/}})\index{b-not})\index{b-not}, {\rm{b-not}}\,({\it{result\/}})\index{b-not})\index{b-nand3}, \\ 
{\rm{b-nand4}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\it{op3\/}})\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\it{op2\/}})\index{b-not}, \\ 
{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\it{op0\/}})\index{b-not})\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\it{op1\/}})\index{b-not})\index{b-not})\index{b-nand}, \\ 
{\it{a0\/}})\-\index{b-nand4})\-\index{b-nand3}, \\ 
{\rm{b-not}}\,({\it{zero\/}})\index{b-not})\-\index{b-and}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$carry-out-help} \\  
\=\+{\rm{f\$carry-out-help}}\,({\it{a0\/}}, {\it{result\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$carry-out-help} \\ 
$=$$\;\;\;\;${\rm{f-and}}\,(\=\+{\rm{f-nand3}}\,(\=\+{\rm{f-nand4}}\,(\=\+{\rm{f-not}}\,({\it{op3\/}})\index{f-not}, \\ 
{\rm{f-nand}}\,({\rm{f-not}}\,({\it{op0\/}})\index{f-not}, {\rm{f-not}}\,({\it{op1\/}})\index{f-not})\index{f-nand}, \\ 
{\rm{f-not}}\,({\it{op2\/}})\index{f-not}, \\ 
{\it{result\/}})\-\index{f-nand4}, \\ 
{\rm{f-nand3}}\,({\rm{f-not}}\,({\it{op3\/}})\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\it{op2\/}})\index{f-not})\index{f-not}, {\rm{f-not}}\,({\it{result\/}})\index{f-not})\index{f-nand3}, \\ 
{\rm{f-nand4}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\it{op3\/}})\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{op2\/}})\index{f-not}, \\ 
{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\it{op0\/}})\index{f-not})\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\it{op1\/}})\index{f-not})\index{f-not})\index{f-nand}, \\ 
{\it{a0\/}})\-\index{f-nand4})\-\index{f-nand3}, \\ 
{\rm{f-not}}\,({\it{zero\/}})\index{f-not})\-\index{f-and}\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$carry-out-help; name this event `f\$carry-out-help-off'.\index{f\$carry-out-help-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{carry-out-help*} \\  
\=\+{\sc{carry-out-help*}}\index{carry-out-help*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{carry-out-help}} \\ 
{\tt{(}}{\tt{a0}}{\tt{ }}{\tt{result}}{\tt{ }}{\tt{zero}}{\tt{ }}{\tt{op0}}{\tt{ }}{\tt{op1}}{\tt{ }}{\tt{op2}}{\tt{ }}{\tt{op3}}{\tt{)}} \\ 
{\tt{(}}{\tt{w-22}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{g-21}}{\tt{ }}{\tt{(}}{\tt{w-21}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{zero}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-16}}{\tt{ }}{\tt{(}}{\tt{w-16}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-17}}{\tt{ }}{\tt{(}}{\tt{w-17}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{w-16}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-14}}{\tt{ }}{\tt{(}}{\tt{w-14}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-15}}{\tt{ }}{\tt{(}}{\tt{w-15}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{w-14}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-18}}{\tt{ }}{\tt{(}}{\tt{w-18}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{w-15}}{\tt{ }}{\tt{w-17}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-13}}{\tt{ }}{\tt{(}}{\tt{w-13}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-11}}{\tt{ }}{\tt{(}}{\tt{w-11}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-12}}{\tt{ }}{\tt{(}}{\tt{w-12}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{w-11}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-19}}{\tt{ }}{\tt{(}}{\tt{w-19}}{\tt{)}}{\tt{ }}{\tt{b-nand4}}{\tt{ }}{\tt{(}}{\tt{w-12}}{\tt{ }}{\tt{w-13}}{\tt{ }}{\tt{w-18}}{\tt{ }}{\tt{a0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-9}}{\tt{ }}{\tt{(}}{\tt{w-9}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{result}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-8}}{\tt{ }}{\tt{(}}{\tt{w-8}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{w-13}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-10}}{\tt{ }}{\tt{(}}{\tt{w-10}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{w-11}}{\tt{ }}{\tt{w-8}}{\tt{ }}{\tt{w-9}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-3}}{\tt{ }}{\tt{(}}{\tt{w-3}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{w-14}}{\tt{ }}{\tt{w-16}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-5}}{\tt{ }}{\tt{(}}{\tt{w-5}}{\tt{)}}{\tt{ }}{\tt{b-nand4}}{\tt{ }}{\tt{(}}{\tt{w-11}}{\tt{ }}{\tt{w-3}}{\tt{ }}{\tt{w-13}}{\tt{ }}{\tt{result}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-20}}{\tt{ }}{\tt{(}}{\tt{w-20}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{w-5}}{\tt{ }}{\tt{w-10}}{\tt{ }}{\tt{w-19}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-22}}{\tt{ }}{\tt{(}}{\tt{w-22}}{\tt{)}}{\tt{ }}{\tt{b-and}}{\tt{ }}{\tt{(}}{\tt{w-20}}{\tt{ }}{\tt{w-21}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{carry-out-help\&} \\  
\=\+{\rm{carry-out-help\&}}\,({\it{netlist\/}})\index{carry-out-help\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{carry-out-help}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{carry-out-help*}}\index{carry-out-help*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{carry-out-help}}, {\it{netlist\/}})\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{carry-out-help}}, {\it{netlist\/}})\index{delete-module})\index{b-nand\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand4\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{carry-out-help}}, {\it{netlist\/}})\index{delete-module})\index{b-nand4\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand3\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{carry-out-help}}, {\it{netlist\/}})\index{delete-module})\index{b-nand3\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-and\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{carry-out-help}}, {\it{netlist\/}})\index{delete-module})\index{b-and\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable carry-out-help\&; name this event `carry-out-help\&-off'.\index{carry-out-help\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{carry-out-help\$netlist} \\  
\=\+{\sc{carry-out-help\$netlist}}\index{carry-out-help\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{carry-out-help*}}\index{carry-out-help*}, \\ 
\=\+(\=\+(({\sc{b-not\$netlist}}\index{b-not\$netlist} $\cup$ {\sc{b-nand\$netlist}}\index{b-nand\$netlist}) $\cup$ {\sc{b-nand4\$netlist}}\index{b-nand4\$netlist}) \\ 
$\cup$$\;\;\;\;${\sc{b-nand3\$netlist}}\index{b-nand3\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-and\$netlist}}\index{b-and\$netlist}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  carry-out-help\$value \\ \index{carry-out-help\$value}
\=\+{\rm{carry-out-help\&}}\,({\it{netlist\/}})\index{carry-out-help\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{carry-out-help}}, \\ 
{\rm{list}}\,({\it{a0\/}}, {\it{result\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}}), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f\$carry-out-help}}\,({\it{a0\/}}, {\it{result\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$carry-out-help}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable carry-out-help\$value; name this event `carry-out-help\$value-off'.\index{carry-out-help\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$carry-out-help=carry-out-help \\ \index{f\$carry-out-help=carry-out-help}
\=\+(\=\+{\rm{boolp}}\,({\it{a0\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{result\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{zero\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op0\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op1\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op2\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op3\/}})\index{boolp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$carry-out-help}}\,({\it{a0\/}}, {\it{result\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$carry-out-help} \\ 
$=$$\;\;\;\;${\rm{carry-out-help}}\,({\it{a0\/}}, {\it{result\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{carry-out-help})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  carry-out-help-congruence \\ \index{carry-out-help-congruence}
{\it{x\/}} $\rightarrow$ (\=\+(\=\+{\rm{carry-out-help}}\,({\it{x\/}}, {\it{a\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{carry-out-help} \\ 
$=$$\;\;\;\;${\rm{carry-out-help}}\,({\bf{t}}, {\it{a\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{carry-out-help})\- \\ 
$=$$\;\;\;\;${\bf{t}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  carry-out-help\$value-zero \\ \index{carry-out-help\$value-zero}
\=\+{\rm{carry-out-help\&}}\,({\it{netlist\/}})\index{carry-out-help\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{carry-out-help}}, \\ 
{\rm{list}}\,({\it{a0\/}}, {\it{result\/}}, {\bf{t}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}}), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\bf{f}}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable carry-out-help\$value-zero; name this event `carry-out-help\$value-zero-off'.\index{carry-out-help\$value-zero-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{overflow-help} \\  
\=\+{\rm{overflow-help}}\,({\it{rn\/}}, {\it{an\/}}, {\it{bn\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{overflow-help} \\ 
$=$$\;\;\;\;${\rm{b-if}}\,(\=\+{\it{rn\/}}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,(\=\+{\rm{b-nor}}\,(\=\+{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\it{op3\/}})\index{b-not}, \\ 
{\rm{b-or3}}\,(\=\+{\rm{b-not}}\,({\it{op1\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\it{op2\/}})\index{b-not}, \\ 
{\rm{b-xor}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\it{an\/}})\index{b-not})\index{b-not}, {\it{bn\/}})\index{b-xor})\-\index{b-or3}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\it{op1\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\it{op2\/}})\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\it{an\/}})\index{b-not})\-\index{b-nand3})\-\index{b-nand3}, \\ 
{\rm{b-nand}}\,(\=\+{\rm{b-nand3}}\,(\=\+{\it{op1\/}}, \\ 
{\rm{b-not}}\,({\it{op2\/}})\index{b-not}, \\ 
{\rm{b-xor}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\it{an\/}})\index{b-not})\index{b-not}, {\it{bn\/}})\index{b-xor})\-\index{b-nand3}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\it{op1\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\it{op2\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\it{an\/}})\index{b-not})\index{b-not})\-\index{b-nand3})\-\index{b-nand})\-\index{b-nor}, \\ 
{\rm{b-not}}\,({\it{zero\/}})\index{b-not})\-\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\it{op2\/}})\index{b-not})\index{b-not}, {\rm{b-not}}\,({\it{an\/}})\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,({\it{op0\/}}, {\rm{b-not}}\,({\it{op1\/}})\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\it{an\/}})\index{b-not})\index{b-not})\index{b-nand3}, \\ 
{\rm{b-nand}}\,({\rm{b-not}}\,({\it{op2\/}})\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\it{an\/}})\index{b-not})\index{b-not})\index{b-nand})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,(\=\+{\rm{b-nor}}\,(\=\+{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\it{op3\/}})\index{b-not}, \\ 
{\rm{b-or3}}\,(\=\+{\rm{b-not}}\,({\it{op1\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\it{op2\/}})\index{b-not}, \\ 
{\rm{b-xor}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\it{an\/}})\index{b-not})\index{b-not}, {\it{bn\/}})\index{b-xor})\-\index{b-or3}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\it{op1\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\it{op2\/}})\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\it{an\/}})\index{b-not})\-\index{b-nand3})\-\index{b-nand3}, \\ 
{\rm{b-nand}}\,(\=\+{\rm{b-nand3}}\,(\=\+{\it{op1\/}}, \\ 
{\rm{b-not}}\,({\it{op2\/}})\index{b-not}, \\ 
{\rm{b-xor}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\it{an\/}})\index{b-not})\index{b-not}, {\it{bn\/}})\index{b-xor})\-\index{b-nand3}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\it{op1\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\it{op2\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\it{an\/}})\index{b-not})\index{b-not})\-\index{b-nand3})\-\index{b-nand})\-\index{b-nor}, \\ 
{\rm{b-not}}\,({\it{zero\/}})\index{b-not})\-\index{b-nand}, \\ 
{\rm{b-not}}\,({\rm{b-nand3}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\it{op2\/}})\index{b-not})\index{b-not}, {\rm{b-not}}\,({\it{an\/}})\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,({\it{op0\/}}, {\rm{b-not}}\,({\it{op1\/}})\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\it{an\/}})\index{b-not})\index{b-not})\index{b-nand3}, \\ 
{\rm{b-nand}}\,({\rm{b-not}}\,({\it{op2\/}})\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\it{an\/}})\index{b-not})\index{b-not})\index{b-nand})\-\index{b-nand3})\index{b-not})\-\index{b-nor})\-\index{b-if}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$overflow-help} \\  
\=\+{\rm{f\$overflow-help}}\,({\it{rn\/}}, {\it{an\/}}, {\it{bn\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$overflow-help} \\ 
$=$$\;\;\;\;${\rm{f-if}}\,(\=\+{\it{rn\/}}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,(\=\+{\rm{f-nor}}\,(\=\+{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\it{op3\/}})\index{f-not}, \\ 
{\rm{f-or3}}\,(\=\+{\rm{f-not}}\,({\it{op1\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{op2\/}})\index{f-not}, \\ 
{\rm{f-xor}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\it{an\/}})\index{f-not})\index{f-not}, {\it{bn\/}})\index{f-xor})\-\index{f-or3}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\it{op1\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\it{op2\/}})\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{an\/}})\index{f-not})\-\index{f-nand3})\-\index{f-nand3}, \\ 
{\rm{f-nand}}\,(\=\+{\rm{f-nand3}}\,(\=\+{\it{op1\/}}, \\ 
{\rm{f-not}}\,({\it{op2\/}})\index{f-not}, \\ 
{\rm{f-xor}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\it{an\/}})\index{f-not})\index{f-not}, {\it{bn\/}})\index{f-xor})\-\index{f-nand3}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\it{op1\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{op2\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\it{an\/}})\index{f-not})\index{f-not})\-\index{f-nand3})\-\index{f-nand})\-\index{f-nor}, \\ 
{\rm{f-not}}\,({\it{zero\/}})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\it{op2\/}})\index{f-not})\index{f-not}, {\rm{f-not}}\,({\it{an\/}})\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,({\it{op0\/}}, {\rm{f-not}}\,({\it{op1\/}})\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\it{an\/}})\index{f-not})\index{f-not})\index{f-nand3}, \\ 
{\rm{f-nand}}\,({\rm{f-not}}\,({\it{op2\/}})\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\it{an\/}})\index{f-not})\index{f-not})\index{f-nand})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,(\=\+{\rm{f-nor}}\,(\=\+{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\it{op3\/}})\index{f-not}, \\ 
{\rm{f-or3}}\,(\=\+{\rm{f-not}}\,({\it{op1\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{op2\/}})\index{f-not}, \\ 
{\rm{f-xor}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\it{an\/}})\index{f-not})\index{f-not}, {\it{bn\/}})\index{f-xor})\-\index{f-or3}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\it{op1\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\it{op2\/}})\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{an\/}})\index{f-not})\-\index{f-nand3})\-\index{f-nand3}, \\ 
{\rm{f-nand}}\,(\=\+{\rm{f-nand3}}\,(\=\+{\it{op1\/}}, \\ 
{\rm{f-not}}\,({\it{op2\/}})\index{f-not}, \\ 
{\rm{f-xor}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\it{an\/}})\index{f-not})\index{f-not}, {\it{bn\/}})\index{f-xor})\-\index{f-nand3}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\it{op1\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{op2\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\it{an\/}})\index{f-not})\index{f-not})\-\index{f-nand3})\-\index{f-nand})\-\index{f-nor}, \\ 
{\rm{f-not}}\,({\it{zero\/}})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f-not}}\,({\rm{f-nand3}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\it{op2\/}})\index{f-not})\index{f-not}, {\rm{f-not}}\,({\it{an\/}})\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,({\it{op0\/}}, {\rm{f-not}}\,({\it{op1\/}})\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\it{an\/}})\index{f-not})\index{f-not})\index{f-nand3}, \\ 
{\rm{f-nand}}\,({\rm{f-not}}\,({\it{op2\/}})\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\it{an\/}})\index{f-not})\index{f-not})\index{f-nand})\-\index{f-nand3})\index{f-not})\-\index{f-nor})\-\index{f-if}\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$overflow-help; name this event `f\$overflow-help-off'.\index{f\$overflow-help-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{overflow-help*} \\  
\=\+{\sc{overflow-help*}}\index{overflow-help*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{overflow-help}} \\ 
{\tt{(}}{\tt{rn}}{\tt{ }}{\tt{an}}{\tt{ }}{\tt{bn}}{\tt{ }}{\tt{zero}}{\tt{ }}{\tt{op0}}{\tt{ }}{\tt{op1}}{\tt{ }}{\tt{op2}}{\tt{ }}{\tt{op3}}{\tt{)}} \\ 
{\tt{(}}{\tt{w-83}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{g-77}}{\tt{ }}{\tt{(}}{\tt{w-77}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{an}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-78}}{\tt{ }}{\tt{(}}{\tt{w-78}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{w-77}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-76}}{\tt{ }}{\tt{(}}{\tt{w-76}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-79}}{\tt{ }}{\tt{(}}{\tt{w-79}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{w-76}}{\tt{ }}{\tt{w-78}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-72}}{\tt{ }}{\tt{(}}{\tt{w-72}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-75}}{\tt{ }}{\tt{(}}{\tt{w-75}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{op0}}{\tt{ }}{\tt{w-72}}{\tt{ }}{\tt{w-78}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-69}}{\tt{ }}{\tt{(}}{\tt{w-69}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{w-76}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-71}}{\tt{ }}{\tt{(}}{\tt{w-71}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{w-69}}{\tt{ }}{\tt{w-77}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-80}}{\tt{ }}{\tt{(}}{\tt{w-80}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{w-71}}{\tt{ }}{\tt{w-75}}{\tt{ }}{\tt{w-79}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-81}}{\tt{ }}{\tt{(}}{\tt{w-81}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{w-80}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-66}}{\tt{ }}{\tt{(}}{\tt{w-66}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{zero}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-63}}{\tt{ }}{\tt{(}}{\tt{w-63}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{w-72}}{\tt{ }}{\tt{w-76}}{\tt{ }}{\tt{w-78}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-57}}{\tt{ }}{\tt{(}}{\tt{w-57}}{\tt{)}}{\tt{ }}{\tt{b-xor}}{\tt{ }}{\tt{(}}{\tt{w-78}}{\tt{ }}{\tt{bn}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-58}}{\tt{ }}{\tt{(}}{\tt{w-58}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{op1}}{\tt{ }}{\tt{w-76}}{\tt{ }}{\tt{w-57}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-64}}{\tt{ }}{\tt{(}}{\tt{w-64}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{w-58}}{\tt{ }}{\tt{w-63}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-52}}{\tt{ }}{\tt{(}}{\tt{w-52}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{w-72}}{\tt{ }}{\tt{w-69}}{\tt{ }}{\tt{w-77}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-47}}{\tt{ }}{\tt{(}}{\tt{w-47}}{\tt{)}}{\tt{ }}{\tt{b-or3}}{\tt{ }}{\tt{(}}{\tt{w-72}}{\tt{ }}{\tt{w-76}}{\tt{ }}{\tt{w-57}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-41}}{\tt{ }}{\tt{(}}{\tt{w-41}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-53}}{\tt{ }}{\tt{(}}{\tt{w-53}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{w-41}}{\tt{ }}{\tt{w-47}}{\tt{ }}{\tt{w-52}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-65}}{\tt{ }}{\tt{(}}{\tt{w-65}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{w-53}}{\tt{ }}{\tt{w-64}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-67}}{\tt{ }}{\tt{(}}{\tt{w-67}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{w-65}}{\tt{ }}{\tt{w-66}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-82}}{\tt{ }}{\tt{(}}{\tt{w-82}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{w-67}}{\tt{ }}{\tt{w-81}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-40}}{\tt{ }}{\tt{(}}{\tt{w-40}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{w-67}}{\tt{ }}{\tt{w-80}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-83}}{\tt{ }}{\tt{(}}{\tt{w-83}}{\tt{)}}{\tt{ }}{\tt{b-if}}{\tt{ }}{\tt{(}}{\tt{rn}}{\tt{ }}{\tt{w-40}}{\tt{ }}{\tt{w-82}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{overflow-help\&} \\  
\=\+{\rm{overflow-help\&}}\,({\it{netlist\/}})\index{overflow-help\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{overflow-help}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{overflow-help*}}\index{overflow-help*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-xor\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{overflow-help}}, {\it{netlist\/}})\index{delete-module})\index{b-xor\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-or3\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{overflow-help}}, {\it{netlist\/}})\index{delete-module})\index{b-or3\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{overflow-help}}, {\it{netlist\/}})\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand3\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{overflow-help}}, {\it{netlist\/}})\index{delete-module})\index{b-nand3\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{overflow-help}}, {\it{netlist\/}})\index{delete-module})\index{b-nand\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nor\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{overflow-help}}, {\it{netlist\/}})\index{delete-module})\index{b-nor\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-if\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{overflow-help}}, {\it{netlist\/}})\index{delete-module})\index{b-if\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable overflow-help\&; name this event `overflow-help\&-off'.\index{overflow-help\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{overflow-help\$netlist} \\  
\=\+{\sc{overflow-help\$netlist}}\index{overflow-help\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{overflow-help*}}\index{overflow-help*}, \\ 
\=\+(\=\+(\=\+(\=\+(({\sc{b-xor\$netlist}}\index{b-xor\$netlist} $\cup$ {\sc{b-or3\$netlist}}\index{b-or3\$netlist}) $\cup$ {\sc{b-not\$netlist}}\index{b-not\$netlist}) \\ 
$\cup$$\;\;\;\;${\sc{b-nand3\$netlist}}\index{b-nand3\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-nand\$netlist}}\index{b-nand\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-nor\$netlist}}\index{b-nor\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-if\$netlist}}\index{b-if\$netlist}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  overflow-help\$value \\ \index{overflow-help\$value}
\=\+{\rm{overflow-help\&}}\,({\it{netlist\/}})\index{overflow-help\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{overflow-help}}, \\ 
{\rm{list}}\,({\it{rn\/}}, {\it{an\/}}, {\it{bn\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}}), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f\$overflow-help}}\,({\it{rn\/}}, {\it{an\/}}, {\it{bn\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$overflow-help}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable overflow-help\$value; name this event `overflow-help\$value-off'.\index{overflow-help\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$overflow-help=overflow-help \\ \index{f\$overflow-help=overflow-help}
\=\+(\=\+{\rm{boolp}}\,({\it{rn\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{an\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{bn\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{zero\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op0\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op1\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op2\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op3\/}})\index{boolp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$overflow-help}}\,({\it{rn\/}}, {\it{an\/}}, {\it{bn\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$overflow-help} \\ 
$=$$\;\;\;\;${\rm{overflow-help}}\,({\it{rn\/}}, {\it{an\/}}, {\it{bn\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{overflow-help})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  overflow-help\$value-zero \\ \index{overflow-help\$value-zero}
\=\+({\rm{overflow-help\&}}\,({\it{netlist\/}})\index{overflow-help\&} $\wedge$ {\rm{boolp}}\,({\it{rn\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{overflow-help}}, \\ 
{\rm{list}}\,({\it{rn\/}}, {\it{an\/}}, {\it{bn\/}}, {\bf{t}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}}), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\bf{f}}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable overflow-help\$value-zero; name this event `overflow-help\$value-zero-off'.\index{overflow-help\$value-zero-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-shift-right-names} \\  
\=\+{\rm{v-shift-right-names}}\,({\it{a\/}}, {\it{si\/}})\index{v-shift-right-names} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{append}}\,({\rm{cdr}}\,({\it{a\/}}), {\rm{list}}\,({\it{si\/}}))$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-v-shift-right-names \\ \index{length-v-shift-right-names}
{\rm{length}}\,({\rm{v-shift-right-names}}\,({\it{a\/}}, {\it{si\/}})\index{v-shift-right-names})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-shift-right-names \\ \index{properp-shift-right-names}
{\rm{properp}}\,({\rm{v-shift-right-names}}\,({\it{a\/}}, {\it{si\/}})\index{v-shift-right-names})\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  collect-value-v-shift-right \\ \index{collect-value-v-shift-right}
\=\+{\rm{v-threefix}}\,({\rm{collect-value}}\,({\rm{v-shift-right-names}}\,({\it{a\/}}, {\it{si\/}})\index{v-shift-right-names}, {\it{alist\/}})\index{collect-value})\index{v-threefix} \\ 
$=$$\;\;\;\;${\rm{fv-shift-right}}\,({\rm{collect-value}}\,({\it{a\/}}, {\it{alist\/}})\index{collect-value}, {\rm{value}}\,({\it{si\/}}, {\it{alist\/}})\index{value})\index{fv-shift-right}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{shift-or-buf-cntl} \\  
\=\+{\rm{shift-or-buf-cntl}}\,({\it{c\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{shift-or-buf-cntl} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{b-or3}}\,({\rm{b-and}}\,({\it{op0\/}}, {\it{op1\/}})\index{b-and}, {\rm{b-nand}}\,({\rm{b-not}}\,({\it{op2\/}})\index{b-not}, {\it{op3\/}})\index{b-nand}, {\it{zero\/}})\index{b-or3}, \\ 
{\rm{b-or}}\,({\rm{b-and}}\,({\it{op0\/}}, {\it{an\/}})\index{b-and}, {\rm{b-and}}\,({\rm{b-and}}\,({\rm{b-not}}\,({\it{op0\/}})\index{b-not}, {\rm{b-not}}\,({\it{op1\/}})\index{b-not})\index{b-and}, {\it{c\/}})\index{b-and})\index{b-or})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$shift-or-buf-cntl} \\  
\=\+{\rm{f\$shift-or-buf-cntl}}\,({\it{c\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$shift-or-buf-cntl} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{f-or3}}\,({\rm{f-and}}\,({\it{op0\/}}, {\it{op1\/}})\index{f-and}, {\rm{f-nand}}\,({\rm{f-not}}\,({\it{op2\/}})\index{f-not}, {\it{op3\/}})\index{f-nand}, {\it{zero\/}})\index{f-or3}, \\ 
{\rm{f-or}}\,({\rm{f-and}}\,({\it{op0\/}}, {\it{an\/}})\index{f-and}, {\rm{f-and}}\,({\rm{f-and}}\,({\rm{f-not}}\,({\it{op0\/}})\index{f-not}, {\rm{f-not}}\,({\it{op1\/}})\index{f-not})\index{f-and}, {\it{c\/}})\index{f-and})\index{f-or})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$shift-or-buf-cntl; name this event `f\$shift-or-buf-cntl-off'.\index{f\$shift-or-buf-cntl-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{shift-or-buf-cntl*} \\  
\=\+{\sc{shift-or-buf-cntl*}}\index{shift-or-buf-cntl*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{shift-or-buf-cntl}} \\ 
{\tt{(}}{\tt{c}}{\tt{ }}{\tt{an}}{\tt{ }}{\tt{zero}}{\tt{ }}{\tt{op0}}{\tt{ }}{\tt{op1}}{\tt{ }}{\tt{op2}}{\tt{ }}{\tt{op3}}{\tt{)}} \\ 
{\tt{(}}{\tt{w-3}}{\tt{ }}{\tt{w-9}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{g-6}}{\tt{ }}{\tt{(}}{\tt{w-6}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-5}}{\tt{ }}{\tt{(}}{\tt{w-5}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-7}}{\tt{ }}{\tt{(}}{\tt{w-7}}{\tt{)}}{\tt{ }}{\tt{b-and}}{\tt{ }}{\tt{(}}{\tt{w-5}}{\tt{ }}{\tt{w-6}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-8}}{\tt{ }}{\tt{(}}{\tt{w-8}}{\tt{)}}{\tt{ }}{\tt{b-and}}{\tt{ }}{\tt{(}}{\tt{w-7}}{\tt{ }}{\tt{c}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-4}}{\tt{ }}{\tt{(}}{\tt{w-4}}{\tt{)}}{\tt{ }}{\tt{b-and}}{\tt{ }}{\tt{(}}{\tt{op0}}{\tt{ }}{\tt{an}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-9}}{\tt{ }}{\tt{(}}{\tt{w-9}}{\tt{)}}{\tt{ }}{\tt{b-or}}{\tt{ }}{\tt{(}}{\tt{w-4}}{\tt{ }}{\tt{w-8}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-1}}{\tt{ }}{\tt{(}}{\tt{w-1}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-2}}{\tt{ }}{\tt{(}}{\tt{w-2}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{w-1}}{\tt{ }}{\tt{op3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-0}}{\tt{ }}{\tt{(}}{\tt{w-0}}{\tt{)}}{\tt{ }}{\tt{b-and}}{\tt{ }}{\tt{(}}{\tt{op0}}{\tt{ }}{\tt{op1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-3}}{\tt{ }}{\tt{(}}{\tt{w-3}}{\tt{)}}{\tt{ }}{\tt{b-or3}}{\tt{ }}{\tt{(}}{\tt{w-0}}{\tt{ }}{\tt{w-2}}{\tt{ }}{\tt{zero}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{shift-or-buf-cntl\&} \\  
\=\+{\rm{shift-or-buf-cntl\&}}\,({\it{netlist\/}})\index{shift-or-buf-cntl\&} \\ 
$=$$\;\;\;\;$(\=\+(\=\+{\rm{lookup-module}}\,({\tt{'}}{\tt{shift-or-buf-cntl}}, {\it{netlist\/}})\index{lookup-module} \\ 
$=$$\;\;\;\;${\sc{shift-or-buf-cntl*}}\index{shift-or-buf-cntl*})\- \\ 
$\wedge$$\;\;\;\;${\rm{b-or\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{shift-or-buf-cntl}}, {\it{netlist\/}})\index{delete-module})\index{b-or\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{shift-or-buf-cntl}}, {\it{netlist\/}})\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{shift-or-buf-cntl}}, {\it{netlist\/}})\index{delete-module})\index{b-nand\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-and\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{shift-or-buf-cntl}}, {\it{netlist\/}})\index{delete-module})\index{b-and\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-or3\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{shift-or-buf-cntl}}, {\it{netlist\/}})\index{delete-module})\index{b-or3\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable shift-or-buf-cntl\&; name this event `shift-or-buf-cntl\&-off'.\index{shift-or-buf-cntl\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{shift-or-buf-cntl\$netlist} \\  
\=\+{\sc{shift-or-buf-cntl\$netlist}}\index{shift-or-buf-cntl\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{shift-or-buf-cntl*}}\index{shift-or-buf-cntl*}, \\ 
\=\+(\=\+(({\sc{b-or\$netlist}}\index{b-or\$netlist} $\cup$ {\sc{b-not\$netlist}}\index{b-not\$netlist}) $\cup$ {\sc{b-nand\$netlist}}\index{b-nand\$netlist}) \\ 
$\cup$$\;\;\;\;${\sc{b-and\$netlist}}\index{b-and\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-or3\$netlist}}\index{b-or3\$netlist}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  shift-or-buf-cntl\$value \\ \index{shift-or-buf-cntl\$value}
\=\+{\rm{shift-or-buf-cntl\&}}\,({\it{netlist\/}})\index{shift-or-buf-cntl\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{shift-or-buf-cntl}}, \\ 
{\rm{list}}\,({\it{c\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}}), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$shift-or-buf-cntl}}\,({\it{c\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$shift-or-buf-cntl})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable shift-or-buf-cntl\$value; name this event `shift-or-buf-cntl\$value-off'.\index{shift-or-buf-cntl\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$shift-or-buf-cntl=shift-or-buf-cntl \\ \index{f\$shift-or-buf-cntl=shift-or-b!uf-cntl}
\=\+(\=\+{\rm{boolp}}\,({\it{c\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{an\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{zero\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op0\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op1\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op2\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op3\/}})\index{boolp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$shift-or-buf-cntl}}\,({\it{c\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$shift-or-buf-cntl} \\ 
$=$$\;\;\;\;${\rm{shift-or-buf-cntl}}\,({\it{c\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{shift-or-buf-cntl})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  shift-or-buf-cntl\$value-zero \\ \index{shift-or-buf-cntl\$value-zero}
\=\+{\rm{shift-or-buf-cntl\&}}\,({\it{netlist\/}})\index{shift-or-buf-cntl\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{car}}\,({\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{shift-or-buf-cntl}}, \\ 
{\rm{list}}\,({\it{c\/}}, {\it{an\/}}, {\bf{t}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}}), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval}) \\ 
$=$$\;\;\;\;${\bf{t}})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$shift-or-buf} \\  
\=\+{\rm{f\$shift-or-buf}}\,({\it{c\/}}, {\it{a\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$shift-or-buf} \\ 
$=$$\;\;\;\;${\rm{fv-if}}\,(\=\+{\rm{car}}\,({\rm{f\$shift-or-buf-cntl}}\,({\it{c\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$shift-or-buf-cntl}), \\ 
{\it{a\/}}, \\ 
{\rm{fv-shift-right}}\,(\=\+{\it{a\/}}, \\ 
{\rm{cadr}}\,({\rm{f\$shift-or-buf-cntl}}\,(\=\+{\it{c\/}}, \\ 
{\it{an\/}}, \\ 
{\it{zero\/}}, \\ 
{\it{op0\/}}, \\ 
{\it{op1\/}}, \\ 
{\it{op2\/}}, \\ 
{\it{op3\/}})\-\index{f\$shift-or-buf-cntl}))\-\index{fv-shift-right})\-\index{fv-if}\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$shift-or-buf; name this event `f\$shift-or-buf-off'.\index{f\$shift-or-buf-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{shift-or-buf} \\  
\=\+{\rm{shift-or-buf}}\,({\it{c\/}}, {\it{a\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{shift-or-buf} \\ 
$=$$\;\;\;\;${\rm{v-if}}\,(\=\+{\rm{car}}\,({\rm{shift-or-buf-cntl}}\,({\it{c\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{shift-or-buf-cntl}), \\ 
{\it{a\/}}, \\ 
{\rm{v-shift-right}}\,(\=\+{\it{a\/}}, \\ 
{\rm{cadr}}\,({\rm{shift-or-buf-cntl}}\,({\it{c\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{shift-or-buf-cntl}))\-\index{v-shift-right})\-\index{v-if}\-
\end{tabbing}


\noindent{\sc Event}:   Enable shift-or-buf; name this event `shift-or-buf-off'.\index{shift-or-buf-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  properp-length-f\$shift-or-buf \\ \index{properp-length-f\$shift-or-buf}
\=\+{\rm{properp}}\,({\rm{f\$shift-or-buf}}\,({\it{c\/}}, {\it{a\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$shift-or-buf})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{f\$shift-or-buf}}\,({\it{c\/}}, {\it{a\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$shift-or-buf})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-shift-or-buf \\ \index{length-shift-or-buf}
{\rm{length}}\,({\rm{shift-or-buf}}\,({\it{c\/}}, {\it{a\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}}, {\it{op4\/}})\index{shift-or-buf})\index{length} $=$ {\rm{length}}\,({\it{a\/}})\index{length}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-shift-or-buf \\ \index{bvp-shift-or-buf}
{\rm{bvp}}\,({\rm{shift-or-buf}}\,({\it{c\/}}, {\it{a\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}}, {\it{op4\/}})\index{shift-or-buf})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f\$shift-or-buf=shift-or-buf \\ \index{f\$shift-or-buf=shift-or-buf}
\=\+(\=\+{\rm{boolp}}\,({\it{c\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{an\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{zero\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op1\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op2\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op3\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{op4\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a\/}})\index{bvp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$shift-or-buf}}\,({\it{c\/}}, {\it{a\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}}, {\it{op4\/}})\index{f\$shift-or-buf} \\ 
$=$$\;\;\;\;${\rm{shift-or-buf}}\,({\it{c\/}}, {\it{a\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}}, {\it{op4\/}})\index{shift-or-buf})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  shift-or-buf-is-buf \\ \index{shift-or-buf-is-buf}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ (({\it{op0\/}} $\wedge$ {\it{op1\/}}) $\vee$ {\it{op2\/}} $\vee$ ($\neg$ {\it{op3\/}}) $\vee$ {\it{zero\/}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{shift-or-buf}}\,({\it{c\/}}, {\it{a\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{shift-or-buf} $=$ {\it{a\/}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  shift-or-buf-is-asr \\ \index{shift-or-buf-is-asr}
\=\+(\=\+{\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\it{an\/}} $=$ {\rm{nth}}\,({\rm{length}}\,({\it{a\/}})\index{length} $-\;1$, {\it{a\/}})\index{nth}) \\ 
$\wedge$$\;\;\;\;${\it{op0\/}} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\it{op1\/}}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\it{op2\/}}) \\ 
$\wedge$$\;\;\;\;${\it{op3\/}} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\it{zero\/}}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{shift-or-buf}}\,({\it{c\/}}, {\it{a\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{shift-or-buf} $=$ {\rm{v-asr}}\,({\it{a\/}})\index{v-asr})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  shift-or-buf-is-ror \\ \index{shift-or-buf-is-ror}
\=\+(\=\+{\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{c\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\it{op0\/}}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\it{op1\/}}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\it{op2\/}}) \\ 
$\wedge$$\;\;\;\;${\it{op3\/}} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\it{zero\/}}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{shift-or-buf}}\,({\it{c\/}}, {\it{a\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{shift-or-buf} $=$ {\rm{v-ror}}\,({\it{a\/}}, {\it{c\/}})\index{v-ror})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  shift-or-buf-is-lsr \\ \index{shift-or-buf-is-lsr}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ($\neg$ {\it{op0\/}}) $\wedge$ {\it{op1\/}} $\wedge$ ($\neg$ {\it{op2\/}}) $\wedge$ {\it{op3\/}} $\wedge$ ($\neg$ {\it{zero\/}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{shift-or-buf}}\,({\it{c\/}}, {\it{a\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{shift-or-buf} $=$ {\rm{v-lsr}}\,({\it{a\/}})\index{v-lsr})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tv-shift-or-buf*} \\  
\=\+{\rm{tv-shift-or-buf*}}\,({\it{tree\/}})\index{tv-shift-or-buf*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{tv-shift-or-buf}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{c}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\tt{'}}{\tt{(}}{\tt{an}}{\tt{ }}{\tt{zero}}{\tt{ }}{\tt{op0}}{\tt{ }}{\tt{op1}}{\tt{ }}{\tt{op2}}{\tt{ }}{\tt{op3}}{\tt{)}})\-)\-, \\ 
{\rm{cons}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{cntl}} \\ 
{\tt{(}}{\tt{ctl}}{\tt{ }}{\tt{si}}{\tt{)}} \\ 
{\tt{shift-or-buf-cntl}} \\ 
{\tt{(}}{\tt{c}}{\tt{ }}{\tt{an}}{\tt{ }}{\tt{zero}}{\tt{ }}{\tt{op0}}{\tt{ }}{\tt{op1}}{\tt{ }}{\tt{op2}}{\tt{ }}{\tt{op3}}{\tt{)}}{\tt{)}}\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{mux}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{tv-if}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{ctl}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,(\=\+{\tt{'}}{\tt{a}}, \\ 
{\tt{0}}, \\ 
{\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\-\index{indices}, \\ 
{\rm{v-shift-right-names}}\,(\=\+{\rm{indices}}\,(\=\+{\tt{'}}{\tt{a}}, \\ 
{\tt{0}}, \\ 
{\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\-\index{indices}, \\ 
{\tt{'}}{\tt{si}})\-\index{v-shift-right-names})\-)\-)\-)\-, \\ 
{\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}})\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tv-shift-or-buf*\$destructure \\ \index{tv-shift-or-buf*\$destructure}
\=\+(\=\+{\rm{car}}\,({\rm{tv-shift-or-buf*}}\,({\it{tree\/}})\index{tv-shift-or-buf*}) \\ 
$=$$\;\;\;\;${\rm{index}}\,({\tt{'}}{\tt{tv-shift-or-buf}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadr}}\,({\rm{tv-shift-or-buf*}}\,({\it{tree\/}})\index{tv-shift-or-buf*}) \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\tt{'}}{\tt{c}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\tt{'}}{\tt{(}}{\tt{an}}{\tt{ }}{\tt{zero}}{\tt{ }}{\tt{op0}}{\tt{ }}{\tt{op1}}{\tt{ }}{\tt{op2}}{\tt{ }}{\tt{op3}}{\tt{)}})\-)\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\rm{tv-shift-or-buf*}}\,({\it{tree\/}})\index{tv-shift-or-buf*}) $=$ {\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadddr}}\,({\rm{tv-shift-or-buf*}}\,({\it{tree\/}})\index{tv-shift-or-buf*}) \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{cntl}} \\ 
{\tt{(}}{\tt{ctl}}{\tt{ }}{\tt{si}}{\tt{)}} \\ 
{\tt{shift-or-buf-cntl}} \\ 
{\tt{(}}{\tt{c}}{\tt{ }}{\tt{an}}{\tt{ }}{\tt{zero}}{\tt{ }}{\tt{op0}}{\tt{ }}{\tt{op1}}{\tt{ }}{\tt{op2}}{\tt{ }}{\tt{op3}}{\tt{)}}{\tt{)}}\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{mux}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{tv-if}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{ctl}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{v-shift-right-names}}\,(\=\+{\rm{indices}}\,(\=\+{\tt{'}}{\tt{a}}, \\ 
{\tt{0}}, \\ 
{\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\-\index{indices}, \\ 
{\tt{'}}{\tt{si}})\-\index{v-shift-right-names})\-)\-)\-)\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{tv-shift-or-buf*}}\,({\it{tree\/}})\index{tv-shift-or-buf*}) $=$ {\bf{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-shift-or-buf*; name this event `tv-shift-or-buf*-off'.\index{tv-shift-or-buf*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable tv-shift-or-buf*\$destructure; name this event `tv-shift-or-buf*\$destructure-off'.\index{tv-shift-or-buf*\$destructure-o!ff}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tv-shift-or-buf\&} \\  
\=\+{\rm{tv-shift-or-buf\&}}\,({\it{netlist\/}}, {\it{tree\/}})\index{tv-shift-or-buf\&} \\ 
$=$$\;\;\;\;$(\=\+(\=\+{\rm{lookup-module}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{tv-shift-or-buf}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\it{netlist\/}})\-\index{lookup-module} \\ 
$=$$\;\;\;\;${\rm{tv-shift-or-buf*}}\,({\it{tree\/}})\index{tv-shift-or-buf*})\- \\ 
$\wedge$$\;\;\;\;${\rm{shift-or-buf-cntl\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-shift-or-buf}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{shift-or-buf-cntl\&} \\ 
$\wedge$$\;\;\;\;${\rm{tv-if\&}}\,(\=\+{\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-shift-or-buf}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\it{tree\/}})\-\index{tv-if\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-shift-or-buf\&; name this event `tv-shift-or-buf\&-off'.\index{tv-shift-or-buf\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tv-shift-or-buf\$netlist} \\  
\=\+{\rm{tv-shift-or-buf\$netlist}}\,({\it{tree\/}})\index{tv-shift-or-buf\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{tv-shift-or-buf*}}\,({\it{tree\/}})\index{tv-shift-or-buf*}, \\ 
{\rm{tv-if\$netlist}}\,({\it{tree\/}})\index{tv-if\$netlist} $\cup$ {\sc{shift-or-buf-cntl\$netlist}}\index{shift-or-buf-cntl\$netlist})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tv-shift-or-buf\$value \\ \index{tv-shift-or-buf\$value}
\=\+(\=\+{\rm{tv-shift-or-buf\&}}\,({\it{netlist\/}}, {\it{tree\/}})\index{tv-shift-or-buf\&} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{a\/}})\index{properp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{tv-shift-or-buf}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\rm{cons}}\,({\it{c\/}}, {\rm{append}}\,({\it{a\/}}, {\rm{list}}\,({\it{an\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}}))), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$shift-or-buf}}\,({\it{c\/}}, {\it{a\/}}, {\it{an\/}}, {\it{zero\/}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}})\index{f\$shift-or-buf})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-shift-or-buf\$value; name this event `tv-shift-or-buf\$value-off'.\index{tv-shift-or-buf\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tv-shift-or-buf\$value-zero \\ \index{tv-shift-or-buf\$value-zero}
\=\+(\=\+{\rm{tv-shift-or-buf\&}}\,({\it{netlist\/}}, {\it{tree\/}})\index{tv-shift-or-buf\&} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a\/}})\index{bvp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{tv-shift-or-buf}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\rm{cons}}\,({\it{c\/}}, {\rm{append}}\,({\it{a\/}}, {\rm{list}}\,({\it{an\/}}, {\bf{t}}, {\it{op0\/}}, {\it{op1\/}}, {\it{op2\/}}, {\it{op3\/}}))), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\it{a\/}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable tv-shift-or-buf\$value-zero; name this event `tv-shift-or-buf\$value-zero-off'.\index{tv-shift-or-buf\$value-zero-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{f\$core-alu} \\  
\=\+{\rm{f\$core-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{zero\/}}, {\it{mpg\/}}, {\it{op\/}}, {\it{tree\/}})\index{f\$core-alu} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{f\$carry-out-help}}\,(\=\+{\rm{nth}}\,({\tt{0}}, {\it{a\/}})\index{nth}, \\ 
{\rm{f\$t-carry}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{f\$tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{f\$tv-alu-help}), \\ 
{\rm{cadr}}\,({\rm{f\$tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{f\$tv-alu-help}))\-\index{f\$t-carry}, \\ 
{\it{zero\/}}, \\ 
{\rm{car}}\,({\it{op\/}}), \\ 
{\rm{cadr}}\,({\it{op\/}}), \\ 
{\rm{caddr}}\,({\it{op\/}}), \\ 
{\rm{cadddr}}\,({\it{op\/}}))\-\index{f\$carry-out-help}, \\ 
{\rm{cons}}\,(\=\+{\rm{f\$overflow-help}}\,(\=\+{\rm{nth}}\,(\=\+{\rm{length}}\,({\it{a\/}})\index{length} $-\;1$, \\ 
{\rm{cddr}}\,({\rm{f\$tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{f\$tv-alu-help}))\-\index{nth}, \\ 
{\rm{nth}}\,({\rm{length}}\,({\it{a\/}})\index{length} $-\;1$, {\it{a\/}})\index{nth}, \\ 
{\rm{nth}}\,({\rm{length}}\,({\it{a\/}})\index{length} $-\;1$, {\it{b\/}})\index{nth}, \\ 
{\it{zero\/}}, \\ 
{\rm{car}}\,({\it{op\/}}), \\ 
{\rm{cadr}}\,({\it{op\/}}), \\ 
{\rm{caddr}}\,({\it{op\/}}), \\ 
{\rm{cadddr}}\,({\it{op\/}}))\-\index{f\$overflow-help}, \\ 
{\rm{cons}}\,(\=\+{\rm{f\$fast-zero}}\,({\rm{f\$shift-or-buf}}\,(\=\+{\it{c\/}}, \\ 
{\rm{cddr}}\,({\rm{f\$tv-alu-help}}\,(\=\+{\it{c\/}}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\it{mpg\/}}, \\ 
{\it{tree\/}})\-\index{f\$tv-alu-help}), \\ 
{\rm{nth}}\,({\rm{length}}\,({\it{a\/}})\index{length} $-\;1$, {\it{a\/}})\index{nth}, \\ 
{\it{zero\/}}, \\ 
{\rm{car}}\,({\it{op\/}}), \\ 
{\rm{cadr}}\,({\it{op\/}}), \\ 
{\rm{caddr}}\,({\it{op\/}}), \\ 
{\rm{cadddr}}\,({\it{op\/}}))\-\index{f\$shift-or-buf})\index{f\$fast-zero}, \\ 
{\rm{f\$shift-or-buf}}\,(\=\+{\it{c\/}}, \\ 
{\rm{cddr}}\,({\rm{f\$tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{f\$tv-alu-help}), \\ 
{\rm{nth}}\,({\rm{length}}\,({\it{a\/}})\index{length} $-\;1$, {\it{a\/}})\index{nth}, \\ 
{\it{zero\/}}, \\ 
{\rm{car}}\,({\it{op\/}}), \\ 
{\rm{cadr}}\,({\it{op\/}}), \\ 
{\rm{caddr}}\,({\it{op\/}}), \\ 
{\rm{cadddr}}\,({\it{op\/}}))\-\index{f\$shift-or-buf})\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$core-alu; name this event `f\$core-alu-off'.\index{f\$core-alu-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{core-alu} \\  
\=\+{\rm{core-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{zero\/}}, {\it{mpg\/}}, {\it{op\/}}, {\it{tree\/}})\index{core-alu} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{carry-out-help}}\,(\=\+{\rm{nth}}\,({\tt{0}}, {\it{a\/}})\index{nth}, \\ 
{\rm{t-carry}}\,(\=\+{\it{c\/}}, \\ 
{\rm{car}}\,({\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help}), \\ 
{\rm{cadr}}\,({\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help}))\-\index{t-carry}, \\ 
{\it{zero\/}}, \\ 
{\rm{car}}\,({\it{op\/}}), \\ 
{\rm{cadr}}\,({\it{op\/}}), \\ 
{\rm{caddr}}\,({\it{op\/}}), \\ 
{\rm{cadddr}}\,({\it{op\/}}))\-\index{carry-out-help}, \\ 
{\rm{cons}}\,(\=\+{\rm{overflow-help}}\,(\=\+{\rm{nth}}\,(\=\+{\rm{length}}\,({\it{a\/}})\index{length} $-\;1$, \\ 
{\rm{cddr}}\,({\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help}))\-\index{nth}, \\ 
{\rm{nth}}\,({\rm{length}}\,({\it{a\/}})\index{length} $-\;1$, {\it{a\/}})\index{nth}, \\ 
{\rm{nth}}\,({\rm{length}}\,({\it{a\/}})\index{length} $-\;1$, {\it{b\/}})\index{nth}, \\ 
{\it{zero\/}}, \\ 
{\rm{car}}\,({\it{op\/}}), \\ 
{\rm{cadr}}\,({\it{op\/}}), \\ 
{\rm{caddr}}\,({\it{op\/}}), \\ 
{\rm{cadddr}}\,({\it{op\/}}))\-\index{overflow-help}, \\ 
{\rm{cons}}\,(\=\+{\rm{v-zerop}}\,({\rm{shift-or-buf}}\,(\=\+{\it{c\/}}, \\ 
{\rm{cddr}}\,({\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help}), \\ 
{\rm{nth}}\,({\rm{length}}\,({\it{a\/}})\index{length} $-\;1$, {\it{a\/}})\index{nth}, \\ 
{\it{zero\/}}, \\ 
{\rm{car}}\,({\it{op\/}}), \\ 
{\rm{cadr}}\,({\it{op\/}}), \\ 
{\rm{caddr}}\,({\it{op\/}}), \\ 
{\rm{cadddr}}\,({\it{op\/}}))\-\index{shift-or-buf})\index{v-zerop}, \\ 
{\rm{shift-or-buf}}\,(\=\+{\it{c\/}}, \\ 
{\rm{cddr}}\,({\rm{tv-alu-help}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{mpg\/}}, {\it{tree\/}})\index{tv-alu-help}), \\ 
{\rm{nth}}\,({\rm{length}}\,({\it{a\/}})\index{length} $-\;1$, {\it{a\/}})\index{nth}, \\ 
{\it{zero\/}}, \\ 
{\rm{car}}\,({\it{op\/}}), \\ 
{\rm{cadr}}\,({\it{op\/}}), \\ 
{\rm{caddr}}\,({\it{op\/}}), \\ 
{\rm{cadddr}}\,({\it{op\/}}))\-\index{shift-or-buf})\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable core-alu; name this event `core-alu-off'.\index{core-alu-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  properp-length-f\$core-alu \\ \index{properp-length-f\$core-alu}
\=\+{\rm{properp}}\,({\rm{f\$core-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{zero\/}}, {\it{mpg\/}}, {\it{op\/}}, {\it{tree\/}})\index{f\$core-alu})\index{properp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{length}}\,({\rm{f\$core-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{zero\/}}, {\it{mpg\/}}, {\it{op\/}}, {\it{tree\/}})\index{f\$core-alu})\index{length} \\ 
$=$$\;\;\;\;$($1\;+$ ($1\;+$ ($1\;+$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}))))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f\$core-alu=core-alu \\ \index{f\$core-alu=core-alu}
\=\+(\=\+{\rm{boolp}}\,({\it{c\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{a\/}})\index{length} $<$ {\tt{3}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{zero\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{mpg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{mpg\/}})\index{length} $=$ {\tt{7}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{op\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{op\/}})\index{length} $=$ {\tt{4}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$core-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{zero\/}}, {\it{mpg\/}}, {\it{op\/}}, {\it{tree\/}})\index{f\$core-alu} \\ 
$=$$\;\;\;\;${\rm{core-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{zero\/}}, {\it{mpg\/}}, {\it{op\/}}, {\it{tree\/}})\index{core-alu})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-core-alu \\ \index{length-core-alu}
\=\+{\rm{length}}\,({\rm{core-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{zero\/}}, {\it{mpg\/}}, {\it{op\/}}, {\it{tree\/}})\index{core-alu})\index{length} \\ 
$=$$\;\;\;\;$($1\;+$ ($1\;+$ ($1\;+$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  boolp-bvp-core-alu \\ \index{boolp-bvp-core-alu}
\=\+{\rm{boolp}}\,({\rm{c}}\,({\rm{core-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{zero\/}}, {\it{mpg\/}}, {\it{op\/}}, {\it{tree\/}})\index{core-alu})\index{c})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{v}}\,({\rm{core-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{zero\/}}, {\it{mpg\/}}, {\it{op\/}}, {\it{tree\/}})\index{core-alu})\index{v})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{zb}}\,({\rm{core-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{zero\/}}, {\it{mpg\/}}, {\it{op\/}}, {\it{tree\/}})\index{core-alu})\index{zb})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{bv}}\,({\rm{core-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{zero\/}}, {\it{mpg\/}}, {\it{op\/}}, {\it{tree\/}})\index{core-alu})\index{bv})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{core-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{zero\/}}, {\it{mpg\/}}, {\it{op\/}}, {\it{tree\/}})\index{core-alu})\index{bvp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  core-alu-works-for-all-normal-cases\$crock \\ \index{core-alu-works-for-all-normal-c!ases\$crock}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{nth}}\,({\tt{0}}, {\it{a\/}})\index{nth}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{nth}}\,({\tt{0}}, {\it{a\/}})\index{nth} $=$ {\bf{t}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable core-alu-works-for-all-normal-cases\$crock; name this event `core-alu-works-for-all-normal-cases\$crock-off'.\index{core-alu-works-for-all-normal-c!ases\$crock-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  core-alu-works-for-all-normal-cases \\ \index{core-alu-works-for-all-normal-c!ases}
\=\+(\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}))\index{v-alu} \\ 
$=$$\;\;\;\;${\rm{core-alu}}\,(\=\+{\rm{carry-in-help}}\,({\rm{list}}\,({\it{c\/}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}))\index{carry-in-help}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\bf{f}}, \\ 
{\rm{mpg}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}))\index{mpg}, \\ 
{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}), \\ 
{\it{tree\/}})\-\index{core-alu})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}))\index{v-alu} \\ 
$=$$\;\;\;\;${\rm{core-alu}}\,(\=\+{\rm{carry-in-help}}\,({\rm{list}}\,({\it{c\/}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}))\index{carry-in-help}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\bf{f}}, \\ 
{\rm{mpg}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}))\index{mpg}, \\ 
{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}), \\ 
{\it{tree\/}})\-\index{core-alu})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}))\index{v-alu} \\ 
$=$$\;\;\;\;${\rm{core-alu}}\,(\=\+{\rm{carry-in-help}}\,({\rm{list}}\,({\it{c\/}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}))\index{carry-in-help}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\bf{f}}, \\ 
{\rm{mpg}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}))\index{mpg}, \\ 
{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}), \\ 
{\it{tree\/}})\-\index{core-alu})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}))\index{v-alu} \\ 
$=$$\;\;\;\;${\rm{core-alu}}\,(\=\+{\rm{carry-in-help}}\,({\rm{list}}\,({\it{c\/}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}))\index{carry-in-help}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\bf{f}}, \\ 
{\rm{mpg}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}))\index{mpg}, \\ 
{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}), \\ 
{\it{tree\/}})\-\index{core-alu})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}))\index{v-alu} \\ 
$=$$\;\;\;\;${\rm{core-alu}}\,(\=\+{\rm{carry-in-help}}\,({\rm{list}}\,({\it{c\/}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}))\index{carry-in-help}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\bf{f}}, \\ 
{\rm{mpg}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}))\index{mpg}, \\ 
{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}), \\ 
{\it{tree\/}})\-\index{core-alu})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}))\index{v-alu} \\ 
$=$$\;\;\;\;${\rm{core-alu}}\,(\=\+{\rm{carry-in-help}}\,({\rm{list}}\,({\it{c\/}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}))\index{carry-in-help}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\bf{f}}, \\ 
{\rm{mpg}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}))\index{mpg}, \\ 
{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}), \\ 
{\it{tree\/}})\-\index{core-alu})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}))\index{v-alu} \\ 
$=$$\;\;\;\;${\rm{core-alu}}\,(\=\+{\rm{carry-in-help}}\,({\rm{list}}\,({\it{c\/}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}))\index{carry-in-help}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\bf{f}}, \\ 
{\rm{mpg}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}))\index{mpg}, \\ 
{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}), \\ 
{\it{tree\/}})\-\index{core-alu})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}))\index{v-alu} \\ 
$=$$\;\;\;\;${\rm{core-alu}}\,(\=\+{\rm{carry-in-help}}\,({\rm{list}}\,({\it{c\/}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}))\index{carry-in-help}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\bf{f}}, \\ 
{\rm{mpg}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}))\index{mpg}, \\ 
{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}), \\ 
{\it{tree\/}})\-\index{core-alu})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}))\index{v-alu} \\ 
$=$$\;\;\;\;${\rm{core-alu}}\,(\=\+{\rm{carry-in-help}}\,({\rm{list}}\,({\it{c\/}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}))\index{carry-in-help}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\bf{f}}, \\ 
{\rm{mpg}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}))\index{mpg}, \\ 
{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}), \\ 
{\it{tree\/}})\-\index{core-alu})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}))\index{v-alu} \\ 
$=$$\;\;\;\;${\rm{core-alu}}\,(\=\+{\rm{carry-in-help}}\,({\rm{list}}\,({\it{c\/}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}))\index{carry-in-help}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\bf{f}}, \\ 
{\rm{mpg}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}))\index{mpg}, \\ 
{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}), \\ 
{\it{tree\/}})\-\index{core-alu})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}))\index{v-alu} \\ 
$=$$\;\;\;\;${\rm{core-alu}}\,(\=\+{\rm{carry-in-help}}\,({\rm{list}}\,({\it{c\/}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}))\index{carry-in-help}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\bf{f}}, \\ 
{\rm{mpg}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}))\index{mpg}, \\ 
{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}), \\ 
{\it{tree\/}})\-\index{core-alu})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}))\index{v-alu} \\ 
$=$$\;\;\;\;${\rm{core-alu}}\,(\=\+{\rm{carry-in-help}}\,({\rm{list}}\,({\it{c\/}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}))\index{carry-in-help}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\bf{f}}, \\ 
{\rm{mpg}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}))\index{mpg}, \\ 
{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}), \\ 
{\it{tree\/}})\-\index{core-alu})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}))\index{v-alu} \\ 
$=$$\;\;\;\;${\rm{core-alu}}\,(\=\+{\rm{carry-in-help}}\,({\rm{list}}\,({\it{c\/}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}))\index{carry-in-help}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\bf{f}}, \\ 
{\rm{mpg}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}))\index{mpg}, \\ 
{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}), \\ 
{\it{tree\/}})\-\index{core-alu})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}))\index{v-alu} \\ 
$=$$\;\;\;\;${\rm{core-alu}}\,(\=\+{\rm{carry-in-help}}\,({\rm{list}}\,({\it{c\/}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}))\index{carry-in-help}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\bf{f}}, \\ 
{\rm{mpg}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}))\index{mpg}, \\ 
{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}), \\ 
{\it{tree\/}})\-\index{core-alu})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}))\index{v-alu} \\ 
$=$$\;\;\;\;${\rm{core-alu}}\,(\=\+{\rm{carry-in-help}}\,({\rm{list}}\,({\it{c\/}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}))\index{carry-in-help}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\bf{f}}, \\ 
{\rm{mpg}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}))\index{mpg}, \\ 
{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}), \\ 
{\it{tree\/}})\-\index{core-alu})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}))\index{v-alu} \\ 
$=$$\;\;\;\;${\rm{core-alu}}\,(\=\+{\rm{carry-in-help}}\,({\rm{list}}\,({\it{c\/}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}))\index{carry-in-help}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\bf{f}}, \\ 
{\rm{mpg}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}))\index{mpg}, \\ 
{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}), \\ 
{\it{tree\/}})\-\index{core-alu})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable core-alu-works-for-all-normal-cases; name this event `core-alu-works-for-all-normal-cases-off'.\index{core-alu-works-for-all-normal-c!ases-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cases-on-a-4-bit-bvp \\ \index{cases-on-a-4-bit-bvp}
\=\+(\=\+{\rm{bvp}}\,({\it{op\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{op\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\it{p\/}} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\it{p\/}} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\it{p\/}} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\it{p\/}} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }{\it{p\/}} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }{\it{p\/}} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }{\it{p\/}} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }{\it{p\/}} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}})$\;\;${\bf then }{\it{p\/}} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}})$\;\;${\bf then }{\it{p\/}} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}})$\;\;${\bf then }{\it{p\/}} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}})$\;\;${\bf then }{\it{p\/}} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}})$\;\;${\bf then }{\it{p\/}} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}})$\;\;${\bf then }{\it{p\/}} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}})$\;\;${\bf then }{\it{p\/}} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}})$\;\;${\bf then }{\it{p\/}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;${\it{p\/}}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  core-alu-is-v-alu \\ \index{core-alu-is-v-alu}
\=\+(\=\+{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{op\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{op\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\it{zero\/}}) \\ 
$\wedge$$\;\;\;\;$({\it{mpg\/}} $=$ {\rm{mpg}}\,({\rm{cons}}\,({\it{zero\/}}, {\rm{cons}}\,({\bf{f}}, {\it{op\/}})))\index{mpg}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{c\/}})\index{boolp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{core-alu}}\,({\rm{carry-in-help}}\,({\rm{cons}}\,({\it{c\/}}, {\rm{cons}}\,({\bf{f}}, {\it{op\/}})))\index{carry-in-help}, {\it{a\/}}, {\it{b\/}}, {\it{zero\/}}, {\it{mpg\/}}, {\it{op\/}}, {\it{tree\/}})\index{core-alu} \\ 
$=$$\;\;\;\;${\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  core-alu-works-for-zero-case \\ \index{core-alu-works-for-zero-case}
\=\+(({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ {\it{zero\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{core-alu}}\,({\bf{t}}, {\it{a\/}}, {\it{b\/}}, {\it{zero\/}}, {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}), {\it{op\/}}, {\it{tree\/}})\index{core-alu} \\ 
$=$$\;\;\;\;${\rm{cvzbv}}\,({\bf{f}}, {\bf{f}}, {\rm{make-list}}\,({\rm{length}}\,({\it{a\/}})\index{length}, {\bf{f}})\index{make-list})\index{cvzbv})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  core-alu-works-as-inc-b \\ \index{core-alu-works-as-inc-b}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ ($\neg$ {\it{zero\/}}) $\wedge$ {\it{swap\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{bv}}\,({\rm{core-alu}}\,(\=\+{\rm{carry-in-help}}\,({\rm{cons}}\,({\it{c\/}}, {\rm{cons}}\,({\it{zero\/}}, {\sc{alu-inc-op}}\index{alu-inc-op})))\index{carry-in-help}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\it{zero\/}}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,({\it{zero\/}}, {\rm{cons}}\,({\it{swap\/}}, {\sc{alu-inc-op}}\index{alu-inc-op})))\index{mpg}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op}, \\ 
{\it{tree\/}})\-\index{core-alu})\index{bv} \\ 
$=$$\;\;\;\;${\rm{v-inc}}\,({\it{b\/}})\index{v-inc})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  core-alu-works-as-dec-b \\ \index{core-alu-works-as-dec-b}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) $\wedge$ ($\neg$ {\it{zero\/}}) $\wedge$ {\it{swap\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{bv}}\,({\rm{core-alu}}\,(\=\+{\rm{carry-in-help}}\,({\rm{cons}}\,({\it{c\/}}, {\rm{cons}}\,({\it{zero\/}}, {\sc{alu-dec-op}}\index{alu-dec-op})))\index{carry-in-help}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\it{zero\/}}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,({\it{zero\/}}, {\rm{cons}}\,({\it{swap\/}}, {\sc{alu-dec-op}}\index{alu-dec-op})))\index{mpg}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op}, \\ 
{\it{tree\/}})\-\index{core-alu})\index{bv} \\ 
$=$$\;\;\;\;${\rm{v-dec}}\,({\it{b\/}})\index{v-dec})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{core-alu*} \\  
\=\+{\rm{core-alu*}}\,({\it{tree\/}})\index{core-alu*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{core-alu}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{c}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{b}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{zero}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{mpg}}, {\tt{0}}, {\tt{7}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{op}}, {\tt{0}}, {\tt{4}})\index{indices})\-)\-)\-)\-)\-, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{carry}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{overflow}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{zerop}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices})\-)\-)\-, \\ 
{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{m-alu}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{p}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{g}}, \\ 
{\rm{indices}}\,(\=\+{\tt{'}}{\tt{alu-out}}, \\ 
{\tt{0}}, \\ 
{\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\-\index{indices})\-)\-, \\ 
{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-alu-help}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{c}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,(\=\+{\tt{'}}{\tt{a}}, \\ 
{\tt{0}}, \\ 
{\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\-\index{indices}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,(\=\+{\tt{'}}{\tt{b}}, \\ 
{\tt{0}}, \\ 
{\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\-\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{mpg}}, {\tt{0}}, {\tt{7}})\index{indices})\-)\-)\-)\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{m-alu-carry}} \\ 
{\tt{(}}{\tt{alu-carry}}{\tt{)}} \\ 
{\tt{t-carry}} \\ 
{\tt{(}}{\tt{c}}{\tt{ }}{\tt{p}}{\tt{ }}{\tt{g}}{\tt{)}}{\tt{)}}\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{m-carry-out-help}}, \\ 
{\tt{'}}{\tt{(}}{\tt{carry}}{\tt{)}}, \\ 
{\tt{'}}{\tt{carry-out-help}}, \\ 
{\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{a}}, {\tt{0}})\index{index}, \\ 
{\tt{'}}{\tt{alu-carry}}, \\ 
{\tt{'}}{\tt{zero}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{0}})\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{1}})\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{2}})\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{3}})\index{index})\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{m-overflow-help}}, \\ 
{\tt{'}}{\tt{(}}{\tt{overflow}}{\tt{)}}, \\ 
{\tt{'}}{\tt{overflow-help}}, \\ 
{\rm{list}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{alu-out}}, \\ 
{\rm{tree-size}}\,({\it{tree\/}})\index{tree-size} $-\;1$)\-\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{a}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size} $-\;1$)\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{b}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size} $-\;1$)\index{index}, \\ 
{\tt{'}}{\tt{zero}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{0}})\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{1}})\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{2}})\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{3}})\index{index})\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{m-shift}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-shift-or-buf}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{c}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,(\=\+{\tt{'}}{\tt{alu-out}}, \\ 
{\tt{0}}, \\ 
{\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\-\index{indices}, \\ 
{\rm{list}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{a}}, \\ 
{\rm{tree-size}}\,({\it{tree\/}})\index{tree-size} $-\;1$)\-\index{index}, \\ 
{\tt{'}}{\tt{zero}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{0}})\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{1}})\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{2}})\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{3}})\index{index})\-)\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{m-zerop}}, \\ 
{\tt{'}}{\tt{(}}{\tt{zerop}}{\tt{)}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{fast-zero}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{index}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices})\-)\-, \\ 
{\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}})\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  core-alu*\$destructure \\ \index{core-alu*\$destructure}
\=\+({\rm{car}}\,({\rm{core-alu*}}\,({\it{tree\/}})\index{core-alu*}) $=$ {\rm{index}}\,({\tt{'}}{\tt{core-alu}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadr}}\,({\rm{core-alu*}}\,({\it{tree\/}})\index{core-alu*}) \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\tt{'}}{\tt{c}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{b}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{zero}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{mpg}}, {\tt{0}}, {\tt{7}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{op}}, {\tt{0}}, {\tt{4}})\index{indices})\-)\-)\-)\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{caddr}}\,({\rm{core-alu*}}\,({\it{tree\/}})\index{core-alu*}) \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\tt{'}}{\tt{carry}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{overflow}}, \\ 
{\rm{cons}}\,({\tt{'}}{\tt{zerop}}, {\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}))\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadddr}}\,({\rm{core-alu*}}\,({\it{tree\/}})\index{core-alu*}) \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{m-alu}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{p}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{g}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{alu-out}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices})\-)\-, \\ 
{\rm{index}}\,({\tt{'}}{\tt{tv-alu-help}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{c}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{a}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{b}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{mpg}}, {\tt{0}}, {\tt{7}})\index{indices})\-)\-)\-)\-, \\ 
{\tt{'}}{\tt{(}}{\tt{m-alu-carry}}{\tt{ }}{\tt{(}}{\tt{alu-carry}}{\tt{)}}{\tt{ }}{\tt{t-carry}}{\tt{ }}{\tt{(}}{\tt{c}}{\tt{ }}{\tt{p}}{\tt{ }}{\tt{g}}{\tt{)}}{\tt{)}}, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{m-carry-out-help}}, \\ 
{\tt{'}}{\tt{(}}{\tt{carry}}{\tt{)}}, \\ 
{\tt{'}}{\tt{carry-out-help}}, \\ 
{\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{a}}, {\tt{0}})\index{index}, \\ 
{\tt{'}}{\tt{alu-carry}}, \\ 
{\tt{'}}{\tt{zero}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{0}})\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{1}})\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{2}})\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{3}})\index{index})\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{m-overflow-help}}, \\ 
{\tt{'}}{\tt{(}}{\tt{overflow}}{\tt{)}}, \\ 
{\tt{'}}{\tt{overflow-help}}, \\ 
{\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{alu-out}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size} $-\;1$)\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{a}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size} $-\;1$)\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{b}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size} $-\;1$)\index{index}, \\ 
{\tt{'}}{\tt{zero}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{0}})\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{1}})\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{2}})\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{3}})\index{index})\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{m-shift}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{tv-shift-or-buf}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{c}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{alu-out}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices}, \\ 
{\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{a}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size} $-\;1$)\index{index}, \\ 
{\tt{'}}{\tt{zero}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{0}})\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{1}})\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{2}})\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{op}}, {\tt{3}})\index{index})\-)\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{m-zerop}}, \\ 
{\tt{'}}{\tt{(}}{\tt{zerop}}{\tt{)}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{fast-zero}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{index}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{indices})\-)\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{core-alu*}}\,({\it{tree\/}})\index{core-alu*}) $=$ {\bf{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable core-alu*; name this event `core-alu*-off'.\index{core-alu*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable core-alu*\$destructure; name this event `core-alu*\$destructure-off'.\index{core-alu*\$destructure-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{core-alu\&} \\  
\=\+{\rm{core-alu\&}}\,({\it{netlist\/}}, {\it{tree\/}})\index{core-alu\&} \\ 
$=$$\;\;\;\;$(\=\+(\=\+{\rm{lookup-module}}\,({\rm{index}}\,({\tt{'}}{\tt{core-alu}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, {\it{netlist\/}})\index{lookup-module} \\ 
$=$$\;\;\;\;${\rm{core-alu*}}\,({\it{tree\/}})\index{core-alu*})\- \\ 
$\wedge$$\;\;\;\;${\rm{tv-alu-help\&}}\,(\=\+{\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{core-alu}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\it{tree\/}})\-\index{tv-alu-help\&} \\ 
$\wedge$$\;\;\;\;${\rm{t-carry\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{core-alu}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{t-carry\&} \\ 
$\wedge$$\;\;\;\;${\rm{carry-out-help\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{core-alu}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{carry-out-help\&} \\ 
$\wedge$$\;\;\;\;${\rm{overflow-help\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{core-alu}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{overflow-help\&} \\ 
$\wedge$$\;\;\;\;${\rm{tv-shift-or-buf\&}}\,(\=\+{\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{core-alu}}, \\ 
{\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\it{tree\/}})\-\index{tv-shift-or-buf\&} \\ 
$\wedge$$\;\;\;\;${\rm{fast-zero\&}}\,(\=\+{\rm{delete-module}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{core-alu}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\-\index{fast-zero\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable core-alu\&; name this event `core-alu\&-off'.\index{core-alu\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{core-alu\$netlist} \\  
\=\+{\rm{core-alu\$netlist}}\,({\it{tree\/}})\index{core-alu\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{core-alu*}}\,({\it{tree\/}})\index{core-alu*}, \\ 
\=\+{\rm{tv-alu-help\$netlist}}\,({\it{tree\/}})\index{tv-alu-help\$netlist} \\ 
$\cup$$\;\;\;\;$(\=\+{\sc{t-carry\$netlist}}\index{t-carry\$netlist} \\ 
$\cup$$\;\;\;\;$(\=\+{\sc{carry-out-help\$netlist}}\index{carry-out-help\$netlist} \\ 
$\cup$$\;\;\;\;$(\=\+{\sc{overflow-help\$netlist}}\index{overflow-help\$netlist} \\ 
$\cup$$\;\;\;\;$(\=\+{\rm{tv-shift-or-buf\$netlist}}\,({\it{tree\/}})\index{tv-shift-or-buf\$netlist} \\ 
$\cup$$\;\;\;\;${\rm{fast-zero\$netlist}}\,({\rm{tree-size}}\,({\it{tree\/}})\index{tree-size})\index{fast-zero\$netlist})\-)\-)\-)\-\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  core-alu\$value \\ \index{core-alu\$value}
\=\+(\=\+{\rm{core-alu\&}}\,({\it{netlist\/}}, {\it{tree\/}})\index{core-alu\&} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b\/}})\index{length} $=$ {\rm{tree-size}}\,({\it{tree\/}})\index{tree-size}) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{a\/}})\index{length} $<$ {\tt{3}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{a\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{b\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{op\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{op\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{mpg\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{mpg\/}})\index{length} $=$ {\tt{7}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{core-alu}}, {\rm{tree-number}}\,({\it{tree\/}})\index{tree-number})\index{index}, \\ 
{\rm{cons}}\,({\it{c\/}}, {\rm{append}}\,({\it{a\/}}, {\rm{append}}\,({\it{b\/}}, {\rm{cons}}\,({\it{zero\/}}, {\rm{append}}\,({\it{mpg\/}}, {\it{op\/}}))))), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$core-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{zero\/}}, {\it{mpg\/}}, {\it{op\/}}, {\it{tree\/}})\index{f\$core-alu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable core-alu\$value; name this event `core-alu\$value-off'.\index{core-alu\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{reg-size}$\;\;$
{\sc{reg-size}}\index{reg-size} $=$ {\tt{4}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{a-immediate-p}$\;\;$
{\rm{a-immediate-p}}\,({\it{instruction\/}})\index{a-immediate-p} $=$ {\rm{nth}}\,({\tt{9}}, {\it{instruction\/}})\index{nth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{a-immediate} \\  
{\rm{a-immediate}}\,({\it{instruction\/}})\index{a-immediate} $=$ {\rm{subrange}}\,({\it{instruction\/}}, {\tt{0}}, {\tt{8}})\index{subrange}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{rn-a}$\;\;$
{\rm{rn-a}}\,({\it{instruction\/}})\index{rn-a} $=$ {\rm{subrange}}\,({\it{instruction\/}}, {\tt{0}}, {\tt{3}})\index{subrange}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{mode-a}$\;\;$
{\rm{mode-a}}\,({\it{instruction\/}})\index{mode-a} $=$ {\rm{subrange}}\,({\it{instruction\/}}, {\tt{4}}, {\tt{5}})\index{subrange}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{rn-b}$\;\;$
{\rm{rn-b}}\,({\it{instruction\/}})\index{rn-b} $=$ {\rm{subrange}}\,({\it{instruction\/}}, {\tt{10}}, {\tt{13}})\index{subrange}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{mode-b}$\;\;$
{\rm{mode-b}}\,({\it{instruction\/}})\index{mode-b} $=$ {\rm{subrange}}\,({\it{instruction\/}}, {\tt{14}}, {\tt{15}})\index{subrange}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{set-flags} \\  
{\rm{set-flags}}\,({\it{instruction\/}})\index{set-flags} $=$ {\rm{subrange}}\,({\it{instruction\/}}, {\tt{16}}, {\tt{19}})\index{subrange}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{store-cc} \\  
{\rm{store-cc}}\,({\it{instruction\/}})\index{store-cc} $=$ {\rm{subrange}}\,({\it{instruction\/}}, {\tt{20}}, {\tt{23}})\index{subrange}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{op-code} \\  
{\rm{op-code}}\,({\it{instruction\/}})\index{op-code} $=$ {\rm{subrange}}\,({\it{instruction\/}}, {\tt{24}}, {\tt{27}})\index{subrange}
\end{tabbing}


\noindent{\sc Event}:   Enable a-immediate-p; name this event `a-immediate-p-off'.\index{a-immediate-p-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable a-immediate; name this event `a-immediate-off'.\index{a-immediate-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable rn-a; name this event `rn-a-off'.\index{rn-a-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable rn-b; name this event `rn-b-off'.\index{rn-b-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable mode-a; name this event `mode-a-off'.\index{mode-a-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable mode-b; name this event `mode-b-off'.\index{mode-b-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable set-flags; name this event `set-flags-off'.\index{set-flags-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable store-cc; name this event `store-cc-off'.\index{store-cc-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable op-code; name this event `op-code-off'.\index{op-code-off}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{ir-fields-theory}} to consist of the following events: a-immediate-p,
a-immediate,
rn-a,
mode-a,
rn-b,
mode-b,
set-flags,
store-cc,
op-code.\index{ir-fields-theory}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{z-set}$\;\;$
{\rm{z-set}}\,({\it{set-flags\/}})\index{z-set} $=$ {\rm{nth}}\,({\tt{0}}, {\it{set-flags\/}})\index{nth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{n-set}$\;\;$
{\rm{n-set}}\,({\it{set-flags\/}})\index{n-set} $=$ {\rm{nth}}\,({\tt{1}}, {\it{set-flags\/}})\index{nth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-set}$\;\;$
{\rm{v-set}}\,({\it{set-flags\/}})\index{v-set} $=$ {\rm{nth}}\,({\tt{2}}, {\it{set-flags\/}})\index{nth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{c-set}$\;\;$
{\rm{c-set}}\,({\it{set-flags\/}})\index{c-set} $=$ {\rm{nth}}\,({\tt{3}}, {\it{set-flags\/}})\index{nth}
\end{tabbing}


\noindent{\sc Event}:   Enable z-set; name this event `z-set-off'.\index{z-set-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable n-set; name this event `n-set-off'.\index{n-set-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-set; name this event `v-set-off'.\index{v-set-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable c-set; name this event `c-set-off'.\index{c-set-off}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{set-flags-theory}} to consist of the following events: z-set,
n-set,
v-set,
c-set.\index{set-flags-theory}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{z-flag}$\;\;$
{\rm{z-flag}}\,({\it{flags\/}})\index{z-flag} $=$ {\rm{nth}}\,({\tt{0}}, {\it{flags\/}})\index{nth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{n-flag}$\;\;$
{\rm{n-flag}}\,({\it{flags\/}})\index{n-flag} $=$ {\rm{nth}}\,({\tt{1}}, {\it{flags\/}})\index{nth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-flag}$\;\;$
{\rm{v-flag}}\,({\it{flags\/}})\index{v-flag} $=$ {\rm{nth}}\,({\tt{2}}, {\it{flags\/}})\index{nth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{c-flag}$\;\;$
{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag} $=$ {\rm{nth}}\,({\tt{3}}, {\it{flags\/}})\index{nth}
\end{tabbing}


\noindent{\sc Event}:   Enable z-flag; name this event `z-flag-off'.\index{z-flag-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable n-flag; name this event `n-flag-off'.\index{n-flag-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-flag; name this event `v-flag-off'.\index{v-flag-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable c-flag; name this event `c-flag-off'.\index{c-flag-off}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{flags-theory}} to consist of the following events: z-flag,
n-flag,
v-flag,
c-flag.\index{flags-theory}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{reg-direct-p}$\;\;$
{\rm{reg-direct-p}}\,({\it{mode\/}})\index{reg-direct-p} $=$ ({\it{mode\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{reg-indirect-p}$\;\;$
{\rm{reg-indirect-p}}\,({\it{mode\/}})\index{reg-indirect-p} $=$ ({\it{mode\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{pre-dec-p}$\;\;$
{\rm{pre-dec-p}}\,({\it{mode\/}})\index{pre-dec-p} $=$ ({\it{mode\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{post-inc-p}$\;\;$
{\rm{post-inc-p}}\,({\it{mode\/}})\index{post-inc-p} $=$ ({\it{mode\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}))
\end{tabbing}


\noindent{\sc Event}:   Enable reg-direct-p; name this event `reg-direct-p-off'.\index{reg-direct-p-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable reg-indirect-p; name this event `reg-indirect-p-off'.\index{reg-indirect-p-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable pre-dec-p; name this event `pre-dec-p-off'.\index{pre-dec-p-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable post-inc-p; name this event `post-inc-p-off'.\index{post-inc-p-off}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{reg-mode-theory}} to consist of the following events: reg-direct-p,
reg-indirect-p,
pre-dec-p,
post-inc-p.\index{reg-mode-theory}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{store-resultp} \\  
\=\+{\rm{store-resultp}}\,({\it{store-cc\/}}, {\it{flags\/}})\index{store-resultp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{store-cc\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }$\neg$ {\rm{c-flag}}\,({\it{flags\/}})\index{c-flag} \\ 
{\bf elseif }{\it{store-cc\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag} \\ 
{\bf elseif }{\it{store-cc\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }$\neg$ {\rm{v-flag}}\,({\it{flags\/}})\index{v-flag} \\ 
{\bf elseif }{\it{store-cc\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\rm{v-flag}}\,({\it{flags\/}})\index{v-flag} \\ 
{\bf elseif }{\it{store-cc\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }$\neg$ {\rm{n-flag}}\,({\it{flags\/}})\index{n-flag} \\ 
{\bf elseif }{\it{store-cc\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }{\rm{n-flag}}\,({\it{flags\/}})\index{n-flag} \\ 
{\bf elseif }{\it{store-cc\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }$\neg$ {\rm{z-flag}}\,({\it{flags\/}})\index{z-flag} \\ 
{\bf elseif }{\it{store-cc\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }{\rm{z-flag}}\,({\it{flags\/}})\index{z-flag} \\ 
{\bf elseif }{\it{store-cc\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf then }($\neg$ {\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}) $\wedge$ ($\neg$ {\rm{z-flag}}\,({\it{flags\/}})\index{z-flag}) \\ 
{\bf elseif }{\it{store-cc\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf then }{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag} $\vee$ {\rm{z-flag}}\,({\it{flags\/}})\index{z-flag} \\ 
{\bf elseif }{\it{store-cc\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf then }\=\+({\rm{n-flag}}\,({\it{flags\/}})\index{n-flag} $\wedge$ {\rm{v-flag}}\,({\it{flags\/}})\index{v-flag}) \\ 
$\vee$$\;\;\;\;$(($\neg$ {\rm{n-flag}}\,({\it{flags\/}})\index{n-flag}) $\wedge$ ($\neg$ {\rm{v-flag}}\,({\it{flags\/}})\index{v-flag}))\- \\ 
{\bf elseif }{\it{store-cc\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf then }\=\+({\rm{n-flag}}\,({\it{flags\/}})\index{n-flag} $\wedge$ ($\neg$ {\rm{v-flag}}\,({\it{flags\/}})\index{v-flag})) \\ 
$\vee$$\;\;\;\;$(($\neg$ {\rm{n-flag}}\,({\it{flags\/}})\index{n-flag}) $\wedge$ {\rm{v-flag}}\,({\it{flags\/}})\index{v-flag})\- \\ 
{\bf elseif }{\it{store-cc\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf then }\=\+({\rm{n-flag}}\,({\it{flags\/}})\index{n-flag} $\wedge$ {\rm{v-flag}}\,({\it{flags\/}})\index{v-flag} $\wedge$ ($\neg$ {\rm{z-flag}}\,({\it{flags\/}})\index{z-flag})) \\ 
$\vee$$\;\;\;\;$(\=\+($\neg$ {\rm{n-flag}}\,({\it{flags\/}})\index{n-flag}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{v-flag}}\,({\it{flags\/}})\index{v-flag}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{z-flag}}\,({\it{flags\/}})\index{z-flag}))\-\- \\ 
{\bf elseif }{\it{store-cc\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf then }\=\+{\rm{z-flag}}\,({\it{flags\/}})\index{z-flag} \\ 
$\vee$$\;\;\;\;$({\rm{n-flag}}\,({\it{flags\/}})\index{n-flag} $\wedge$ ($\neg$ {\rm{v-flag}}\,({\it{flags\/}})\index{v-flag})) \\ 
$\vee$$\;\;\;\;$(($\neg$ {\rm{n-flag}}\,({\it{flags\/}})\index{n-flag}) $\wedge$ {\rm{v-flag}}\,({\it{flags\/}})\index{v-flag})\- \\ 
{\bf elseif }{\it{store-cc\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}})$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable store-resultp; name this event `store-resultp-off'.\index{store-resultp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{update-flags} \\  
\=\+{\rm{update-flags}}\,({\it{flags\/}}, {\it{set-flags\/}}, {\it{cvzbv\/}})\index{update-flags} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{b-if}}\,({\rm{z-set}}\,({\it{set-flags\/}})\index{z-set}, {\rm{zb}}\,({\it{cvzbv\/}})\index{zb}, {\rm{z-flag}}\,({\it{flags\/}})\index{z-flag})\index{b-if}, \\ 
{\rm{b-if}}\,({\rm{n-set}}\,({\it{set-flags\/}})\index{n-set}, {\rm{n}}\,({\it{cvzbv\/}})\index{n}, {\rm{n-flag}}\,({\it{flags\/}})\index{n-flag})\index{b-if}, \\ 
{\rm{b-if}}\,({\rm{v-set}}\,({\it{set-flags\/}})\index{v-set}, {\rm{v}}\,({\it{cvzbv\/}})\index{v}, {\rm{v-flag}}\,({\it{flags\/}})\index{v-flag})\index{b-if}, \\ 
{\rm{b-if}}\,({\rm{c-set}}\,({\it{set-flags\/}})\index{c-set}, {\rm{c}}\,({\it{cvzbv\/}})\index{c}, {\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{b-if})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable update-flags; name this event `update-flags-off'.\index{update-flags-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{regs}$\;\;$
{\rm{regs}}\,({\it{state\/}})\index{regs} $=$ {\rm{nth}}\,({\tt{0}}, {\it{state\/}})\index{nth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{flags}$\;\;$
{\rm{flags}}\,({\it{state\/}})\index{flags} $=$ {\rm{nth}}\,({\tt{1}}, {\it{state\/}})\index{nth}
\end{tabbing}


\noindent{\sc Event}:   Enable regs; name this event `regs-off'.\index{regs-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable flags; name this event `flags-off'.\index{flags-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fm9001-alu-operation} \\  
\=\+{\rm{fm9001-alu-operation}}\,({\it{regs\/}}, {\it{flags\/}}, {\it{mem\/}}, {\it{ins\/}}, {\it{operand-a\/}}, {\it{operand-b\/}}, {\it{b-address\/}})\index{fm9001-alu-operation} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+\=\+{\bf if }\=\+{\rm{store-resultp}}\,({\rm{store-cc}}\,({\it{ins\/}})\index{store-cc}, {\it{flags\/}})\index{store-resultp} \\ 
$\wedge$$\;\;\;\;${\rm{reg-direct-p}}\,({\rm{mode-b}}\,({\it{ins\/}})\index{mode-b})\index{reg-direct-p}\- \\ 
{\bf then }{\rm{write-mem}}\,(\=\+{\rm{rn-b}}\,({\it{ins\/}})\index{rn-b}, \\ 
{\it{regs\/}}, \\ 
{\rm{bv}}\,({\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{operand-a\/}}, \\ 
{\it{operand-b\/}}, \\ 
{\rm{op-code}}\,({\it{ins\/}})\index{op-code})\-\index{v-alu})\index{bv})\-\index{write-mem} \\ 
{\bf else }{\it{regs\/}}$\;${\bf  endif}\-, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\rm{set-flags}}\,({\it{ins\/}})\index{set-flags}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{operand-a\/}}, \\ 
{\it{operand-b\/}}, \\ 
{\rm{op-code}}\,({\it{ins\/}})\index{op-code})\-\index{v-alu})\-\index{update-flags})\-, \\ 
\=\+{\bf if }\=\+{\rm{store-resultp}}\,({\rm{store-cc}}\,({\it{ins\/}})\index{store-cc}, {\it{flags\/}})\index{store-resultp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{reg-direct-p}}\,({\rm{mode-b}}\,({\it{ins\/}})\index{mode-b})\index{reg-direct-p})\- \\ 
{\bf then }{\rm{write-mem}}\,(\=\+{\it{b-address\/}}, \\ 
{\it{mem\/}}, \\ 
{\rm{bv}}\,({\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{operand-a\/}}, \\ 
{\it{operand-b\/}}, \\ 
{\rm{op-code}}\,({\it{ins\/}})\index{op-code})\-\index{v-alu})\index{bv})\-\index{write-mem} \\ 
{\bf else }{\it{mem\/}}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fm9001-operand-b} \\  
\=\+{\rm{fm9001-operand-b}}\,({\it{regs\/}}, {\it{flags\/}}, {\it{mem\/}}, {\it{ins\/}}, {\it{operand-a\/}})\index{fm9001-operand-b} \\ 
$=$$\;\;\;\;${\rm{fm9001-alu-operation}}\,(\=\+\=\+{\bf if }{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{ins\/}})\index{mode-b})\index{pre-dec-p} \\ 
{\bf then }{\rm{write-mem}}\,(\=\+{\rm{rn-b}}\,({\it{ins\/}})\index{rn-b}, \\ 
{\it{regs\/}}, \\ 
{\rm{v-dec}}\,({\rm{read-mem}}\,({\rm{rn-b}}\,({\it{ins\/}})\index{rn-b}, {\it{regs\/}})\index{read-mem})\index{v-dec})\-\index{write-mem} \\ 
{\bf elseif }{\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{ins\/}})\index{mode-b})\index{post-inc-p} \\ 
{\bf then }{\rm{write-mem}}\,(\=\+{\rm{rn-b}}\,({\it{ins\/}})\index{rn-b}, \\ 
{\it{regs\/}}, \\ 
{\rm{v-inc}}\,({\rm{read-mem}}\,({\rm{rn-b}}\,({\it{ins\/}})\index{rn-b}, {\it{regs\/}})\index{read-mem})\index{v-inc})\-\index{write-mem} \\ 
{\bf else }{\it{regs\/}}$\;${\bf  endif}\-, \\ 
{\it{flags\/}}, \\ 
{\it{mem\/}}, \\ 
{\it{ins\/}}, \\ 
{\it{operand-a\/}}, \\ 
\=\+{\bf if }{\rm{reg-direct-p}}\,({\rm{mode-b}}\,({\it{ins\/}})\index{mode-b})\index{reg-direct-p} \\ 
{\bf then }{\rm{read-mem}}\,({\rm{rn-b}}\,({\it{ins\/}})\index{rn-b}, {\it{regs\/}})\index{read-mem} \\ 
{\bf else }{\rm{read-mem}}\,(\=\+\=\+{\bf if }{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{ins\/}})\index{mode-b})\index{pre-dec-p} \\ 
{\bf then }{\rm{v-dec}}\,({\rm{read-mem}}\,(\=\+{\rm{rn-b}}\,({\it{ins\/}})\index{rn-b}, \\ 
{\it{regs\/}})\-\index{read-mem})\index{v-dec} \\ 
{\bf else }{\rm{read-mem}}\,(\=\+{\rm{rn-b}}\,({\it{ins\/}})\index{rn-b}, \\ 
{\it{regs\/}})\-\index{read-mem}$\;${\bf  endif}\-, \\ 
{\it{mem\/}})\-\index{read-mem}$\;${\bf  endif}\-, \\ 
\=\+{\bf if }{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{ins\/}})\index{mode-b})\index{pre-dec-p} \\ 
{\bf then }{\rm{v-dec}}\,({\rm{read-mem}}\,({\rm{rn-b}}\,({\it{ins\/}})\index{rn-b}, {\it{regs\/}})\index{read-mem})\index{v-dec} \\ 
{\bf else }{\rm{read-mem}}\,({\rm{rn-b}}\,({\it{ins\/}})\index{rn-b}, {\it{regs\/}})\index{read-mem}$\;${\bf  endif}\-)\-\index{fm9001-alu-operation}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fm9001-operand-a} \\  
\=\+{\rm{fm9001-operand-a}}\,({\it{regs\/}}, {\it{flags\/}}, {\it{mem\/}}, {\it{ins\/}})\index{fm9001-operand-a} \\ 
$=$$\;\;\;\;${\rm{fm9001-operand-b}}\,(\=\+\=\+{\bf if }{\rm{a-immediate-p}}\,({\it{ins\/}})\index{a-immediate-p}$\;\;${\bf then }{\it{regs\/}} \\ 
{\bf elseif }{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{ins\/}})\index{mode-a})\index{pre-dec-p} \\ 
{\bf then }{\rm{write-mem}}\,(\=\+{\rm{rn-a}}\,({\it{ins\/}})\index{rn-a}, \\ 
{\it{regs\/}}, \\ 
{\rm{v-dec}}\,({\rm{read-mem}}\,({\rm{rn-a}}\,({\it{ins\/}})\index{rn-a}, {\it{regs\/}})\index{read-mem})\index{v-dec})\-\index{write-mem} \\ 
{\bf elseif }{\rm{post-inc-p}}\,({\rm{mode-a}}\,({\it{ins\/}})\index{mode-a})\index{post-inc-p} \\ 
{\bf then }{\rm{write-mem}}\,(\=\+{\rm{rn-a}}\,({\it{ins\/}})\index{rn-a}, \\ 
{\it{regs\/}}, \\ 
{\rm{v-inc}}\,({\rm{read-mem}}\,({\rm{rn-a}}\,({\it{ins\/}})\index{rn-a}, {\it{regs\/}})\index{read-mem})\index{v-inc})\-\index{write-mem} \\ 
{\bf else }{\it{regs\/}}$\;${\bf  endif}\-, \\ 
{\it{flags\/}}, \\ 
{\it{mem\/}}, \\ 
{\it{ins\/}}, \\ 
\=\+{\bf if }{\rm{a-immediate-p}}\,({\it{ins\/}})\index{a-immediate-p} \\ 
{\bf then }{\rm{sign-extend}}\,({\rm{a-immediate}}\,({\it{ins\/}})\index{a-immediate}, {\tt{32}})\index{sign-extend} \\ 
{\bf elseif }{\rm{reg-direct-p}}\,({\rm{mode-a}}\,({\it{ins\/}})\index{mode-a})\index{reg-direct-p} \\ 
{\bf then }{\rm{read-mem}}\,({\rm{rn-a}}\,({\it{ins\/}})\index{rn-a}, {\it{regs\/}})\index{read-mem} \\ 
{\bf elseif }{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{ins\/}})\index{mode-a})\index{pre-dec-p} \\ 
{\bf then }{\rm{read-mem}}\,({\rm{v-dec}}\,({\rm{read-mem}}\,({\rm{rn-a}}\,({\it{ins\/}})\index{rn-a}, {\it{regs\/}})\index{read-mem})\index{v-dec}, {\it{mem\/}})\index{read-mem} \\ 
{\bf else }{\rm{read-mem}}\,({\rm{read-mem}}\,({\rm{rn-a}}\,({\it{ins\/}})\index{rn-a}, {\it{regs\/}})\index{read-mem}, {\it{mem\/}})\index{read-mem}$\;${\bf  endif}\-)\-\index{fm9001-operand-b}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fm9001-fetch} \\  
\=\+{\rm{fm9001-fetch}}\,({\it{regs\/}}, {\it{flags\/}}, {\it{mem\/}}, {\it{pc-reg\/}})\index{fm9001-fetch} \\ 
$=$$\;\;\;\;${\rm{fm9001-operand-a}}\,(\=\+{\rm{write-mem}}\,({\it{pc-reg\/}}, {\it{regs\/}}, {\rm{v-inc}}\,({\rm{read-mem}}\,({\it{pc-reg\/}}, {\it{regs\/}})\index{read-mem})\index{v-inc})\index{write-mem}, \\ 
{\it{flags\/}}, \\ 
{\it{mem\/}}, \\ 
{\rm{read-mem}}\,({\rm{read-mem}}\,({\it{pc-reg\/}}, {\it{regs\/}})\index{read-mem}, {\it{mem\/}})\index{read-mem})\-\index{fm9001-operand-a}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fm9001-step} \\  
\=\+{\rm{fm9001-step}}\,({\it{state\/}}, {\it{pc-reg\/}})\index{fm9001-step} \\ 
$=$$\;\;\;\;${\rm{fm9001-fetch}}\,({\rm{regs}}\,({\rm{car}}\,({\it{state\/}}))\index{regs}, {\rm{flags}}\,({\rm{car}}\,({\it{state\/}}))\index{flags}, {\rm{cadr}}\,({\it{state\/}}), {\it{pc-reg\/}})\index{fm9001-fetch}\-
\end{tabbing}


\noindent{\sc Event}:   Enable fm9001-step; name this event `fm9001-step-off'.\index{fm9001-step-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fm9001} \\  
\=\+{\rm{fm9001}}\,({\it{state\/}}, {\it{n\/}})\index{fm9001} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\it{state\/}} \\ 
{\bf else }{\rm{fm9001}}\,({\rm{fm9001-step}}\,({\it{state\/}}, {\rm{nat-to-v}}\,({\tt{15}}, {\sc{reg-size}}\index{reg-size})\index{nat-to-v})\index{fm9001-step}, {\it{n\/}} $-\;1$)\index{fm9001}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fm9001; name this event `fm9001-off'.\index{fm9001-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fm9001-interpreter} \\  
\=\+{\rm{fm9001-interpreter}}\,({\it{state\/}}, {\it{pc-reg\/}}, {\it{n\/}})\index{fm9001-interpreter} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\it{state\/}} \\ 
{\bf else }{\rm{fm9001-interpreter}}\,({\rm{fm9001-step}}\,({\it{state\/}}, {\it{pc-reg\/}})\index{fm9001-step}, {\it{pc-reg\/}}, {\it{n\/}} $-\;1$)\index{fm9001-interpreter}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fm9001-interpreter; name this event `fm9001-interpreter-off'.\index{fm9001-interpreter-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-fm9001-interpreter \\ \index{open-fm9001-interpreter}
\=\+(({\it{n\/}} $\simeq {\tt{0}}$) $\rightarrow$ ({\rm{fm9001-interpreter}}\,({\it{state\/}}, {\it{pc-reg\/}}, {\it{n\/}})\index{fm9001-interpreter} $=$ {\it{state\/}})) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{fm9001-interpreter}}\,({\it{state\/}}, {\it{pc-reg\/}}, {\it{n\/}})\index{fm9001-interpreter} \\ 
$=$$\;\;\;\;${\rm{fm9001-interpreter}}\,(\=\+{\rm{fm9001-step}}\,({\it{state\/}}, {\it{pc-reg\/}})\index{fm9001-step}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{n\/}} $-\;1$)\-\index{fm9001-interpreter})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fm9001-intr} \\  
\=\+{\rm{fm9001-intr}}\,({\it{state\/}}, {\it{pc-reg-input\/}})\index{fm9001-intr} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{pc-reg-input\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{state\/}} \\ 
{\bf else }{\rm{fm9001-intr}}\,(\=\+{\rm{fm9001-step}}\,({\it{state\/}}, {\rm{car}}\,({\it{pc-reg-input\/}}))\index{fm9001-step}, \\ 
{\rm{cdr}}\,({\it{pc-reg-input\/}}))\-\index{fm9001-intr}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fm9001-intr; name this event `fm9001-intr-off'.\index{fm9001-intr-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  properp-length-ir-accessors \\ \index{properp-length-ir-accessors}
\=\+{\rm{properp}}\,({\rm{a-immediate}}\,({\it{i-reg\/}})\index{a-immediate})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{a-immediate}}\,({\it{i-reg\/}})\index{a-immediate})\index{length} $=$ {\tt{9}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{rn-a}}\,({\it{i-reg\/}})\index{rn-a})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{rn-a}}\,({\it{i-reg\/}})\index{rn-a})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{length} $=$ {\tt{2}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{length} $=$ {\tt{2}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{set-flags}}\,({\it{i-reg\/}})\index{set-flags})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{set-flags}}\,({\it{i-reg\/}})\index{set-flags})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{length} $=$ {\tt{4}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-ir-accessors \\ \index{bvp-ir-accessors}
\=\+({\rm{bvp}}\,({\it{i-reg\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{i-reg\/}})\index{length} $=$ {\tt{32}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{bvp}}\,({\rm{a-immediate}}\,({\it{i-reg\/}})\index{a-immediate})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{rn-a}}\,({\it{i-reg\/}})\index{rn-a})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{set-flags}}\,({\it{i-reg\/}})\index{set-flags})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{bvp})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  boolp-a-immediate-p \\ \index{boolp-a-immediate-p}
({\rm{bvp}}\,({\it{ir\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{ir\/}})\index{length} $=$ {\tt{32}})) $\rightarrow$ {\rm{boolp}}\,({\rm{a-immediate-p}}\,({\it{ir\/}})\index{a-immediate-p})\index{boolp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-length-update-flags \\ \index{bvp-length-update-flags}
\=\+{\rm{bvp}}\,({\rm{update-flags}}\,({\it{flags\/}}, {\it{set-flags\/}}, {\it{cvzbv\/}})\index{update-flags})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{update-flags}}\,({\it{flags\/}}, {\it{set-flags\/}}, {\it{cvzbv\/}})\index{update-flags})\index{length} $=$ {\tt{4}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  boolp-c-flag-update-flags \\ \index{boolp-c-flag-update-flags}
{\rm{boolp}}\,({\rm{c-flag}}\,({\rm{update-flags}}\,({\it{flags\/}}, {\it{set-flags\/}}, {\it{cvzbv\/}})\index{update-flags})\index{c-flag})\index{boolp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-a-immediate \\ \index{bvp-a-immediate}
({\rm{bvp}}\,({\it{ir\/}})\index{bvp} $\wedge$ ({\tt{8}} $<$ {\rm{length}}\,({\it{ir\/}})\index{length})) $\rightarrow$ {\rm{bvp}}\,({\rm{a-immediate}}\,({\it{ir\/}})\index{a-immediate})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  reg-direct-$>$not-reg-indirect \\ \index{reg-direct-$>$not-reg-indirect}
\=\+{\rm{reg-direct-p}}\,({\it{mode\/}})\index{reg-direct-p} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{reg-indirect-p}}\,({\it{mode\/}})\index{reg-indirect-p} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$({\rm{pre-dec-p}}\,({\it{mode\/}})\index{pre-dec-p} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$({\rm{post-inc-p}}\,({\it{mode\/}})\index{post-inc-p} $=$ {\bf{f}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  boolp-store-result-p \\ \index{boolp-store-result-p}
\=\+({\rm{bvp}}\,({\it{flags\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{flags\/}})\index{length} $=$ {\tt{4}})) \\ 
$\rightarrow$$\;\;\;\;${\rm{boolp}}\,({\rm{store-resultp}}\,({\it{store-cc\/}}, {\it{flags\/}})\index{store-resultp})\index{boolp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  unary-op-code-p-op-code-$>$v-alu=v-alu-1 \\ \index{unary-op-code-p-op-code-$>$v-al!u=v-alu-1}
\=\+{\rm{unary-op-code-p}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{unary-op-code-p} \\ 
$\rightarrow$$\;\;\;\;$({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{v-alu} $=$ {\rm{v-alu-1}}\,({\it{c\/}}, {\it{a\/}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{v-alu-1})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{intp}$\;\;$
{\rm{intp}}\,({\it{x\/}})\index{intp} $=$ (({\it{x\/}} $\in\;${\bf{N}}${}$) $\vee$ {\rm{negativep}}\,({\it{x\/}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{int-to-bv} \\  
\=\+{\rm{int-to-bv}}\,({\it{x\/}}, {\it{size\/}})\index{int-to-bv} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{negativep}}\,({\it{x\/}}) \\ 
{\bf then }{\rm{v-subtracter-output}}\,(\=\+{\bf{f}}, \\ 
{\rm{nat-to-v}}\,({\rm{negative-guts}}\,({\it{x\/}}), {\it{size\/}})\index{nat-to-v}, \\ 
{\rm{nat-to-v}}\,({\tt{0}}, {\it{size\/}})\index{nat-to-v})\-\index{v-subtracter-output} \\ 
{\bf else }{\rm{nat-to-v}}\,({\it{x\/}}, {\it{size\/}})\index{nat-to-v}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{bv-to-int} \\  
\=\+{\rm{bv-to-int}}\,({\it{x\/}})\index{bv-to-int} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{nth}}\,({\rm{length}}\,({\it{x\/}})\index{length} $-\;1$, {\it{x\/}})\index{nth}$\;\;${\bf then }$-$ {\rm{v-to-nat}}\,({\rm{v-inc}}\,({\rm{v-not}}\,({\it{x\/}})\index{v-not})\index{v-inc})\index{v-to-nat} \\ 
{\bf else }{\rm{v-to-nat}}\,({\it{x\/}})\index{v-to-nat}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{c10-tf} \\  
\=\+{\rm{c10-tf}}\,({\it{x\/}})\index{c10-tf} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+\=\+{\bf if }{\rm{car}}\,({\it{x\/}}) $=$ {\tt{0}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-, \\ 
{\rm{c10-tf}}\,({\rm{cdr}}\,({\it{x\/}}))\index{c10-tf})\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{c10-int}$\;\;$
{\rm{c10-int}}\,({\it{x\/}})\index{c10-int} $=$ {\rm{bv-to-int}}\,({\rm{c10-tf}}\,({\it{x\/}})\index{c10-tf})\index{bv-to-int}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{add} \\  
\=\+{\rm{add}}\,({\it{x\/}}, {\it{y\/}})\index{add} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{negativep}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{negativep}}\,({\it{y\/}})$\;\;${\bf then }$-$ ({\rm{negative-guts}}\,({\it{x\/}}) $+$ {\rm{negative-guts}}\,({\it{y\/}})) \\ 
{\bf elseif }{\it{y\/}} $<$ {\rm{negative-guts}}\,({\it{x\/}})$\;\;${\bf then }$-$ ({\rm{negative-guts}}\,({\it{x\/}}) $-$ {\it{y\/}}) \\ 
{\bf else }{\it{y\/}} $-$ {\rm{negative-guts}}\,({\it{x\/}})$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{negativep}}\,({\it{y\/}}) \\ 
{\bf then }\=\+{\bf if }{\it{x\/}} $<$ {\rm{negative-guts}}\,({\it{y\/}})$\;\;${\bf then }$-$ ({\rm{negative-guts}}\,({\it{y\/}}) $-$ {\it{x\/}}) \\ 
{\bf else }{\it{x\/}} $-$ {\rm{negative-guts}}\,({\it{y\/}})$\;${\bf  endif}\- \\ 
{\bf else }{\it{x\/}} $+$ {\it{y\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{integer-minus} \\  
\=\+{\rm{integer-minus}}\,({\it{x\/}})\index{integer-minus} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{negativep}}\,({\it{x\/}})$\;\;${\bf then }{\rm{negative-guts}}\,({\it{x\/}}) \\ 
{\bf elseif }{\it{x\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }$-$ {\it{x\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{sub}$\;\;$
{\rm{sub}}\,({\it{x\/}}, {\it{y\/}})\index{sub} $=$ {\rm{add}}\,({\it{x\/}}, {\rm{integer-minus}}\,({\it{y\/}})\index{integer-minus})\index{add}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{exp2} \\  
\=\+{\rm{exp2}}\,({\it{y\/}})\index{exp2} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{y\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{1}} \\ 
{\bf else }{\tt{2}} $*$ {\rm{exp2}}\,({\it{y\/}} $-\;1$)\index{exp2}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-stuff \\ \index{quotient-stuff}
(({\it{n\/}} $\not=$ {\tt{0}}) $\wedge$ ({\it{n\/}} $\in\;${\bf{N}}${}$)) $\rightarrow$ (({\it{n\/}} $\div$ {\tt{2}}) $<$ {\it{n\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{log2} \\  
\=\+{\rm{log2}}\,({\it{n\/}})\index{log2} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{n\/}} $\simeq {\tt{0}}$) $\vee$ ({\it{n\/}} $=$ {\tt{1}})$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }$1\;+$ {\rm{log2}}\,({\it{n\/}} $\div$ {\tt{2}})\index{log2}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm-register} \\  
\=\+{\rm{asm-register}}\,({\it{x\/}})\index{asm-register} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{x\/}}: \\ 
{\bf case = }{\it{r0\/}} \\ 
{\bf then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{r1\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{r2\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{r3\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{r4\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{r5\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{r6\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{r7\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{r8\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{r9\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{r10\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{r11\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{r12\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{r13\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{lnk\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{r14\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{tos\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{r15\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{pc\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\sc{r0}}\index{r0} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\sc{r1}}\index{r1} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\sc{r2}}\index{r2} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\sc{r3}}\index{r3} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\sc{r4}}\index{r4} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\sc{r5}}\index{r5} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\sc{r6}}\index{r6} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\sc{r7}}\index{r7} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\sc{r8}}\index{r8} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\sc{r9}}\index{r9} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\sc{r10}}\index{r10} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\sc{r11}}\index{r11} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\sc{r12}}\index{r12} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\sc{r13}}\index{r13} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\sc{lnk}}\index{lnk} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\sc{r14}}\index{r14} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\sc{tos}}\index{tos} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\sc{r15}}\index{r15} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\sc{pc}}\index{pc} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\sc{r0-}}\index{r0-} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r1-}}\index{r1-} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r2-}}\index{r2-} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r3-}}\index{r3-} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r4-}}\index{r4-} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r5-}}\index{r5-} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r6-}}\index{r6-} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r7-}}\index{r7-} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r8-}}\index{r8-} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r9-}}\index{r9-} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r10-}}\index{r10-} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r11-}}\index{r11-} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r12-}}\index{r12-} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r13-}}\index{r13-} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\sc{lnk-}}\index{lnk-} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r14-}}\index{r14-} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\sc{tos-}}\index{tos-} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r15-}}\index{r15-} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\sc{pc-}}\index{pc-} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r0+}}\index{r0+} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r1+}}\index{r1+} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r2+}}\index{r2+} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r3+}}\index{r3+} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r4+}}\index{r4+} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r5+}}\index{r5+} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r6+}}\index{r6+} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r7+}}\index{r7+} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r8+}}\index{r8+} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r9+}}\index{r9+} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r10+}}\index{r10+} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r11+}}\index{r11+} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r12+}}\index{r12+} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r13+}}\index{r13+} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\sc{lnk+}}\index{lnk+} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r14+}}\index{r14+} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\sc{tos+}}\index{tos+} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\sc{r15+}}\index{r15+} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\sc{pc+}}\index{pc+} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf otherwise }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}})$\;${\bf  endcase}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm-register-a} \\  
\=\+{\rm{asm-register-a}}\,({\it{x\/}})\index{asm-register-a} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{intp}}\,({\it{x\/}})\index{intp}$\;\;${\bf then }{\rm{append}}\,({\rm{int-to-bv}}\,({\it{x\/}}, {\tt{9}})\index{int-to-bv}, {\rm{list}}\,({\bf{t}})) \\ 
{\bf else }{\rm{append}}\,({\rm{asm-register}}\,({\it{x\/}})\index{asm-register}, {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}))$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm-op-code} \\  
\=\+{\rm{asm-op-code}}\,({\it{x\/}})\index{asm-op-code} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{x\/}}: \\ 
{\bf case = }{\it{move\/}} \\ 
{\bf then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{inc\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{addc\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{add\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{neg\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\it{dec\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\it{subb\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\it{sub\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\it{ror\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\it{asr\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\it{lsr\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\it{xor\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\it{or\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\it{and\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\it{not\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\it{m15\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf otherwise }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}})$\;${\bf  endcase}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm-store-cc} \\  
\=\+{\rm{asm-store-cc}}\,({\it{x\/}})\index{asm-store-cc} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{x\/}}: \\ 
{\bf case = }{\it{cc\/}} \\ 
{\bf then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{cs\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{vc\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{vs\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}) \\ 
{\bf case = }{\it{pl\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\it{nc\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\it{mi\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\it{ns\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\it{ne\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\it{zc\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\it{eq\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\it{zs\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}) \\ 
{\bf case = }{\it{hi\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\it{ls\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\it{ge\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\it{lt\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}) \\ 
{\bf case = }{\it{gt\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\it{le\/}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\bf{t}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf case = }{\bf{f}} \\ 
{\bf $\;\;$then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf otherwise }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}})$\;${\bf  endcase}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm-flags} \\  
\=\+{\rm{asm-flags}}\,({\it{x\/}})\index{asm-flags} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $=$ {\tt{'}}{\tt{t}}$\;\;${\bf then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf else }{\rm{list}}\,(\=\+{\rm{car}}\,({\rm{unpack}}\,({\tt{'}}{\tt{z}})) $\in$ {\rm{unpack}}\,({\it{x\/}}), \\ 
{\rm{car}}\,({\rm{unpack}}\,({\tt{'}}{\tt{n}})) $\in$ {\rm{unpack}}\,({\it{x\/}}), \\ 
{\rm{car}}\,({\rm{unpack}}\,({\tt{'}}{\tt{v}})) $\in$ {\rm{unpack}}\,({\it{x\/}}), \\ 
{\rm{car}}\,({\rm{unpack}}\,({\tt{'}}{\tt{c}})) $\in$ {\rm{unpack}}\,({\it{x\/}}))\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{resolve-names} \\  
\=\+{\rm{resolve-names}}\,({\it{list\/}}, {\it{cnt\/}}, {\it{alist\/}})\index{resolve-names} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{list\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{alist\/}} \\ 
{\bf elseif }{\rm{litatom}}\,({\rm{car}}\,({\it{list\/}})) \\ 
{\bf then }{\rm{resolve-names}}\,({\rm{cdr}}\,({\it{list\/}}), {\it{cnt\/}}, {\rm{cons}}\,({\rm{cons}}\,({\rm{car}}\,({\it{list\/}}), {\it{cnt\/}}), {\it{alist\/}}))\index{resolve-names} \\ 
{\bf else }{\rm{resolve-names}}\,({\rm{cdr}}\,({\it{list\/}}), $1\;+$ {\it{cnt\/}}, {\it{alist\/}})\index{resolve-names}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{update-list} \\  
\=\+{\rm{update-list}}\,({\it{list\/}}, {\it{alist\/}})\index{update-list} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{list\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+\=\+{\bf if }{\rm{listp}}\,({\rm{car}}\,({\it{list\/}})) $\wedge$ ({\rm{caar}}\,({\it{list\/}}) $=$ {\tt{'}}{\tt{value}}) \\ 
{\bf then }{\rm{eval\$}}\,({\bf{t}}, {\rm{cadar}}\,({\it{list\/}}), {\it{alist\/}}) \\ 
{\bf else }{\rm{car}}\,({\it{list\/}})$\;${\bf  endif}\-, \\ 
{\rm{update-list}}\,({\rm{cdr}}\,({\it{list\/}}), {\it{alist\/}})\index{update-list})\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm-line} \\  
\=\+{\rm{asm-line}}\,({\it{line\/}})\index{asm-line} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{intp}}\,({\it{line\/}})\index{intp}$\;\;${\bf then }{\rm{int-to-bv}}\,({\it{line\/}}, {\tt{32}})\index{int-to-bv} \\ 
{\bf else }{\rm{append}}\,(\=\+{\rm{asm-register-a}}\,({\rm{caddddr}}\,({\it{line\/}}))\index{asm-register-a}, \\ 
{\rm{append}}\,(\=\+{\rm{asm-register}}\,({\rm{cadddr}}\,({\it{line\/}}))\index{asm-register}, \\ 
{\rm{append}}\,(\=\+{\rm{asm-flags}}\,({\rm{caddr}}\,({\it{line\/}}))\index{asm-flags}, \\ 
{\rm{append}}\,(\=\+{\rm{asm-store-cc}}\,({\rm{cadr}}\,({\it{line\/}}))\index{asm-store-cc}, \\ 
{\rm{append}}\,(\=\+{\rm{asm-op-code}}\,({\rm{car}}\,({\it{line\/}}))\index{asm-op-code}, \\ 
{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}))\-)\-)\-)\-)\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm-list} \\  
\=\+{\rm{asm-list}}\,({\it{list\/}})\index{asm-list} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{list\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf elseif }{\rm{litatom}}\,({\rm{car}}\,({\it{list\/}}))$\;\;${\bf then }{\rm{asm-list}}\,({\rm{cdr}}\,({\it{list\/}}))\index{asm-list} \\ 
{\bf else }{\rm{cons}}\,({\rm{asm-line}}\,({\rm{car}}\,({\it{list\/}}))\index{asm-line}, {\rm{asm-list}}\,({\rm{cdr}}\,({\it{list\/}}))\index{asm-list})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm} \\  
{\rm{asm}}\,({\it{list\/}})\index{asm} $=$ {\rm{asm-list}}\,({\rm{update-list}}\,({\it{list\/}}, {\rm{resolve-names}}\,({\it{list\/}}, {\tt{0}}, {\bf{nil}})\index{resolve-names})\index{update-list})\index{asm-list}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{t-and-f-to-1-and-0} \\  
\=\+{\rm{t-and-f-to-1-and-0}}\,({\it{list\/}})\index{t-and-f-to-1-and-0} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{list\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+\=\+{\bf if }{\rm{falsep}}\,({\rm{car}}\,({\it{list\/}}))$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }{\tt{1}}$\;${\bf  endif}\-, \\ 
{\rm{t-and-f-to-1-and-0}}\,({\rm{cdr}}\,({\it{list\/}}))\index{t-and-f-to-1-and-0})\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm-to-1-and-0} \\  
\=\+{\rm{asm-to-1-and-0}}\,({\it{list\/}})\index{asm-to-1-and-0} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{list\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{t-and-f-to-1-and-0}}\,({\rm{car}}\,({\it{list\/}}))\index{t-and-f-to-1-and-0}, \\ 
{\rm{asm-to-1-and-0}}\,({\rm{cdr}}\,({\it{list\/}}))\index{asm-to-1-and-0})\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-to-nat-all} \\  
\=\+{\rm{v-to-nat-all}}\,({\it{x\/}})\index{v-to-nat-all} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{v-to-nat}}\,({\rm{car}}\,({\it{x\/}}))\index{v-to-nat}, {\rm{v-to-nat-all}}\,({\rm{cdr}}\,({\it{x\/}}))\index{v-to-nat-all})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-to-0s-through-fs} \\  
\=\+{\rm{v-to-0s-through-fs}}\,({\it{x\/}}, {\it{collect\/}})\index{v-to-0s-through-fs} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{collect\/}} \\ 
{\bf else }{\rm{v-to-0s-through-fs}}\,(\=\+{\rm{cddddr}}\,({\it{x\/}}), \\ 
{\rm{cons}}\,(\=\+\=\+{\bf case on }{\rm{v-to-nat}}\,({\rm{firstn}}\,({\tt{4}}, {\it{x\/}})\index{firstn})\index{v-to-nat}: \\ 
{\bf case = }{\tt{0}} \\ 
{\bf then }{\rm{cadr}}\,({\rm{unpack}}\,({\tt{'}}{\tt{x0}})) \\ 
{\bf case = }{\tt{1}} \\ 
{\bf $\;\;$then }{\rm{cadr}}\,({\rm{unpack}}\,({\tt{'}}{\tt{x1}})) \\ 
{\bf case = }{\tt{2}} \\ 
{\bf $\;\;$then }{\rm{cadr}}\,({\rm{unpack}}\,({\tt{'}}{\tt{x2}})) \\ 
{\bf case = }{\tt{3}} \\ 
{\bf $\;\;$then }{\rm{cadr}}\,({\rm{unpack}}\,({\tt{'}}{\tt{x3}})) \\ 
{\bf case = }{\tt{4}} \\ 
{\bf $\;\;$then }{\rm{cadr}}\,({\rm{unpack}}\,({\tt{'}}{\tt{x4}})) \\ 
{\bf case = }{\tt{5}} \\ 
{\bf $\;\;$then }{\rm{cadr}}\,({\rm{unpack}}\,({\tt{'}}{\tt{x5}})) \\ 
{\bf case = }{\tt{6}} \\ 
{\bf $\;\;$then }{\rm{cadr}}\,({\rm{unpack}}\,({\tt{'}}{\tt{x6}})) \\ 
{\bf case = }{\tt{7}} \\ 
{\bf $\;\;$then }{\rm{cadr}}\,({\rm{unpack}}\,({\tt{'}}{\tt{x7}})) \\ 
{\bf case = }{\tt{8}} \\ 
{\bf $\;\;$then }{\rm{cadr}}\,({\rm{unpack}}\,({\tt{'}}{\tt{x8}})) \\ 
{\bf case = }{\tt{9}} \\ 
{\bf $\;\;$then }{\rm{cadr}}\,({\rm{unpack}}\,({\tt{'}}{\tt{x9}})) \\ 
{\bf case = }{\tt{10}} \\ 
{\bf $\;\;$then }{\rm{cadr}}\,({\rm{unpack}}\,({\tt{'}}{\tt{xa}})) \\ 
{\bf case = }{\tt{11}} \\ 
{\bf $\;\;$then }{\rm{cadr}}\,({\rm{unpack}}\,({\tt{'}}{\tt{xb}})) \\ 
{\bf case = }{\tt{12}} \\ 
{\bf $\;\;$then }{\rm{cadr}}\,({\rm{unpack}}\,({\tt{'}}{\tt{xc}})) \\ 
{\bf case = }{\tt{13}} \\ 
{\bf $\;\;$then }{\rm{cadr}}\,({\rm{unpack}}\,({\tt{'}}{\tt{xd}})) \\ 
{\bf case = }{\tt{14}} \\ 
{\bf $\;\;$then }{\rm{cadr}}\,({\rm{unpack}}\,({\tt{'}}{\tt{xe}})) \\ 
{\bf otherwise }{\rm{cadr}}\,({\rm{unpack}}\,({\tt{'}}{\tt{xf}}))$\;${\bf  endcase}\-, \\ 
{\it{collect\/}})\-)\-\index{v-to-0s-through-fs}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-to-hex} \\  
{\rm{v-to-hex}}\,({\it{x\/}})\index{v-to-hex} $=$ {\rm{pack}}\,({\rm{cons}}\,({\rm{car}}\,({\rm{unpack}}\,({\tt{'}}{\tt{x}})), {\rm{v-to-0s-through-fs}}\,({\it{x\/}}, {\tt{0}})\index{v-to-0s-through-fs}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-to-hex-all} \\  
\=\+{\rm{v-to-hex-all}}\,({\it{x\/}})\index{v-to-hex-all} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{v-to-hex}}\,({\rm{car}}\,({\it{x\/}}))\index{v-to-hex}, {\rm{v-to-hex-all}}\,({\rm{cdr}}\,({\it{x\/}}))\index{v-to-hex-all})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{make-pairs} \\  
\=\+{\rm{make-pairs}}\,({\it{list\/}})\index{make-pairs} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{list\/}} $\simeq\;${{\bf{nil}}}${}$) $\vee$ ({\rm{cdr}}\,({\it{list\/}}) $\simeq\;${{\bf{nil}}}${}$)$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{cons}}\,({\rm{car}}\,({\it{list\/}}), {\rm{cadr}}\,({\it{list\/}})), {\rm{make-pairs}}\,({\rm{cddr}}\,({\it{list\/}}))\index{make-pairs})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{add-ram-marker} \\  
\=\+{\rm{add-ram-marker}}\,({\it{list-mem\/}})\index{add-ram-marker} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{list-mem\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{ram}}\,({\rm{car}}\,({\it{list-mem\/}}))\index{ram}, {\rm{add-ram-marker}}\,({\rm{cdr}}\,({\it{list-mem\/}}))\index{add-ram-marker})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{list-to-mem3} \\  
\=\+{\rm{list-to-mem3}}\,({\it{mem\/}}, {\it{depth\/}})\index{list-to-mem3} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{depth\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\it{mem\/}} \\ 
{\bf else }{\rm{list-to-mem3}}\,({\rm{make-pairs}}\,({\it{mem\/}})\index{make-pairs}, {\it{depth\/}} $-\;1$)\index{list-to-mem3}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{list-to-mem2} \\  
{\rm{list-to-mem2}}\,({\it{mem\/}}, {\it{depth\/}})\index{list-to-mem2} $=$ {\rm{car}}\,({\rm{list-to-mem3}}\,({\it{mem\/}}, {\it{depth\/}})\index{list-to-mem3})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{list-to-mem1} \\  
\=\+{\rm{list-to-mem1}}\,({\it{mem\/}}, {\it{default\/}})\index{list-to-mem1} \\ 
$=$$\;\;\;\;${\rm{list-to-mem2}}\,(\=\+{\rm{add-ram-marker}}\,({\rm{append}}\,(\=\+{\it{mem\/}}, \\ 
{\rm{make-list}}\,(\=\+\=\+{\rm{exp2}}\,($1\;+$ {\rm{log2}}\,({\rm{length}}\,({\it{mem\/}})\index{length})\index{log2})\index{exp2} \\ 
$-$$\;\;\;\;${\rm{length}}\,({\it{mem\/}})\index{length}\-, \\ 
{\it{default\/}})\-\index{make-list})\-)\index{add-ram-marker}, \\ 
$1\;+$ {\rm{log2}}\,({\rm{length}}\,({\it{mem\/}})\index{length})\index{log2})\-\index{list-to-mem2}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{stub-right} \\  
\=\+{\rm{stub-right}}\,({\it{mem\/}}, {\it{levels\/}}, {\it{default\/}})\index{stub-right} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{levels\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\it{mem\/}} \\ 
{\bf else }{\rm{cons}}\,({\rm{stub-right}}\,({\it{mem\/}}, {\it{levels\/}} $-\;1$, {\it{default\/}})\index{stub-right}, {\rm{stub}}\,({\it{default\/}})\index{stub})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{list-to-mem} \\  
\=\+{\rm{list-to-mem}}\,({\it{mem\/}}, {\it{size\/}}, {\it{default\/}})\index{list-to-mem} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{size\/}} $<$ ($1\;+$ {\rm{log2}}\,({\rm{length}}\,({\it{mem\/}})\index{length})\index{log2}) \\ 
{\bf then }{\tt{'}}{\tt{(}}{\tt{list-to-mem=}}{\tt{ }}{\tt{insufficient-size}}{\tt{)}} \\ 
{\bf else }{\rm{stub-right}}\,(\=\+{\rm{list-to-mem1}}\,({\it{mem\/}}, {\it{default\/}})\index{list-to-mem1}, \\ 
{\it{size\/}} $-$ ($1\;+$ {\rm{log2}}\,({\rm{length}}\,({\it{mem\/}})\index{length})\index{log2}), \\ 
{\it{default\/}})\-\index{stub-right}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{list-to-tree-mem} \\  
{\rm{list-to-tree-mem}}\,({\it{mem\/}})\index{list-to-tree-mem} $=$ {\rm{list-to-mem}}\,({\it{mem\/}}, {\tt{32}}, {\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list})\index{list-to-mem}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{mem-to-list} \\  
\=\+{\rm{mem-to-list}}\,({\it{mem\/}})\index{mem-to-list} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{mem\/}}) \\ 
{\bf then }{\rm{append}}\,({\rm{mem-to-list}}\,({\rm{car}}\,({\it{mem\/}}))\index{mem-to-list}, {\rm{mem-to-list}}\,({\rm{cdr}}\,({\it{mem\/}}))\index{mem-to-list}) \\ 
{\bf elseif }{\rm{stubp}}\,({\it{mem\/}})\index{stubp}$\;\;${\bf then }{\bf{nil}} \\ 
{\bf elseif }{\rm{ramp}}\,({\it{mem\/}})\index{ramp}$\;\;${\bf then }{\rm{list}}\,({\rm{ram-guts}}\,({\it{mem\/}})\index{ram-guts}) \\ 
{\bf elseif }{\rm{romp}}\,({\it{mem\/}})\index{romp}$\;\;${\bf then }{\rm{list}}\,({\rm{rom-guts}}\,({\it{mem\/}})\index{rom-guts}) \\ 
{\bf else }{\it{mem\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{un-fm9001} \\  
\=\+{\rm{un-fm9001}}\,({\it{state\/}})\index{un-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{v-to-nat-all}}\,({\rm{mem-to-list}}\,({\rm{regs}}\,({\rm{car}}\,({\it{state\/}}))\index{regs})\index{mem-to-list})\index{v-to-nat-all}, \\ 
{\rm{z-flag}}\,({\rm{flags}}\,({\rm{car}}\,({\it{state\/}}))\index{flags})\index{z-flag}, \\ 
{\rm{n-flag}}\,({\rm{flags}}\,({\rm{car}}\,({\it{state\/}}))\index{flags})\index{n-flag}, \\ 
{\rm{v-flag}}\,({\rm{flags}}\,({\rm{car}}\,({\it{state\/}}))\index{flags})\index{v-flag}, \\ 
{\rm{c-flag}}\,({\rm{flags}}\,({\rm{car}}\,({\it{state\/}}))\index{flags})\index{c-flag})\-, \\ 
{\rm{v-to-hex-all}}\,({\rm{mem-to-list}}\,({\rm{cadr}}\,({\it{state\/}}))\index{mem-to-list})\index{v-to-hex-all})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{execute-fm9001} \\  
\=\+{\rm{execute-fm9001}}\,({\it{n\/}}, {\it{tree-pgm\/}})\index{execute-fm9001} \\ 
$=$$\;\;\;\;${\rm{un-fm9001}}\,({\rm{fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list-to-mem}}\,(\=\+{\rm{make-list}}\,({\tt{15}}, {\rm{nat-to-v}}\,({\tt{0}}, {\tt{32}})\index{nat-to-v})\index{make-list}, \\ 
{\tt{4}}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list})\-\index{list-to-mem}, \\ 
{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}))\-, \\ 
{\it{tree-pgm\/}})\-, \\ 
{\it{n\/}})\-\index{fm9001})\index{un-fm9001}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm-and-fm9001} \\  
\=\+{\rm{asm-and-fm9001}}\,({\it{n\/}}, {\it{program\/}})\index{asm-and-fm9001} \\ 
$=$$\;\;\;\;${\rm{execute-fm9001}}\,({\it{n\/}}, {\rm{list-to-mem}}\,({\rm{asm}}\,({\it{program\/}})\index{asm}, {\tt{32}}, {\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list})\index{list-to-mem})\index{execute-fm9001}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{store-resultp-mux} \\  
\=\+{\rm{store-resultp-mux}}\,({\it{s0\/}}, {\it{s1\/}}, {\it{s2\/}}, {\it{d0\/}}, {\it{d1\/}}, {\it{d2\/}}, {\it{d3\/}}, {\it{d4\/}}, {\it{d5\/}}, {\it{d6\/}})\index{store-resultp-mux} \\ 
$=$$\;\;\;\;${\rm{ao2}}\,(\=\+{\rm{b-not}}\,({\it{s2\/}})\index{b-not}, \\ 
{\rm{ao2}}\,({\rm{b-not}}\,({\it{s1\/}})\index{b-not}, {\rm{ao2}}\,({\rm{b-not}}\,({\it{s0\/}})\index{b-not}, {\it{d0\/}}, {\it{s0\/}}, {\it{d1\/}})\index{ao2}, {\it{s1\/}}, {\rm{ao2}}\,({\rm{b-not}}\,({\it{s0\/}})\index{b-not}, {\it{d2\/}}, {\it{s0\/}}, {\it{d3\/}})\index{ao2})\index{ao2}, \\ 
{\it{s2\/}}, \\ 
{\rm{ao2}}\,({\rm{b-not}}\,({\it{s1\/}})\index{b-not}, {\rm{ao2}}\,({\rm{b-not}}\,({\it{s0\/}})\index{b-not}, {\it{d4\/}}, {\it{s0\/}}, {\it{d5\/}})\index{ao2}, {\it{s1\/}}, {\rm{b-nand}}\,({\rm{b-not}}\,({\it{s0\/}})\index{b-not}, {\it{d6\/}})\index{b-nand})\index{ao2})\-\index{ao2}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$store-resultp-mux} \\  
\=\+{\rm{f\$store-resultp-mux}}\,({\it{s0\/}}, {\it{s1\/}}, {\it{s2\/}}, {\it{d0\/}}, {\it{d1\/}}, {\it{d2\/}}, {\it{d3\/}}, {\it{d4\/}}, {\it{d5\/}}, {\it{d6\/}})\index{f\$store-resultp-mux} \\ 
$=$$\;\;\;\;${\rm{f\$ao2}}\,(\=\+{\rm{f-not}}\,({\it{s2\/}})\index{f-not}, \\ 
{\rm{f\$ao2}}\,(\=\+{\rm{f-not}}\,({\it{s1\/}})\index{f-not}, \\ 
{\rm{f\$ao2}}\,({\rm{f-not}}\,({\it{s0\/}})\index{f-not}, {\it{d0\/}}, {\it{s0\/}}, {\it{d1\/}})\index{f\$ao2}, \\ 
{\it{s1\/}}, \\ 
{\rm{f\$ao2}}\,({\rm{f-not}}\,({\it{s0\/}})\index{f-not}, {\it{d2\/}}, {\it{s0\/}}, {\it{d3\/}})\index{f\$ao2})\-\index{f\$ao2}, \\ 
{\it{s2\/}}, \\ 
{\rm{f\$ao2}}\,(\=\+{\rm{f-not}}\,({\it{s1\/}})\index{f-not}, \\ 
{\rm{f\$ao2}}\,({\rm{f-not}}\,({\it{s0\/}})\index{f-not}, {\it{d4\/}}, {\it{s0\/}}, {\it{d5\/}})\index{f\$ao2}, \\ 
{\it{s1\/}}, \\ 
{\rm{f-nand}}\,({\rm{f-not}}\,({\it{s0\/}})\index{f-not}, {\it{d6\/}})\index{f-nand})\-\index{f\$ao2})\-\index{f\$ao2}\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$store-resultp-mux; name this event `f\$store-resultp-mux-off'.\index{f\$store-resultp-mux-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{store-resultp-mux*} \\  
\=\+{\sc{store-resultp-mux*}}\index{store-resultp-mux*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{store-resultp-mux}} \\ 
{\tt{(}}{\tt{s0}}{\tt{ }}{\tt{s1}}{\tt{ }}{\tt{s2}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}}{\tt{ }}{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{)}} \\ 
{\tt{(}}{\tt{w-13}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{g-10}}{\tt{ }}{\tt{(}}{\tt{w-10}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{s0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-11}}{\tt{ }}{\tt{(}}{\tt{w-11}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{w-10}}{\tt{ }}{\tt{d6}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-9}}{\tt{ }}{\tt{(}}{\tt{w-9}}{\tt{)}}{\tt{ }}{\tt{ao2}}{\tt{ }}{\tt{(}}{\tt{w-10}}{\tt{ }}{\tt{d4}}{\tt{ }}{\tt{s0}}{\tt{ }}{\tt{d5}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-7}}{\tt{ }}{\tt{(}}{\tt{w-7}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{s1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-12}}{\tt{ }}{\tt{(}}{\tt{w-12}}{\tt{)}}{\tt{ }}{\tt{ao2}}{\tt{ }}{\tt{(}}{\tt{w-7}}{\tt{ }}{\tt{w-9}}{\tt{ }}{\tt{s1}}{\tt{ }}{\tt{w-11}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-5}}{\tt{ }}{\tt{(}}{\tt{w-5}}{\tt{)}}{\tt{ }}{\tt{ao2}}{\tt{ }}{\tt{(}}{\tt{w-10}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{s0}}{\tt{ }}{\tt{d3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-3}}{\tt{ }}{\tt{(}}{\tt{w-3}}{\tt{)}}{\tt{ }}{\tt{ao2}}{\tt{ }}{\tt{(}}{\tt{w-10}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{s0}}{\tt{ }}{\tt{d1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-6}}{\tt{ }}{\tt{(}}{\tt{w-6}}{\tt{)}}{\tt{ }}{\tt{ao2}}{\tt{ }}{\tt{(}}{\tt{w-7}}{\tt{ }}{\tt{w-3}}{\tt{ }}{\tt{s1}}{\tt{ }}{\tt{w-5}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-0}}{\tt{ }}{\tt{(}}{\tt{w-0}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{s2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-13}}{\tt{ }}{\tt{(}}{\tt{w-13}}{\tt{)}}{\tt{ }}{\tt{ao2}}{\tt{ }}{\tt{(}}{\tt{w-0}}{\tt{ }}{\tt{w-6}}{\tt{ }}{\tt{s2}}{\tt{ }}{\tt{w-12}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{store-resultp-mux\&} \\  
\=\+{\rm{store-resultp-mux\&}}\,({\it{netlist\/}})\index{store-resultp-mux\&} \\ 
$=$$\;\;\;\;$(\=\+(\=\+{\rm{lookup-module}}\,({\tt{'}}{\tt{store-resultp-mux}}, {\it{netlist\/}})\index{lookup-module} \\ 
$=$$\;\;\;\;${\sc{store-resultp-mux*}}\index{store-resultp-mux*})\- \\ 
$\wedge$$\;\;\;\;${\rm{b-nand\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{store-resultp-mux}}, {\it{netlist\/}})\index{delete-module})\index{b-nand\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{store-resultp-mux}}, {\it{netlist\/}})\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{ao2\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{store-resultp-mux}}, {\it{netlist\/}})\index{delete-module})\index{ao2\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable store-resultp-mux\&; name this event `store-resultp-mux\&-off'.\index{store-resultp-mux\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{store-resultp-mux\$netlist} \\  
\=\+{\sc{store-resultp-mux\$netlist}}\index{store-resultp-mux\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{store-resultp-mux*}}\index{store-resultp-mux*}, \\ 
({\sc{b-nand\$netlist}}\index{b-nand\$netlist} $\cup$ {\sc{b-not\$netlist}}\index{b-not\$netlist}) $\cup$ {\sc{ao2\$netlist}}\index{ao2\$netlist})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  store-resultp-mux\$value \\ \index{store-resultp-mux\$value}
\=\+{\rm{store-resultp-mux\&}}\,({\it{netlist\/}})\index{store-resultp-mux\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{store-resultp-mux}}, \\ 
{\rm{list}}\,({\it{s0\/}}, {\it{s1\/}}, {\it{s2\/}}, {\it{d0\/}}, {\it{d1\/}}, {\it{d2\/}}, {\it{d3\/}}, {\it{d4\/}}, {\it{d5\/}}, {\it{d6\/}}), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f\$store-resultp-mux}}\,({\it{s0\/}}, {\it{s1\/}}, {\it{s2\/}}, {\it{d0\/}}, {\it{d1\/}}, {\it{d2\/}}, {\it{d3\/}}, {\it{d4\/}}, {\it{d5\/}}, {\it{d6\/}})\index{f\$store-resultp-mux}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable store-resultp-mux\$value; name this event `store-resultp-mux\$value-off'.\index{store-resultp-mux\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$store-resultp-mux=store-resultp-mux \\ \index{f\$store-resultp-mux=store-resu!ltp-mux}
\=\+(\=\+{\rm{boolp}}\,({\it{s0\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s1\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s2\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{d0\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{d1\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{d2\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{d3\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{d4\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{d5\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{d6\/}})\index{boolp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$store-resultp-mux}}\,({\it{s0\/}}, {\it{s1\/}}, {\it{s2\/}}, {\it{d0\/}}, {\it{d1\/}}, {\it{d2\/}}, {\it{d3\/}}, {\it{d4\/}}, {\it{d5\/}}, {\it{d6\/}})\index{f\$store-resultp-mux} \\ 
$=$$\;\;\;\;${\rm{store-resultp-mux}}\,({\it{s0\/}}, {\it{s1\/}}, {\it{s2\/}}, {\it{d0\/}}, {\it{d1\/}}, {\it{d2\/}}, {\it{d3\/}}, {\it{d4\/}}, {\it{d5\/}}, {\it{d6\/}})\index{store-resultp-mux})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-store-resultp} \\  
\=\+{\rm{b-store-resultp}}\,({\it{store-cc\/}}, {\it{flags\/}})\index{b-store-resultp} \\ 
$=$$\;\;\;\;${\rm{b-xor}}\,(\=\+{\rm{car}}\,({\it{store-cc\/}}), \\ 
{\rm{store-resultp-mux}}\,(\=\+{\rm{cadr}}\,({\it{store-cc\/}}), \\ 
{\rm{caddr}}\,({\it{store-cc\/}}), \\ 
{\rm{cadddr}}\,({\it{store-cc\/}}), \\ 
{\rm{cadddr}}\,({\it{flags\/}}), \\ 
{\rm{caddr}}\,({\it{flags\/}}), \\ 
{\rm{cadr}}\,({\it{flags\/}}), \\ 
{\rm{car}}\,({\it{flags\/}}), \\ 
{\rm{b-or}}\,({\rm{cadddr}}\,({\it{flags\/}}), {\rm{car}}\,({\it{flags\/}}))\index{b-or}, \\ 
{\rm{b-xor}}\,({\rm{cadr}}\,({\it{flags\/}}), {\rm{caddr}}\,({\it{flags\/}}))\index{b-xor}, \\ 
{\rm{b-or}}\,(\=\+{\rm{car}}\,({\it{flags\/}}), \\ 
{\rm{b-xor}}\,({\rm{cadr}}\,({\it{flags\/}}), {\rm{caddr}}\,({\it{flags\/}}))\index{b-xor})\-\index{b-or})\-\index{store-resultp-mux})\-\index{b-xor}\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-store-resultp; name this event `b-store-resultp-off'.\index{b-store-resultp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{f\$b-store-resultp} \\  
\=\+{\rm{f\$b-store-resultp}}\,({\it{store-cc\/}}, {\it{flags\/}})\index{f\$b-store-resultp} \\ 
$=$$\;\;\;\;${\rm{f-xor}}\,(\=\+{\rm{car}}\,({\it{store-cc\/}}), \\ 
{\rm{f\$store-resultp-mux}}\,(\=\+{\rm{cadr}}\,({\it{store-cc\/}}), \\ 
{\rm{caddr}}\,({\it{store-cc\/}}), \\ 
{\rm{cadddr}}\,({\it{store-cc\/}}), \\ 
{\rm{cadddr}}\,({\it{flags\/}}), \\ 
{\rm{caddr}}\,({\it{flags\/}}), \\ 
{\rm{cadr}}\,({\it{flags\/}}), \\ 
{\rm{car}}\,({\it{flags\/}}), \\ 
{\rm{f-or}}\,({\rm{cadddr}}\,({\it{flags\/}}), {\rm{car}}\,({\it{flags\/}}))\index{f-or}, \\ 
{\rm{f-xor}}\,({\rm{cadr}}\,({\it{flags\/}}), {\rm{caddr}}\,({\it{flags\/}}))\index{f-xor}, \\ 
{\rm{f-or}}\,(\=\+{\rm{car}}\,({\it{flags\/}}), \\ 
{\rm{f-xor}}\,({\rm{cadr}}\,({\it{flags\/}}), {\rm{caddr}}\,({\it{flags\/}}))\index{f-xor})\-\index{f-or})\-\index{f\$store-resultp-mux})\-\index{f-xor}\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$b-store-resultp; name this event `f\$b-store-resultp-off'.\index{f\$b-store-resultp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$b-store-resultp=b-store-resultp \\ \index{f\$b-store-resultp=b-store-resu!ltp}
\=\+(\=\+{\rm{bvp}}\,({\it{store-cc\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{store-cc\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{flags\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{flags\/}})\index{length} $=$ {\tt{4}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$b-store-resultp}}\,({\it{store-cc\/}}, {\it{flags\/}})\index{f\$b-store-resultp} \\ 
$=$$\;\;\;\;${\rm{b-store-resultp}}\,({\it{store-cc\/}}, {\it{flags\/}})\index{b-store-resultp})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-store-resultp*} \\  
\=\+{\sc{b-store-resultp*}}\index{b-store-resultp*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{b-store-resultp}} \\ 
{\tt{(}}{\tt{s0}}{\tt{ }}{\tt{s1}}{\tt{ }}{\tt{s2}}{\tt{ }}{\tt{s3}}{\tt{ }}{\tt{z}}{\tt{ }}{\tt{n}}{\tt{ }}{\tt{v}}{\tt{ }}{\tt{c}}{\tt{)}} \\ 
{\tt{(}}{\tt{result}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{g0}}{\tt{ }}{\tt{(}}{\tt{cz}}{\tt{)}}{\tt{ }}{\tt{b-or}}{\tt{ }}{\tt{(}}{\tt{c}}{\tt{ }}{\tt{z}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g1}}{\tt{ }}{\tt{(}}{\tt{nv}}{\tt{)}}{\tt{ }}{\tt{b-xor}}{\tt{ }}{\tt{(}}{\tt{n}}{\tt{ }}{\tt{v}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g2}}{\tt{ }}{\tt{(}}{\tt{znv}}{\tt{)}}{\tt{ }}{\tt{b-or}}{\tt{ }}{\tt{(}}{\tt{z}}{\tt{ }}{\tt{nv}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g3}} \\ 
{\tt{(}}{\tt{mux}}{\tt{)}} \\ 
{\tt{store-resultp-mux}} \\ 
{\tt{(}}{\tt{s1}}{\tt{ }}{\tt{s2}}{\tt{ }}{\tt{s3}}{\tt{ }}{\tt{c}}{\tt{ }}{\tt{v}}{\tt{ }}{\tt{n}}{\tt{ }}{\tt{z}}{\tt{ }}{\tt{cz}}{\tt{ }}{\tt{nv}}{\tt{ }}{\tt{znv}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g4}}{\tt{ }}{\tt{(}}{\tt{result}}{\tt{)}}{\tt{ }}{\tt{b-xor}}{\tt{ }}{\tt{(}}{\tt{s0}}{\tt{ }}{\tt{mux}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-store-resultp\&} \\  
\=\+{\rm{b-store-resultp\&}}\,({\it{netlist\/}})\index{b-store-resultp\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{b-store-resultp}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{b-store-resultp*}}\index{b-store-resultp*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-or\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{b-store-resultp}}, {\it{netlist\/}})\index{delete-module})\index{b-or\&} \\ 
$\wedge$$\;\;\;\;${\rm{store-resultp-mux\&}}\,({\rm{delete-module}}\,(\=\+{\tt{'}}{\tt{b-store-resultp}}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{store-resultp-mux\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-xor\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{b-store-resultp}}, {\it{netlist\/}})\index{delete-module})\index{b-xor\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-store-resultp\&; name this event `b-store-resultp\&-off'.\index{b-store-resultp\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-store-resultp\$netlist} \\  
\=\+{\sc{b-store-resultp\$netlist}}\index{b-store-resultp\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{b-store-resultp*}}\index{b-store-resultp*}, \\ 
({\sc{b-or\$netlist}}\index{b-or\$netlist} $\cup$ {\sc{store-resultp-mux\$netlist}}\index{store-resultp-mux\$netlist}) $\cup$ {\sc{b-xor\$netlist}}\index{b-xor\$netlist})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-store-resultp=store-resultp\$help \\ \index{b-store-resultp=store-resultp\$!help}
\=\+(\=\+{\rm{boolp}}\,({\it{s0\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s1\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s2\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s3\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s4\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s5\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s6\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s7\/}})\index{boolp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{b-store-resultp}}\,({\rm{list}}\,({\it{s0\/}}, {\it{s1\/}}, {\it{s2\/}}, {\it{s3\/}}), {\rm{list}}\,({\it{s4\/}}, {\it{s5\/}}, {\it{s6\/}}, {\it{s7\/}}))\index{b-store-resultp} \\ 
$=$$\;\;\;\;${\rm{store-resultp}}\,({\rm{list}}\,({\it{s0\/}}, {\it{s1\/}}, {\it{s2\/}}, {\it{s3\/}}), {\rm{list}}\,({\it{s4\/}}, {\it{s5\/}}, {\it{s6\/}}, {\it{s7\/}}))\index{store-resultp})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-store-resultp=store-resultp \\ \index{b-store-resultp=store-resultp}
\=\+(\=\+{\rm{bvp}}\,({\it{store-cc\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{store-cc\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{flags\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{flags\/}})\index{length} $=$ {\tt{4}}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{b-store-resultp}}\,({\it{store-cc\/}}, {\it{flags\/}})\index{b-store-resultp} $=$ {\rm{store-resultp}}\,({\it{store-cc\/}}, {\it{flags\/}})\index{store-resultp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-store-resultp\$value \\ \index{b-store-resultp\$value}
\=\+(\=\+{\rm{b-store-resultp\&}}\,({\it{netlist\/}})\index{b-store-resultp\&} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{store-cc\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{store-cc\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{store-cc\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{flags\/}})\index{length} $=$ {\tt{4}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{b-store-resultp}}, \\ 
{\rm{append}}\,({\it{store-cc\/}}, {\it{flags\/}}), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f\$b-store-resultp}}\,({\it{store-cc\/}}, {\it{flags\/}})\index{f\$b-store-resultp}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$unary-op-code-p} \\  
\=\+{\rm{f\$unary-op-code-p}}\,({\it{op\/}})\index{f\$unary-op-code-p} \\ 
$=$$\;\;\;\;${\rm{f-nand4}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{cadddr}}\,({\it{op\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{cadr}}\,({\it{op\/}}))\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{op\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{cadr}}\,({\it{op\/}}))\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,({\rm{cadddr}}\,({\it{op\/}}), {\rm{cadr}}\,({\it{op\/}}), {\rm{f-not}}\,({\rm{car}}\,({\it{op\/}}))\index{f-not})\index{f-nand3}, \\ 
{\rm{f-nand3}}\,({\rm{cadddr}}\,({\it{op\/}}), {\rm{caddr}}\,({\it{op\/}}), {\rm{cadr}}\,({\it{op\/}}))\index{f-nand3})\-\index{f-nand4}\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$unary-op-code-p; name this event `f\$unary-op-code-p-off'.\index{f\$unary-op-code-p-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$unary-op-code-p=unary-op-code-p \\ \index{f\$unary-op-code-p=unary-op-code!-p}
\=\+({\rm{bvp}}\,({\it{op\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{op\/}})\index{length} $=$ {\tt{4}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f\$unary-op-code-p}}\,({\it{op\/}})\index{f\$unary-op-code-p} $=$ {\rm{unary-op-code-p}}\,({\it{op\/}})\index{unary-op-code-p})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{unary-op-code-p*} \\  
\=\+{\sc{unary-op-code-p*}}\index{unary-op-code-p*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{unary-op-code-p}} \\ 
{\tt{(}}{\tt{op0}}{\tt{ }}{\tt{op1}}{\tt{ }}{\tt{op2}}{\tt{ }}{\tt{op3}}{\tt{)}} \\ 
{\tt{(}}{\tt{z}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{g0}}{\tt{ }}{\tt{(}}{\tt{op0-}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g1}}{\tt{ }}{\tt{(}}{\tt{op1-}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g2}}{\tt{ }}{\tt{(}}{\tt{op2-}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g3}}{\tt{ }}{\tt{(}}{\tt{op3-}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g4}}{\tt{ }}{\tt{(}}{\tt{s0}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{op3-}}{\tt{ }}{\tt{op1-}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g5}}{\tt{ }}{\tt{(}}{\tt{s1}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{op2-}}{\tt{ }}{\tt{op1-}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g6}}{\tt{ }}{\tt{(}}{\tt{s2}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{op3}}{\tt{ }}{\tt{op1}}{\tt{ }}{\tt{op0-}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g7}}{\tt{ }}{\tt{(}}{\tt{s3}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{op3}}{\tt{ }}{\tt{op2}}{\tt{ }}{\tt{op1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g8}}{\tt{ }}{\tt{(}}{\tt{z}}{\tt{)}}{\tt{ }}{\tt{b-nand4}}{\tt{ }}{\tt{(}}{\tt{s0}}{\tt{ }}{\tt{s1}}{\tt{ }}{\tt{s2}}{\tt{ }}{\tt{s3}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{unary-op-code-p\&} \\  
\=\+{\rm{unary-op-code-p\&}}\,({\it{netlist\/}})\index{unary-op-code-p\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{unary-op-code-p}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{unary-op-code-p*}}\index{unary-op-code-p*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{unary-op-code-p}}, {\it{netlist\/}})\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{unary-op-code-p}}, {\it{netlist\/}})\index{delete-module})\index{b-nand\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand3\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{unary-op-code-p}}, {\it{netlist\/}})\index{delete-module})\index{b-nand3\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand4\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{unary-op-code-p}}, {\it{netlist\/}})\index{delete-module})\index{b-nand4\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable unary-op-code-p\&; name this event `unary-op-code-p\&-off'.\index{unary-op-code-p\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{unary-op-code-p\$netlist} \\  
\=\+{\sc{unary-op-code-p\$netlist}}\index{unary-op-code-p\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{unary-op-code-p*}}\index{unary-op-code-p*}, \\ 
\=\+(({\sc{b-not\$netlist}}\index{b-not\$netlist} $\cup$ {\sc{b-nand\$netlist}}\index{b-nand\$netlist}) $\cup$ {\sc{b-nand3\$netlist}}\index{b-nand3\$netlist}) \\ 
$\cup$$\;\;\;\;${\sc{b-nand4\$netlist}}\index{b-nand4\$netlist}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  unary-op-code-p\$value \\ \index{unary-op-code-p\$value}
\=\+{\rm{unary-op-code-p\&}}\,({\it{netlist\/}})\index{unary-op-code-p\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{unary-op-code-p}}, {\it{op-code\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f\$unary-op-code-p}}\,({\it{op-code\/}})\index{f\$unary-op-code-p}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable unary-op-code-p\$value; name this event `unary-op-code-p\$value-off'.\index{unary-op-code-p\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{f\$decode-reg-mode} \\  
\=\+{\rm{f\$decode-reg-mode}}\,({\it{m\/}})\index{f\$decode-reg-mode} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nor}}\,({\rm{car}}\,({\it{m\/}}), {\rm{cadr}}\,({\it{m\/}}))\index{f-nor}, {\rm{f-nor}}\,({\rm{car}}\,({\it{m\/}}), {\rm{f-not}}\,({\rm{cadr}}\,({\it{m\/}}))\index{f-not})\index{f-nor}, {\rm{id}}\,({\rm{cadr}}\,({\it{m\/}}))\index{id})\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$decode-reg-mode; name this event `f\$decode-reg-mode-off'.\index{f\$decode-reg-mode-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{decode-reg-mode*} \\  
\=\+{\sc{decode-reg-mode*}}\index{decode-reg-mode*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{decode-reg-mode}} \\ 
{\tt{(}}{\tt{m0}}{\tt{ }}{\tt{m1}}{\tt{)}} \\ 
{\tt{(}}{\tt{direct}}{\tt{ }}{\tt{pre-dec}}{\tt{ }}{\tt{side-effect}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{g0}}{\tt{ }}{\tt{(}}{\tt{direct}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{m0}}{\tt{ }}{\tt{m1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g1}}{\tt{ }}{\tt{(}}{\tt{m1-}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{m1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g2}}{\tt{ }}{\tt{(}}{\tt{pre-dec}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{m0}}{\tt{ }}{\tt{m1-}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g3}}{\tt{ }}{\tt{(}}{\tt{side-effect}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{m1}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{decode-reg-mode\&} \\  
\=\+{\rm{decode-reg-mode\&}}\,({\it{netlist\/}})\index{decode-reg-mode\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{decode-reg-mode}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{decode-reg-mode*}}\index{decode-reg-mode*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-reg-mode}}, {\it{netlist\/}})\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nor\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-reg-mode}}, {\it{netlist\/}})\index{delete-module})\index{b-nor\&} \\ 
$\wedge$$\;\;\;\;${\rm{id\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-reg-mode}}, {\it{netlist\/}})\index{delete-module})\index{id\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable decode-reg-mode\&; name this event `decode-reg-mode\&-off'.\index{decode-reg-mode\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{decode-reg-mode\$netlist} \\  
\=\+{\sc{decode-reg-mode\$netlist}}\index{decode-reg-mode\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{decode-reg-mode*}}\index{decode-reg-mode*}, \\ 
({\sc{b-not\$netlist}}\index{b-not\$netlist} $\cup$ {\sc{b-nor\$netlist}}\index{b-nor\$netlist}) $\cup$ {\sc{id\$netlist}}\index{id\$netlist})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  decode-reg-mode\$value \\ \index{decode-reg-mode\$value}
\=\+{\rm{decode-reg-mode\&}}\,({\it{netlist\/}})\index{decode-reg-mode\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{decode-reg-mode}}, {\it{mode\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$decode-reg-mode}}\,({\it{mode\/}})\index{f\$decode-reg-mode})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable decode-reg-mode\$value; name this event `decode-reg-mode\$value-off'.\index{decode-reg-mode\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$decode-reg-mode-as-reg-mode \\ \index{f\$decode-reg-mode-as-reg-mode}
\=\+({\rm{bvp}}\,({\it{mode\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{mode\/}})\index{length} $=$ {\tt{2}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$decode-reg-mode}}\,({\it{mode\/}})\index{f\$decode-reg-mode} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{reg-direct-p}}\,({\it{mode\/}})\index{reg-direct-p}, \\ 
{\rm{pre-dec-p}}\,({\it{mode\/}})\index{pre-dec-p}, \\ 
{\rm{pre-dec-p}}\,({\it{mode\/}})\index{pre-dec-p} $\vee$ {\rm{post-inc-p}}\,({\it{mode\/}})\index{post-inc-p})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$select-op-code} \\  
\=\+{\rm{f\$select-op-code}}\,({\it{select\/}}, {\it{dec\/}}, {\it{op\/}})\index{f\$select-op-code} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{f-nand}}\,({\it{select\/}}, {\rm{f-not}}\,({\rm{car}}\,({\it{op\/}}))\index{f-not})\index{f-nand}, \\ 
{\rm{f-and}}\,({\it{select\/}}, {\rm{cadr}}\,({\it{op\/}}))\index{f-and}, \\ 
{\rm{f-if}}\,({\it{select\/}}, {\rm{caddr}}\,({\it{op\/}}), {\it{dec\/}})\index{f-if}, \\ 
{\rm{f-and}}\,({\it{select\/}}, {\rm{cadddr}}\,({\it{op\/}}))\index{f-and})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$select-op-code; name this event `f\$select-op-code-off'.\index{f\$select-op-code-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  properp-length-f\$select-op-code \\ \index{properp-length-f\$select-op-code}
\=\+{\rm{properp}}\,({\rm{f\$select-op-code}}\,({\it{select\/}}, {\it{dec\/}}, {\it{op\/}})\index{f\$select-op-code})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{f\$select-op-code}}\,({\it{select\/}}, {\it{dec\/}}, {\it{op\/}})\index{f\$select-op-code})\index{length} $=$ {\tt{4}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f\$select-op-code-selects \\ \index{f\$select-op-code-selects}
\=\+({\rm{boolp}}\,({\it{select\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{dec\/}})\index{boolp} $\wedge$ {\rm{bvp}}\,({\it{op\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{op\/}})\index{length} $=$ {\tt{4}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$select-op-code}}\,({\it{select\/}}, {\it{dec\/}}, {\it{op\/}})\index{f\$select-op-code} \\ 
$=$$\;\;\;\;${\rm{v-if}}\,({\it{select\/}}, {\it{op\/}}, {\rm{v-if}}\,({\it{dec\/}}, {\sc{alu-dec-op}}\index{alu-dec-op}, {\sc{alu-inc-op}}\index{alu-inc-op})\index{v-if})\index{v-if})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{select-op-code*} \\  
\=\+{\sc{select-op-code*}}\index{select-op-code*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{select-op-code}} \\ 
{\tt{(}}{\tt{select}}{\tt{ }}{\tt{dec}}{\tt{ }}{\tt{op0}}{\tt{ }}{\tt{op1}}{\tt{ }}{\tt{op2}}{\tt{ }}{\tt{op3}}{\tt{)}} \\ 
{\tt{(}}{\tt{z0}}{\tt{ }}{\tt{z1}}{\tt{ }}{\tt{z2}}{\tt{ }}{\tt{z3}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{i0}}{\tt{ }}{\tt{(}}{\tt{op0-}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{op0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g0}}{\tt{ }}{\tt{(}}{\tt{z0}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{select}}{\tt{ }}{\tt{op0-}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g1}}{\tt{ }}{\tt{(}}{\tt{z1}}{\tt{)}}{\tt{ }}{\tt{b-and}}{\tt{ }}{\tt{(}}{\tt{select}}{\tt{ }}{\tt{op1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g2}}{\tt{ }}{\tt{(}}{\tt{z2}}{\tt{)}}{\tt{ }}{\tt{b-if}}{\tt{ }}{\tt{(}}{\tt{select}}{\tt{ }}{\tt{op2}}{\tt{ }}{\tt{dec}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g3}}{\tt{ }}{\tt{(}}{\tt{z3}}{\tt{)}}{\tt{ }}{\tt{b-and}}{\tt{ }}{\tt{(}}{\tt{select}}{\tt{ }}{\tt{op3}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{select-op-code\&} \\  
\=\+{\rm{select-op-code\&}}\,({\it{netlist\/}})\index{select-op-code\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{select-op-code}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{select-op-code*}}\index{select-op-code*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{select-op-code}}, {\it{netlist\/}})\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{select-op-code}}, {\it{netlist\/}})\index{delete-module})\index{b-nand\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-if\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{select-op-code}}, {\it{netlist\/}})\index{delete-module})\index{b-if\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-and\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{select-op-code}}, {\it{netlist\/}})\index{delete-module})\index{b-and\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable select-op-code\&; name this event `select-op-code\&-off'.\index{select-op-code\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{select-op-code\$netlist} \\  
\=\+{\sc{select-op-code\$netlist}}\index{select-op-code\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{select-op-code*}}\index{select-op-code*}, \\ 
\=\+(({\sc{b-not\$netlist}}\index{b-not\$netlist} $\cup$ {\sc{b-nand\$netlist}}\index{b-nand\$netlist}) $\cup$ {\sc{b-if\$netlist}}\index{b-if\$netlist}) \\ 
$\cup$$\;\;\;\;${\sc{b-and\$netlist}}\index{b-and\$netlist}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  select-op-code\$value \\ \index{select-op-code\$value}
\=\+({\rm{select-op-code\&}}\,({\it{netlist\/}})\index{select-op-code\&} $\wedge$ {\rm{properp}}\,({\it{op\/}})\index{properp} $\wedge$ ({\rm{length}}\,({\it{op\/}})\index{length} $=$ {\tt{4}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{select-op-code}}, \\ 
{\rm{cons}}\,({\it{select\/}}, {\rm{cons}}\,({\it{dec\/}}, {\it{op\/}})), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$select-op-code}}\,({\it{select\/}}, {\it{dec\/}}, {\it{op\/}})\index{f\$select-op-code})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable select-op-code\$value; name this event `select-op-code\$value-off'.\index{select-op-code\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-if-f-4*} \\  
\=\+{\sc{v-if-f-4*}}\index{v-if-f-4*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{v-if-f-4}} \\ 
{\tt{(}}{\tt{c}}{\tt{ }}{\tt{a0}}{\tt{ }}{\tt{a1}}{\tt{ }}{\tt{a2}}{\tt{ }}{\tt{a3}}{\tt{)}} \\ 
{\tt{(}}{\tt{z0}}{\tt{ }}{\tt{z1}}{\tt{ }}{\tt{z2}}{\tt{ }}{\tt{z3}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{cb}}{\tt{ }}{\tt{(}}{\tt{c-}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{c}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g0}}{\tt{ }}{\tt{(}}{\tt{z0}}{\tt{)}}{\tt{ }}{\tt{b-and}}{\tt{ }}{\tt{(}}{\tt{c-}}{\tt{ }}{\tt{a0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g1}}{\tt{ }}{\tt{(}}{\tt{z1}}{\tt{)}}{\tt{ }}{\tt{b-and}}{\tt{ }}{\tt{(}}{\tt{c-}}{\tt{ }}{\tt{a1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g2}}{\tt{ }}{\tt{(}}{\tt{z2}}{\tt{)}}{\tt{ }}{\tt{b-and}}{\tt{ }}{\tt{(}}{\tt{c-}}{\tt{ }}{\tt{a2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g3}}{\tt{ }}{\tt{(}}{\tt{z3}}{\tt{)}}{\tt{ }}{\tt{b-and}}{\tt{ }}{\tt{(}}{\tt{c-}}{\tt{ }}{\tt{a3}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-if-f-4\&} \\  
\=\+{\rm{v-if-f-4\&}}\,({\it{netlist\/}})\index{v-if-f-4\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{v-if-f-4}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{v-if-f-4*}}\index{v-if-f-4*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{v-if-f-4}}, {\it{netlist\/}})\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-and\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{v-if-f-4}}, {\it{netlist\/}})\index{delete-module})\index{b-and\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-if-f-4\&; name this event `v-if-f-4\&-off'.\index{v-if-f-4\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-if-f-4\$netlist} \\  
{\sc{v-if-f-4\$netlist}}\index{v-if-f-4\$netlist} $=$ {\rm{cons}}\,({\sc{v-if-f-4*}}\index{v-if-f-4*}, {\sc{b-not\$netlist}}\index{b-not\$netlist} $\cup$ {\sc{b-and\$netlist}}\index{b-and\$netlist})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$v-if-f-4} \\  
\=\+{\rm{f\$v-if-f-4}}\,({\it{c\/}}, {\it{a\/}})\index{f\$v-if-f-4} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{f-and}}\,({\rm{f-not}}\,({\it{c\/}})\index{f-not}, {\rm{car}}\,({\it{a\/}}))\index{f-and}, \\ 
{\rm{f-and}}\,({\rm{f-not}}\,({\it{c\/}})\index{f-not}, {\rm{cadr}}\,({\it{a\/}}))\index{f-and}, \\ 
{\rm{f-and}}\,({\rm{f-not}}\,({\it{c\/}})\index{f-not}, {\rm{caddr}}\,({\it{a\/}}))\index{f-and}, \\ 
{\rm{f-and}}\,({\rm{f-not}}\,({\it{c\/}})\index{f-not}, {\rm{cadddr}}\,({\it{a\/}}))\index{f-and})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$v-if-f-4; name this event `f\$v-if-f-4-off'.\index{f\$v-if-f-4-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  properp-length-f\$v-if-f-4 \\ \index{properp-length-f\$v-if-f-4}
{\rm{properp}}\,({\rm{f\$v-if-f-4}}\,({\it{c\/}}, {\it{a\/}})\index{f\$v-if-f-4})\index{properp} $\wedge$ ({\rm{length}}\,({\rm{f\$v-if-f-4}}\,({\it{c\/}}, {\it{a\/}})\index{f\$v-if-f-4})\index{length} $=$ {\tt{4}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-if-f-4\$value \\ \index{v-if-f-4\$value}
\=\+{\rm{v-if-f-4\&}}\,({\it{netlist\/}})\index{v-if-f-4\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{v-if-f-4}}, {\rm{cons}}\,({\it{c\/}}, {\it{a\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$v-if-f-4}}\,({\it{c\/}}, {\it{a\/}})\index{f\$v-if-f-4})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f\$v-if-f-4=fv-if \\ \index{f\$v-if-f-4=fv-if}
{\rm{boolp}}\,({\it{c\/}})\index{boolp} $\rightarrow$ ({\rm{f\$v-if-f-4}}\,({\it{c\/}}, {\it{a\/}})\index{f\$v-if-f-4} $=$ {\rm{fv-if}}\,({\it{c\/}}, {\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list}, {\it{a\/}})\index{fv-if})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-if-f-4\$reset-value \\ \index{v-if-f-4\$reset-value}
\=\+{\rm{v-if-f-4\&}}\,({\it{netlist\/}})\index{v-if-f-4\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{v-if-f-4}}, {\rm{cons}}\,({\bf{t}}, {\it{a\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-if-f-4\$reset-value; name this event `v-if-f-4\$reset-value-off'.\index{v-if-f-4\$reset-value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fanout-4*} \\  
\=\+{\sc{fanout-4*}}\index{fanout-4*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{fanout-4}} \\ 
{\tt{(}}{\tt{a}}{\tt{)}} \\ 
{\tt{(}}{\tt{z0}}{\tt{ }}{\tt{z1}}{\tt{ }}{\tt{z2}}{\tt{ }}{\tt{z3}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{aa}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{ }}{\tt{b-buf}}{\tt{ }}{\tt{(}}{\tt{a}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g0}}{\tt{ }}{\tt{(}}{\tt{z0}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g1}}{\tt{ }}{\tt{(}}{\tt{z1}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g2}}{\tt{ }}{\tt{(}}{\tt{z2}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g3}}{\tt{ }}{\tt{(}}{\tt{z3}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fanout-4\&} \\  
\=\+{\rm{fanout-4\&}}\,({\it{netlist\/}})\index{fanout-4\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{fanout-4}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{fanout-4*}}\index{fanout-4*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-buf\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{fanout-4}}, {\it{netlist\/}})\index{delete-module})\index{b-buf\&} \\ 
$\wedge$$\;\;\;\;${\rm{id\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{fanout-4}}, {\it{netlist\/}})\index{delete-module})\index{id\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fanout-4\&; name this event `fanout-4\&-off'.\index{fanout-4\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fanout-4\$netlist} \\  
{\sc{fanout-4\$netlist}}\index{fanout-4\$netlist} $=$ {\rm{cons}}\,({\sc{fanout-4*}}\index{fanout-4*}, {\sc{b-buf\$netlist}}\index{b-buf\$netlist} $\cup$ {\sc{id\$netlist}}\index{id\$netlist})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fanout-4\$value \\ \index{fanout-4\$value}
\=\+{\rm{fanout-4\&}}\,({\it{netlist\/}})\index{fanout-4\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{fanout-4}}, {\rm{list}}\,({\it{a\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\rm{threefix}}\,({\it{a\/}})\index{threefix})\index{make-list})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fanout-4\$value; name this event `fanout-4\$value-off'.\index{fanout-4\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fanout-5*} \\  
\=\+{\sc{fanout-5*}}\index{fanout-5*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{fanout-5}} \\ 
{\tt{(}}{\tt{a}}{\tt{)}} \\ 
{\tt{(}}{\tt{z0}}{\tt{ }}{\tt{z1}}{\tt{ }}{\tt{z2}}{\tt{ }}{\tt{z3}}{\tt{ }}{\tt{z4}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{aa}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{ }}{\tt{b-buf}}{\tt{ }}{\tt{(}}{\tt{a}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g0}}{\tt{ }}{\tt{(}}{\tt{z0}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g1}}{\tt{ }}{\tt{(}}{\tt{z1}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g2}}{\tt{ }}{\tt{(}}{\tt{z2}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g3}}{\tt{ }}{\tt{(}}{\tt{z3}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g4}}{\tt{ }}{\tt{(}}{\tt{z4}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fanout-5\&} \\  
\=\+{\rm{fanout-5\&}}\,({\it{netlist\/}})\index{fanout-5\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{fanout-5}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{fanout-5*}}\index{fanout-5*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-buf\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{fanout-5}}, {\it{netlist\/}})\index{delete-module})\index{b-buf\&} \\ 
$\wedge$$\;\;\;\;${\rm{id\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{fanout-5}}, {\it{netlist\/}})\index{delete-module})\index{id\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fanout-5\&; name this event `fanout-5\&-off'.\index{fanout-5\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fanout-5\$netlist} \\  
{\sc{fanout-5\$netlist}}\index{fanout-5\$netlist} $=$ {\rm{cons}}\,({\sc{fanout-5*}}\index{fanout-5*}, {\sc{b-buf\$netlist}}\index{b-buf\$netlist} $\cup$ {\sc{id\$netlist}}\index{id\$netlist})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fanout-5\$value \\ \index{fanout-5\$value}
\=\+{\rm{fanout-5\&}}\,({\it{netlist\/}})\index{fanout-5\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{fanout-5}}, {\rm{list}}\,({\it{a\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{5}}, {\rm{threefix}}\,({\it{a\/}})\index{threefix})\index{make-list})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fanout-5\$value; name this event `fanout-5\$value-off'.\index{fanout-5\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fanout-32*} \\  
\=\+{\sc{fanout-32*}}\index{fanout-32*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{fanout-32}} \\ 
{\tt{(}}{\tt{a}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{s0}}{\tt{ }}{\tt{s1}}{\tt{ }}{\tt{s2}}{\tt{ }}{\tt{s3}}{\tt{ }}{\tt{s4}}{\tt{ }}{\tt{s5}}{\tt{ }}{\tt{s6}}{\tt{ }}{\tt{s7}}{\tt{ }}{\tt{s8}}{\tt{ }}{\tt{s9}}{\tt{ }}{\tt{s10}}{\tt{ }}{\tt{s11}}{\tt{ }}{\tt{s12}}{\tt{ }}{\tt{s13}}{\tt{ }}{\tt{s14}} \\ 
{\tt{s15}}{\tt{ }}{\tt{s16}}{\tt{ }}{\tt{s17}}{\tt{ }}{\tt{s18}}{\tt{ }}{\tt{s19}}{\tt{ }}{\tt{s20}}{\tt{ }}{\tt{s21}}{\tt{ }}{\tt{s22}}{\tt{ }}{\tt{s23}}{\tt{ }}{\tt{s24}}{\tt{ }}{\tt{s25}}{\tt{ }}{\tt{s26}}{\tt{ }}{\tt{s27}} \\ 
{\tt{s28}}{\tt{ }}{\tt{s29}}{\tt{ }}{\tt{s30}}{\tt{ }}{\tt{s31}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{ga}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{ }}{\tt{b-buf-pwr}}{\tt{ }}{\tt{(}}{\tt{a}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g0}}{\tt{ }}{\tt{(}}{\tt{s0}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g1}}{\tt{ }}{\tt{(}}{\tt{s1}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g2}}{\tt{ }}{\tt{(}}{\tt{s2}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g3}}{\tt{ }}{\tt{(}}{\tt{s3}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g4}}{\tt{ }}{\tt{(}}{\tt{s4}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g5}}{\tt{ }}{\tt{(}}{\tt{s5}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g6}}{\tt{ }}{\tt{(}}{\tt{s6}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g7}}{\tt{ }}{\tt{(}}{\tt{s7}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g8}}{\tt{ }}{\tt{(}}{\tt{s8}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g9}}{\tt{ }}{\tt{(}}{\tt{s9}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g10}}{\tt{ }}{\tt{(}}{\tt{s10}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g11}}{\tt{ }}{\tt{(}}{\tt{s11}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g12}}{\tt{ }}{\tt{(}}{\tt{s12}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g13}}{\tt{ }}{\tt{(}}{\tt{s13}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g14}}{\tt{ }}{\tt{(}}{\tt{s14}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g15}}{\tt{ }}{\tt{(}}{\tt{s15}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g16}}{\tt{ }}{\tt{(}}{\tt{s16}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g17}}{\tt{ }}{\tt{(}}{\tt{s17}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g18}}{\tt{ }}{\tt{(}}{\tt{s18}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g19}}{\tt{ }}{\tt{(}}{\tt{s19}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g20}}{\tt{ }}{\tt{(}}{\tt{s20}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g21}}{\tt{ }}{\tt{(}}{\tt{s21}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g22}}{\tt{ }}{\tt{(}}{\tt{s22}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g23}}{\tt{ }}{\tt{(}}{\tt{s23}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g24}}{\tt{ }}{\tt{(}}{\tt{s24}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g25}}{\tt{ }}{\tt{(}}{\tt{s25}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g26}}{\tt{ }}{\tt{(}}{\tt{s26}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g27}}{\tt{ }}{\tt{(}}{\tt{s27}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g28}}{\tt{ }}{\tt{(}}{\tt{s28}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g29}}{\tt{ }}{\tt{(}}{\tt{s29}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g30}}{\tt{ }}{\tt{(}}{\tt{s30}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g31}}{\tt{ }}{\tt{(}}{\tt{s31}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{aa}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fanout-32\&} \\  
\=\+{\rm{fanout-32\&}}\,({\it{netlist\/}})\index{fanout-32\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{fanout-32}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{fanout-32*}}\index{fanout-32*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-buf-pwr\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{fanout-32}}, {\it{netlist\/}})\index{delete-module})\index{b-buf-pwr\&} \\ 
$\wedge$$\;\;\;\;${\rm{id\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{fanout-32}}, {\it{netlist\/}})\index{delete-module})\index{id\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fanout-32\&; name this event `fanout-32\&-off'.\index{fanout-32\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fanout-32\$netlist} \\  
{\sc{fanout-32\$netlist}}\index{fanout-32\$netlist} $=$ {\rm{cons}}\,({\sc{fanout-32*}}\index{fanout-32*}, {\sc{b-buf-pwr\$netlist}}\index{b-buf-pwr\$netlist} $\cup$ {\sc{id\$netlist}}\index{id\$netlist})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fanout-32\$value \\ \index{fanout-32\$value}
\=\+{\rm{fanout-32\&}}\,({\it{netlist\/}})\index{fanout-32\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{fanout-32}}, {\rm{list}}\,({\it{a\/}}), {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{32}}, {\rm{threefix}}\,({\it{a\/}})\index{threefix})\index{make-list})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fanout-32\$value; name this event `fanout-32\$value-off'.\index{fanout-32\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{f\$decode-5} \\  
\=\+{\rm{f\$decode-5}}\,({\it{s\/}})\index{f\$decode-5} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not})\index{f-not}, {\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not})\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not})\index{f-not}, {\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not})\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not})\index{f-not}, {\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not})\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not})\index{f-not}, {\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not})\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not})\index{f-not}, {\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not})\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not})\index{f-not}, {\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not})\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not})\index{f-not}, {\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not})\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not})\index{f-not}, {\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\-\index{f-nand3})\-\index{f-nor}, \\ 
{\rm{f-nor}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{s\/}}))\index{f-not})\index{f-not}, {\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{f-not})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{f-not})\index{f-not})\-\index{f-nand3})\-\index{f-nor})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$decode-5; name this event `f\$decode-5-off'.\index{f\$decode-5-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{decode-5} \\  
\=\+{\rm{decode-5}}\,({\it{s\/}})\index{decode-5} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,({\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not})\index{b-not}, {\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,({\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,({\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not})\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,({\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not})\index{b-not}, {\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not})\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not})\index{b-not}, {\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not})\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not})\index{b-not}, {\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not})\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not})\index{b-not}, {\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not})\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not})\index{b-not}, {\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not})\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not})\index{b-not}, {\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not})\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not})\index{b-not}, {\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\-\index{b-nand3})\-\index{b-nor}, \\ 
{\rm{b-nor}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\rm{b-not}}\,({\rm{car}}\,({\it{s\/}}))\index{b-not})\index{b-not}, {\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{cadddr}}\,({\it{s\/}}))\index{b-not})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-not}}\,({\rm{caddddr}}\,({\it{s\/}}))\index{b-not})\index{b-not})\-\index{b-nand3})\-\index{b-nor})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable decode-5; name this event `decode-5-off'.\index{decode-5-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  bvp-length-decode-5 \\ \index{bvp-length-decode-5}
{\rm{bvp}}\,({\rm{decode-5}}\,({\it{s\/}})\index{decode-5})\index{bvp} $\wedge$ ({\rm{length}}\,({\rm{decode-5}}\,({\it{s\/}})\index{decode-5})\index{length} $=$ {\tt{32}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{decode-5*} \\  
\=\+{\sc{decode-5*}}\index{decode-5*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{decode-5}} \\ 
{\tt{(}}{\tt{s0}}{\tt{ }}{\tt{s1}}{\tt{ }}{\tt{s2}}{\tt{ }}{\tt{s3}}{\tt{ }}{\tt{s4}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{x00}}{\tt{ }}{\tt{x10}}{\tt{ }}{\tt{x20}}{\tt{ }}{\tt{x30}}{\tt{ }}{\tt{x01}}{\tt{ }}{\tt{x11}}{\tt{ }}{\tt{x21}}{\tt{ }}{\tt{x31}}{\tt{ }}{\tt{x02}}{\tt{ }}{\tt{x12}}{\tt{ }}{\tt{x22}}{\tt{ }}{\tt{x32}}{\tt{ }}{\tt{x03}} \\ 
{\tt{x13}}{\tt{ }}{\tt{x23}}{\tt{ }}{\tt{x33}}{\tt{ }}{\tt{x04}}{\tt{ }}{\tt{x14}}{\tt{ }}{\tt{x24}}{\tt{ }}{\tt{x34}}{\tt{ }}{\tt{x05}}{\tt{ }}{\tt{x15}}{\tt{ }}{\tt{x25}}{\tt{ }}{\tt{x35}}{\tt{ }}{\tt{x06}}{\tt{ }}{\tt{x16}} \\ 
{\tt{x26}}{\tt{ }}{\tt{x36}}{\tt{ }}{\tt{x07}}{\tt{ }}{\tt{x17}}{\tt{ }}{\tt{x27}}{\tt{ }}{\tt{x37}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{gs0-}}{\tt{ }}{\tt{(}}{\tt{s0-}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{s0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gs1-}}{\tt{ }}{\tt{(}}{\tt{s1-}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{s1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gs2-}}{\tt{ }}{\tt{(}}{\tt{s2-}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{s2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gs3-}}{\tt{ }}{\tt{(}}{\tt{s3-}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{s3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gs4-}}{\tt{ }}{\tt{(}}{\tt{s4-}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{s4}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gs0}}{\tt{ }}{\tt{(}}{\tt{bs0}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{s0-}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gs1}}{\tt{ }}{\tt{(}}{\tt{bs1}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{s1-}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gs2}}{\tt{ }}{\tt{(}}{\tt{bs2}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{s2-}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gs3}}{\tt{ }}{\tt{(}}{\tt{bs3}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{s3-}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gs4}}{\tt{ }}{\tt{(}}{\tt{bs4}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{s4-}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gl0}}{\tt{ }}{\tt{(}}{\tt{l0}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{s0-}}{\tt{ }}{\tt{s1-}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gl1}}{\tt{ }}{\tt{(}}{\tt{l1}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{bs0}}{\tt{ }}{\tt{s1-}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gl2}}{\tt{ }}{\tt{(}}{\tt{l2}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{s0-}}{\tt{ }}{\tt{bs1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gl3}}{\tt{ }}{\tt{(}}{\tt{l3}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{bs0}}{\tt{ }}{\tt{bs1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gh0}}{\tt{ }}{\tt{(}}{\tt{h0}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{s2-}}{\tt{ }}{\tt{s3-}}{\tt{ }}{\tt{s4-}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gh1}}{\tt{ }}{\tt{(}}{\tt{h1}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{bs2}}{\tt{ }}{\tt{s3-}}{\tt{ }}{\tt{s4-}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gh2}}{\tt{ }}{\tt{(}}{\tt{h2}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{s2-}}{\tt{ }}{\tt{bs3}}{\tt{ }}{\tt{s4-}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gh3}}{\tt{ }}{\tt{(}}{\tt{h3}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{bs2}}{\tt{ }}{\tt{bs3}}{\tt{ }}{\tt{s4-}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gh4}}{\tt{ }}{\tt{(}}{\tt{h4}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{s2-}}{\tt{ }}{\tt{s3-}}{\tt{ }}{\tt{bs4}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gh5}}{\tt{ }}{\tt{(}}{\tt{h5}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{bs2}}{\tt{ }}{\tt{s3-}}{\tt{ }}{\tt{bs4}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gh6}}{\tt{ }}{\tt{(}}{\tt{h6}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{s2-}}{\tt{ }}{\tt{bs3}}{\tt{ }}{\tt{bs4}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gh7}}{\tt{ }}{\tt{(}}{\tt{h7}}{\tt{)}}{\tt{ }}{\tt{b-nand3}}{\tt{ }}{\tt{(}}{\tt{bs2}}{\tt{ }}{\tt{bs3}}{\tt{ }}{\tt{bs4}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx00}}{\tt{ }}{\tt{(}}{\tt{x00}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l0}}{\tt{ }}{\tt{h0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx10}}{\tt{ }}{\tt{(}}{\tt{x10}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l1}}{\tt{ }}{\tt{h0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx20}}{\tt{ }}{\tt{(}}{\tt{x20}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l2}}{\tt{ }}{\tt{h0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx30}}{\tt{ }}{\tt{(}}{\tt{x30}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l3}}{\tt{ }}{\tt{h0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx01}}{\tt{ }}{\tt{(}}{\tt{x01}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l0}}{\tt{ }}{\tt{h1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx11}}{\tt{ }}{\tt{(}}{\tt{x11}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l1}}{\tt{ }}{\tt{h1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx21}}{\tt{ }}{\tt{(}}{\tt{x21}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l2}}{\tt{ }}{\tt{h1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx31}}{\tt{ }}{\tt{(}}{\tt{x31}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l3}}{\tt{ }}{\tt{h1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx02}}{\tt{ }}{\tt{(}}{\tt{x02}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l0}}{\tt{ }}{\tt{h2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx12}}{\tt{ }}{\tt{(}}{\tt{x12}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l1}}{\tt{ }}{\tt{h2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx22}}{\tt{ }}{\tt{(}}{\tt{x22}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l2}}{\tt{ }}{\tt{h2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx32}}{\tt{ }}{\tt{(}}{\tt{x32}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l3}}{\tt{ }}{\tt{h2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx03}}{\tt{ }}{\tt{(}}{\tt{x03}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l0}}{\tt{ }}{\tt{h3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx13}}{\tt{ }}{\tt{(}}{\tt{x13}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l1}}{\tt{ }}{\tt{h3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx23}}{\tt{ }}{\tt{(}}{\tt{x23}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l2}}{\tt{ }}{\tt{h3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx33}}{\tt{ }}{\tt{(}}{\tt{x33}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l3}}{\tt{ }}{\tt{h3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx04}}{\tt{ }}{\tt{(}}{\tt{x04}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l0}}{\tt{ }}{\tt{h4}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx14}}{\tt{ }}{\tt{(}}{\tt{x14}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l1}}{\tt{ }}{\tt{h4}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx24}}{\tt{ }}{\tt{(}}{\tt{x24}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l2}}{\tt{ }}{\tt{h4}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx34}}{\tt{ }}{\tt{(}}{\tt{x34}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l3}}{\tt{ }}{\tt{h4}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx05}}{\tt{ }}{\tt{(}}{\tt{x05}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l0}}{\tt{ }}{\tt{h5}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx15}}{\tt{ }}{\tt{(}}{\tt{x15}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l1}}{\tt{ }}{\tt{h5}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx25}}{\tt{ }}{\tt{(}}{\tt{x25}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l2}}{\tt{ }}{\tt{h5}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx35}}{\tt{ }}{\tt{(}}{\tt{x35}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l3}}{\tt{ }}{\tt{h5}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx06}}{\tt{ }}{\tt{(}}{\tt{x06}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l0}}{\tt{ }}{\tt{h6}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx16}}{\tt{ }}{\tt{(}}{\tt{x16}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l1}}{\tt{ }}{\tt{h6}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx26}}{\tt{ }}{\tt{(}}{\tt{x26}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l2}}{\tt{ }}{\tt{h6}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx36}}{\tt{ }}{\tt{(}}{\tt{x36}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l3}}{\tt{ }}{\tt{h6}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx07}}{\tt{ }}{\tt{(}}{\tt{x07}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l0}}{\tt{ }}{\tt{h7}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx17}}{\tt{ }}{\tt{(}}{\tt{x17}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l1}}{\tt{ }}{\tt{h7}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx27}}{\tt{ }}{\tt{(}}{\tt{x27}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l2}}{\tt{ }}{\tt{h7}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{gx37}}{\tt{ }}{\tt{(}}{\tt{x37}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{l3}}{\tt{ }}{\tt{h7}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{decode-5\&} \\  
\=\+{\rm{decode-5\&}}\,({\it{netlist\/}})\index{decode-5\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{decode-5}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{decode-5*}}\index{decode-5*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-5}}, {\it{netlist\/}})\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-5}}, {\it{netlist\/}})\index{delete-module})\index{b-nand\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand3\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-5}}, {\it{netlist\/}})\index{delete-module})\index{b-nand3\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nor\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{decode-5}}, {\it{netlist\/}})\index{delete-module})\index{b-nor\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable decode-5\&; name this event `decode-5\&-off'.\index{decode-5\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{decode-5\$netlist} \\  
\=\+{\sc{decode-5\$netlist}}\index{decode-5\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{decode-5*}}\index{decode-5*}, \\ 
\=\+(({\sc{b-not\$netlist}}\index{b-not\$netlist} $\cup$ {\sc{b-nand\$netlist}}\index{b-nand\$netlist}) $\cup$ {\sc{b-nand3\$netlist}}\index{b-nand3\$netlist}) \\ 
$\cup$$\;\;\;\;${\sc{b-nor\$netlist}}\index{b-nor\$netlist}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-length-f\$decode-5 \\ \index{properp-length-f\$decode-5}
{\rm{properp}}\,({\rm{f\$decode-5}}\,({\it{s\/}})\index{f\$decode-5})\index{properp} $\wedge$ ({\rm{length}}\,({\rm{f\$decode-5}}\,({\it{s\/}})\index{f\$decode-5})\index{length} $=$ {\tt{32}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  decode-5\$value \\ \index{decode-5\$value}
\=\+({\rm{decode-5\&}}\,({\it{netlist\/}})\index{decode-5\&} $\wedge$ ({\rm{length}}\,({\it{s\/}})\index{length} $=$ {\tt{5}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{decode-5}}, {\it{s\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{f\$decode-5}}\,({\it{s\/}})\index{f\$decode-5})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f\$decode-5=decode-5 \\ \index{f\$decode-5=decode-5}
({\rm{bvp}}\,({\it{s\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{s\/}})\index{length} $=$ {\tt{5}})) $\rightarrow$ ({\rm{f\$decode-5}}\,({\it{s\/}})\index{f\$decode-5} $=$ {\rm{decode-5}}\,({\it{s\/}})\index{decode-5})
\end{tabbing}


\noindent{\sc Event}:   Enable decode-5\$value; name this event `decode-5\$value-off'.\index{decode-5\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{encode-32} \\  
\=\+{\rm{encode-32}}\,(\=\+{\it{s0\/}}, \\ 
{\it{s1\/}}, \\ 
{\it{s2\/}}, \\ 
{\it{s3\/}}, \\ 
{\it{s4\/}}, \\ 
{\it{s5\/}}, \\ 
{\it{s6\/}}, \\ 
{\it{s7\/}}, \\ 
{\it{s8\/}}, \\ 
{\it{s9\/}}, \\ 
{\it{s10\/}}, \\ 
{\it{s11\/}}, \\ 
{\it{s12\/}}, \\ 
{\it{s13\/}}, \\ 
{\it{s14\/}}, \\ 
{\it{s15\/}}, \\ 
{\it{s16\/}}, \\ 
{\it{s17\/}}, \\ 
{\it{s18\/}}, \\ 
{\it{s19\/}}, \\ 
{\it{s20\/}}, \\ 
{\it{s21\/}}, \\ 
{\it{s22\/}}, \\ 
{\it{s23\/}}, \\ 
{\it{s24\/}}, \\ 
{\it{s25\/}}, \\ 
{\it{s26\/}}, \\ 
{\it{s27\/}}, \\ 
{\it{s28\/}}, \\ 
{\it{s29\/}}, \\ 
{\it{s30\/}}, \\ 
{\it{s31\/}})\-\index{encode-32} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{b-nand4}}\,(\=\+{\rm{b-nor4}}\,({\it{s1\/}}, {\it{s3\/}}, {\it{s5\/}}, {\it{s7\/}})\index{b-nor4}, \\ 
{\rm{b-nor4}}\,({\it{s9\/}}, {\it{s11\/}}, {\it{s13\/}}, {\it{s15\/}})\index{b-nor4}, \\ 
{\rm{b-nor4}}\,({\it{s17\/}}, {\it{s19\/}}, {\it{s21\/}}, {\it{s23\/}})\index{b-nor4}, \\ 
{\rm{b-nor}}\,({\it{s25\/}}, {\it{s29\/}})\index{b-nor})\-\index{b-nand4}, \\ 
{\rm{b-nand4}}\,(\=\+{\rm{b-nor4}}\,({\it{s2\/}}, {\it{s3\/}}, {\it{s6\/}}, {\it{s7\/}})\index{b-nor4}, \\ 
{\rm{b-nor4}}\,({\it{s10\/}}, {\it{s11\/}}, {\it{s14\/}}, {\it{s15\/}})\index{b-nor4}, \\ 
{\rm{b-nor4}}\,({\it{s18\/}}, {\it{s19\/}}, {\it{s22\/}}, {\it{s23\/}})\index{b-nor4}, \\ 
{\rm{b-not}}\,({\it{s30\/}})\index{b-not})\-\index{b-nand4}, \\ 
{\rm{b-nand4}}\,(\=\+{\rm{b-nor4}}\,({\it{s4\/}}, {\it{s5\/}}, {\it{s6\/}}, {\it{s7\/}})\index{b-nor4}, \\ 
{\rm{b-nor4}}\,({\it{s12\/}}, {\it{s13\/}}, {\it{s14\/}}, {\it{s15\/}})\index{b-nor4}, \\ 
{\rm{b-nor4}}\,({\it{s20\/}}, {\it{s21\/}}, {\it{s22\/}}, {\it{s23\/}})\index{b-nor4}, \\ 
{\rm{b-nor3}}\,({\it{s28\/}}, {\it{s29\/}}, {\it{s30\/}})\index{b-nor3})\-\index{b-nand4}, \\ 
{\rm{b-nand4}}\,(\=\+{\rm{b-nor4}}\,({\it{s8\/}}, {\it{s9\/}}, {\it{s10\/}}, {\it{s11\/}})\index{b-nor4}, \\ 
{\rm{b-nor4}}\,({\it{s12\/}}, {\it{s13\/}}, {\it{s14\/}}, {\it{s15\/}})\index{b-nor4}, \\ 
{\rm{b-nor}}\,({\it{s24\/}}, {\it{s25\/}})\index{b-nor}, \\ 
{\rm{b-nor3}}\,({\it{s28\/}}, {\it{s29\/}}, {\it{s30\/}})\index{b-nor3})\-\index{b-nand4}, \\ 
{\rm{b-nand4}}\,(\=\+{\rm{b-nor4}}\,({\it{s16\/}}, {\it{s17\/}}, {\it{s18\/}}, {\it{s19\/}})\index{b-nor4}, \\ 
{\rm{b-nor4}}\,({\it{s20\/}}, {\it{s21\/}}, {\it{s22\/}}, {\it{s23\/}})\index{b-nor4}, \\ 
{\rm{b-nor}}\,({\it{s24\/}}, {\it{s25\/}})\index{b-nor}, \\ 
{\rm{b-nor3}}\,({\it{s28\/}}, {\it{s29\/}}, {\it{s30\/}})\index{b-nor3})\-\index{b-nand4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable encode-32; name this event `encode-32-off'.\index{encode-32-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{f\$encode-32} \\  
\=\+{\rm{f\$encode-32}}\,(\=\+{\it{s0\/}}, \\ 
{\it{s1\/}}, \\ 
{\it{s2\/}}, \\ 
{\it{s3\/}}, \\ 
{\it{s4\/}}, \\ 
{\it{s5\/}}, \\ 
{\it{s6\/}}, \\ 
{\it{s7\/}}, \\ 
{\it{s8\/}}, \\ 
{\it{s9\/}}, \\ 
{\it{s10\/}}, \\ 
{\it{s11\/}}, \\ 
{\it{s12\/}}, \\ 
{\it{s13\/}}, \\ 
{\it{s14\/}}, \\ 
{\it{s15\/}}, \\ 
{\it{s16\/}}, \\ 
{\it{s17\/}}, \\ 
{\it{s18\/}}, \\ 
{\it{s19\/}}, \\ 
{\it{s20\/}}, \\ 
{\it{s21\/}}, \\ 
{\it{s22\/}}, \\ 
{\it{s23\/}}, \\ 
{\it{s24\/}}, \\ 
{\it{s25\/}}, \\ 
{\it{s26\/}}, \\ 
{\it{s27\/}}, \\ 
{\it{s28\/}}, \\ 
{\it{s29\/}}, \\ 
{\it{s30\/}}, \\ 
{\it{s31\/}})\-\index{f\$encode-32} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{f-nand4}}\,(\=\+{\rm{f-nor4}}\,({\it{s1\/}}, {\it{s3\/}}, {\it{s5\/}}, {\it{s7\/}})\index{f-nor4}, \\ 
{\rm{f-nor4}}\,({\it{s9\/}}, {\it{s11\/}}, {\it{s13\/}}, {\it{s15\/}})\index{f-nor4}, \\ 
{\rm{f-nor4}}\,({\it{s17\/}}, {\it{s19\/}}, {\it{s21\/}}, {\it{s23\/}})\index{f-nor4}, \\ 
{\rm{f-nor}}\,({\it{s25\/}}, {\it{s29\/}})\index{f-nor})\-\index{f-nand4}, \\ 
{\rm{f-nand4}}\,(\=\+{\rm{f-nor4}}\,({\it{s2\/}}, {\it{s3\/}}, {\it{s6\/}}, {\it{s7\/}})\index{f-nor4}, \\ 
{\rm{f-nor4}}\,({\it{s10\/}}, {\it{s11\/}}, {\it{s14\/}}, {\it{s15\/}})\index{f-nor4}, \\ 
{\rm{f-nor4}}\,({\it{s18\/}}, {\it{s19\/}}, {\it{s22\/}}, {\it{s23\/}})\index{f-nor4}, \\ 
{\rm{f-not}}\,({\it{s30\/}})\index{f-not})\-\index{f-nand4}, \\ 
{\rm{f-nand4}}\,(\=\+{\rm{f-nor4}}\,({\it{s4\/}}, {\it{s5\/}}, {\it{s6\/}}, {\it{s7\/}})\index{f-nor4}, \\ 
{\rm{f-nor4}}\,({\it{s12\/}}, {\it{s13\/}}, {\it{s14\/}}, {\it{s15\/}})\index{f-nor4}, \\ 
{\rm{f-nor4}}\,({\it{s20\/}}, {\it{s21\/}}, {\it{s22\/}}, {\it{s23\/}})\index{f-nor4}, \\ 
{\rm{f-nor3}}\,({\it{s28\/}}, {\it{s29\/}}, {\it{s30\/}})\index{f-nor3})\-\index{f-nand4}, \\ 
{\rm{f-nand4}}\,(\=\+{\rm{f-nor4}}\,({\it{s8\/}}, {\it{s9\/}}, {\it{s10\/}}, {\it{s11\/}})\index{f-nor4}, \\ 
{\rm{f-nor4}}\,({\it{s12\/}}, {\it{s13\/}}, {\it{s14\/}}, {\it{s15\/}})\index{f-nor4}, \\ 
{\rm{f-nor}}\,({\it{s24\/}}, {\it{s25\/}})\index{f-nor}, \\ 
{\rm{f-nor3}}\,({\it{s28\/}}, {\it{s29\/}}, {\it{s30\/}})\index{f-nor3})\-\index{f-nand4}, \\ 
{\rm{f-nand4}}\,(\=\+{\rm{f-nor4}}\,({\it{s16\/}}, {\it{s17\/}}, {\it{s18\/}}, {\it{s19\/}})\index{f-nor4}, \\ 
{\rm{f-nor4}}\,({\it{s20\/}}, {\it{s21\/}}, {\it{s22\/}}, {\it{s23\/}})\index{f-nor4}, \\ 
{\rm{f-nor}}\,({\it{s24\/}}, {\it{s25\/}})\index{f-nor}, \\ 
{\rm{f-nor3}}\,({\it{s28\/}}, {\it{s29\/}}, {\it{s30\/}})\index{f-nor3})\-\index{f-nand4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$encode-32; name this event `f\$encode-32-off'.\index{f\$encode-32-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{encode-32*} \\  
\=\+{\sc{encode-32*}}\index{encode-32*} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{encode-32}} \\ 
{\tt{(}}\=\+{\tt{s0}}{\tt{ }}{\tt{s1}}{\tt{ }}{\tt{s2}}{\tt{ }}{\tt{s3}}{\tt{ }}{\tt{s4}}{\tt{ }}{\tt{s5}}{\tt{ }}{\tt{s6}}{\tt{ }}{\tt{s7}}{\tt{ }}{\tt{s8}}{\tt{ }}{\tt{s9}}{\tt{ }}{\tt{s10}}{\tt{ }}{\tt{s11}}{\tt{ }}{\tt{s12}}{\tt{ }}{\tt{s13}}{\tt{ }}{\tt{s14}} \\ 
{\tt{s15}}{\tt{ }}{\tt{s16}}{\tt{ }}{\tt{s17}}{\tt{ }}{\tt{s18}}{\tt{ }}{\tt{s19}}{\tt{ }}{\tt{s20}}{\tt{ }}{\tt{s21}}{\tt{ }}{\tt{s22}}{\tt{ }}{\tt{s23}}{\tt{ }}{\tt{s24}}{\tt{ }}{\tt{s25}}{\tt{ }}{\tt{s26}}{\tt{ }}{\tt{s27}} \\ 
{\tt{s28}}{\tt{ }}{\tt{s29}}{\tt{ }}{\tt{s30}}{\tt{ }}{\tt{s31}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{w-4}}{\tt{ }}{\tt{w-9}}{\tt{ }}{\tt{w-14}}{\tt{ }}{\tt{w-19}}{\tt{ }}{\tt{w-24}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{(}}{\tt{g-23}}{\tt{ }}{\tt{(}}{\tt{w-23}}{\tt{)}}{\tt{ }}{\tt{b-nor3}}{\tt{ }}{\tt{(}}{\tt{s28}}{\tt{ }}{\tt{s29}}{\tt{ }}{\tt{s30}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-22}}{\tt{ }}{\tt{(}}{\tt{w-22}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{s24}}{\tt{ }}{\tt{s25}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-21}}{\tt{ }}{\tt{(}}{\tt{w-21}}{\tt{)}}{\tt{ }}{\tt{b-nor4}}{\tt{ }}{\tt{(}}{\tt{s20}}{\tt{ }}{\tt{s21}}{\tt{ }}{\tt{s22}}{\tt{ }}{\tt{s23}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-20}}{\tt{ }}{\tt{(}}{\tt{w-20}}{\tt{)}}{\tt{ }}{\tt{b-nor4}}{\tt{ }}{\tt{(}}{\tt{s16}}{\tt{ }}{\tt{s17}}{\tt{ }}{\tt{s18}}{\tt{ }}{\tt{s19}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-24}}{\tt{ }}{\tt{(}}{\tt{w-24}}{\tt{)}}{\tt{ }}{\tt{b-nand4}}{\tt{ }}{\tt{(}}{\tt{w-20}}{\tt{ }}{\tt{w-21}}{\tt{ }}{\tt{w-22}}{\tt{ }}{\tt{w-23}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-16}}{\tt{ }}{\tt{(}}{\tt{w-16}}{\tt{)}}{\tt{ }}{\tt{b-nor4}}{\tt{ }}{\tt{(}}{\tt{s12}}{\tt{ }}{\tt{s13}}{\tt{ }}{\tt{s14}}{\tt{ }}{\tt{s15}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-15}}{\tt{ }}{\tt{(}}{\tt{w-15}}{\tt{)}}{\tt{ }}{\tt{b-nor4}}{\tt{ }}{\tt{(}}{\tt{s8}}{\tt{ }}{\tt{s9}}{\tt{ }}{\tt{s10}}{\tt{ }}{\tt{s11}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-19}}{\tt{ }}{\tt{(}}{\tt{w-19}}{\tt{)}}{\tt{ }}{\tt{b-nand4}}{\tt{ }}{\tt{(}}{\tt{w-15}}{\tt{ }}{\tt{w-16}}{\tt{ }}{\tt{w-22}}{\tt{ }}{\tt{w-23}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-10}}{\tt{ }}{\tt{(}}{\tt{w-10}}{\tt{)}}{\tt{ }}{\tt{b-nor4}}{\tt{ }}{\tt{(}}{\tt{s4}}{\tt{ }}{\tt{s5}}{\tt{ }}{\tt{s6}}{\tt{ }}{\tt{s7}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-14}}{\tt{ }}{\tt{(}}{\tt{w-14}}{\tt{)}}{\tt{ }}{\tt{b-nand4}}{\tt{ }}{\tt{(}}{\tt{w-10}}{\tt{ }}{\tt{w-16}}{\tt{ }}{\tt{w-21}}{\tt{ }}{\tt{w-23}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-8}}{\tt{ }}{\tt{(}}{\tt{w-8}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{s30}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-7}}{\tt{ }}{\tt{(}}{\tt{w-7}}{\tt{)}}{\tt{ }}{\tt{b-nor4}}{\tt{ }}{\tt{(}}{\tt{s18}}{\tt{ }}{\tt{s19}}{\tt{ }}{\tt{s22}}{\tt{ }}{\tt{s23}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-6}}{\tt{ }}{\tt{(}}{\tt{w-6}}{\tt{)}}{\tt{ }}{\tt{b-nor4}}{\tt{ }}{\tt{(}}{\tt{s10}}{\tt{ }}{\tt{s11}}{\tt{ }}{\tt{s14}}{\tt{ }}{\tt{s15}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-5}}{\tt{ }}{\tt{(}}{\tt{w-5}}{\tt{)}}{\tt{ }}{\tt{b-nor4}}{\tt{ }}{\tt{(}}{\tt{s2}}{\tt{ }}{\tt{s3}}{\tt{ }}{\tt{s6}}{\tt{ }}{\tt{s7}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-9}}{\tt{ }}{\tt{(}}{\tt{w-9}}{\tt{)}}{\tt{ }}{\tt{b-nand4}}{\tt{ }}{\tt{(}}{\tt{w-5}}{\tt{ }}{\tt{w-6}}{\tt{ }}{\tt{w-7}}{\tt{ }}{\tt{w-8}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-3}}{\tt{ }}{\tt{(}}{\tt{w-3}}{\tt{)}}{\tt{ }}{\tt{b-nor}}{\tt{ }}{\tt{(}}{\tt{s25}}{\tt{ }}{\tt{s29}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-2}}{\tt{ }}{\tt{(}}{\tt{w-2}}{\tt{)}}{\tt{ }}{\tt{b-nor4}}{\tt{ }}{\tt{(}}{\tt{s17}}{\tt{ }}{\tt{s19}}{\tt{ }}{\tt{s21}}{\tt{ }}{\tt{s23}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-1}}{\tt{ }}{\tt{(}}{\tt{w-1}}{\tt{)}}{\tt{ }}{\tt{b-nor4}}{\tt{ }}{\tt{(}}{\tt{s9}}{\tt{ }}{\tt{s11}}{\tt{ }}{\tt{s13}}{\tt{ }}{\tt{s15}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-0}}{\tt{ }}{\tt{(}}{\tt{w-0}}{\tt{)}}{\tt{ }}{\tt{b-nor4}}{\tt{ }}{\tt{(}}{\tt{s1}}{\tt{ }}{\tt{s3}}{\tt{ }}{\tt{s5}}{\tt{ }}{\tt{s7}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-4}}{\tt{ }}{\tt{(}}{\tt{w-4}}{\tt{)}}{\tt{ }}{\tt{b-nand4}}{\tt{ }}{\tt{(}}{\tt{w-0}}{\tt{ }}{\tt{w-1}}{\tt{ }}{\tt{w-2}}{\tt{ }}{\tt{w-3}}{\tt{)}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{nil}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{encode-32\&} \\  
\=\+{\rm{encode-32\&}}\,({\it{netlist\/}})\index{encode-32\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{encode-32}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{encode-32*}}\index{encode-32*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-nor3\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{encode-32}}, {\it{netlist\/}})\index{delete-module})\index{b-nor3\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{encode-32}}, {\it{netlist\/}})\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nor\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{encode-32}}, {\it{netlist\/}})\index{delete-module})\index{b-nor\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nor4\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{encode-32}}, {\it{netlist\/}})\index{delete-module})\index{b-nor4\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand4\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{encode-32}}, {\it{netlist\/}})\index{delete-module})\index{b-nand4\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable encode-32\&; name this event `encode-32\&-off'.\index{encode-32\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{encode-32\$netlist} \\  
\=\+{\sc{encode-32\$netlist}}\index{encode-32\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{encode-32*}}\index{encode-32*}, \\ 
\=\+(\=\+(({\sc{b-nor3\$netlist}}\index{b-nor3\$netlist} $\cup$ {\sc{b-not\$netlist}}\index{b-not\$netlist}) $\cup$ {\sc{b-nor\$netlist}}\index{b-nor\$netlist}) \\ 
$\cup$$\;\;\;\;${\sc{b-nor4\$netlist}}\index{b-nor4\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-nand4\$netlist}}\index{b-nand4\$netlist}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  encode-32\$value \\ \index{encode-32\$value}
\=\+{\rm{encode-32\&}}\,({\it{netlist\/}})\index{encode-32\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{encode-32}}, \\ 
{\rm{list}}\,(\=\+{\it{s0\/}}, \\ 
{\it{s1\/}}, \\ 
{\it{s2\/}}, \\ 
{\it{s3\/}}, \\ 
{\it{s4\/}}, \\ 
{\it{s5\/}}, \\ 
{\it{s6\/}}, \\ 
{\it{s7\/}}, \\ 
{\it{s8\/}}, \\ 
{\it{s9\/}}, \\ 
{\it{s10\/}}, \\ 
{\it{s11\/}}, \\ 
{\it{s12\/}}, \\ 
{\it{s13\/}}, \\ 
{\it{s14\/}}, \\ 
{\it{s15\/}}, \\ 
{\it{s16\/}}, \\ 
{\it{s17\/}}, \\ 
{\it{s18\/}}, \\ 
{\it{s19\/}}, \\ 
{\it{s20\/}}, \\ 
{\it{s21\/}}, \\ 
{\it{s22\/}}, \\ 
{\it{s23\/}}, \\ 
{\it{s24\/}}, \\ 
{\it{s25\/}}, \\ 
{\it{s26\/}}, \\ 
{\it{s27\/}}, \\ 
{\it{s28\/}}, \\ 
{\it{s29\/}}, \\ 
{\it{s30\/}}, \\ 
{\it{s31\/}})\-, \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$encode-32}}\,(\=\+{\it{s0\/}}, \\ 
{\it{s1\/}}, \\ 
{\it{s2\/}}, \\ 
{\it{s3\/}}, \\ 
{\it{s4\/}}, \\ 
{\it{s5\/}}, \\ 
{\it{s6\/}}, \\ 
{\it{s7\/}}, \\ 
{\it{s8\/}}, \\ 
{\it{s9\/}}, \\ 
{\it{s10\/}}, \\ 
{\it{s11\/}}, \\ 
{\it{s12\/}}, \\ 
{\it{s13\/}}, \\ 
{\it{s14\/}}, \\ 
{\it{s15\/}}, \\ 
{\it{s16\/}}, \\ 
{\it{s17\/}}, \\ 
{\it{s18\/}}, \\ 
{\it{s19\/}}, \\ 
{\it{s20\/}}, \\ 
{\it{s21\/}}, \\ 
{\it{s22\/}}, \\ 
{\it{s23\/}}, \\ 
{\it{s24\/}}, \\ 
{\it{s25\/}}, \\ 
{\it{s26\/}}, \\ 
{\it{s27\/}}, \\ 
{\it{s28\/}}, \\ 
{\it{s29\/}}, \\ 
{\it{s30\/}}, \\ 
{\it{s31\/}})\-\index{f\$encode-32})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable encode-32\$value; name this event `encode-32\$value-off'.\index{encode-32\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$encode-32=encode-32 \\ \index{f\$encode-32=encode-32}
\=\+(\=\+{\rm{boolp}}\,({\it{s0\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s1\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s2\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s3\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s4\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s5\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s6\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s7\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s8\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s9\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s10\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s11\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s12\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s13\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s14\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s15\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s16\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s17\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s18\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s19\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s20\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s21\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s22\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s23\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s24\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s25\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s26\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s27\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s28\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s29\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s30\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{s31\/}})\index{boolp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$encode-32}}\,(\=\+{\it{s0\/}}, \\ 
{\it{s1\/}}, \\ 
{\it{s2\/}}, \\ 
{\it{s3\/}}, \\ 
{\it{s4\/}}, \\ 
{\it{s5\/}}, \\ 
{\it{s6\/}}, \\ 
{\it{s7\/}}, \\ 
{\it{s8\/}}, \\ 
{\it{s9\/}}, \\ 
{\it{s10\/}}, \\ 
{\it{s11\/}}, \\ 
{\it{s12\/}}, \\ 
{\it{s13\/}}, \\ 
{\it{s14\/}}, \\ 
{\it{s15\/}}, \\ 
{\it{s16\/}}, \\ 
{\it{s17\/}}, \\ 
{\it{s18\/}}, \\ 
{\it{s19\/}}, \\ 
{\it{s20\/}}, \\ 
{\it{s21\/}}, \\ 
{\it{s22\/}}, \\ 
{\it{s23\/}}, \\ 
{\it{s24\/}}, \\ 
{\it{s25\/}}, \\ 
{\it{s26\/}}, \\ 
{\it{s27\/}}, \\ 
{\it{s28\/}}, \\ 
{\it{s29\/}}, \\ 
{\it{s30\/}}, \\ 
{\it{s31\/}})\-\index{f\$encode-32} \\ 
$=$$\;\;\;\;${\rm{encode-32}}\,(\=\+{\it{s0\/}}, \\ 
{\it{s1\/}}, \\ 
{\it{s2\/}}, \\ 
{\it{s3\/}}, \\ 
{\it{s4\/}}, \\ 
{\it{s5\/}}, \\ 
{\it{s6\/}}, \\ 
{\it{s7\/}}, \\ 
{\it{s8\/}}, \\ 
{\it{s9\/}}, \\ 
{\it{s10\/}}, \\ 
{\it{s11\/}}, \\ 
{\it{s12\/}}, \\ 
{\it{s13\/}}, \\ 
{\it{s14\/}}, \\ 
{\it{s15\/}}, \\ 
{\it{s16\/}}, \\ 
{\it{s17\/}}, \\ 
{\it{s18\/}}, \\ 
{\it{s19\/}}, \\ 
{\it{s20\/}}, \\ 
{\it{s21\/}}, \\ 
{\it{s22\/}}, \\ 
{\it{s23\/}}, \\ 
{\it{s24\/}}, \\ 
{\it{s25\/}}, \\ 
{\it{s26\/}}, \\ 
{\it{s27\/}}, \\ 
{\it{s28\/}}, \\ 
{\it{s29\/}}, \\ 
{\it{s30\/}}, \\ 
{\it{s31\/}})\-\index{encode-32})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-length-encode-32 \\ \index{bvp-length-encode-32}
\=\+{\rm{bvp}}\,({\rm{encode-32}}\,(\=\+{\it{s0\/}}, \\ 
{\it{s1\/}}, \\ 
{\it{s2\/}}, \\ 
{\it{s3\/}}, \\ 
{\it{s4\/}}, \\ 
{\it{s5\/}}, \\ 
{\it{s6\/}}, \\ 
{\it{s7\/}}, \\ 
{\it{s8\/}}, \\ 
{\it{s9\/}}, \\ 
{\it{s10\/}}, \\ 
{\it{s11\/}}, \\ 
{\it{s12\/}}, \\ 
{\it{s13\/}}, \\ 
{\it{s14\/}}, \\ 
{\it{s15\/}}, \\ 
{\it{s16\/}}, \\ 
{\it{s17\/}}, \\ 
{\it{s18\/}}, \\ 
{\it{s19\/}}, \\ 
{\it{s20\/}}, \\ 
{\it{s21\/}}, \\ 
{\it{s22\/}}, \\ 
{\it{s23\/}}, \\ 
{\it{s24\/}}, \\ 
{\it{s25\/}}, \\ 
{\it{s26\/}}, \\ 
{\it{s27\/}}, \\ 
{\it{s28\/}}, \\ 
{\it{s29\/}}, \\ 
{\it{s30\/}}, \\ 
{\it{s31\/}})\-\index{encode-32})\index{bvp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{length}}\,({\rm{encode-32}}\,(\=\+{\it{s0\/}}, \\ 
{\it{s1\/}}, \\ 
{\it{s2\/}}, \\ 
{\it{s3\/}}, \\ 
{\it{s4\/}}, \\ 
{\it{s5\/}}, \\ 
{\it{s6\/}}, \\ 
{\it{s7\/}}, \\ 
{\it{s8\/}}, \\ 
{\it{s9\/}}, \\ 
{\it{s10\/}}, \\ 
{\it{s11\/}}, \\ 
{\it{s12\/}}, \\ 
{\it{s13\/}}, \\ 
{\it{s14\/}}, \\ 
{\it{s15\/}}, \\ 
{\it{s16\/}}, \\ 
{\it{s17\/}}, \\ 
{\it{s18\/}}, \\ 
{\it{s19\/}}, \\ 
{\it{s20\/}}, \\ 
{\it{s21\/}}, \\ 
{\it{s22\/}}, \\ 
{\it{s23\/}}, \\ 
{\it{s24\/}}, \\ 
{\it{s25\/}}, \\ 
{\it{s26\/}}, \\ 
{\it{s27\/}}, \\ 
{\it{s28\/}}, \\ 
{\it{s29\/}}, \\ 
{\it{s30\/}}, \\ 
{\it{s31\/}})\-\index{encode-32})\index{length} \\ 
$=$$\;\;\;\;${\tt{5}})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-length-f\$encode-32 \\ \index{properp-length-f\$encode-32}
\=\+{\rm{properp}}\,({\rm{f\$encode-32}}\,(\=\+{\it{s0\/}}, \\ 
{\it{s1\/}}, \\ 
{\it{s2\/}}, \\ 
{\it{s3\/}}, \\ 
{\it{s4\/}}, \\ 
{\it{s5\/}}, \\ 
{\it{s6\/}}, \\ 
{\it{s7\/}}, \\ 
{\it{s8\/}}, \\ 
{\it{s9\/}}, \\ 
{\it{s10\/}}, \\ 
{\it{s11\/}}, \\ 
{\it{s12\/}}, \\ 
{\it{s13\/}}, \\ 
{\it{s14\/}}, \\ 
{\it{s15\/}}, \\ 
{\it{s16\/}}, \\ 
{\it{s17\/}}, \\ 
{\it{s18\/}}, \\ 
{\it{s19\/}}, \\ 
{\it{s20\/}}, \\ 
{\it{s21\/}}, \\ 
{\it{s22\/}}, \\ 
{\it{s23\/}}, \\ 
{\it{s24\/}}, \\ 
{\it{s25\/}}, \\ 
{\it{s26\/}}, \\ 
{\it{s27\/}}, \\ 
{\it{s28\/}}, \\ 
{\it{s29\/}}, \\ 
{\it{s30\/}}, \\ 
{\it{s31\/}})\-\index{f\$encode-32})\index{properp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{length}}\,({\rm{f\$encode-32}}\,(\=\+{\it{s0\/}}, \\ 
{\it{s1\/}}, \\ 
{\it{s2\/}}, \\ 
{\it{s3\/}}, \\ 
{\it{s4\/}}, \\ 
{\it{s5\/}}, \\ 
{\it{s6\/}}, \\ 
{\it{s7\/}}, \\ 
{\it{s8\/}}, \\ 
{\it{s9\/}}, \\ 
{\it{s10\/}}, \\ 
{\it{s11\/}}, \\ 
{\it{s12\/}}, \\ 
{\it{s13\/}}, \\ 
{\it{s14\/}}, \\ 
{\it{s15\/}}, \\ 
{\it{s16\/}}, \\ 
{\it{s17\/}}, \\ 
{\it{s18\/}}, \\ 
{\it{s19\/}}, \\ 
{\it{s20\/}}, \\ 
{\it{s21\/}}, \\ 
{\it{s22\/}}, \\ 
{\it{s23\/}}, \\ 
{\it{s24\/}}, \\ 
{\it{s25\/}}, \\ 
{\it{s26\/}}, \\ 
{\it{s27\/}}, \\ 
{\it{s28\/}}, \\ 
{\it{s29\/}}, \\ 
{\it{s30\/}}, \\ 
{\it{s31\/}})\-\index{f\$encode-32})\index{length} \\ 
$=$$\;\;\;\;${\tt{5}})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-on-collected-nth-32 \\ \index{dual-eval-on-collected-nth-32}
\=\+(({\rm{length}}\,({\it{args\/}})\index{length} $=$ {\tt{32}}) $\wedge$ {\rm{properp}}\,({\it{args\/}})\index{properp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\it{flag\/}}, {\it{name\/}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{dual-eval}}\,(\=\+{\it{flag\/}}, \\ 
{\it{name\/}}, \\ 
{\rm{list}}\,(\=\+{\rm{nth}}\,({\tt{0}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{1}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{2}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{3}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{4}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{5}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{6}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{7}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{8}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{9}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{10}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{11}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{12}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{13}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{14}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{15}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{16}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{17}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{18}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{19}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{20}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{21}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{22}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{23}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{24}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{25}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{26}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{27}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{28}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{29}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{30}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{31}}, {\it{args\/}})\index{nth})\-, \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  encode-32\$value-on-a-vector \\ \index{encode-32\$value-on-a-vector}
\=\+({\rm{encode-32\&}}\,({\it{netlist\/}})\index{encode-32\&} $\wedge$ {\rm{properp}}\,({\it{args\/}})\index{properp} $\wedge$ ({\rm{length}}\,({\it{args\/}})\index{length} $=$ {\tt{32}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{encode-32}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$encode-32}}\,(\=\+{\rm{nth}}\,({\tt{0}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{1}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{2}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{3}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{4}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{5}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{6}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{7}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{8}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{9}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{10}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{11}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{12}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{13}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{14}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{15}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{16}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{17}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{18}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{19}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{20}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{21}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{22}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{23}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{24}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{25}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{26}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{27}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{28}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{29}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{30}}, {\it{args\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{31}}, {\it{args\/}})\index{nth})\-\index{f\$encode-32})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable encode-32\$value-on-a-vector; name this event `encode-32\$value-on-a-vector-off'.\index{encode-32\$value-on-a-vector-of!f}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{set-some-flags} \\  
\=\+{\rm{set-some-flags}}\,({\it{set-flags\/}})\index{set-some-flags} \\ 
$=$$\;\;\;\;$(\=\+{\rm{z-set}}\,({\it{set-flags\/}})\index{z-set} \\ 
$\vee$$\;\;\;\;${\rm{n-set}}\,({\it{set-flags\/}})\index{n-set} \\ 
$\vee$$\;\;\;\;${\rm{v-set}}\,({\it{set-flags\/}})\index{v-set} \\ 
$\vee$$\;\;\;\;${\rm{c-set}}\,({\it{set-flags\/}})\index{c-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable set-some-flags; name this event `set-some-flags-off'.\index{set-some-flags-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-set-some-flags-make-list-4-f \\ \index{not-set-some-flags-make-list-4-!f}
$\neg$ {\rm{set-some-flags}}\,({\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\index{set-some-flags}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{flags-hyps} \\  
{\rm{flags-hyps}}\,({\it{flags\/}})\index{flags-hyps} $=$ (({\rm{length}}\,({\it{flags\/}})\index{length} $=$ {\tt{4}}) $\wedge$ {\rm{bvp}}\,({\it{flags\/}})\index{bvp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  not-set-some-flags-update-flags \\ \index{not-set-some-flags-update-flags}
\=\+({\rm{flags-hyps}}\,({\it{flags\/}})\index{flags-hyps} $\wedge$ ($\neg$ {\rm{set-some-flags}}\,({\it{set-flags\/}})\index{set-some-flags})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{update-flags}}\,({\it{flags\/}}, {\it{set-flags\/}}, {\it{cvzbv\/}})\index{update-flags} $=$ {\it{flags\/}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  boolp-c-flag \\ \index{boolp-c-flag}
{\rm{flags-hyps}}\,({\it{flags\/}})\index{flags-hyps} $\rightarrow$ {\rm{boolp}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{boolp}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$set-some-flags} \\  
\=\+{\rm{f\$set-some-flags}}\,({\it{set-flags\/}})\index{f\$set-some-flags} \\ 
$=$$\;\;\;\;${\rm{f-or4}}\,(\=\+{\rm{car}}\,({\it{set-flags\/}}), \\ 
{\rm{cadr}}\,({\it{set-flags\/}}), \\ 
{\rm{caddr}}\,({\it{set-flags\/}}), \\ 
{\rm{cadddr}}\,({\it{set-flags\/}}))\-\index{f-or4}\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$set-some-flags; name this event `f\$set-some-flags-off'.\index{f\$set-some-flags-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$set-some-flags=set-some=flags \\ \index{f\$set-some-flags=set-some=flag!s}
\=\+({\rm{bvp}}\,({\it{set-flags\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{set-flags\/}})\index{length} $=$ {\tt{4}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{f\$set-some-flags}}\,({\it{set-flags\/}})\index{f\$set-some-flags} $=$ {\rm{set-some-flags}}\,({\it{set-flags\/}})\index{set-some-flags})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-or4\$value-as-f\$set-some-flags \\ \index{b-or4\$value-as-f\$set-some-fla!gs}
\=\+({\rm{b-or4\&}}\,({\it{netlist\/}})\index{b-or4\&} $\wedge$ {\rm{properp}}\,({\it{set-flags\/}})\index{properp} $\wedge$ ({\rm{length}}\,({\it{set-flags\/}})\index{length} $=$ {\tt{4}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-or4}}, {\it{set-flags\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f\$set-some-flags}}\,({\it{set-flags\/}})\index{f\$set-some-flags}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-or4\$value-as-f\$set-some-flags; name this event `b-or4\$value-as-f\$set-some-flags-off'.\index{b-or4\$value-as-f\$set-some-fla!gs-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{f\$all-t-regs-address} \\  
\=\+{\rm{f\$all-t-regs-address}}\,({\it{regs-address\/}})\index{f\$all-t-regs-address} \\ 
$=$$\;\;\;\;${\rm{f-and4}}\,(\=\+{\rm{car}}\,({\it{regs-address\/}}), \\ 
{\rm{cadr}}\,({\it{regs-address\/}}), \\ 
{\rm{caddr}}\,({\it{regs-address\/}}), \\ 
{\rm{cadddr}}\,({\it{regs-address\/}}))\-\index{f-and4}\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$all-t-regs-address; name this event `f\$all-t-regs-address-off'.\index{f\$all-t-regs-address-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$all-t-regs-address=set-some=flags \\ \index{f\$all-t-regs-address=set-some=!flags}
\=\+({\rm{bvp}}\,({\it{regs-address\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{regs-address\/}})\index{length} $=$ {\tt{4}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$all-t-regs-address}}\,({\it{regs-address\/}})\index{f\$all-t-regs-address} \\ 
$=$$\;\;\;\;$({\it{regs-address\/}} $=$ {\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-and4\$value-as-f\$all-t-regs-address \\ \index{b-and4\$value-as-f\$all-t-regs-!address}
\=\+(\=\+{\rm{b-and4\&}}\,({\it{netlist\/}})\index{b-and4\&} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{regs-address\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{regs-address\/}})\index{length} $=$ {\tt{4}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-and4}}, {\it{regs-address\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f\$all-t-regs-address}}\,({\it{regs-address\/}})\index{f\$all-t-regs-address}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable b-and4\$value-as-f\$all-t-regs-address; name this event `b-and4\$value-as-f\$all-t-regs-address-off'.\index{b-and4\$value-as-f\$all-t-regs-!address-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{cv-hyps} \\  
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$=$$\;\;\;\;$(\=\+{\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{regs-address\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{regs-address\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{i-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{i-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{flags-hyps}}\,({\it{flags\/}})\index{flags-hyps} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{pc-reg\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{pc-reg\/}})\index{bvp})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v\_fetch0}$\;\;$
{\sc{v\_fetch0}}\index{v\_fetch0} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_fetch0; name this event `v\_fetch0-off'.\index{v\_fetch0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_fetch0; name this event `g*1*v\_fetch0-off'.\index{g*1*v\_fetch0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_fetch0}$\;\;$
{\sc{n\_fetch0}}\index{n\_fetch0} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_fetch0; name this event `n\_fetch0-off'.\index{n\_fetch0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_fetch0; name this event `g*1*n\_fetch0-off'.\index{g*1*n\_fetch0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_fetch1}$\;\;$
{\sc{v\_fetch1}}\index{v\_fetch1} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_fetch1; name this event `v\_fetch1-off'.\index{v\_fetch1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_fetch1; name this event `g*1*v\_fetch1-off'.\index{g*1*v\_fetch1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_fetch1}$\;\;$
{\sc{n\_fetch1}}\index{n\_fetch1} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_fetch1; name this event `n\_fetch1-off'.\index{n\_fetch1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_fetch1; name this event `g*1*n\_fetch1-off'.\index{g*1*n\_fetch1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_fetch2}$\;\;$
{\sc{v\_fetch2}}\index{v\_fetch2} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_fetch2; name this event `v\_fetch2-off'.\index{v\_fetch2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_fetch2; name this event `g*1*v\_fetch2-off'.\index{g*1*v\_fetch2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_fetch2}$\;\;$
{\sc{n\_fetch2}}\index{n\_fetch2} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_fetch2; name this event `n\_fetch2-off'.\index{n\_fetch2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_fetch2; name this event `g*1*n\_fetch2-off'.\index{g*1*n\_fetch2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_fetch3}$\;\;$
{\sc{v\_fetch3}}\index{v\_fetch3} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_fetch3; name this event `v\_fetch3-off'.\index{v\_fetch3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_fetch3; name this event `g*1*v\_fetch3-off'.\index{g*1*v\_fetch3-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_fetch3}$\;\;$
{\sc{n\_fetch3}}\index{n\_fetch3} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_fetch3; name this event `n\_fetch3-off'.\index{n\_fetch3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_fetch3; name this event `g*1*n\_fetch3-off'.\index{g*1*n\_fetch3-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_decode}$\;\;$
{\sc{v\_decode}}\index{v\_decode} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_decode; name this event `v\_decode-off'.\index{v\_decode-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_decode; name this event `g*1*v\_decode-off'.\index{g*1*v\_decode-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_decode}$\;\;$
{\sc{n\_decode}}\index{n\_decode} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_decode; name this event `n\_decode-off'.\index{n\_decode-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_decode; name this event `g*1*n\_decode-off'.\index{g*1*n\_decode-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_rega}$\;\;$
{\sc{v\_rega}}\index{v\_rega} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_rega; name this event `v\_rega-off'.\index{v\_rega-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_rega; name this event `g*1*v\_rega-off'.\index{g*1*v\_rega-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_rega}$\;\;$
{\sc{n\_rega}}\index{n\_rega} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_rega; name this event `n\_rega-off'.\index{n\_rega-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_rega; name this event `g*1*n\_rega-off'.\index{g*1*n\_rega-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_regb}$\;\;$
{\sc{v\_regb}}\index{v\_regb} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_regb; name this event `v\_regb-off'.\index{v\_regb-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_regb; name this event `g*1*v\_regb-off'.\index{g*1*v\_regb-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_regb}$\;\;$
{\sc{n\_regb}}\index{n\_regb} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_regb; name this event `n\_regb-off'.\index{n\_regb-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_regb; name this event `g*1*n\_regb-off'.\index{g*1*n\_regb-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_update}$\;\;$
{\sc{v\_update}}\index{v\_update} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_update; name this event `v\_update-off'.\index{v\_update-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_update; name this event `g*1*v\_update-off'.\index{g*1*v\_update-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_update}$\;\;$
{\sc{n\_update}}\index{n\_update} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_update; name this event `n\_update-off'.\index{n\_update-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_update; name this event `g*1*n\_update-off'.\index{g*1*n\_update-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_reada0}$\;\;$
{\sc{v\_reada0}}\index{v\_reada0} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_reada0; name this event `v\_reada0-off'.\index{v\_reada0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_reada0; name this event `g*1*v\_reada0-off'.\index{g*1*v\_reada0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_reada0}$\;\;$
{\sc{n\_reada0}}\index{n\_reada0} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_reada0; name this event `n\_reada0-off'.\index{n\_reada0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_reada0; name this event `g*1*n\_reada0-off'.\index{g*1*n\_reada0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_reada1}$\;\;$
{\sc{v\_reada1}}\index{v\_reada1} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_reada1; name this event `v\_reada1-off'.\index{v\_reada1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_reada1; name this event `g*1*v\_reada1-off'.\index{g*1*v\_reada1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_reada1}$\;\;$
{\sc{n\_reada1}}\index{n\_reada1} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_reada1; name this event `n\_reada1-off'.\index{n\_reada1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_reada1; name this event `g*1*n\_reada1-off'.\index{g*1*n\_reada1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_reada2}$\;\;$
{\sc{v\_reada2}}\index{v\_reada2} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_reada2; name this event `v\_reada2-off'.\index{v\_reada2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_reada2; name this event `g*1*v\_reada2-off'.\index{g*1*v\_reada2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_reada2}$\;\;$
{\sc{n\_reada2}}\index{n\_reada2} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_reada2; name this event `n\_reada2-off'.\index{n\_reada2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_reada2; name this event `g*1*n\_reada2-off'.\index{g*1*n\_reada2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_reada3}$\;\;$
{\sc{v\_reada3}}\index{v\_reada3} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_reada3; name this event `v\_reada3-off'.\index{v\_reada3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_reada3; name this event `g*1*v\_reada3-off'.\index{g*1*v\_reada3-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_reada3}$\;\;$
{\sc{n\_reada3}}\index{n\_reada3} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_reada3; name this event `n\_reada3-off'.\index{n\_reada3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_reada3; name this event `g*1*n\_reada3-off'.\index{g*1*n\_reada3-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_readb0}$\;\;$
{\sc{v\_readb0}}\index{v\_readb0} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_readb0; name this event `v\_readb0-off'.\index{v\_readb0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_readb0; name this event `g*1*v\_readb0-off'.\index{g*1*v\_readb0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_readb0}$\;\;$
{\sc{n\_readb0}}\index{n\_readb0} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_readb0; name this event `n\_readb0-off'.\index{n\_readb0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_readb0; name this event `g*1*n\_readb0-off'.\index{g*1*n\_readb0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_readb1}$\;\;$
{\sc{v\_readb1}}\index{v\_readb1} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_readb1; name this event `v\_readb1-off'.\index{v\_readb1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_readb1; name this event `g*1*v\_readb1-off'.\index{g*1*v\_readb1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_readb1}$\;\;$
{\sc{n\_readb1}}\index{n\_readb1} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_readb1; name this event `n\_readb1-off'.\index{n\_readb1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_readb1; name this event `g*1*n\_readb1-off'.\index{g*1*n\_readb1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_readb2}$\;\;$
{\sc{v\_readb2}}\index{v\_readb2} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_readb2; name this event `v\_readb2-off'.\index{v\_readb2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_readb2; name this event `g*1*v\_readb2-off'.\index{g*1*v\_readb2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_readb2}$\;\;$
{\sc{n\_readb2}}\index{n\_readb2} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_readb2; name this event `n\_readb2-off'.\index{n\_readb2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_readb2; name this event `g*1*n\_readb2-off'.\index{g*1*n\_readb2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_readb3}$\;\;$
{\sc{v\_readb3}}\index{v\_readb3} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_readb3; name this event `v\_readb3-off'.\index{v\_readb3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_readb3; name this event `g*1*v\_readb3-off'.\index{g*1*v\_readb3-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_readb3}$\;\;$
{\sc{n\_readb3}}\index{n\_readb3} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_readb3; name this event `n\_readb3-off'.\index{n\_readb3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_readb3; name this event `g*1*n\_readb3-off'.\index{g*1*n\_readb3-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_write0}$\;\;$
{\sc{v\_write0}}\index{v\_write0} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_write0; name this event `v\_write0-off'.\index{v\_write0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_write0; name this event `g*1*v\_write0-off'.\index{g*1*v\_write0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_write0}$\;\;$
{\sc{n\_write0}}\index{n\_write0} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_write0; name this event `n\_write0-off'.\index{n\_write0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_write0; name this event `g*1*n\_write0-off'.\index{g*1*n\_write0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_write1}$\;\;$
{\sc{v\_write1}}\index{v\_write1} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_write1; name this event `v\_write1-off'.\index{v\_write1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_write1; name this event `g*1*v\_write1-off'.\index{g*1*v\_write1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_write1}$\;\;$
{\sc{n\_write1}}\index{n\_write1} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_write1; name this event `n\_write1-off'.\index{n\_write1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_write1; name this event `g*1*n\_write1-off'.\index{g*1*n\_write1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_write2}$\;\;$
{\sc{v\_write2}}\index{v\_write2} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_write2; name this event `v\_write2-off'.\index{v\_write2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_write2; name this event `g*1*v\_write2-off'.\index{g*1*v\_write2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_write2}$\;\;$
{\sc{n\_write2}}\index{n\_write2} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_write2; name this event `n\_write2-off'.\index{n\_write2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_write2; name this event `g*1*n\_write2-off'.\index{g*1*n\_write2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_write3}$\;\;$
{\sc{v\_write3}}\index{v\_write3} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_write3; name this event `v\_write3-off'.\index{v\_write3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_write3; name this event `g*1*v\_write3-off'.\index{g*1*v\_write3-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_write3}$\;\;$
{\sc{n\_write3}}\index{n\_write3} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_write3; name this event `n\_write3-off'.\index{n\_write3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_write3; name this event `g*1*n\_write3-off'.\index{g*1*n\_write3-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_sefa0}$\;\;$
{\sc{v\_sefa0}}\index{v\_sefa0} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_sefa0; name this event `v\_sefa0-off'.\index{v\_sefa0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_sefa0; name this event `g*1*v\_sefa0-off'.\index{g*1*v\_sefa0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_sefa0}$\;\;$
{\sc{n\_sefa0}}\index{n\_sefa0} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_sefa0; name this event `n\_sefa0-off'.\index{n\_sefa0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_sefa0; name this event `g*1*n\_sefa0-off'.\index{g*1*n\_sefa0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_sefa1}$\;\;$
{\sc{v\_sefa1}}\index{v\_sefa1} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_sefa1; name this event `v\_sefa1-off'.\index{v\_sefa1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_sefa1; name this event `g*1*v\_sefa1-off'.\index{g*1*v\_sefa1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_sefa1}$\;\;$
{\sc{n\_sefa1}}\index{n\_sefa1} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_sefa1; name this event `n\_sefa1-off'.\index{n\_sefa1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_sefa1; name this event `g*1*n\_sefa1-off'.\index{g*1*n\_sefa1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_sefb0}$\;\;$
{\sc{v\_sefb0}}\index{v\_sefb0} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_sefb0; name this event `v\_sefb0-off'.\index{v\_sefb0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_sefb0; name this event `g*1*v\_sefb0-off'.\index{g*1*v\_sefb0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_sefb0}$\;\;$
{\sc{n\_sefb0}}\index{n\_sefb0} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_sefb0; name this event `n\_sefb0-off'.\index{n\_sefb0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_sefb0; name this event `g*1*n\_sefb0-off'.\index{g*1*n\_sefb0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_sefb1}$\;\;$
{\sc{v\_sefb1}}\index{v\_sefb1} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_sefb1; name this event `v\_sefb1-off'.\index{v\_sefb1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_sefb1; name this event `g*1*v\_sefb1-off'.\index{g*1*v\_sefb1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_sefb1}$\;\;$
{\sc{n\_sefb1}}\index{n\_sefb1} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_sefb1; name this event `n\_sefb1-off'.\index{n\_sefb1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_sefb1; name this event `g*1*n\_sefb1-off'.\index{g*1*n\_sefb1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_hold0}$\;\;$
{\sc{v\_hold0}}\index{v\_hold0} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_hold0; name this event `v\_hold0-off'.\index{v\_hold0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_hold0; name this event `g*1*v\_hold0-off'.\index{g*1*v\_hold0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_hold0}$\;\;$
{\sc{n\_hold0}}\index{n\_hold0} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_hold0; name this event `n\_hold0-off'.\index{n\_hold0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_hold0; name this event `g*1*n\_hold0-off'.\index{g*1*n\_hold0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_hold1}$\;\;$
{\sc{v\_hold1}}\index{v\_hold1} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_hold1; name this event `v\_hold1-off'.\index{v\_hold1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_hold1; name this event `g*1*v\_hold1-off'.\index{g*1*v\_hold1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_hold1}$\;\;$
{\sc{n\_hold1}}\index{n\_hold1} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_hold1; name this event `n\_hold1-off'.\index{n\_hold1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_hold1; name this event `g*1*n\_hold1-off'.\index{g*1*n\_hold1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_v11010}$\;\;$
{\sc{v\_v11010}}\index{v\_v11010} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_v11010; name this event `v\_v11010-off'.\index{v\_v11010-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_v11010; name this event `g*1*v\_v11010-off'.\index{g*1*v\_v11010-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_v11010}$\;\;$
{\sc{n\_v11010}}\index{n\_v11010} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_v11010; name this event `n\_v11010-off'.\index{n\_v11010-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_v11010; name this event `g*1*n\_v11010-off'.\index{g*1*n\_v11010-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_v11011}$\;\;$
{\sc{v\_v11011}}\index{v\_v11011} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_v11011; name this event `v\_v11011-off'.\index{v\_v11011-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_v11011; name this event `g*1*v\_v11011-off'.\index{g*1*v\_v11011-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_v11011}$\;\;$
{\sc{n\_v11011}}\index{n\_v11011} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_v11011; name this event `n\_v11011-off'.\index{n\_v11011-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_v11011; name this event `g*1*n\_v11011-off'.\index{g*1*n\_v11011-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_reset0}$\;\;$
{\sc{v\_reset0}}\index{v\_reset0} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_reset0; name this event `v\_reset0-off'.\index{v\_reset0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_reset0; name this event `g*1*v\_reset0-off'.\index{g*1*v\_reset0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_reset0}$\;\;$
{\sc{n\_reset0}}\index{n\_reset0} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_reset0; name this event `n\_reset0-off'.\index{n\_reset0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_reset0; name this event `g*1*n\_reset0-off'.\index{g*1*n\_reset0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_reset1}$\;\;$
{\sc{v\_reset1}}\index{v\_reset1} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_reset1; name this event `v\_reset1-off'.\index{v\_reset1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_reset1; name this event `g*1*v\_reset1-off'.\index{g*1*v\_reset1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_reset1}$\;\;$
{\sc{n\_reset1}}\index{n\_reset1} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_reset1; name this event `n\_reset1-off'.\index{n\_reset1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_reset1; name this event `g*1*n\_reset1-off'.\index{g*1*n\_reset1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_reset2}$\;\;$
{\sc{v\_reset2}}\index{v\_reset2} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_reset2; name this event `v\_reset2-off'.\index{v\_reset2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_reset2; name this event `g*1*v\_reset2-off'.\index{g*1*v\_reset2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_reset2}$\;\;$
{\sc{n\_reset2}}\index{n\_reset2} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_reset2; name this event `n\_reset2-off'.\index{n\_reset2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_reset2; name this event `g*1*n\_reset2-off'.\index{g*1*n\_reset2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v\_v11111}$\;\;$
{\sc{v\_v11111}}\index{v\_v11111} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}})
\end{tabbing}


\noindent{\sc Event}:   Enable v\_v11111; name this event `v\_v11111-off'.\index{v\_v11111-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v\_v11111; name this event `g*1*v\_v11111-off'.\index{g*1*v\_v11111-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{n\_v11111}$\;\;$
{\sc{n\_v11111}}\index{n\_v11111} $=$ {\rm{v-to-nat}}\,({\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}))\index{v-to-nat}
\end{tabbing}


\noindent{\sc Event}:   Enable n\_v11111; name this event `n\_v11111-off'.\index{n\_v11111-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*n\_v11111; name this event `g*1*n\_v11111-off'.\index{g*1*n\_v11111-off}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{vector-state-theory}} to consist of the following events: v\_fetch0,
v\_fetch1,
v\_fetch2,
v\_fetch3,
v\_decode,
v\_rega,
v\_regb,
v\_update,
v\_reada0,
v\_reada1,
v\_reada2,
v\_reada3,
v\_readb0,
v\_readb1,
v\_readb2,
v\_readb3,
v\_write0,
v\_write1,
v\_write2,
v\_write3,
v\_sefa0,
v\_sefa1,
v\_sefb0,
v\_sefb1,
v\_hold0,
v\_hold1,
v\_v11010,
v\_v11011,
v\_reset0,
v\_reset1,
v\_reset2,
v\_v11111.\index{vector-state-theory}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{natural-state-theory}} to consist of the following events: n\_fetch0,
n\_fetch1,
n\_fetch2,
n\_fetch3,
n\_decode,
n\_rega,
n\_regb,
n\_update,
n\_reada0,
n\_reada1,
n\_reada2,
n\_reada3,
n\_readb0,
n\_readb1,
n\_readb2,
n\_readb3,
n\_write0,
n\_write1,
n\_write2,
n\_write3,
n\_sefa0,
n\_sefa1,
n\_sefb0,
n\_sefb1,
n\_hold0,
n\_hold1,
n\_v11010,
n\_v11011,
n\_reset0,
n\_reset1,
n\_reset2,
n\_v11111.\index{natural-state-theory}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  bvp-length-state-vectors \\ \index{bvp-length-state-vectors}
\=\+({\rm{length}}\,({\sc{v\_fetch0}}\index{v\_fetch0})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_fetch0}}\index{v\_fetch0})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_fetch1}}\index{v\_fetch1})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_fetch1}}\index{v\_fetch1})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_fetch2}}\index{v\_fetch2})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_fetch2}}\index{v\_fetch2})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_fetch3}}\index{v\_fetch3})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_fetch3}}\index{v\_fetch3})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_decode}}\index{v\_decode})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_decode}}\index{v\_decode})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_rega}}\index{v\_rega})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_rega}}\index{v\_rega})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_regb}}\index{v\_regb})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_regb}}\index{v\_regb})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_update}}\index{v\_update})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_update}}\index{v\_update})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_reada0}}\index{v\_reada0})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_reada0}}\index{v\_reada0})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_reada1}}\index{v\_reada1})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_reada1}}\index{v\_reada1})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_reada2}}\index{v\_reada2})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_reada2}}\index{v\_reada2})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_reada3}}\index{v\_reada3})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_reada3}}\index{v\_reada3})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_readb0}}\index{v\_readb0})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_readb0}}\index{v\_readb0})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_readb1}}\index{v\_readb1})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_readb1}}\index{v\_readb1})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_readb2}}\index{v\_readb2})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_readb2}}\index{v\_readb2})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_readb3}}\index{v\_readb3})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_readb3}}\index{v\_readb3})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_write0}}\index{v\_write0})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_write0}}\index{v\_write0})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_write1}}\index{v\_write1})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_write1}}\index{v\_write1})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_write2}}\index{v\_write2})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_write2}}\index{v\_write2})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_write3}}\index{v\_write3})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_write3}}\index{v\_write3})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_sefa0}}\index{v\_sefa0})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_sefa0}}\index{v\_sefa0})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_sefa1}}\index{v\_sefa1})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_sefa1}}\index{v\_sefa1})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_sefb0}}\index{v\_sefb0})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_sefb0}}\index{v\_sefb0})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_sefb1}}\index{v\_sefb1})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_sefb1}}\index{v\_sefb1})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_hold0}}\index{v\_hold0})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_hold0}}\index{v\_hold0})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_hold1}}\index{v\_hold1})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_hold1}}\index{v\_hold1})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_v11010}}\index{v\_v11010})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_v11010}}\index{v\_v11010})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_v11011}}\index{v\_v11011})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_v11011}}\index{v\_v11011})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_reset0}}\index{v\_reset0})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_reset0}}\index{v\_reset0})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_reset1}}\index{v\_reset1})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_reset1}}\index{v\_reset1})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_reset2}}\index{v\_reset2})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_reset2}}\index{v\_reset2})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\sc{v\_v11111}}\index{v\_v11111})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\sc{v\_v11111}}\index{v\_v11111})\index{bvp}\-
\end{tabbing}


\noindent{\sc Event}:   Enable bvp-length-state-vectors; name this event `bvp-length-state-vectors-off'.\index{bvp-length-state-vectors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{rw-}$\;\;$
{\rm{rw-}}\,({\it{cntl-state\/}})\index{rw-} $=$ {\rm{nth}}\,({\tt{0}}, {\it{cntl-state\/}})\index{nth}
\end{tabbing}


\noindent{\sc Event}:   Enable rw-; name this event `rw--off'.\index{rw--off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{strobe-}$\;\;$
{\rm{strobe-}}\,({\it{cntl-state\/}})\index{strobe-} $=$ {\rm{nth}}\,({\tt{1}}, {\it{cntl-state\/}})\index{nth}
\end{tabbing}


\noindent{\sc Event}:   Enable strobe-; name this event `strobe--off'.\index{strobe--off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{hdack-}$\;\;$
{\rm{hdack-}}\,({\it{cntl-state\/}})\index{hdack-} $=$ {\rm{nth}}\,({\tt{2}}, {\it{cntl-state\/}})\index{nth}
\end{tabbing}


\noindent{\sc Event}:   Enable hdack-; name this event `hdack--off'.\index{hdack--off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{we-regs}$\;\;$
{\rm{we-regs}}\,({\it{cntl-state\/}})\index{we-regs} $=$ {\rm{nth}}\,({\tt{3}}, {\it{cntl-state\/}})\index{nth}
\end{tabbing}


\noindent{\sc Event}:   Enable we-regs; name this event `we-regs-off'.\index{we-regs-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{we-a-reg}$\;\;$
{\rm{we-a-reg}}\,({\it{cntl-state\/}})\index{we-a-reg} $=$ {\rm{nth}}\,({\tt{4}}, {\it{cntl-state\/}})\index{nth}
\end{tabbing}


\noindent{\sc Event}:   Enable we-a-reg; name this event `we-a-reg-off'.\index{we-a-reg-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{we-b-reg}$\;\;$
{\rm{we-b-reg}}\,({\it{cntl-state\/}})\index{we-b-reg} $=$ {\rm{nth}}\,({\tt{5}}, {\it{cntl-state\/}})\index{nth}
\end{tabbing}


\noindent{\sc Event}:   Enable we-b-reg; name this event `we-b-reg-off'.\index{we-b-reg-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{we-i-reg}$\;\;$
{\rm{we-i-reg}}\,({\it{cntl-state\/}})\index{we-i-reg} $=$ {\rm{nth}}\,({\tt{6}}, {\it{cntl-state\/}})\index{nth}
\end{tabbing}


\noindent{\sc Event}:   Enable we-i-reg; name this event `we-i-reg-off'.\index{we-i-reg-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{we-data-out}$\;\;$
{\rm{we-data-out}}\,({\it{cntl-state\/}})\index{we-data-out} $=$ {\rm{nth}}\,({\tt{7}}, {\it{cntl-state\/}})\index{nth}
\end{tabbing}


\noindent{\sc Event}:   Enable we-data-out; name this event `we-data-out-off'.\index{we-data-out-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{we-addr-out}$\;\;$
{\rm{we-addr-out}}\,({\it{cntl-state\/}})\index{we-addr-out} $=$ {\rm{nth}}\,({\tt{8}}, {\it{cntl-state\/}})\index{nth}
\end{tabbing}


\noindent{\sc Event}:   Enable we-addr-out; name this event `we-addr-out-off'.\index{we-addr-out-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{we-hold-}$\;\;$
{\rm{we-hold-}}\,({\it{cntl-state\/}})\index{we-hold-} $=$ {\rm{nth}}\,({\tt{9}}, {\it{cntl-state\/}})\index{nth}
\end{tabbing}


\noindent{\sc Event}:   Enable we-hold-; name this event `we-hold--off'.\index{we-hold--off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{we-pc-reg}$\;\;$
{\rm{we-pc-reg}}\,({\it{cntl-state\/}})\index{we-pc-reg} $=$ {\rm{nth}}\,({\tt{10}}, {\it{cntl-state\/}})\index{nth}
\end{tabbing}


\noindent{\sc Event}:   Enable we-pc-reg; name this event `we-pc-reg-off'.\index{we-pc-reg-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{data-in-select}$\;\;$
{\rm{data-in-select}}\,({\it{cntl-state\/}})\index{data-in-select} $=$ {\rm{nth}}\,({\tt{11}}, {\it{cntl-state\/}})\index{nth}
\end{tabbing}


\noindent{\sc Event}:   Enable data-in-select; name this event `data-in-select-off'.\index{data-in-select-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{dec-addr-out}$\;\;$
{\rm{dec-addr-out}}\,({\it{cntl-state\/}})\index{dec-addr-out} $=$ {\rm{nth}}\,({\tt{12}}, {\it{cntl-state\/}})\index{nth}
\end{tabbing}


\noindent{\sc Event}:   Enable dec-addr-out; name this event `dec-addr-out-off'.\index{dec-addr-out-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{select-immediate}$\;\;$
{\rm{select-immediate}}\,({\it{cntl-state\/}})\index{select-immediate} $=$ {\rm{nth}}\,({\tt{13}}, {\it{cntl-state\/}})\index{nth}
\end{tabbing}


\noindent{\sc Event}:   Enable select-immediate; name this event `select-immediate-off'.\index{select-immediate-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{alu-c}$\;\;$
{\rm{alu-c}}\,({\it{cntl-state\/}})\index{alu-c} $=$ {\rm{nth}}\,({\tt{14}}, {\it{cntl-state\/}})\index{nth}
\end{tabbing}


\noindent{\sc Event}:   Enable alu-c; name this event `alu-c-off'.\index{alu-c-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{alu-zero}$\;\;$
{\rm{alu-zero}}\,({\it{cntl-state\/}})\index{alu-zero} $=$ {\rm{nth}}\,({\tt{15}}, {\it{cntl-state\/}})\index{nth}
\end{tabbing}


\noindent{\sc Event}:   Enable alu-zero; name this event `alu-zero-off'.\index{alu-zero-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{state}$\;\;$
{\rm{state}}\,({\it{cntl-state\/}})\index{state} $=$ {\rm{subrange}}\,({\it{cntl-state\/}}, {\tt{16}}, {\tt{20}})\index{subrange}
\end{tabbing}


\noindent{\sc Event}:   Enable state; name this event `state-off'.\index{state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{we-flags}$\;\;$
{\rm{we-flags}}\,({\it{cntl-state\/}})\index{we-flags} $=$ {\rm{subrange}}\,({\it{cntl-state\/}}, {\tt{21}}, {\tt{24}})\index{subrange}
\end{tabbing}


\noindent{\sc Event}:   Enable we-flags; name this event `we-flags-off'.\index{we-flags-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{regs-address} \\  
{\rm{regs-address}}\,({\it{cntl-state\/}})\index{regs-address} $=$ {\rm{subrange}}\,({\it{cntl-state\/}}, {\tt{25}}, {\tt{28}})\index{subrange}
\end{tabbing}


\noindent{\sc Event}:   Enable regs-address; name this event `regs-address-off'.\index{regs-address-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{alu-op}$\;\;$
{\rm{alu-op}}\,({\it{cntl-state\/}})\index{alu-op} $=$ {\rm{subrange}}\,({\it{cntl-state\/}}, {\tt{29}}, {\tt{32}})\index{subrange}
\end{tabbing}


\noindent{\sc Event}:   Enable alu-op; name this event `alu-op-off'.\index{alu-op-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{alu-mpg}$\;\;$
{\rm{alu-mpg}}\,({\it{cntl-state\/}})\index{alu-mpg} $=$ {\rm{subrange}}\,({\it{cntl-state\/}}, {\tt{33}}, {\tt{39}})\index{subrange}
\end{tabbing}


\noindent{\sc Event}:   Enable alu-mpg; name this event `alu-mpg-off'.\index{alu-mpg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{control-state-accessor-theory}} to consist of the following events: rw-,
strobe-,
hdack-,
we-regs,
we-a-reg,
we-b-reg,
we-i-reg,
we-data-out,
we-addr-out,
we-hold-,
we-pc-reg,
data-in-select,
dec-addr-out,
select-immediate,
alu-c,
alu-zero,
state,
we-flags,
regs-address,
alu-op,
alu-mpg.\index{control-state-accessor-theory}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_FETCH0
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS RW-
  (CONS T
   (CONS T
    (CONS F
     (CONS T
      (CONS F
       (CONS F
        (CONS F
         (CONS T
          (CONS T
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS T (ALU-INC-OP))))
                (CONS T
                 (APPEND
                  (V_FETCH0)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND PC-REG
                           (APPEND (ALU-INC-OP)
                                   (APPEND (MPG (CONS T (CONS F (ALU-INC-OP))))
                                           NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_fetch0; name this event `cv\_fetch0-off'.\index{cv\_fetch0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_fetch0\$destructure \\ \index{cv\_fetch0\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\index{rw-} $=$ {\it{rw-\/}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\index{we-regs} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_fetch0}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch0})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\rm{cons}}\,({\bf{t}}, {\sc{alu-inc-op}}\index{alu-inc-op})))\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_fetch0}}\index{v\_fetch0})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\index{regs-address} \\ 
$=$$\;\;\;\;${\it{pc-reg\/}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\index{alu-op} \\ 
$=$$\;\;\;\;${\sc{alu-inc-op}}\index{alu-inc-op})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{t}}, {\rm{cons}}\,({\bf{f}}, {\sc{alu-inc-op}}\index{alu-inc-op})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_fetch0\$destructure; name this event `cv\_fetch0\$destructure-off'.\index{cv\_fetch0\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_FETCH1
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS T
    (CONS F
     (CONS F
      (CONS F
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_FETCH1)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND PC-REG
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_fetch1; name this event `cv\_fetch1-off'.\index{cv\_fetch1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_fetch1\$destructure \\ \index{cv\_fetch1\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{we-regs} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_fetch1}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch1})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_fetch1}}\index{v\_fetch1})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{regs-address} \\ 
$=$$\;\;\;\;${\it{pc-reg\/}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_fetch1\$destructure; name this event `cv\_fetch1\$destructure-off'.\index{cv\_fetch1\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_FETCH2
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS F
   (CONS T
    (CONS T
     (CONS F
      (CONS F
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (ALU-INC-OP))))
                (CONS F
                 (APPEND
                  (V_FETCH2)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND PC-REG
                           (APPEND (ALU-INC-OP)
                                   (APPEND (MPG (CONS F (CONS F (ALU-INC-OP))))
                                           NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_fetch2; name this event `cv\_fetch2-off'.\index{cv\_fetch2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_fetch2\$destructure \\ \index{cv\_fetch2\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2})\index{we-regs} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_fetch2}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch2})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\rm{cons}}\,({\bf{f}}, {\sc{alu-inc-op}}\index{alu-inc-op})))\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_fetch2}}\index{v\_fetch2})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2})\index{regs-address} \\ 
$=$$\;\;\;\;${\it{pc-reg\/}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2})\index{alu-op} \\ 
$=$$\;\;\;\;${\sc{alu-inc-op}}\index{alu-inc-op})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\sc{alu-inc-op}}\index{alu-inc-op})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_fetch2\$destructure; name this event `cv\_fetch2\$destructure-off'.\index{cv\_fetch2\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_FETCH3
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS F
   (CONS T
    (CONS F
     (CONS F
      (CONS F
       (CONS T
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS T
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_FETCH3)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND PC-REG
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_fetch3; name this event `cv\_fetch3-off'.\index{cv\_fetch3-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_fetch3\$destructure \\ \index{cv\_fetch3\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\index{we-regs} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_fetch3}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch3})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_fetch3}}\index{v\_fetch3})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\index{regs-address} \\ 
$=$$\;\;\;\;${\it{pc-reg\/}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_fetch3\$destructure; name this event `cv\_fetch3\$destructure-off'.\index{cv\_fetch3\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_DECODE
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS T
    (CONS F
     (CONS F
      (CONS F
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_DECODE)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND PC-REG
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_decode; name this event `cv\_decode-off'.\index{cv\_decode-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_decode\$destructure \\ \index{cv\_decode\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\index{we-regs} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_decode}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_decode})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_decode}}\index{v\_decode})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\index{regs-address} \\ 
$=$$\;\;\;\;${\it{pc-reg\/}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_decode\$destructure; name this event `cv\_decode\$destructure-off'.\index{cv\_decode\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_REGA
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS T
    (CONS F
     (CONS T
      (CONS F
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS
               (A-IMMEDIATE-P I-REG)
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_REGA)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND
                        (RN-A I-REG)
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_rega; name this event `cv\_rega-off'.\index{cv\_rega-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_rega\$destructure \\ \index{cv\_rega\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{strobe-}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{strobe-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{we-regs}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{we-regs} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$({\rm{we-a-reg}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{we-a-reg} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{we-b-reg}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{we-b-reg} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$({\rm{we-i-reg}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{we-i-reg} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{we-hold-}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{we-hold-} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{select-immediate} \\ 
$=$$\;\;\;\;${\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$({\rm{alu-zero}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{alu-zero} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_rega}}\index{v\_rega})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{regs-address} \\ 
$=$$\;\;\;\;${\rm{rn-a}}\,({\it{i-reg\/}})\index{rn-a})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_rega\$destructure; name this event `cv\_rega\$destructure-off'.\index{cv\_rega\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_REGB
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS T
    (CONS F
     (CONS F
      (CONS T
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_REGB)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND
                        (RN-B I-REG)
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_regb; name this event `cv\_regb-off'.\index{cv\_regb-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_regb\$destructure \\ \index{cv\_regb\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{strobe-}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{strobe-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{we-regs}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{we-regs} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$({\rm{we-a-reg}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{we-a-reg} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$({\rm{we-b-reg}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{we-b-reg} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{we-i-reg}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{we-i-reg} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{we-hold-}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{we-hold-} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$({\rm{alu-zero}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{alu-zero} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_regb}}\index{v\_regb})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{regs-address} \\ 
$=$$\;\;\;\;${\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_regb\$destructure; name this event `cv\_regb\$destructure-off'.\index{cv\_regb\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_UPDATE
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS T
    (CONS
     (STORE-RESULTP (STORE-CC I-REG) FLAGS)
     (CONS F
      (CONS T
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_UPDATE)
                  (APPEND
                   (SET-FLAGS I-REG)
                   (APPEND
                        (RN-B I-REG)
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_update; name this event `cv\_update-off'.\index{cv\_update-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_update\$destructure \\ \index{cv\_update\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\index{we-regs} \\ 
$=$$\;\;\;\;${\rm{store-resultp}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, {\it{flags\/}})\index{store-resultp})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_update}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_update})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_update}}\index{v\_update})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{set-flags}}\,({\it{i-reg\/}})\index{set-flags})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\index{regs-address} \\ 
$=$$\;\;\;\;${\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_update\$destructure; name this event `cv\_update\$destructure-off'.\index{cv\_update\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_READA0
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS T
    (CONS F
     (CONS T
      (CONS F
       (CONS F
        (CONS F
         (CONS T
          (CONS F
           (CONS F
            (CONS F
             (CONS
              (PRE-DEC-P (MODE-A I-REG))
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_READA0)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND
                        (RN-A I-REG)
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_reada0; name this event `cv\_reada0-off'.\index{cv\_reada0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_reada0\$destructure \\ \index{cv\_reada0\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\index{we-regs} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_reada0}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_reada0})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_reada0}}\index{v\_reada0})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\index{regs-address} \\ 
$=$$\;\;\;\;${\rm{rn-a}}\,({\it{i-reg\/}})\index{rn-a})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_reada0\$destructure; name this event `cv\_reada0\$destructure-off'.\index{cv\_reada0\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_READA1
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS T
    (CONS
     (AND* (NOT* (A-IMMEDIATE-P I-REG))
           (OR* (PRE-DEC-P (MODE-A I-REG))
                (POST-INC-P (MODE-A I-REG))))
     (CONS F
      (CONS F
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (IF* (PRE-DEC-P (MODE-A I-REG))
                     (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                          (CONS F (ALU-DEC-OP))))
                     (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                          (CONS F (ALU-INC-OP)))))
                (CONS F
                 (APPEND
                  (V_READA1)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND
                     (RN-A I-REG)
                     (APPEND (IF* (PRE-DEC-P (MODE-A I-REG))
                                  (ALU-DEC-OP)
                                  (ALU-INC-OP))
                             (APPEND (IF* (PRE-DEC-P (MODE-A I-REG))
                                          (MPG (CONS F (CONS F (ALU-DEC-OP))))
                                          (MPG (CONS F (CONS F (ALU-INC-OP)))))
                                     NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_reada1; name this event `cv\_reada1-off'.\index{cv\_reada1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_reada1\$destructure \\ \index{cv\_reada1\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\index{we-regs} \\ 
$=$$\;\;\;\;${\rm{and*}}\,(\=\+{\rm{not*}}\,({\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p})\index{not*}, \\ 
{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{post-inc-p})\-\index{or*})\-\index{and*})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_reada1}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_reada1})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\sc{alu-dec-op}}\index{alu-dec-op}))\-)\index{carry-in-help}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\sc{alu-inc-op}}\index{alu-inc-op}))\-)\index{carry-in-help})\-\index{if*})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_reada1}}\index{v\_reada1})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\index{regs-address} \\ 
$=$$\;\;\;\;${\rm{rn-a}}\,({\it{i-reg\/}})\index{rn-a})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{if*}}\,({\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, {\sc{alu-dec-op}}\index{alu-dec-op}, {\sc{alu-inc-op}}\index{alu-inc-op})\index{if*})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\sc{alu-dec-op}}\index{alu-dec-op})))\index{mpg}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\sc{alu-inc-op}}\index{alu-inc-op})))\index{mpg})\-\index{if*})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_reada1\$destructure; name this event `cv\_reada1\$destructure-off'.\index{cv\_reada1\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_READA2
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS F
   (CONS T
    (CONS F
     (CONS F
      (CONS T
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_READA2)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND
                        (RN-B I-REG)
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_reada2; name this event `cv\_reada2-off'.\index{cv\_reada2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_reada2\$destructure \\ \index{cv\_reada2\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\index{we-regs} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_reada2}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_reada2})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_reada2}}\index{v\_reada2})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\index{regs-address} \\ 
$=$$\;\;\;\;${\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_reada2\$destructure; name this event `cv\_reada2\$destructure-off'.\index{cv\_reada2\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_READA3
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS F
   (CONS T
    (CONS F
     (CONS T
      (CONS F
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS T
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_READA3)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND PC-REG
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_reada3; name this event `cv\_reada3-off'.\index{cv\_reada3-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_reada3\$destructure \\ \index{cv\_reada3\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\index{we-regs} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_reada3}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_reada3})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_reada3}}\index{v\_reada3})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\index{regs-address} \\ 
$=$$\;\;\;\;${\it{pc-reg\/}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_reada3\$destructure; name this event `cv\_reada3\$destructure-off'.\index{cv\_reada3\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_READB0
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS T
    (CONS F
     (CONS F
      (CONS T
       (CONS F
        (CONS F
         (CONS T
          (CONS F
           (CONS F
            (CONS F
             (CONS
              (PRE-DEC-P (MODE-B I-REG))
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_READB0)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND
                        (RN-B I-REG)
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_readb0; name this event `cv\_readb0-off'.\index{cv\_readb0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_readb0\$destructure \\ \index{cv\_readb0\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\index{we-regs} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_readb0}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_readb0})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_readb0}}\index{v\_readb0})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\index{regs-address} \\ 
$=$$\;\;\;\;${\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_readb0\$destructure; name this event `cv\_readb0\$destructure-off'.\index{cv\_readb0\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_READB1
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS T
    (CONS F
     (CONS
      (OR* (A-IMMEDIATE-P I-REG)
           (REG-DIRECT-P (MODE-A I-REG)))
      (CONS F
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS
               (A-IMMEDIATE-P I-REG)
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_READB1)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND
                        (RN-A I-REG)
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_readb1; name this event `cv\_readb1-off'.\index{cv\_readb1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_readb1\$destructure \\ \index{cv\_readb1\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\index{we-regs} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\rm{or*}}\,({\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p}, {\rm{reg-direct-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{reg-direct-p})\index{or*})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_readb1}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_readb1})\index{select-immediate} \\ 
$=$$\;\;\;\;${\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_readb1}}\index{v\_readb1})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\index{regs-address} \\ 
$=$$\;\;\;\;${\rm{rn-a}}\,({\it{i-reg\/}})\index{rn-a})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_readb1\$destructure; name this event `cv\_readb1\$destructure-off'.\index{cv\_readb1\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_READB2
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS F
   (CONS T
    (CONS
     (AND* (NOT* (STORE-RESULTP (STORE-CC I-REG)
                                FLAGS))
           (OR* (PRE-DEC-P (MODE-B I-REG))
                (POST-INC-P (MODE-B I-REG))))
     (CONS F
      (CONS F
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (IF* (PRE-DEC-P (MODE-B I-REG))
                     (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                          (CONS F (ALU-DEC-OP))))
                     (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                          (CONS F (ALU-INC-OP)))))
                (CONS F
                 (APPEND
                  (V_READB2)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND
                     (RN-B I-REG)
                     (APPEND (IF* (PRE-DEC-P (MODE-B I-REG))
                                  (ALU-DEC-OP)
                                  (ALU-INC-OP))
                             (APPEND (IF* (PRE-DEC-P (MODE-B I-REG))
                                          (MPG (CONS F (CONS T (ALU-DEC-OP))))
                                          (MPG (CONS F (CONS T (ALU-INC-OP)))))
                                     NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_readb2; name this event `cv\_readb2-off'.\index{cv\_readb2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_readb2\$destructure \\ \index{cv\_readb2\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\index{we-regs} \\ 
$=$$\;\;\;\;${\rm{and*}}\,(\=\+{\rm{not*}}\,({\rm{store-resultp}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, {\it{flags\/}})\index{store-resultp})\index{not*}, \\ 
{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{post-inc-p})\-\index{or*})\-\index{and*})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_readb2}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_readb2})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\sc{alu-dec-op}}\index{alu-dec-op}))\-)\index{carry-in-help}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\sc{alu-inc-op}}\index{alu-inc-op}))\-)\index{carry-in-help})\-\index{if*})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_readb2}}\index{v\_readb2})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\index{regs-address} \\ 
$=$$\;\;\;\;${\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{if*}}\,({\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, {\sc{alu-dec-op}}\index{alu-dec-op}, {\sc{alu-inc-op}}\index{alu-inc-op})\index{if*})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{t}}, {\sc{alu-dec-op}}\index{alu-dec-op})))\index{mpg}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{t}}, {\sc{alu-inc-op}}\index{alu-inc-op})))\index{mpg})\-\index{if*})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_readb2\$destructure; name this event `cv\_readb2\$destructure-off'.\index{cv\_readb2\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_READB3
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS F
   (CONS T
    (CONS F
     (CONS F
      (CONS T
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS T
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_READB3)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND PC-REG
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_readb3; name this event `cv\_readb3-off'.\index{cv\_readb3-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_readb3\$destructure \\ \index{cv\_readb3\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\index{we-regs} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_readb3}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_readb3})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_readb3}}\index{v\_readb3})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\index{regs-address} \\ 
$=$$\;\;\;\;${\it{pc-reg\/}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_readb3\$destructure; name this event `cv\_readb3\$destructure-off'.\index{cv\_readb3\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_WRITE0
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS T
    (CONS F
     (CONS F
      (CONS T
       (CONS F
        (CONS T
         (CONS T
          (CONS F
           (CONS F
            (CONS F
             (CONS
              (PRE-DEC-P (MODE-B I-REG))
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_WRITE0)
                  (APPEND
                   (SET-FLAGS I-REG)
                   (APPEND
                        (RN-B I-REG)
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_write0; name this event `cv\_write0-off'.\index{cv\_write0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_write0\$destructure \\ \index{cv\_write0\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0})\index{we-regs} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_write0}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_write0})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_write0}}\index{v\_write0})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{set-flags}}\,({\it{i-reg\/}})\index{set-flags})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0})\index{regs-address} \\ 
$=$$\;\;\;\;${\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_write0\$destructure; name this event `cv\_write0\$destructure-off'.\index{cv\_write0\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_WRITE1
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS F
  (CONS T
   (CONS T
    (CONS
     (OR* (PRE-DEC-P (MODE-B I-REG))
          (POST-INC-P (MODE-B I-REG)))
     (CONS F
      (CONS F
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (IF* (PRE-DEC-P (MODE-B I-REG))
                     (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                          (CONS F (ALU-DEC-OP))))
                     (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                          (CONS F (ALU-INC-OP)))))
                (CONS F
                 (APPEND
                  (V_WRITE1)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND
                     (RN-B I-REG)
                     (APPEND (IF* (PRE-DEC-P (MODE-B I-REG))
                                  (ALU-DEC-OP)
                                  (ALU-INC-OP))
                             (APPEND (IF* (PRE-DEC-P (MODE-B I-REG))
                                          (MPG (CONS F (CONS T (ALU-DEC-OP))))
                                          (MPG (CONS F (CONS T (ALU-INC-OP)))))
                                     NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_write1; name this event `cv\_write1-off'.\index{cv\_write1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_write1\$destructure \\ \index{cv\_write1\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\index{rw-} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\index{we-regs} \\ 
$=$$\;\;\;\;${\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{post-inc-p})\-\index{or*})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_write1}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_write1})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\sc{alu-dec-op}}\index{alu-dec-op}))\-)\index{carry-in-help}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\sc{alu-inc-op}}\index{alu-inc-op}))\-)\index{carry-in-help})\-\index{if*})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_write1}}\index{v\_write1})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\index{regs-address} \\ 
$=$$\;\;\;\;${\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{if*}}\,({\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, {\sc{alu-dec-op}}\index{alu-dec-op}, {\sc{alu-inc-op}}\index{alu-inc-op})\index{if*})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{t}}, {\sc{alu-dec-op}}\index{alu-dec-op})))\index{mpg}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{t}}, {\sc{alu-inc-op}}\index{alu-inc-op})))\index{mpg})\-\index{if*})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_write1\$destructure; name this event `cv\_write1\$destructure-off'.\index{cv\_write1\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_WRITE2
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS F
  (CONS F
   (CONS T
    (CONS F
     (CONS F
      (CONS F
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_WRITE2)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND PC-REG
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_write2; name this event `cv\_write2-off'.\index{cv\_write2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_write2\$destructure \\ \index{cv\_write2\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\index{rw-} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\index{we-regs} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_write2}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_write2})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_write2}}\index{v\_write2})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\index{regs-address} \\ 
$=$$\;\;\;\;${\it{pc-reg\/}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_write2\$destructure; name this event `cv\_write2\$destructure-off'.\index{cv\_write2\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_WRITE3
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS F
  (CONS F
   (CONS T
    (CONS F
     (CONS F
      (CONS F
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_WRITE3)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND PC-REG
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_write3; name this event `cv\_write3-off'.\index{cv\_write3-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_write3\$destructure \\ \index{cv\_write3\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\index{rw-} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\index{we-regs} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_write3}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_write3})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_write3}}\index{v\_write3})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\index{regs-address} \\ 
$=$$\;\;\;\;${\it{pc-reg\/}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_write3\$destructure; name this event `cv\_write3\$destructure-off'.\index{cv\_write3\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_SEFA0
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS T
    (CONS F
     (CONS T
      (CONS F
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_SEFA0)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND
                        (RN-A I-REG)
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_sefa0; name this event `cv\_sefa0-off'.\index{cv\_sefa0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_sefa0\$destructure \\ \index{cv\_sefa0\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{strobe-}}\,({\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0})\index{strobe-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{we-regs}}\,({\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0})\index{we-regs} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_sefa0}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_sefa0})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_sefa0}}\index{v\_sefa0})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0})\index{regs-address} \\ 
$=$$\;\;\;\;${\rm{rn-a}}\,({\it{i-reg\/}})\index{rn-a})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_sefa0\$destructure; name this event `cv\_sefa0\$destructure-off'.\index{cv\_sefa0\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_SEFA1
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS T
    (CONS T
     (CONS F
      (CONS F
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (IF* (PRE-DEC-P (MODE-A I-REG))
                     (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                          (CONS F (ALU-DEC-OP))))
                     (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                          (CONS F (ALU-INC-OP)))))
                (CONS F
                 (APPEND
                  (V_SEFA1)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND
                     (RN-A I-REG)
                     (APPEND (IF* (PRE-DEC-P (MODE-A I-REG))
                                  (ALU-DEC-OP)
                                  (ALU-INC-OP))
                             (APPEND (IF* (PRE-DEC-P (MODE-A I-REG))
                                          (MPG (CONS F (CONS F (ALU-DEC-OP))))
                                          (MPG (CONS F (CONS F (ALU-INC-OP)))))
                                     NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_sefa1; name this event `cv\_sefa1-off'.\index{cv\_sefa1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_sefa1\$destructure \\ \index{cv\_sefa1\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{strobe-}}\,({\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\index{strobe-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{we-regs}}\,({\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\index{we-regs} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_sefa1}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_sefa1})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\sc{alu-dec-op}}\index{alu-dec-op}))\-)\index{carry-in-help}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\sc{alu-inc-op}}\index{alu-inc-op}))\-)\index{carry-in-help})\-\index{if*})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_sefa1}}\index{v\_sefa1})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\index{regs-address} \\ 
$=$$\;\;\;\;${\rm{rn-a}}\,({\it{i-reg\/}})\index{rn-a})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{if*}}\,({\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, {\sc{alu-dec-op}}\index{alu-dec-op}, {\sc{alu-inc-op}}\index{alu-inc-op})\index{if*})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\sc{alu-dec-op}}\index{alu-dec-op})))\index{mpg}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\sc{alu-inc-op}}\index{alu-inc-op})))\index{mpg})\-\index{if*})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_sefa1\$destructure; name this event `cv\_sefa1\$destructure-off'.\index{cv\_sefa1\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_SEFB0
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS T
    (CONS F
     (CONS F
      (CONS T
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_SEFB0)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND
                        (RN-B I-REG)
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_sefb0; name this event `cv\_sefb0-off'.\index{cv\_sefb0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_sefb0\$destructure \\ \index{cv\_sefb0\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{strobe-}}\,({\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0})\index{strobe-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{we-regs}}\,({\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0})\index{we-regs} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_sefb0}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_sefb0})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_sefb0}}\index{v\_sefb0})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0})\index{regs-address} \\ 
$=$$\;\;\;\;${\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_sefb0\$destructure; name this event `cv\_sefb0\$destructure-off'.\index{cv\_sefb0\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_SEFB1
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS T
    (CONS T
     (CONS F
      (CONS F
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (IF* (PRE-DEC-P (MODE-B I-REG))
                     (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                          (CONS F (ALU-DEC-OP))))
                     (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                          (CONS F (ALU-INC-OP)))))
                (CONS F
                 (APPEND
                  (V_SEFB1)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND
                     (RN-B I-REG)
                     (APPEND (IF* (PRE-DEC-P (MODE-B I-REG))
                                  (ALU-DEC-OP)
                                  (ALU-INC-OP))
                             (APPEND (IF* (PRE-DEC-P (MODE-B I-REG))
                                          (MPG (CONS F (CONS T (ALU-DEC-OP))))
                                          (MPG (CONS F (CONS T (ALU-INC-OP)))))
                                     NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_sefb1; name this event `cv\_sefb1-off'.\index{cv\_sefb1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_sefb1\$destructure \\ \index{cv\_sefb1\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{strobe-}}\,({\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\index{strobe-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{we-regs}}\,({\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\index{we-regs} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_sefb1}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_sefb1})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\sc{alu-dec-op}}\index{alu-dec-op}))\-)\index{carry-in-help}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\sc{alu-inc-op}}\index{alu-inc-op}))\-)\index{carry-in-help})\-\index{if*})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_sefb1}}\index{v\_sefb1})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\index{regs-address} \\ 
$=$$\;\;\;\;${\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{if*}}\,({\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, {\sc{alu-dec-op}}\index{alu-dec-op}, {\sc{alu-inc-op}}\index{alu-inc-op})\index{if*})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{t}}, {\sc{alu-dec-op}}\index{alu-dec-op})))\index{mpg}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{t}}, {\sc{alu-inc-op}}\index{alu-inc-op})))\index{mpg})\-\index{if*})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_sefb1\$destructure; name this event `cv\_sefb1\$destructure-off'.\index{cv\_sefb1\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_HOLD0
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS F
    (CONS F
     (CONS F
      (CONS F
       (CONS F
        (CONS F
         (CONS F
          (CONS T
           (CONS T
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_HOLD0)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND PC-REG
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_hold0; name this event `cv\_hold0-off'.\index{cv\_hold0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_hold0\$destructure \\ \index{cv\_hold0\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{strobe-}}\,({\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\index{strobe-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\index{hdack-} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$({\rm{we-regs}}\,({\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\index{we-regs} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_hold0}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_hold0})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_hold0}}\index{v\_hold0})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\index{regs-address} \\ 
$=$$\;\;\;\;${\it{pc-reg\/}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_hold0\$destructure; name this event `cv\_hold0\$destructure-off'.\index{cv\_hold0\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_HOLD1
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS T
    (CONS F
     (CONS F
      (CONS F
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_HOLD1)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND PC-REG
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_hold1; name this event `cv\_hold1-off'.\index{cv\_hold1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_hold1\$destructure \\ \index{cv\_hold1\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{strobe-}}\,({\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1})\index{strobe-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{we-regs}}\,({\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1})\index{we-regs} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_hold1}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_hold1})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_hold1}}\index{v\_hold1})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1})\index{regs-address} \\ 
$=$$\;\;\;\;${\it{pc-reg\/}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_hold1\$destructure; name this event `cv\_hold1\$destructure-off'.\index{cv\_hold1\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_V11010
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS T
    (CONS F
     (CONS F
      (CONS F
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_V11010)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND PC-REG
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_v11010; name this event `cv\_v11010-off'.\index{cv\_v11010-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_v11010\$destructure \\ \index{cv\_v11010\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_v11010}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11010})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_v11010}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11010})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_v11010}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11010})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_v11010}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11010})\index{we-regs} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_v11010}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11010})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_v11010}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11010})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_v11010}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11010})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_v11010}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11010})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_v11010}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11010})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_v11010}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11010})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_v11010}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11010})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_v11010}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11010})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_v11010}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11010})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_v11010}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_v11010})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_v11010}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11010})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_v11010}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11010})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_v11010}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11010})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_v11010}}\index{v\_v11010})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_v11010}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11010})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_v11010}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11010})\index{regs-address} \\ 
$=$$\;\;\;\;${\it{pc-reg\/}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_v11010}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11010})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_v11010}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11010})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_v11010\$destructure; name this event `cv\_v11010\$destructure-off'.\index{cv\_v11010\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_V11011
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS T
    (CONS F
     (CONS F
      (CONS F
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_V11011)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND PC-REG
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_v11011; name this event `cv\_v11011-off'.\index{cv\_v11011-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_v11011\$destructure \\ \index{cv\_v11011\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_v11011}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11011})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_v11011}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11011})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_v11011}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11011})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_v11011}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11011})\index{we-regs} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_v11011}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11011})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_v11011}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11011})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_v11011}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11011})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_v11011}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11011})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_v11011}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11011})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_v11011}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11011})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_v11011}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11011})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_v11011}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11011})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_v11011}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11011})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_v11011}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_v11011})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_v11011}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11011})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_v11011}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11011})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_v11011}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11011})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_v11011}}\index{v\_v11011})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_v11011}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11011})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_v11011}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11011})\index{regs-address} \\ 
$=$$\;\;\;\;${\it{pc-reg\/}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_v11011}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11011})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_v11011}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11011})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_v11011\$destructure; name this event `cv\_v11011\$destructure-off'.\index{cv\_v11011\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_RESET0
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS T
    (CONS T
     (CONS F
      (CONS F
       (CONS F
        (CONS T
         (CONS F
          (CONS T
           (CONS T
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS T (ALU-INC-OP))))
                (CONS T
                 (APPEND
                  (V_RESET0)
                  (APPEND
                   (MAKE-LIST 4 T)
                   (APPEND (MAKE-LIST 4 F)
                           (APPEND (ALU-INC-OP)
                                   (APPEND (MPG (CONS T (CONS F (ALU-INC-OP))))
                                           NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_reset0; name this event `cv\_reset0-off'.\index{cv\_reset0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_reset0\$destructure \\ \index{cv\_reset0\$destructure}
{\bf{t}} $\rightarrow$ (\=\+({\rm{rw-}}\,({\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{strobe-}}\,({\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\index{strobe-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{we-regs}}\,({\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\index{we-regs} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_reset0}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_reset0})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\rm{cons}}\,({\bf{t}}, {\sc{alu-inc-op}}\index{alu-inc-op})))\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_reset0}}\index{v\_reset0})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\index{regs-address} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\index{alu-op} \\ 
$=$$\;\;\;\;${\sc{alu-inc-op}}\index{alu-inc-op})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{t}}, {\rm{cons}}\,({\bf{f}}, {\sc{alu-inc-op}}\index{alu-inc-op})))\index{mpg})\-)\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_reset0\$destructure; name this event `cv\_reset0\$destructure-off'.\index{cv\_reset0\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_RESET1
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS T
    (CONS F
     (CONS T
      (CONS T
       (CONS T
        (CONS F
         (CONS T
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS T (ALU-INC-OP))))
                (CONS T
                 (APPEND
                  (V_RESET1)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND (MAKE-LIST 4 F)
                           (APPEND (ALU-INC-OP)
                                   (APPEND (MPG (CONS T (CONS F (ALU-INC-OP))))
                                           NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_reset1; name this event `cv\_reset1-off'.\index{cv\_reset1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_reset1\$destructure \\ \index{cv\_reset1\$destructure}
{\bf{t}} $\rightarrow$ (\=\+({\rm{rw-}}\,({\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{strobe-}}\,({\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\index{strobe-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{we-regs}}\,({\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\index{we-regs} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_reset1}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_reset1})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\rm{cons}}\,({\bf{t}}, {\sc{alu-inc-op}}\index{alu-inc-op})))\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_reset1}}\index{v\_reset1})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\index{regs-address} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\index{alu-op} \\ 
$=$$\;\;\;\;${\sc{alu-inc-op}}\index{alu-inc-op})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{t}}, {\rm{cons}}\,({\bf{f}}, {\sc{alu-inc-op}}\index{alu-inc-op})))\index{mpg})\-)\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_reset1\$destructure; name this event `cv\_reset1\$destructure-off'.\index{cv\_reset1\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_RESET2
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS T
    (CONS T
     (CONS F
      (CONS F
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS T (ALU-INC-OP))))
                (CONS T
                 (APPEND
                  (V_RESET2)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND (V-INC REGS-ADDRESS)
                           (APPEND (ALU-INC-OP)
                                   (APPEND (MPG (CONS T (CONS F (ALU-INC-OP))))
                                           NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_reset2; name this event `cv\_reset2-off'.\index{cv\_reset2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_reset2\$destructure \\ \index{cv\_reset2\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\index{we-regs} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_reset2}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_reset2})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\rm{cons}}\,({\bf{t}}, {\sc{alu-inc-op}}\index{alu-inc-op})))\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_reset2}}\index{v\_reset2})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\index{regs-address} \\ 
$=$$\;\;\;\;${\rm{v-inc}}\,({\it{regs-address\/}})\index{v-inc})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\index{alu-op} \\ 
$=$$\;\;\;\;${\sc{alu-inc-op}}\index{alu-inc-op})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{t}}, {\rm{cons}}\,({\bf{f}}, {\sc{alu-inc-op}}\index{alu-inc-op})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_reset2\$destructure; name this event `cv\_reset2\$destructure-off'.\index{cv\_reset2\$destructure-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV_V11111
 (RW- REGS-ADDRESS I-REG FLAGS PC-REG)
 (CONS T
  (CONS T
   (CONS T
    (CONS F
     (CONS F
      (CONS F
       (CONS F
        (CONS F
         (CONS F
          (CONS F
           (CONS F
            (CONS F
             (CONS F
              (CONS F
               (CONS
                (CARRY-IN-HELP (CONS (C-FLAG FLAGS)
                                     (CONS F (OP-CODE I-REG))))
                (CONS F
                 (APPEND
                  (V_V11111)
                  (APPEND
                   (MAKE-LIST 4 F)
                   (APPEND PC-REG
                        (APPEND (OP-CODE I-REG)
                                (APPEND (MPG (CONS F (CONS F (OP-CODE I-REG))))
                                        NIL))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv\_v11111; name this event `cv\_v11111-off'.\index{cv\_v11111-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_v11111\$destructure \\ \index{cv\_v11111\$destructure}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{rw-}}\,({\rm{cv\_v11111}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11111})\index{rw-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{strobe-}}\,({\rm{cv\_v11111}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11111})\index{strobe-} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$({\rm{hdack-}}\,({\rm{cv\_v11111}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11111})\index{hdack-} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-regs}}\,({\rm{cv\_v11111}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11111})\index{we-regs} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-a-reg}}\,({\rm{cv\_v11111}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11111})\index{we-a-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-b-reg}}\,({\rm{cv\_v11111}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11111})\index{we-b-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-i-reg}}\,({\rm{cv\_v11111}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11111})\index{we-i-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-data-out}}\,({\rm{cv\_v11111}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11111})\index{we-data-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-addr-out}}\,({\rm{cv\_v11111}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11111})\index{we-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-hold-}}\,({\rm{cv\_v11111}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11111})\index{we-hold-} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-pc-reg}}\,({\rm{cv\_v11111}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11111})\index{we-pc-reg} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{data-in-select}}\,({\rm{cv\_v11111}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11111})\index{data-in-select} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{dec-addr-out}}\,({\rm{cv\_v11111}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11111})\index{dec-addr-out} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{select-immediate}}\,({\rm{cv\_v11111}}\,(\=\+{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_v11111})\index{select-immediate} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-c}}\,({\rm{cv\_v11111}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11111})\index{alu-c} \\ 
$=$$\;\;\;\;${\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}))\-)\index{carry-in-help})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-zero}}\,({\rm{cv\_v11111}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11111})\index{alu-zero} \\ 
$=$$\;\;\;\;${\bf{f}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{state}}\,({\rm{cv\_v11111}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11111})\index{state} \\ 
$=$$\;\;\;\;${\sc{v\_v11111}}\index{v\_v11111})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{we-flags}}\,({\rm{cv\_v11111}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11111})\index{we-flags} \\ 
$=$$\;\;\;\;${\rm{make-list}}\,({\tt{4}}, {\bf{f}})\index{make-list})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{regs-address}}\,({\rm{cv\_v11111}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11111})\index{regs-address} \\ 
$=$$\;\;\;\;${\it{pc-reg\/}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-op}}\,({\rm{cv\_v11111}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11111})\index{alu-op} \\ 
$=$$\;\;\;\;${\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{alu-mpg}}\,({\rm{cv\_v11111}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11111})\index{alu-mpg} \\ 
$=$$\;\;\;\;${\rm{mpg}}\,({\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})))\index{mpg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\_v11111\$destructure; name this event `cv\_v11111\$destructure-off'.\index{cv\_v11111\$destructure-off}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{cv-theory}} to consist of the following events: cv\_fetch0,
cv\_fetch1,
cv\_fetch2,
cv\_fetch3,
cv\_decode,
cv\_rega,
cv\_regb,
cv\_update,
cv\_reada0,
cv\_reada1,
cv\_reada2,
cv\_reada3,
cv\_readb0,
cv\_readb1,
cv\_readb2,
cv\_readb3,
cv\_write0,
cv\_write1,
cv\_write2,
cv\_write3,
cv\_sefa0,
cv\_sefa1,
cv\_sefb0,
cv\_sefb1,
cv\_hold0,
cv\_hold1,
cv\_v11010,
cv\_v11011,
cv\_reset0,
cv\_reset1,
cv\_reset2,
cv\_v11111.\index{cv-theory}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{cv-destructure-theory}} to consist of the following events: cv\_fetch0\$destructure,
cv\_fetch1\$destructure,
cv\_fetch2\$destructure,
cv\_fetch3\$destructure,
cv\_decode\$destructure,
cv\_rega\$destructure,
cv\_regb\$destructure,
cv\_update\$destructure,
cv\_reada0\$destructure,
cv\_reada1\$destructure,
cv\_reada2\$destructure,
cv\_reada3\$destructure,
cv\_readb0\$destructure,
cv\_readb1\$destructure,
cv\_readb2\$destructure,
cv\_readb3\$destructure,
cv\_write0\$destructure,
cv\_write1\$destructure,
cv\_write2\$destructure,
cv\_write3\$destructure,
cv\_sefa0\$destructure,
cv\_sefa1\$destructure,
cv\_sefb0\$destructure,
cv\_sefb1\$destructure,
cv\_hold0\$destructure,
cv\_hold1\$destructure,
cv\_v11010\$destructure,
cv\_v11011\$destructure,
cv\_reset0\$destructure,
cv\_reset1\$destructure,
cv\_reset2\$destructure,
cv\_v11111\$destructure.\index{cv-destructure-theory}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  bvp-cv-vectors \\ \index{bvp-cv-vectors}
\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{bvp}}\,({\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_v11010}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11010})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_v11011}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11011})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cv\_v11111}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_v11111})\index{bvp})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable bvp-cv-vectors; name this event `bvp-cv-vectors-off'.\index{bvp-cv-vectors-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cv\_fetch1\$rw-doan-matta \\ \index{cv\_fetch1\$rw-doan-matta}
\=\+{\rm{cv\_fetch1}}\,({\bf{f}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1} \\ 
$=$$\;\;\;\;${\rm{cv\_fetch1}}\,({\bf{t}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-length-cv\_fetch1 \\ \index{properp-length-cv\_fetch1}
\=\+(\=\+{\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\rightarrow$$\;\;\;\;$({\rm{length}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{length} $=$ {\tt{40}}))\- \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\index{properp}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$control-let} \\  
\=\+{\rm{f\$control-let}}\,({\it{i-reg\/}}, {\it{flags\/}}, {\it{regs-address\/}})\index{f\$control-let} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{id}}\,({\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p})\index{id}, \\ 
{\rm{f\$b-store-resultp}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, {\it{flags\/}})\index{f\$b-store-resultp}, \\ 
{\rm{f\$set-some-flags}}\,({\rm{set-flags}}\,({\it{i-reg\/}})\index{set-flags})\index{f\$set-some-flags}, \\ 
{\rm{f-or}}\,(\=\+{\rm{id}}\,({\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p})\index{id}, \\ 
{\rm{car}}\,({\rm{f\$decode-reg-mode}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{f\$decode-reg-mode}))\-\index{f-or}, \\ 
{\rm{car}}\,({\rm{f\$decode-reg-mode}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{f\$decode-reg-mode}), \\ 
{\rm{f\$unary-op-code-p}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{f\$unary-op-code-p}, \\ 
{\rm{cadr}}\,({\rm{f\$decode-reg-mode}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{f\$decode-reg-mode}), \\ 
{\rm{cadr}}\,({\rm{f\$decode-reg-mode}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{f\$decode-reg-mode}), \\ 
{\rm{id}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{id}, \\ 
{\rm{f\$all-t-regs-address}}\,({\it{regs-address\/}})\index{f\$all-t-regs-address}, \\ 
{\rm{f-and}}\,(\=\+{\rm{f-not}}\,({\rm{id}}\,({\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p})\index{id})\index{f-not}, \\ 
{\rm{caddr}}\,({\rm{f\$decode-reg-mode}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{f\$decode-reg-mode}))\-\index{f-and}, \\ 
{\rm{caddr}}\,({\rm{f\$decode-reg-mode}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{f\$decode-reg-mode}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$control-let; name this event `f\$control-let-off'.\index{f\$control-let-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CONTROL-LET* NIL
 (CONS 'CONTROL-LET
  (CONS
   (APPEND (INDICES 'I-REG 0 32)
           (APPEND (INDICES 'FLAGS 0 4)
                   (INDICES 'REGS-ADDRESS 0 4)))
   (CONS
    '(A-IMMEDIATE-P STORE SET-SOME-FLAGS DIRECT-A DIRECT-B UNARY PRE-DEC-A
                    PRE-DEC-B C ALL-T-REGS-ADDRESS SIDE-EFFECT-A SIDE-EFFECT-B)
    (CONS
     (CONS
      (LIST 'G0
            '(A-IMMEDIATE-P)
            'ID
            (LIST (A-IMMEDIATE-P (INDICES 'I-REG 0 32))))
      (CONS
       '(G1 (A-IMMEDIATE-P-)
            B-NOT
            (A-IMMEDIATE-P))
       (CONS
        (LIST 'G2
              '(STORE)
              'B-STORE-RESULTP
              (APPEND (STORE-CC (INDICES 'I-REG 0 32))
                      (INDICES 'FLAGS 0 4)))
        (CONS
         (LIST 'G3
               '(SET-SOME-FLAGS)
               'B-OR4
               (SET-FLAGS (INDICES 'I-REG 0 32)))
         (CONS
          (LIST 'G4
                '(ALMOST-DIRECT-A PRE-DEC-A ALMOST-SIDE-EFFECT-A)
                'DECODE-REG-MODE
                (MODE-A (INDICES 'I-REG 0 32)))
          (CONS
             (LIST 'G5
                   '(DIRECT-B PRE-DEC-B SIDE-EFFECT-B)
                   'DECODE-REG-MODE
                   (MODE-B (INDICES 'I-REG 0 32)))
             (CONS (LIST 'G6
                         '(UNARY)
                         'UNARY-OP-CODE-P
                         (OP-CODE (INDICES 'I-REG 0 32)))
                   (CONS (LIST 'G7
                               '(C)
                               'ID
                               (LIST (C-FLAG (INDICES 'FLAGS 0 4))))
                         (CONS (LIST 'G8
                                     '(ALL-T-REGS-ADDRESS)
                                     'B-AND4
                                     (INDICES 'REGS-ADDRESS 0 4))
                               '((G9 (SIDE-EFFECT-A)
                                     B-AND
                                     (A-IMMEDIATE-P- ALMOST-SIDE-EFFECT-A))
                                 (GA (DIRECT-A)
                                     B-OR
                                     (A-IMMEDIATE-P ALMOST-DIRECT-A))))))))))))
     '(NIL))))))
\end{verbatim}


\begin{tabbing}{\sc Definition}:\index{control-let\&} \\  
\=\+{\rm{control-let\&}}\,({\it{netlist\/}})\index{control-let\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{control-let}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{control-let*}}\index{control-let*}) \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{control-let}}, {\it{netlist\/}})\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-store-resultp\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{control-let}}, {\it{netlist\/}})\index{delete-module})\index{b-store-resultp\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-or4\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{control-let}}, {\it{netlist\/}})\index{delete-module})\index{b-or4\&} \\ 
$\wedge$$\;\;\;\;${\rm{decode-reg-mode\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{control-let}}, {\it{netlist\/}})\index{delete-module})\index{decode-reg-mode\&} \\ 
$\wedge$$\;\;\;\;${\rm{unary-op-code-p\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{control-let}}, {\it{netlist\/}})\index{delete-module})\index{unary-op-code-p\&} \\ 
$\wedge$$\;\;\;\;${\rm{id\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{control-let}}, {\it{netlist\/}})\index{delete-module})\index{id\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-and4\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{control-let}}, {\it{netlist\/}})\index{delete-module})\index{b-and4\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-and\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{control-let}}, {\it{netlist\/}})\index{delete-module})\index{b-and\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-or\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{control-let}}, {\it{netlist\/}})\index{delete-module})\index{b-or\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable control-let\&; name this event `control-let\&-off'.\index{control-let\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{control-let\$netlist} \\  
\=\+{\sc{control-let\$netlist}}\index{control-let\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{control-let*}}\index{control-let*}, \\ 
\=\+(\=\+(\=\+(\=\+(\=\+(\=\+(\=\+({\sc{b-not\$netlist}}\index{b-not\$netlist} $\cup$ {\sc{b-store-resultp\$netlist}}\index{b-store-resultp\$netlist}) \\ 
$\cup$$\;\;\;\;${\sc{b-or4\$netlist}}\index{b-or4\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{decode-reg-mode\$netlist}}\index{decode-reg-mode\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{unary-op-code-p\$netlist}}\index{unary-op-code-p\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{id\$netlist}}\index{id\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-and4\$netlist}}\index{b-and4\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-and\$netlist}}\index{b-and\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-or\$netlist}}\index{b-or\$netlist}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  control-let\$value \\ \index{control-let\$value}
\=\+(\=\+{\rm{control-let\&}}\,({\it{netlist\/}})\index{control-let\&} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{i-reg\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{i-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{flags\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{flags\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{regs-address\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{regs-address\/}})\index{length} $=$ {\tt{4}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{control-let}}, \\ 
{\rm{append}}\,({\it{i-reg\/}}, {\rm{append}}\,({\it{flags\/}}, {\it{regs-address\/}})), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$control-let}}\,({\it{i-reg\/}}, {\it{flags\/}}, {\it{regs-address\/}})\index{f\$control-let})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable control-let\$value; name this event `control-let\$value-off'.\index{control-let\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$control-let=control-let \\ \index{f\$control-let=control-let}
\=\+(\=\+{\rm{bvp}}\,({\it{i-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{i-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{flags\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{flags\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{regs-address\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{regs-address\/}})\index{length} $=$ {\tt{4}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$control-let}}\,({\it{i-reg\/}}, {\it{flags\/}}, {\it{regs-address\/}})\index{f\$control-let} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p}, \\ 
{\rm{store-resultp}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, {\it{flags\/}})\index{store-resultp}, \\ 
{\rm{set-some-flags}}\,({\rm{set-flags}}\,({\it{i-reg\/}})\index{set-flags})\index{set-some-flags}, \\ 
{\rm{or*}}\,({\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p}, {\rm{reg-direct-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{reg-direct-p})\index{or*}, \\ 
{\rm{reg-direct-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{reg-direct-p}, \\ 
{\rm{unary-op-code-p}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{unary-op-code-p}, \\ 
{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{regs-address\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}), \\ 
{\rm{and*}}\,(\=\+{\rm{not*}}\,({\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p})\index{not*}, \\ 
{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{post-inc-p})\-\index{or*})\-\index{and*}, \\ 
{\rm{or*}}\,({\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, {\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{post-inc-p})\index{or*})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{next-state} \\  
\=\+{\rm{next-state}}\,(\=\+{\it{decoded-state\/}}, \\ 
{\it{store\/}}, \\ 
{\it{set-some-flags\/}}, \\ 
{\it{unary\/}}, \\ 
{\it{direct-a\/}}, \\ 
{\it{direct-b\/}}, \\ 
{\it{side-effect-a\/}}, \\ 
{\it{side-effect-b\/}}, \\ 
{\it{all-t-regs-address\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}})\-\index{next-state} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{b-nand}}\,(\=\+{\rm{b-and4}}\,(\=\+{\rm{b-nand}}\,({\it{all-t-regs-address\/}}, {\rm{nth}}\,({\tt{30}}, {\it{decoded-state\/}})\index{nth})\index{b-nand}, \\ 
{\rm{b-not}}\,({\rm{nth}}\,({\tt{25}}, {\it{decoded-state\/}})\index{nth})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{nth}}\,({\tt{23}}, {\it{decoded-state\/}})\index{nth})\index{b-not}, \\ 
{\rm{b-nand}}\,({\rm{b-not}}\,({\it{side-effect-b\/}})\index{b-not}, {\rm{nth}}\,({\tt{21}}, {\it{decoded-state\/}})\index{nth})\index{b-nand})\-\index{b-and4}, \\ 
{\rm{b-and3}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\it{dtack-\/}})\index{b-not}, {\rm{nth}}\,({\tt{19}}, {\it{decoded-state\/}})\index{nth})\index{b-nand}, \\ 
{\rm{b-nand}}\,(\=\+{\rm{b-not}}\,({\rm{b-and}}\,({\it{side-effect-b\/}}, {\it{unary\/}})\index{b-and})\index{b-not}, \\ 
{\rm{nth}}\,({\tt{7}}, {\it{decoded-state\/}})\index{nth})\-\index{b-nand}, \\ 
{\rm{b-nand4}}\,(\=\+{\rm{b-not}}\,({\it{side-effect-b\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\it{side-effect-a\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-or}}\,({\it{store\/}}, {\it{set-some-flags\/}})\index{b-or})\index{b-not}, \\ 
{\rm{nth}}\,({\tt{4}}, {\it{decoded-state\/}})\index{nth})\-\index{b-nand4})\-\index{b-and3})\-\index{b-nand}, \\ 
{\rm{nth}}\,({\tt{0}}, {\it{decoded-state\/}})\index{nth}, \\ 
{\rm{b-and}}\,({\it{hold-\/}}, {\rm{nth}}\,({\tt{1}}, {\it{decoded-state\/}})\index{nth})\index{b-and}, \\ 
{\rm{b-nand}}\,(\=\+{\rm{b-nand}}\,({\it{dtack-\/}}, {\rm{nth}}\,({\tt{3}}, {\it{decoded-state\/}})\index{nth})\index{b-nand}, \\ 
{\rm{b-not}}\,({\rm{nth}}\,({\tt{2}}, {\it{decoded-state\/}})\index{nth})\index{b-not})\-\index{b-nand}, \\ 
{\rm{b-and}}\,({\rm{b-not}}\,({\it{dtack-\/}})\index{b-not}, {\rm{nth}}\,({\tt{3}}, {\it{decoded-state\/}})\index{nth})\index{b-and}, \\ 
{\rm{b-and4}}\,(\=\+{\rm{b-or}}\,({\it{direct-b\/}}, {\it{unary\/}})\index{b-or}, \\ 
{\it{direct-a\/}}, \\ 
{\rm{b-or}}\,({\it{store\/}}, {\it{set-some-flags\/}})\index{b-or}, \\ 
{\rm{nth}}\,({\tt{4}}, {\it{decoded-state\/}})\index{nth})\-\index{b-and4}, \\ 
{\rm{b-and3}}\,({\rm{b-not}}\,({\it{unary\/}})\index{b-not}, {\it{direct-b\/}}, {\rm{nth}}\,({\tt{5}}, {\it{decoded-state\/}})\index{nth})\index{b-and3}, \\ 
{\rm{b-nand6}}\,(\=\+{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\it{store\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\it{dtack-\/}})\index{b-not}, \\ 
{\rm{nth}}\,({\tt{15}}, {\it{decoded-state\/}})\index{nth})\-\index{b-nand3}, \\ 
{\rm{b-nand5}}\,(\=\+{\rm{b-not}}\,({\it{store\/}})\index{b-not}, \\ 
{\it{unary\/}}, \\ 
{\rm{b-not}}\,({\it{direct-b\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\it{dtack-\/}})\index{b-not}, \\ 
{\rm{nth}}\,({\tt{11}}, {\it{decoded-state\/}})\index{nth})\-\index{b-nand5}, \\ 
{\rm{b-nand3}}\,({\it{direct-b\/}}, {\rm{b-not}}\,({\it{dtack-\/}})\index{b-not}, {\rm{nth}}\,({\tt{11}}, {\it{decoded-state\/}})\index{nth})\index{b-nand3}, \\ 
{\rm{b-not}}\,({\rm{nth}}\,({\tt{6}}, {\it{decoded-state\/}})\index{nth})\index{b-not}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\it{store\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\it{direct-b\/}})\index{b-not}, \\ 
{\rm{nth}}\,({\tt{5}}, {\it{decoded-state\/}})\index{nth})\-\index{b-nand3}, \\ 
{\rm{b-nand3}}\,({\it{unary\/}}, {\it{direct-b\/}}, {\rm{nth}}\,({\tt{5}}, {\it{decoded-state\/}})\index{nth})\index{b-nand3})\-\index{b-nand6}, \\ 
{\rm{b-and3}}\,(\=\+{\rm{b-not}}\,({\it{direct-a\/}})\index{b-not}, \\ 
{\rm{b-or}}\,({\it{store\/}}, {\it{set-some-flags\/}})\index{b-or}, \\ 
{\rm{nth}}\,({\tt{4}}, {\it{decoded-state\/}})\index{nth})\-\index{b-and3}, \\ 
{\rm{nth}}\,({\tt{8}}, {\it{decoded-state\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{9}}, {\it{decoded-state\/}})\index{nth}, \\ 
{\rm{b-nand}}\,(\=\+{\rm{b-nand}}\,({\it{dtack-\/}}, {\rm{nth}}\,({\tt{11}}, {\it{decoded-state\/}})\index{nth})\index{b-nand}, \\ 
{\rm{b-not}}\,({\rm{nth}}\,({\tt{10}}, {\it{decoded-state\/}})\index{nth})\index{b-not})\-\index{b-nand}, \\ 
{\rm{b-nand}}\,(\=\+{\rm{b-nand4}}\,(\=\+{\rm{b-not}}\,({\it{unary\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\it{direct-b\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\it{dtack-\/}})\index{b-not}, \\ 
{\rm{nth}}\,({\tt{11}}, {\it{decoded-state\/}})\index{nth})\-\index{b-nand4}, \\ 
{\rm{b-nand4}}\,(\=\+{\rm{b-not}}\,({\rm{b-or}}\,({\it{direct-b\/}}, {\it{unary\/}})\index{b-or})\index{b-not}, \\ 
{\it{direct-a\/}}, \\ 
{\rm{b-or}}\,({\it{store\/}}, {\it{set-some-flags\/}})\index{b-or}, \\ 
{\rm{nth}}\,({\tt{4}}, {\it{decoded-state\/}})\index{nth})\-\index{b-nand4})\-\index{b-nand}, \\ 
{\rm{nth}}\,({\tt{12}}, {\it{decoded-state\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{13}}, {\it{decoded-state\/}})\index{nth}, \\ 
{\rm{b-nand}}\,(\=\+{\rm{b-nand}}\,({\it{dtack-\/}}, {\rm{nth}}\,({\tt{15}}, {\it{decoded-state\/}})\index{nth})\index{b-nand}, \\ 
{\rm{b-not}}\,({\rm{nth}}\,({\tt{14}}, {\it{decoded-state\/}})\index{nth})\index{b-not})\-\index{b-nand}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-nand3}}\,({\it{store\/}}, {\rm{b-not}}\,({\it{dtack-\/}})\index{b-not}, {\rm{nth}}\,({\tt{15}}, {\it{decoded-state\/}})\index{nth})\index{b-nand3}, \\ 
{\rm{b-nand5}}\,(\=\+{\it{store\/}}, \\ 
{\it{unary\/}}, \\ 
{\rm{b-not}}\,({\it{direct-b\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\it{dtack-\/}})\index{b-not}, \\ 
{\rm{nth}}\,({\tt{11}}, {\it{decoded-state\/}})\index{nth})\-\index{b-nand5}, \\ 
{\rm{b-nand3}}\,({\it{store\/}}, {\rm{b-not}}\,({\it{direct-b\/}})\index{b-not}, {\rm{nth}}\,({\tt{5}}, {\it{decoded-state\/}})\index{nth})\index{b-nand3})\-\index{b-nand3}, \\ 
{\rm{nth}}\,({\tt{16}}, {\it{decoded-state\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{17}}, {\it{decoded-state\/}})\index{nth}, \\ 
{\rm{b-nand}}\,(\=\+{\rm{b-nand}}\,({\it{dtack-\/}}, {\rm{nth}}\,({\tt{19}}, {\it{decoded-state\/}})\index{nth})\index{b-nand}, \\ 
{\rm{b-not}}\,({\rm{nth}}\,({\tt{18}}, {\it{decoded-state\/}})\index{nth})\index{b-not})\-\index{b-nand}, \\ 
{\rm{b-and3}}\,(\=\+{\it{side-effect-a\/}}, \\ 
{\rm{b-not}}\,({\rm{b-or}}\,({\it{store\/}}, {\it{set-some-flags\/}})\index{b-or})\index{b-not}, \\ 
{\rm{nth}}\,({\tt{4}}, {\it{decoded-state\/}})\index{nth})\-\index{b-and3}, \\ 
{\rm{nth}}\,({\tt{20}}, {\it{decoded-state\/}})\index{nth}, \\ 
{\rm{b-nand}}\,(\=\+{\rm{b-nand}}\,({\it{side-effect-b\/}}, {\rm{nth}}\,({\tt{21}}, {\it{decoded-state\/}})\index{nth})\index{b-nand}, \\ 
{\rm{b-nand4}}\,(\=\+{\it{side-effect-b\/}}, \\ 
{\rm{b-not}}\,({\it{side-effect-a\/}})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{b-or}}\,({\it{store\/}}, {\it{set-some-flags\/}})\index{b-or})\index{b-not}, \\ 
{\rm{nth}}\,({\tt{4}}, {\it{decoded-state\/}})\index{nth})\-\index{b-nand4})\-\index{b-nand}, \\ 
{\rm{b-nand}}\,(\=\+{\rm{b-not}}\,({\rm{nth}}\,({\tt{22}}, {\it{decoded-state\/}})\index{nth})\index{b-not}, \\ 
{\rm{b-nand}}\,({\rm{b-and}}\,({\it{side-effect-b\/}}, {\it{unary\/}})\index{b-and}, {\rm{nth}}\,({\tt{7}}, {\it{decoded-state\/}})\index{nth})\index{b-nand})\-\index{b-nand}, \\ 
{\rm{b-nand}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\it{hold-\/}})\index{b-not}, {\rm{nth}}\,({\tt{24}}, {\it{decoded-state\/}})\index{nth})\index{b-nand}, \\ 
{\rm{b-nand}}\,({\rm{b-not}}\,({\it{hold-\/}})\index{b-not}, {\rm{nth}}\,({\tt{1}}, {\it{decoded-state\/}})\index{nth})\index{b-nand})\-\index{b-nand}, \\ 
{\rm{b-and}}\,({\it{hold-\/}}, {\rm{nth}}\,({\tt{24}}, {\it{decoded-state\/}})\index{nth})\index{b-and}, \\ 
{\sc{vss}}\index{vss}, \\ 
{\sc{vss}}\index{vss}, \\ 
{\rm{b-nand3}}\,(\=\+{\rm{b-not}}\,({\rm{nth}}\,({\tt{31}}, {\it{decoded-state\/}})\index{nth})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{nth}}\,({\tt{27}}, {\it{decoded-state\/}})\index{nth})\index{b-not}, \\ 
{\rm{b-not}}\,({\rm{nth}}\,({\tt{26}}, {\it{decoded-state\/}})\index{nth})\index{b-not})\-\index{b-nand3}, \\ 
{\rm{nth}}\,({\tt{28}}, {\it{decoded-state\/}})\index{nth}, \\ 
{\rm{b-nand}}\,(\=\+{\rm{b-nand}}\,({\rm{b-not}}\,({\it{all-t-regs-address\/}})\index{b-not}, {\rm{nth}}\,({\tt{30}}, {\it{decoded-state\/}})\index{nth})\index{b-nand}, \\ 
{\rm{b-not}}\,({\rm{nth}}\,({\tt{29}}, {\it{decoded-state\/}})\index{nth})\index{b-not})\-\index{b-nand}, \\ 
{\sc{vss}}\index{vss})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$next-state} \\  
\=\+{\rm{f\$next-state}}\,(\=\+{\it{decoded-state\/}}, \\ 
{\it{store\/}}, \\ 
{\it{set-some-flags\/}}, \\ 
{\it{unary\/}}, \\ 
{\it{direct-a\/}}, \\ 
{\it{direct-b\/}}, \\ 
{\it{side-effect-a\/}}, \\ 
{\it{side-effect-b\/}}, \\ 
{\it{all-t-regs-address\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}})\-\index{f\$next-state} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{f-nand}}\,(\=\+{\rm{f-and4}}\,(\=\+{\rm{f-nand}}\,({\it{all-t-regs-address\/}}, {\rm{nth}}\,({\tt{30}}, {\it{decoded-state\/}})\index{nth})\index{f-nand}, \\ 
{\rm{f-not}}\,({\rm{nth}}\,({\tt{25}}, {\it{decoded-state\/}})\index{nth})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{nth}}\,({\tt{23}}, {\it{decoded-state\/}})\index{nth})\index{f-not}, \\ 
{\rm{f-nand}}\,({\rm{f-not}}\,({\it{side-effect-b\/}})\index{f-not}, {\rm{nth}}\,({\tt{21}}, {\it{decoded-state\/}})\index{nth})\index{f-nand})\-\index{f-and4}, \\ 
{\rm{f-and3}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\it{dtack-\/}})\index{f-not}, {\rm{nth}}\,({\tt{19}}, {\it{decoded-state\/}})\index{nth})\index{f-nand}, \\ 
{\rm{f-nand}}\,(\=\+{\rm{f-not}}\,({\rm{f-and}}\,({\it{side-effect-b\/}}, {\it{unary\/}})\index{f-and})\index{f-not}, \\ 
{\rm{nth}}\,({\tt{7}}, {\it{decoded-state\/}})\index{nth})\-\index{f-nand}, \\ 
{\rm{f-nand4}}\,(\=\+{\rm{f-not}}\,({\it{side-effect-b\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{side-effect-a\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-or}}\,({\it{store\/}}, {\it{set-some-flags\/}})\index{f-or})\index{f-not}, \\ 
{\rm{nth}}\,({\tt{4}}, {\it{decoded-state\/}})\index{nth})\-\index{f-nand4})\-\index{f-and3})\-\index{f-nand}, \\ 
{\rm{nth}}\,({\tt{0}}, {\it{decoded-state\/}})\index{nth}, \\ 
{\rm{f-and}}\,({\it{hold-\/}}, {\rm{nth}}\,({\tt{1}}, {\it{decoded-state\/}})\index{nth})\index{f-and}, \\ 
{\rm{f-nand}}\,(\=\+{\rm{f-nand}}\,({\it{dtack-\/}}, {\rm{nth}}\,({\tt{3}}, {\it{decoded-state\/}})\index{nth})\index{f-nand}, \\ 
{\rm{f-not}}\,({\rm{nth}}\,({\tt{2}}, {\it{decoded-state\/}})\index{nth})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f-and}}\,({\rm{f-not}}\,({\it{dtack-\/}})\index{f-not}, {\rm{nth}}\,({\tt{3}}, {\it{decoded-state\/}})\index{nth})\index{f-and}, \\ 
{\rm{f-and4}}\,(\=\+{\rm{f-or}}\,({\it{direct-b\/}}, {\it{unary\/}})\index{f-or}, \\ 
{\it{direct-a\/}}, \\ 
{\rm{f-or}}\,({\it{store\/}}, {\it{set-some-flags\/}})\index{f-or}, \\ 
{\rm{nth}}\,({\tt{4}}, {\it{decoded-state\/}})\index{nth})\-\index{f-and4}, \\ 
{\rm{f-and3}}\,({\rm{f-not}}\,({\it{unary\/}})\index{f-not}, {\it{direct-b\/}}, {\rm{nth}}\,({\tt{5}}, {\it{decoded-state\/}})\index{nth})\index{f-and3}, \\ 
{\rm{f-nand6}}\,(\=\+{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\it{store\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{dtack-\/}})\index{f-not}, \\ 
{\rm{nth}}\,({\tt{15}}, {\it{decoded-state\/}})\index{nth})\-\index{f-nand3}, \\ 
{\rm{f-nand5}}\,(\=\+{\rm{f-not}}\,({\it{store\/}})\index{f-not}, \\ 
{\it{unary\/}}, \\ 
{\rm{f-not}}\,({\it{direct-b\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{dtack-\/}})\index{f-not}, \\ 
{\rm{nth}}\,({\tt{11}}, {\it{decoded-state\/}})\index{nth})\-\index{f-nand5}, \\ 
{\rm{f-nand3}}\,({\it{direct-b\/}}, {\rm{f-not}}\,({\it{dtack-\/}})\index{f-not}, {\rm{nth}}\,({\tt{11}}, {\it{decoded-state\/}})\index{nth})\index{f-nand3}, \\ 
{\rm{f-not}}\,({\rm{nth}}\,({\tt{6}}, {\it{decoded-state\/}})\index{nth})\index{f-not}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\it{store\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{direct-b\/}})\index{f-not}, \\ 
{\rm{nth}}\,({\tt{5}}, {\it{decoded-state\/}})\index{nth})\-\index{f-nand3}, \\ 
{\rm{f-nand3}}\,({\it{unary\/}}, {\it{direct-b\/}}, {\rm{nth}}\,({\tt{5}}, {\it{decoded-state\/}})\index{nth})\index{f-nand3})\-\index{f-nand6}, \\ 
{\rm{f-and3}}\,(\=\+{\rm{f-not}}\,({\it{direct-a\/}})\index{f-not}, \\ 
{\rm{f-or}}\,({\it{store\/}}, {\it{set-some-flags\/}})\index{f-or}, \\ 
{\rm{nth}}\,({\tt{4}}, {\it{decoded-state\/}})\index{nth})\-\index{f-and3}, \\ 
{\rm{nth}}\,({\tt{8}}, {\it{decoded-state\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{9}}, {\it{decoded-state\/}})\index{nth}, \\ 
{\rm{f-nand}}\,(\=\+{\rm{f-nand}}\,({\it{dtack-\/}}, {\rm{nth}}\,({\tt{11}}, {\it{decoded-state\/}})\index{nth})\index{f-nand}, \\ 
{\rm{f-not}}\,({\rm{nth}}\,({\tt{10}}, {\it{decoded-state\/}})\index{nth})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f-nand}}\,(\=\+{\rm{f-nand4}}\,(\=\+{\rm{f-not}}\,({\it{unary\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{direct-b\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{dtack-\/}})\index{f-not}, \\ 
{\rm{nth}}\,({\tt{11}}, {\it{decoded-state\/}})\index{nth})\-\index{f-nand4}, \\ 
{\rm{f-nand4}}\,(\=\+{\rm{f-not}}\,({\rm{f-or}}\,({\it{direct-b\/}}, {\it{unary\/}})\index{f-or})\index{f-not}, \\ 
{\it{direct-a\/}}, \\ 
{\rm{f-or}}\,({\it{store\/}}, {\it{set-some-flags\/}})\index{f-or}, \\ 
{\rm{nth}}\,({\tt{4}}, {\it{decoded-state\/}})\index{nth})\-\index{f-nand4})\-\index{f-nand}, \\ 
{\rm{nth}}\,({\tt{12}}, {\it{decoded-state\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{13}}, {\it{decoded-state\/}})\index{nth}, \\ 
{\rm{f-nand}}\,(\=\+{\rm{f-nand}}\,({\it{dtack-\/}}, {\rm{nth}}\,({\tt{15}}, {\it{decoded-state\/}})\index{nth})\index{f-nand}, \\ 
{\rm{f-not}}\,({\rm{nth}}\,({\tt{14}}, {\it{decoded-state\/}})\index{nth})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-nand3}}\,({\it{store\/}}, {\rm{f-not}}\,({\it{dtack-\/}})\index{f-not}, {\rm{nth}}\,({\tt{15}}, {\it{decoded-state\/}})\index{nth})\index{f-nand3}, \\ 
{\rm{f-nand5}}\,(\=\+{\it{store\/}}, \\ 
{\it{unary\/}}, \\ 
{\rm{f-not}}\,({\it{direct-b\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\it{dtack-\/}})\index{f-not}, \\ 
{\rm{nth}}\,({\tt{11}}, {\it{decoded-state\/}})\index{nth})\-\index{f-nand5}, \\ 
{\rm{f-nand3}}\,({\it{store\/}}, {\rm{f-not}}\,({\it{direct-b\/}})\index{f-not}, {\rm{nth}}\,({\tt{5}}, {\it{decoded-state\/}})\index{nth})\index{f-nand3})\-\index{f-nand3}, \\ 
{\rm{nth}}\,({\tt{16}}, {\it{decoded-state\/}})\index{nth}, \\ 
{\rm{nth}}\,({\tt{17}}, {\it{decoded-state\/}})\index{nth}, \\ 
{\rm{f-nand}}\,(\=\+{\rm{f-nand}}\,({\it{dtack-\/}}, {\rm{nth}}\,({\tt{19}}, {\it{decoded-state\/}})\index{nth})\index{f-nand}, \\ 
{\rm{f-not}}\,({\rm{nth}}\,({\tt{18}}, {\it{decoded-state\/}})\index{nth})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f-and3}}\,(\=\+{\it{side-effect-a\/}}, \\ 
{\rm{f-not}}\,({\rm{f-or}}\,({\it{store\/}}, {\it{set-some-flags\/}})\index{f-or})\index{f-not}, \\ 
{\rm{nth}}\,({\tt{4}}, {\it{decoded-state\/}})\index{nth})\-\index{f-and3}, \\ 
{\rm{nth}}\,({\tt{20}}, {\it{decoded-state\/}})\index{nth}, \\ 
{\rm{f-nand}}\,(\=\+{\rm{f-nand}}\,({\it{side-effect-b\/}}, {\rm{nth}}\,({\tt{21}}, {\it{decoded-state\/}})\index{nth})\index{f-nand}, \\ 
{\rm{f-nand4}}\,(\=\+{\it{side-effect-b\/}}, \\ 
{\rm{f-not}}\,({\it{side-effect-a\/}})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{f-or}}\,({\it{store\/}}, {\it{set-some-flags\/}})\index{f-or})\index{f-not}, \\ 
{\rm{nth}}\,({\tt{4}}, {\it{decoded-state\/}})\index{nth})\-\index{f-nand4})\-\index{f-nand}, \\ 
{\rm{f-nand}}\,(\=\+{\rm{f-not}}\,({\rm{nth}}\,({\tt{22}}, {\it{decoded-state\/}})\index{nth})\index{f-not}, \\ 
{\rm{f-nand}}\,({\rm{f-and}}\,({\it{side-effect-b\/}}, {\it{unary\/}})\index{f-and}, {\rm{nth}}\,({\tt{7}}, {\it{decoded-state\/}})\index{nth})\index{f-nand})\-\index{f-nand}, \\ 
{\rm{f-nand}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\it{hold-\/}})\index{f-not}, {\rm{nth}}\,({\tt{24}}, {\it{decoded-state\/}})\index{nth})\index{f-nand}, \\ 
{\rm{f-nand}}\,({\rm{f-not}}\,({\it{hold-\/}})\index{f-not}, {\rm{nth}}\,({\tt{1}}, {\it{decoded-state\/}})\index{nth})\index{f-nand})\-\index{f-nand}, \\ 
{\rm{f-and}}\,({\it{hold-\/}}, {\rm{nth}}\,({\tt{24}}, {\it{decoded-state\/}})\index{nth})\index{f-and}, \\ 
{\sc{vss}}\index{vss}, \\ 
{\sc{vss}}\index{vss}, \\ 
{\rm{f-nand3}}\,(\=\+{\rm{f-not}}\,({\rm{nth}}\,({\tt{31}}, {\it{decoded-state\/}})\index{nth})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{nth}}\,({\tt{27}}, {\it{decoded-state\/}})\index{nth})\index{f-not}, \\ 
{\rm{f-not}}\,({\rm{nth}}\,({\tt{26}}, {\it{decoded-state\/}})\index{nth})\index{f-not})\-\index{f-nand3}, \\ 
{\rm{nth}}\,({\tt{28}}, {\it{decoded-state\/}})\index{nth}, \\ 
{\rm{f-nand}}\,(\=\+{\rm{f-nand}}\,({\rm{f-not}}\,({\it{all-t-regs-address\/}})\index{f-not}, {\rm{nth}}\,({\tt{30}}, {\it{decoded-state\/}})\index{nth})\index{f-nand}, \\ 
{\rm{f-not}}\,({\rm{nth}}\,({\tt{29}}, {\it{decoded-state\/}})\index{nth})\index{f-not})\-\index{f-nand}, \\ 
{\sc{vss}}\index{vss})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$next-state; name this event `f\$next-state-off'.\index{f\$next-state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$next-state=next-state \\ \index{f\$next-state=next-state}
\=\+(\=\+{\rm{bvp}}\,({\it{decoded-state\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{decoded-state\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{store\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{set-some-flags\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{unary\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{direct-a\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{direct-b\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{side-effect-a\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{side-effect-b\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{all-t-regs-address\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$next-state}}\,(\=\+{\it{decoded-state\/}}, \\ 
{\it{store\/}}, \\ 
{\it{set-some-flags\/}}, \\ 
{\it{unary\/}}, \\ 
{\it{direct-a\/}}, \\ 
{\it{direct-b\/}}, \\ 
{\it{side-effect-a\/}}, \\ 
{\it{side-effect-b\/}}, \\ 
{\it{all-t-regs-address\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}})\-\index{f\$next-state} \\ 
$=$$\;\;\;\;${\rm{next-state}}\,(\=\+{\it{decoded-state\/}}, \\ 
{\it{store\/}}, \\ 
{\it{set-some-flags\/}}, \\ 
{\it{unary\/}}, \\ 
{\it{direct-a\/}}, \\ 
{\it{direct-b\/}}, \\ 
{\it{side-effect-a\/}}, \\ 
{\it{side-effect-b\/}}, \\ 
{\it{all-t-regs-address\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}})\-\index{next-state})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{next-state*} \\  
\=\+{\sc{next-state*}}\index{next-state*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\tt{'}}{\tt{next-state}}, \\ 
{\rm{cons}}\,(\=\+{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{s}}, {\tt{0}}, {\tt{32}})\index{indices}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{store}}{\tt{ }}{\tt{set-some-flags}}{\tt{ }}{\tt{unary}}{\tt{ }}{\tt{direct-a}} \\ 
{\tt{direct-b}}{\tt{ }}{\tt{side-effect-a}}{\tt{ }}{\tt{side-effect-b}} \\ 
{\tt{all-t-regs-address}}{\tt{ }}{\tt{dtack-}}{\tt{ }}{\tt{hold-}}{\tt{)}}\-)\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{w-17}}{\tt{ }}{\tt{w-18}}{\tt{ }}{\tt{w-19}}{\tt{ }}{\tt{w-22}}{\tt{ }}{\tt{w-24}}{\tt{ }}{\tt{w-27}}{\tt{ }}{\tt{w-29}}{\tt{ }}{\tt{w-44}} \\ 
{\tt{w-47}}{\tt{ }}{\tt{w-48}}{\tt{ }}{\tt{w-49}}{\tt{ }}{\tt{w-52}}{\tt{ }}{\tt{w-61}}{\tt{ }}{\tt{w-62}}{\tt{ }}{\tt{w-63}}{\tt{ }}{\tt{w-66}} \\ 
{\tt{w-74}}{\tt{ }}{\tt{w-75}}{\tt{ }}{\tt{w-76}}{\tt{ }}{\tt{w-79}}{\tt{ }}{\tt{w-82}}{\tt{ }}{\tt{w-83}}{\tt{ }}{\tt{w-89}}{\tt{ }}{\tt{w-93}} \\ 
{\tt{w-98}}{\tt{ }}{\tt{w-99}}{\tt{ }}{\tt{w-112}}{\tt{ }}{\tt{w-113}}{\tt{ }}{\tt{w-105}}{\tt{ }}{\tt{w-106}}{\tt{ }}{\tt{w-110}} \\ 
{\tt{w-111}}{\tt{)}}\-, \\ 
{\rm{cons}}\,(\=\+{\rm{append}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-0}}, \\ 
{\tt{'}}{\tt{(}}{\tt{fetch0}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{0}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-1}}, \\ 
{\tt{'}}{\tt{(}}{\tt{fetch1}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{1}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-2}}, \\ 
{\tt{'}}{\tt{(}}{\tt{fetch2}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{2}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-3}}, \\ 
{\tt{'}}{\tt{(}}{\tt{fetch3}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{3}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-4}}, \\ 
{\tt{'}}{\tt{(}}{\tt{decode}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{4}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-5}}, \\ 
{\tt{'}}{\tt{(}}{\tt{rega}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{5}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-6}}, \\ 
{\tt{'}}{\tt{(}}{\tt{regb}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{6}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-7}}, \\ 
{\tt{'}}{\tt{(}}{\tt{update}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{7}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-8}}, \\ 
{\tt{'}}{\tt{(}}{\tt{reada0}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{8}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-9}}, \\ 
{\tt{'}}{\tt{(}}{\tt{reada1}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{9}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-10}}, \\ 
{\tt{'}}{\tt{(}}{\tt{reada2}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{10}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-11}}, \\ 
{\tt{'}}{\tt{(}}{\tt{reada3}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{11}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-12}}, \\ 
{\tt{'}}{\tt{(}}{\tt{readb0}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{12}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-13}}, \\ 
{\tt{'}}{\tt{(}}{\tt{readb1}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{13}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-14}}, \\ 
{\tt{'}}{\tt{(}}{\tt{readb2}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{14}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-15}}, \\ 
{\tt{'}}{\tt{(}}{\tt{readb3}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{15}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-16}}, \\ 
{\tt{'}}{\tt{(}}{\tt{write0}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{16}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-17}}, \\ 
{\tt{'}}{\tt{(}}{\tt{write1}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{17}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-18}}, \\ 
{\tt{'}}{\tt{(}}{\tt{write2}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{18}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-19}}, \\ 
{\tt{'}}{\tt{(}}{\tt{write3}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{19}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-20}}, \\ 
{\tt{'}}{\tt{(}}{\tt{sefa0}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{20}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-21}}, \\ 
{\tt{'}}{\tt{(}}{\tt{sefa1}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{21}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-22}}, \\ 
{\tt{'}}{\tt{(}}{\tt{sefb0}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{22}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-23}}, \\ 
{\tt{'}}{\tt{(}}{\tt{sefb1}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{23}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-24}}, \\ 
{\tt{'}}{\tt{(}}{\tt{hold0}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{24}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-25}}, \\ 
{\tt{'}}{\tt{(}}{\tt{hold1}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{25}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-26}}, \\ 
{\tt{'}}{\tt{(}}{\tt{v11010}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{26}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-27}}, \\ 
{\tt{'}}{\tt{(}}{\tt{v11011}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{27}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-28}}, \\ 
{\tt{'}}{\tt{(}}{\tt{reset0}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{28}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-29}}, \\ 
{\tt{'}}{\tt{(}}{\tt{reset1}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{29}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-30}}, \\ 
{\tt{'}}{\tt{(}}{\tt{reset2}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{30}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{r-31}}, \\ 
{\tt{'}}{\tt{(}}{\tt{v11111}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{s}}, {\tt{31}})\index{index}))\-)\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{(}}{\tt{g-111}}{\tt{ }}{\tt{(}}{\tt{w-111}}{\tt{)}}{\tt{ }}{\tt{vss}}{\tt{ }}{\tt{nil}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-109}}{\tt{ }}{\tt{(}}{\tt{w-109}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{reset1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g-107}} \\ 
{\tt{(}}{\tt{w-107}}{\tt{)}} \\ 
{\tt{b-not}} \\ 
{\tt{(}}{\tt{all-t-regs-address}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-108}} \\ 
{\tt{(}}{\tt{w-108}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{w-107}}{\tt{ }}{\tt{reset2}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-110}} \\ 
{\tt{(}}{\tt{w-110}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{w-108}}{\tt{ }}{\tt{w-109}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g-106}}{\tt{ }}{\tt{(}}{\tt{w-106}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{reset0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-104}}{\tt{ }}{\tt{(}}{\tt{w-104}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{v11010}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-103}}{\tt{ }}{\tt{(}}{\tt{w-103}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{v11011}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-102}}{\tt{ }}{\tt{(}}{\tt{w-102}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{v11111}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g-105}} \\ 
{\tt{(}}{\tt{w-105}}{\tt{)}} \\ 
{\tt{b-nand3}} \\ 
{\tt{(}}{\tt{w-102}}{\tt{ }}{\tt{w-103}}{\tt{ }}{\tt{w-104}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-99}} \\ 
{\tt{(}}{\tt{w-99}}{\tt{)}} \\ 
{\tt{b-and}} \\ 
{\tt{(}}{\tt{hold-}}{\tt{ }}{\tt{hold0}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g-96}}{\tt{ }}{\tt{(}}{\tt{w-96}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{hold-}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g-97}} \\ 
{\tt{(}}{\tt{w-97}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{w-96}}{\tt{ }}{\tt{fetch1}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-95}} \\ 
{\tt{(}}{\tt{w-95}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{w-96}}{\tt{ }}{\tt{hold0}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-98}} \\ 
{\tt{(}}{\tt{w-98}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{w-95}}{\tt{ }}{\tt{w-97}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-91}} \\ 
{\tt{(}}{\tt{w-91}}{\tt{)}} \\ 
{\tt{b-and}} \\ 
{\tt{(}}{\tt{side-effect-b}}{\tt{ }}{\tt{unary}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-92}} \\ 
{\tt{(}}{\tt{w-92}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{w-91}}{\tt{ }}{\tt{update}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g-90}}{\tt{ }}{\tt{(}}{\tt{w-90}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{sefb0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g-93}} \\ 
{\tt{(}}{\tt{w-93}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{w-90}}{\tt{ }}{\tt{w-92}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-86}} \\ 
{\tt{(}}{\tt{w-86}}{\tt{)}} \\ 
{\tt{b-or}} \\ 
{\tt{(}}{\tt{store}}{\tt{ }}{\tt{set-some-flags}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g-87}}{\tt{ }}{\tt{(}}{\tt{w-87}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{w-86}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g-85}} \\ 
{\tt{(}}{\tt{w-85}}{\tt{)}} \\ 
{\tt{b-not}} \\ 
{\tt{(}}{\tt{side-effect-a}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-88}} \\ 
{\tt{(}}{\tt{w-88}}{\tt{)}} \\ 
{\tt{b-nand4}} \\ 
{\tt{(}}\=\+{\tt{side-effect-b}}{\tt{ }}{\tt{w-85}}{\tt{ }}{\tt{w-87}}{\tt{ }}{\tt{decode}}{\tt{)}}\-{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-84}} \\ 
{\tt{(}}{\tt{w-84}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{side-effect-b}}{\tt{ }}{\tt{sefa1}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-89}} \\ 
{\tt{(}}{\tt{w-89}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{w-84}}{\tt{ }}{\tt{w-88}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g-83}}{\tt{ }}{\tt{(}}{\tt{w-83}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{sefa0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g-82}} \\ 
{\tt{(}}{\tt{w-82}}{\tt{)}} \\ 
{\tt{b-and3}} \\ 
{\tt{(}}{\tt{side-effect-a}}{\tt{ }}{\tt{w-87}}{\tt{ }}{\tt{decode}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g-78}}{\tt{ }}{\tt{(}}{\tt{w-78}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{write2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g-77}} \\ 
{\tt{(}}{\tt{w-77}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{dtack-}}{\tt{ }}{\tt{write3}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-79}} \\ 
{\tt{(}}{\tt{w-79}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{w-77}}{\tt{ }}{\tt{w-78}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g-76}}{\tt{ }}{\tt{(}}{\tt{w-76}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{write1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-75}}{\tt{ }}{\tt{(}}{\tt{w-75}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{write0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-72}}{\tt{ }}{\tt{(}}{\tt{w-72}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{direct-b}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g-73}} \\ 
{\tt{(}}{\tt{w-73}}{\tt{)}} \\ 
{\tt{b-nand3}} \\ 
{\tt{(}}{\tt{store}}{\tt{ }}{\tt{w-72}}{\tt{ }}{\tt{rega}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g-70}}{\tt{ }}{\tt{(}}{\tt{w-70}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{dtack-}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g-71}} \\ 
{\tt{(}}{\tt{w-71}}{\tt{)}} \\ 
{\tt{b-nand5}} \\ 
{\tt{(}}\=\+{\tt{store}}{\tt{ }}{\tt{unary}}{\tt{ }}{\tt{w-72}}{\tt{ }}{\tt{w-70}}{\tt{ }}{\tt{reada3}}{\tt{)}}\-{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-68}} \\ 
{\tt{(}}{\tt{w-68}}{\tt{)}} \\ 
{\tt{b-nand3}} \\ 
{\tt{(}}{\tt{store}}{\tt{ }}{\tt{w-70}}{\tt{ }}{\tt{readb3}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-74}} \\ 
{\tt{(}}{\tt{w-74}}{\tt{)}} \\ 
{\tt{b-nand3}} \\ 
{\tt{(}}{\tt{w-68}}{\tt{ }}{\tt{w-71}}{\tt{ }}{\tt{w-73}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g-65}}{\tt{ }}{\tt{(}}{\tt{w-65}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{readb2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g-64}} \\ 
{\tt{(}}{\tt{w-64}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{dtack-}}{\tt{ }}{\tt{readb3}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-66}} \\ 
{\tt{(}}{\tt{w-66}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{w-64}}{\tt{ }}{\tt{w-65}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g-63}}{\tt{ }}{\tt{(}}{\tt{w-63}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{readb1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-62}}{\tt{ }}{\tt{(}}{\tt{w-62}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{readb0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g-57}} \\ 
{\tt{(}}{\tt{w-57}}{\tt{)}} \\ 
{\tt{b-or}} \\ 
{\tt{(}}{\tt{direct-b}}{\tt{ }}{\tt{unary}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g-58}}{\tt{ }}{\tt{(}}{\tt{w-58}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{w-57}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g-60}} \\ 
{\tt{(}}{\tt{w-60}}{\tt{)}} \\ 
{\tt{b-nand4}} \\ 
{\tt{(}}{\tt{w-58}}{\tt{ }}{\tt{direct-a}}{\tt{ }}{\tt{w-86}}{\tt{ }}{\tt{decode}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g-53}}{\tt{ }}{\tt{(}}{\tt{w-53}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{unary}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g-56}} \\ 
{\tt{(}}{\tt{w-56}}{\tt{)}} \\ 
{\tt{b-nand4}} \\ 
{\tt{(}}{\tt{w-53}}{\tt{ }}{\tt{w-72}}{\tt{ }}{\tt{w-70}}{\tt{ }}{\tt{reada3}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-61}} \\ 
{\tt{(}}{\tt{w-61}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{w-56}}{\tt{ }}{\tt{w-60}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g-51}}{\tt{ }}{\tt{(}}{\tt{w-51}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{reada2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g-50}} \\ 
{\tt{(}}{\tt{w-50}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{dtack-}}{\tt{ }}{\tt{reada3}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-52}} \\ 
{\tt{(}}{\tt{w-52}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{w-50}}{\tt{ }}{\tt{w-51}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g-49}}{\tt{ }}{\tt{(}}{\tt{w-49}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{reada1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-48}}{\tt{ }}{\tt{(}}{\tt{w-48}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{reada0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-45}}{\tt{ }}{\tt{(}}{\tt{w-45}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{direct-a}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g-47}} \\ 
{\tt{(}}{\tt{w-47}}{\tt{)}} \\ 
{\tt{b-and3}} \\ 
{\tt{(}}{\tt{w-45}}{\tt{ }}{\tt{w-86}}{\tt{ }}{\tt{decode}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-43}} \\ 
{\tt{(}}{\tt{w-43}}{\tt{)}} \\ 
{\tt{b-nand3}} \\ 
{\tt{(}}{\tt{unary}}{\tt{ }}{\tt{direct-b}}{\tt{ }}{\tt{rega}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g-40}}{\tt{ }}{\tt{(}}{\tt{w-40}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{store}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g-42}} \\ 
{\tt{(}}{\tt{w-42}}{\tt{)}} \\ 
{\tt{b-nand3}} \\ 
{\tt{(}}{\tt{w-40}}{\tt{ }}{\tt{w-72}}{\tt{ }}{\tt{rega}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g-39}}{\tt{ }}{\tt{(}}{\tt{w-39}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{regb}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g-38}} \\ 
{\tt{(}}{\tt{w-38}}{\tt{)}} \\ 
{\tt{b-nand3}} \\ 
{\tt{(}}{\tt{direct-b}}{\tt{ }}{\tt{w-70}}{\tt{ }}{\tt{reada3}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-36}} \\ 
{\tt{(}}{\tt{w-36}}{\tt{)}} \\ 
{\tt{b-nand5}} \\ 
{\tt{(}}{\tt{w-40}}{\tt{ }}{\tt{unary}}{\tt{ }}{\tt{w-72}}{\tt{ }}{\tt{w-70}}{\tt{ }}{\tt{reada3}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-32}} \\ 
{\tt{(}}{\tt{w-32}}{\tt{)}} \\ 
{\tt{b-nand3}} \\ 
{\tt{(}}{\tt{w-40}}{\tt{ }}{\tt{w-70}}{\tt{ }}{\tt{readb3}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-44}} \\ 
{\tt{(}}{\tt{w-44}}{\tt{)}} \\ 
{\tt{b-nand6}} \\ 
{\tt{(}}\=\+{\tt{w-32}}{\tt{ }}{\tt{w-36}}{\tt{ }}{\tt{w-38}}{\tt{ }}{\tt{w-39}}{\tt{ }}{\tt{w-42}}{\tt{ }}{\tt{w-43}}{\tt{)}}\-{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-29}} \\ 
{\tt{(}}{\tt{w-29}}{\tt{)}} \\ 
{\tt{b-and3}} \\ 
{\tt{(}}{\tt{w-53}}{\tt{ }}{\tt{direct-b}}{\tt{ }}{\tt{rega}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-27}} \\ 
{\tt{(}}{\tt{w-27}}{\tt{)}} \\ 
{\tt{b-and4}} \\ 
{\tt{(}}{\tt{w-57}}{\tt{ }}{\tt{direct-a}}{\tt{ }}{\tt{w-86}}{\tt{ }}{\tt{decode}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-24}} \\ 
{\tt{(}}{\tt{w-24}}{\tt{)}} \\ 
{\tt{b-and}} \\ 
{\tt{(}}{\tt{w-70}}{\tt{ }}{\tt{fetch3}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g-21}}{\tt{ }}{\tt{(}}{\tt{w-21}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{fetch2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g-20}} \\ 
{\tt{(}}{\tt{w-20}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{dtack-}}{\tt{ }}{\tt{fetch3}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-22}} \\ 
{\tt{(}}{\tt{w-22}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{w-20}}{\tt{ }}{\tt{w-21}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-19}} \\ 
{\tt{(}}{\tt{w-19}}{\tt{)}} \\ 
{\tt{b-and}} \\ 
{\tt{(}}{\tt{hold-}}{\tt{ }}{\tt{fetch1}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g-18}}{\tt{ }}{\tt{(}}{\tt{w-18}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{fetch0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g-11}} \\ 
{\tt{(}}{\tt{w-11}}{\tt{)}} \\ 
{\tt{b-not}} \\ 
{\tt{(}}{\tt{side-effect-b}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-15}} \\ 
{\tt{(}}{\tt{w-15}}{\tt{)}} \\ 
{\tt{b-nand4}} \\ 
{\tt{(}}{\tt{w-11}}{\tt{ }}{\tt{w-85}}{\tt{ }}{\tt{w-87}}{\tt{ }}{\tt{decode}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g-9}}{\tt{ }}{\tt{(}}{\tt{w-9}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{w-91}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g-10}} \\ 
{\tt{(}}{\tt{w-10}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{w-9}}{\tt{ }}{\tt{update}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-7}} \\ 
{\tt{(}}{\tt{w-7}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{w-70}}{\tt{ }}{\tt{write3}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-16}} \\ 
{\tt{(}}{\tt{w-16}}{\tt{)}} \\ 
{\tt{b-and3}} \\ 
{\tt{(}}{\tt{w-7}}{\tt{ }}{\tt{w-10}}{\tt{ }}{\tt{w-15}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-4}} \\ 
{\tt{(}}{\tt{w-4}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{w-11}}{\tt{ }}{\tt{sefa1}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g-2}}{\tt{ }}{\tt{(}}{\tt{w-2}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{sefb1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-1}}{\tt{ }}{\tt{(}}{\tt{w-1}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{hold1}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{g-0}} \\ 
{\tt{(}}{\tt{w-0}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{all-t-regs-address}}{\tt{ }}{\tt{reset2}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-5}} \\ 
{\tt{(}}{\tt{w-5}}{\tt{)}} \\ 
{\tt{b-and4}} \\ 
{\tt{(}}{\tt{w-0}}{\tt{ }}{\tt{w-1}}{\tt{ }}{\tt{w-2}}{\tt{ }}{\tt{w-4}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{g-17}} \\ 
{\tt{(}}{\tt{w-17}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{w-5}}{\tt{ }}{\tt{w-16}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{g-112}}{\tt{ }}{\tt{(}}{\tt{w-112}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{w-111}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{g-113}}{\tt{ }}{\tt{(}}{\tt{w-113}}{\tt{)}}{\tt{ }}{\tt{id}}{\tt{ }}{\tt{(}}{\tt{w-111}}{\tt{)}}{\tt{)}}{\tt{)}}\-)\-, \\ 
{\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}})\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{next-state\&} \\  
\=\+{\rm{next-state\&}}\,({\it{netlist\/}})\index{next-state\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{next-state}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{next-state*}}\index{next-state*}) \\ 
$\wedge$$\;\;\;\;${\rm{vss\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{next-state}}, {\it{netlist\/}})\index{delete-module})\index{vss\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-or\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{next-state}}, {\it{netlist\/}})\index{delete-module})\index{b-or\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand5\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{next-state}}, {\it{netlist\/}})\index{delete-module})\index{b-nand5\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand3\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{next-state}}, {\it{netlist\/}})\index{delete-module})\index{b-nand3\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand6\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{next-state}}, {\it{netlist\/}})\index{delete-module})\index{b-nand6\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-and\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{next-state}}, {\it{netlist\/}})\index{delete-module})\index{b-and\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand4\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{next-state}}, {\it{netlist\/}})\index{delete-module})\index{b-nand4\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-and3\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{next-state}}, {\it{netlist\/}})\index{delete-module})\index{b-and3\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{next-state}}, {\it{netlist\/}})\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-and4\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{next-state}}, {\it{netlist\/}})\index{delete-module})\index{b-and4\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{next-state}}, {\it{netlist\/}})\index{delete-module})\index{b-nand\&} \\ 
$\wedge$$\;\;\;\;${\rm{id\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{next-state}}, {\it{netlist\/}})\index{delete-module})\index{id\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable next-state\&; name this event `next-state\&-off'.\index{next-state\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{next-state\$netlist} \\  
\=\+{\sc{next-state\$netlist}}\index{next-state\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{next-state*}}\index{next-state*}, \\ 
\=\+(\=\+(\=\+(\=\+(\=\+(\=\+(\=\+(\=\+(\=\+(({\sc{vss\$netlist}}\index{vss\$netlist} $\cup$ {\sc{b-or\$netlist}}\index{b-or\$netlist}) $\cup$ {\sc{b-nand5\$netlist}}\index{b-nand5\$netlist}) \\ 
$\cup$$\;\;\;\;${\sc{b-nand3\$netlist}}\index{b-nand3\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-nand6\$netlist}}\index{b-nand6\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-and\$netlist}}\index{b-and\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-nand4\$netlist}}\index{b-nand4\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-and3\$netlist}}\index{b-and3\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-not\$netlist}}\index{b-not\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-and4\$netlist}}\index{b-and4\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{b-nand\$netlist}}\index{b-nand\$netlist})\- \\ 
$\cup$$\;\;\;\;${\sc{id\$netlist}}\index{id\$netlist}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-length-next-state \\ \index{bvp-length-next-state}
\=\+(\=\+{\rm{length}}\,({\rm{next-state}}\,(\=\+{\it{decoded-state\/}}, \\ 
{\it{store\/}}, \\ 
{\it{set-some-flags\/}}, \\ 
{\it{unary\/}}, \\ 
{\it{direct-a\/}}, \\ 
{\it{direct-b\/}}, \\ 
{\it{side-effect-a\/}}, \\ 
{\it{side-effect-b\/}}, \\ 
{\it{all-t-regs-address\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}})\-\index{next-state})\index{length} \\ 
$=$$\;\;\;\;${\tt{32}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{bvp}}\,({\it{decoded-state\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{decoded-state\/}})\index{length} $=$ {\tt{32}})) \\ 
$\rightarrow$$\;\;\;\;${\rm{bvp}}\,({\rm{next-state}}\,(\=\+{\it{decoded-state\/}}, \\ 
{\it{store\/}}, \\ 
{\it{set-some-flags\/}}, \\ 
{\it{unary\/}}, \\ 
{\it{direct-a\/}}, \\ 
{\it{direct-b\/}}, \\ 
{\it{side-effect-a\/}}, \\ 
{\it{side-effect-b\/}}, \\ 
{\it{all-t-regs-address\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}})\-\index{next-state})\index{bvp})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-length-f\$next-state \\ \index{properp-length-f\$next-state}
\=\+(\=\+{\rm{length}}\,({\rm{f\$next-state}}\,(\=\+{\it{decoded-state\/}}, \\ 
{\it{store\/}}, \\ 
{\it{set-some-flags\/}}, \\ 
{\it{unary\/}}, \\ 
{\it{direct-a\/}}, \\ 
{\it{direct-b\/}}, \\ 
{\it{side-effect-a\/}}, \\ 
{\it{side-effect-b\/}}, \\ 
{\it{all-t-regs-address\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}})\-\index{f\$next-state})\index{length} \\ 
$=$$\;\;\;\;${\tt{32}})\- \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{f\$next-state}}\,(\=\+{\it{decoded-state\/}}, \\ 
{\it{store\/}}, \\ 
{\it{set-some-flags\/}}, \\ 
{\it{unary\/}}, \\ 
{\it{direct-a\/}}, \\ 
{\it{direct-b\/}}, \\ 
{\it{side-effect-a\/}}, \\ 
{\it{side-effect-b\/}}, \\ 
{\it{all-t-regs-address\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}})\-\index{f\$next-state})\index{properp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-state\$value \\ \index{next-state\$value}
\=\+(\=\+{\rm{next-state\&}}\,({\it{netlist\/}})\index{next-state\&} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{decoded-state\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{decoded-state\/}})\index{length} $=$ {\tt{32}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{next-state}}, \\ 
{\rm{append}}\,(\=\+{\it{decoded-state\/}}, \\ 
{\rm{list}}\,(\=\+{\it{store\/}}, \\ 
{\it{set-some-flags\/}}, \\ 
{\it{unary\/}}, \\ 
{\it{direct-a\/}}, \\ 
{\it{direct-b\/}}, \\ 
{\it{side-effect-a\/}}, \\ 
{\it{side-effect-b\/}}, \\ 
{\it{all-t-regs-address\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}})\-)\-, \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$next-state}}\,(\=\+{\it{decoded-state\/}}, \\ 
{\it{store\/}}, \\ 
{\it{set-some-flags\/}}, \\ 
{\it{unary\/}}, \\ 
{\it{direct-a\/}}, \\ 
{\it{direct-b\/}}, \\ 
{\it{side-effect-a\/}}, \\ 
{\it{side-effect-b\/}}, \\ 
{\it{all-t-regs-address\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}})\-\index{f\$next-state})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable next-state\$value; name this event `next-state\$value-off'.\index{next-state\$value-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN CV
 (DECODED-STATE RN-A RN-B OP-CODE PC-REG REGS-ADDRESS SET-FLAGS STORE C
                A-IMMEDIATE-P RW- DIRECT-A SIDE-EFFECT-A SIDE-EFFECT-B
                PRE-DEC-A PRE-DEC-B)
 (CONS
  (B-AND (B-NAND (B-NOT RW-)
                 (NTH 0 DECODED-STATE))
         (B-NOR3 (NTH 17 DECODED-STATE)
                 (NTH 18 DECODED-STATE)
                 (NTH 19 DECODED-STATE)))
  (CONS
   (B-NOR8 (NTH 2 DECODED-STATE)
           (NTH 3 DECODED-STATE)
           (NTH 10 DECODED-STATE)
           (NTH 11 DECODED-STATE)
           (NTH 14 DECODED-STATE)
           (NTH 15 DECODED-STATE)
           (NTH 18 DECODED-STATE)
           (NTH 19 DECODED-STATE))
   (CONS
    (B-NOT (NTH 24 DECODED-STATE))
    (CONS
     (B-NAND5 (B-NAND STORE (NTH 7 DECODED-STATE))
              (B-NAND SIDE-EFFECT-A
                      (NTH 9 DECODED-STATE))
              (B-NAND3 (B-NOT STORE)
                       SIDE-EFFECT-B
                       (NTH 14 DECODED-STATE))
              (B-NAND SIDE-EFFECT-B
                      (NTH 17 DECODED-STATE))
              (B-NOR5 (NTH 2 DECODED-STATE)
                      (NTH 21 DECODED-STATE)
                      (NTH 23 DECODED-STATE)
                      (NTH 28 DECODED-STATE)
                      (NTH 30 DECODED-STATE)))
     (CONS
      (B-NAND (B-NAND DIRECT-A
                      (NTH 13 DECODED-STATE))
              (B-NOR6 (NTH 0 DECODED-STATE)
                      (NTH 5 DECODED-STATE)
                      (NTH 8 DECODED-STATE)
                      (NTH 11 DECODED-STATE)
                      (NTH 20 DECODED-STATE)
                      (NTH 29 DECODED-STATE)))
      (CONS
       (B-NAND (B-NOR4 (NTH 6 DECODED-STATE)
                       (NTH 7 DECODED-STATE)
                       (NTH 10 DECODED-STATE)
                       (NTH 12 DECODED-STATE))
               (B-NOR4 (NTH 15 DECODED-STATE)
                       (NTH 16 DECODED-STATE)
                       (NTH 22 DECODED-STATE)
                       (NTH 29 DECODED-STATE)))
       (CONS
        (B-OR (NTH 3 DECODED-STATE)
              (NTH 29 DECODED-STATE))
        (CONS
         (B-OR (NTH 16 DECODED-STATE)
               (NTH 28 DECODED-STATE))
         (CONS
          (B-NAND (B-NOR3 (NTH 0 DECODED-STATE)
                          (NTH 8 DECODED-STATE)
                          (NTH 12 DECODED-STATE))
                  (B-NOR (NTH 16 DECODED-STATE)
                         (NTH 29 DECODED-STATE)))
          (CONS
           (B-OR3 (NTH 0 DECODED-STATE)
                  (NTH 24 DECODED-STATE)
                  (NTH 28 DECODED-STATE))
           (CONS
            (B-OR (NTH 24 DECODED-STATE)
                  (NTH 28 DECODED-STATE))
            (CONS
             (B-OR3 (NTH 3 DECODED-STATE)
                    (NTH 11 DECODED-STATE)
                    (NTH 15 DECODED-STATE))
             (CONS
              (B-NAND (B-NAND PRE-DEC-A
                              (NTH 8 DECODED-STATE))
                      (B-NAND PRE-DEC-B
                              (B-OR (NTH 12 DECODED-STATE)
                                    (NTH 16 DECODED-STATE))))
              (CONS
               (B-AND A-IMMEDIATE-P
                      (B-OR (NTH 5 DECODED-STATE)
                            (NTH 13 DECODED-STATE)))
               (CONS
                (CARRY-IN-HELP
                 (CONS C
                  (CONS
                     (B-OR4 (NTH 0 DECODED-STATE)
                            (NTH 28 DECODED-STATE)
                            (NTH 29 DECODED-STATE)
                            (NTH 30 DECODED-STATE))
                     (V-IF (B-NOR4 (NTH 2 DECODED-STATE)
                                   (B-OR (NTH 9 DECODED-STATE)
                                         (NTH 21 DECODED-STATE))
                                   (B-OR3 (NTH 14 DECODED-STATE)
                                          (NTH 17 DECODED-STATE)
                                          (NTH 23 DECODED-STATE))
                                   (B-OR4 (NTH 0 DECODED-STATE)
                                          (NTH 28 DECODED-STATE)
                                          (NTH 29 DECODED-STATE)
                                          (NTH 30 DECODED-STATE)))
                           OP-CODE
                           (V-IF (B-NAND (B-NAND (B-OR (NTH 9 DECODED-STATE)
                                                       (NTH 21 DECODED-STATE))
                                                 PRE-DEC-A)
                                         (B-NAND (B-OR3 (NTH 14 DECODED-STATE)
                                                        (NTH 17 DECODED-STATE)
                                                        (NTH 23 DECODED-STATE))
                                                 PRE-DEC-B))
                                 (ALU-DEC-OP)
                                 (ALU-INC-OP))))))
                (CONS
                 (B-OR4 (NTH 0 DECODED-STATE)
                        (NTH 28 DECODED-STATE)
                        (NTH 29 DECODED-STATE)
                        (NTH 30 DECODED-STATE))
                 (APPEND
                  (ENCODE-32 (NTH 0 DECODED-STATE)
                             (NTH 1 DECODED-STATE)
                             (NTH 2 DECODED-STATE)
                             (NTH 3 DECODED-STATE)
                             (NTH 4 DECODED-STATE)
                             (NTH 5 DECODED-STATE)
                             (NTH 6 DECODED-STATE)
                             (NTH 7 DECODED-STATE)
                             (NTH 8 DECODED-STATE)
                             (NTH 9 DECODED-STATE)
                             (NTH 10 DECODED-STATE)
                             (NTH 11 DECODED-STATE)
                             (NTH 12 DECODED-STATE)
                             (NTH 13 DECODED-STATE)
                             (NTH 14 DECODED-STATE)
                             (NTH 15 DECODED-STATE)
                             (NTH 16 DECODED-STATE)
                             (NTH 17 DECODED-STATE)
                             (NTH 18 DECODED-STATE)
                             (NTH 19 DECODED-STATE)
                             (NTH 20 DECODED-STATE)
                             (NTH 21 DECODED-STATE)
                             (NTH 22 DECODED-STATE)
                             (NTH 23 DECODED-STATE)
                             (NTH 24 DECODED-STATE)
                             (NTH 25 DECODED-STATE)
                             (NTH 26 DECODED-STATE)
                             (NTH 27 DECODED-STATE)
                             (NTH 28 DECODED-STATE)
                             (NTH 29 DECODED-STATE)
                             (NTH 30 DECODED-STATE)
                             (NTH 31 DECODED-STATE))
                  (APPEND
                   (V-IF (B-NOR (NTH 7 DECODED-STATE)
                                (NTH 16 DECODED-STATE))
                         (V-IF (NTH 28 DECODED-STATE)
                               (MAKE-LIST 4 T)
                               (MAKE-LIST 4 F))
                         SET-FLAGS)
                   (APPEND
                    (V-IF (B-NAND (B-NOR3 (NTH 5 DECODED-STATE)
                                          (NTH 8 DECODED-STATE)
                                          (NTH 9 DECODED-STATE))
                                  (B-NOR3 (NTH 13 DECODED-STATE)
                                          (NTH 20 DECODED-STATE)
                                          (NTH 21 DECODED-STATE)))
                          RN-A
                          (V-IF (B-NAND (B-NOR5 (NTH 6 DECODED-STATE)
                                                (NTH 7 DECODED-STATE)
                                                (NTH 10 DECODED-STATE)
                                                (NTH 12 DECODED-STATE)
                                                (NTH 14 DECODED-STATE))
                                        (B-NOR4 (NTH 16 DECODED-STATE)
                                                (NTH 17 DECODED-STATE)
                                                (NTH 22 DECODED-STATE)
                                                (NTH 23 DECODED-STATE)))
                                RN-B
                                (V-IF (B-OR (NTH 28 DECODED-STATE)
                                            (NTH 29 DECODED-STATE))
                                      (MAKE-LIST 4 F)
                                      (V-IF (NTH 30 DECODED-STATE)
                                            (V-INC REGS-ADDRESS)
                                            PC-REG))))
                    (APPEND
                     (V-IF (B-NOR4 (NTH 2 DECODED-STATE)
                                   (B-OR (NTH 9 DECODED-STATE)
                                         (NTH 21 DECODED-STATE))
                                   (B-OR3 (NTH 14 DECODED-STATE)
                                          (NTH 17 DECODED-STATE)
                                          (NTH 23 DECODED-STATE))
                                   (B-OR4 (NTH 0 DECODED-STATE)
                                          (NTH 28 DECODED-STATE)
                                          (NTH 29 DECODED-STATE)
                                          (NTH 30 DECODED-STATE)))
                           OP-CODE
                           (V-IF (B-NAND (B-NAND (B-OR (NTH 9 DECODED-STATE)
                                                       (NTH 21 DECODED-STATE))
                                                 PRE-DEC-A)
                                         (B-NAND (B-OR3 (NTH 14 DECODED-STATE)
                                                        (NTH 17 DECODED-STATE)
                                                        (NTH 23 DECODED-STATE))
                                                 PRE-DEC-B))
                                 (ALU-DEC-OP)
                                 (ALU-INC-OP)))
                     (MPG
                      (CONS
                       (B-OR4 (NTH 0 DECODED-STATE)
                              (NTH 28 DECODED-STATE)
                              (NTH 29 DECODED-STATE)
                              (NTH 30 DECODED-STATE))
                       (CONS
                        (B-OR3 (NTH 14 DECODED-STATE)
                               (NTH 17 DECODED-STATE)
                               (NTH 23 DECODED-STATE))
                        (V-IF
                           (B-NOR4 (NTH 2 DECODED-STATE)
                                   (B-OR (NTH 9 DECODED-STATE)
                                         (NTH 21 DECODED-STATE))
                                   (B-OR3 (NTH 14 DECODED-STATE)
                                          (NTH 17 DECODED-STATE)
                                          (NTH 23 DECODED-STATE))
                                   (B-OR4 (NTH 0 DECODED-STATE)
                                          (NTH 28 DECODED-STATE)
                                          (NTH 29 DECODED-STATE)
                                          (NTH 30 DECODED-STATE)))
                           OP-CODE
                           (V-IF (B-NAND (B-NAND (B-OR (NTH 9 DECODED-STATE)
                                                       (NTH 21 DECODED-STATE))
                                                 PRE-DEC-A)
                                         (B-NAND (B-OR3 (NTH 14 DECODED-STATE)
                                                        (NTH 17 DECODED-STATE)
                                                        (NTH 23 DECODED-STATE))
                                                 PRE-DEC-B))
                                 (ALU-DEC-OP)
                                 (ALU-INC-OP)))))))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable cv; name this event `cv-off'.\index{cv-off}

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN F$CV
 (DECODED-STATE RN-A RN-B OP-CODE PC-REG REGS-ADDRESS SET-FLAGS STORE C
                A-IMMEDIATE-P RW- DIRECT-A SIDE-EFFECT-A SIDE-EFFECT-B
                PRE-DEC-A PRE-DEC-B)
 (CONS
  (F-AND (F-NAND (F-NOT RW-)
                 (NTH 0 DECODED-STATE))
         (F-NOR3 (NTH 17 DECODED-STATE)
                 (NTH 18 DECODED-STATE)
                 (NTH 19 DECODED-STATE)))
  (CONS
   (F-NOR8 (NTH 2 DECODED-STATE)
           (NTH 3 DECODED-STATE)
           (NTH 10 DECODED-STATE)
           (NTH 11 DECODED-STATE)
           (NTH 14 DECODED-STATE)
           (NTH 15 DECODED-STATE)
           (NTH 18 DECODED-STATE)
           (NTH 19 DECODED-STATE))
   (CONS
    (F-NOT (NTH 24 DECODED-STATE))
    (CONS
     (F-NAND5 (F-NAND STORE (NTH 7 DECODED-STATE))
              (F-NAND SIDE-EFFECT-A
                      (NTH 9 DECODED-STATE))
              (F-NAND3 (F-NOT STORE)
                       SIDE-EFFECT-B
                       (NTH 14 DECODED-STATE))
              (F-NAND SIDE-EFFECT-B
                      (NTH 17 DECODED-STATE))
              (F-NOR5 (NTH 2 DECODED-STATE)
                      (NTH 21 DECODED-STATE)
                      (NTH 23 DECODED-STATE)
                      (NTH 28 DECODED-STATE)
                      (NTH 30 DECODED-STATE)))
     (CONS
      (F-NAND (F-NAND DIRECT-A
                      (NTH 13 DECODED-STATE))
              (F-NOR6 (NTH 0 DECODED-STATE)
                      (NTH 5 DECODED-STATE)
                      (NTH 8 DECODED-STATE)
                      (NTH 11 DECODED-STATE)
                      (NTH 20 DECODED-STATE)
                      (NTH 29 DECODED-STATE)))
      (CONS
       (F-NAND (F-NOR4 (NTH 6 DECODED-STATE)
                       (NTH 7 DECODED-STATE)
                       (NTH 10 DECODED-STATE)
                       (NTH 12 DECODED-STATE))
               (F-NOR4 (NTH 15 DECODED-STATE)
                       (NTH 16 DECODED-STATE)
                       (NTH 22 DECODED-STATE)
                       (NTH 29 DECODED-STATE)))
       (CONS
        (F-OR (NTH 3 DECODED-STATE)
              (NTH 29 DECODED-STATE))
        (CONS
         (F-OR (NTH 16 DECODED-STATE)
               (NTH 28 DECODED-STATE))
         (CONS
          (F-NAND (F-NOR3 (NTH 0 DECODED-STATE)
                          (NTH 8 DECODED-STATE)
                          (NTH 12 DECODED-STATE))
                  (F-NOR (NTH 16 DECODED-STATE)
                         (NTH 29 DECODED-STATE)))
          (CONS
           (F-OR3 (NTH 0 DECODED-STATE)
                  (NTH 24 DECODED-STATE)
                  (NTH 28 DECODED-STATE))
           (CONS
            (F-OR (NTH 24 DECODED-STATE)
                  (NTH 28 DECODED-STATE))
            (CONS
             (F-OR3 (NTH 3 DECODED-STATE)
                    (NTH 11 DECODED-STATE)
                    (NTH 15 DECODED-STATE))
             (CONS
              (F-NAND (F-NAND PRE-DEC-A
                              (NTH 8 DECODED-STATE))
                      (F-NAND PRE-DEC-B
                              (F-OR (NTH 12 DECODED-STATE)
                                    (NTH 16 DECODED-STATE))))
              (CONS
               (F-AND A-IMMEDIATE-P
                      (F-OR (NTH 5 DECODED-STATE)
                            (NTH 13 DECODED-STATE)))
               (CONS
                (F$CARRY-IN-HELP
                 (CONS C
                  (CONS
                   (F-OR4 (NTH 0 DECODED-STATE)
                          (NTH 28 DECODED-STATE)
                          (NTH 29 DECODED-STATE)
                          (NTH 30 DECODED-STATE))
                   (F$SELECT-OP-CODE
                                 (F-NOR4 (NTH 2 DECODED-STATE)
                                         (F-OR (NTH 9 DECODED-STATE)
                                               (NTH 21 DECODED-STATE))
                                         (F-OR3 (NTH 14 DECODED-STATE)
                                                (NTH 17 DECODED-STATE)
                                                (NTH 23 DECODED-STATE))
                                         (F-OR4 (NTH 0 DECODED-STATE)
                                                (NTH 28 DECODED-STATE)
                                                (NTH 29 DECODED-STATE)
                                                (NTH 30 DECODED-STATE)))
                                 (F-NAND (F-NAND (F-OR (NTH 9 DECODED-STATE)
                                                       (NTH 21 DECODED-STATE))
                                                 PRE-DEC-A)
                                         (F-NAND (F-OR3 (NTH 14 DECODED-STATE)
                                                        (NTH 17 DECODED-STATE)
                                                        (NTH 23 DECODED-STATE))
                                                 PRE-DEC-B))
                                 OP-CODE))))
                (CONS
                 (F-OR4 (NTH 0 DECODED-STATE)
                        (NTH 28 DECODED-STATE)
                        (NTH 29 DECODED-STATE)
                        (NTH 30 DECODED-STATE))
                 (APPEND
                  (F$ENCODE-32 (NTH 0 DECODED-STATE)
                               (NTH 1 DECODED-STATE)
                               (NTH 2 DECODED-STATE)
                               (NTH 3 DECODED-STATE)
                               (NTH 4 DECODED-STATE)
                               (NTH 5 DECODED-STATE)
                               (NTH 6 DECODED-STATE)
                               (NTH 7 DECODED-STATE)
                               (NTH 8 DECODED-STATE)
                               (NTH 9 DECODED-STATE)
                               (NTH 10 DECODED-STATE)
                               (NTH 11 DECODED-STATE)
                               (NTH 12 DECODED-STATE)
                               (NTH 13 DECODED-STATE)
                               (NTH 14 DECODED-STATE)
                               (NTH 15 DECODED-STATE)
                               (NTH 16 DECODED-STATE)
                               (NTH 17 DECODED-STATE)
                               (NTH 18 DECODED-STATE)
                               (NTH 19 DECODED-STATE)
                               (NTH 20 DECODED-STATE)
                               (NTH 21 DECODED-STATE)
                               (NTH 22 DECODED-STATE)
                               (NTH 23 DECODED-STATE)
                               (NTH 24 DECODED-STATE)
                               (NTH 25 DECODED-STATE)
                               (NTH 26 DECODED-STATE)
                               (NTH 27 DECODED-STATE)
                               (NTH 28 DECODED-STATE)
                               (NTH 29 DECODED-STATE)
                               (NTH 30 DECODED-STATE)
                               (NTH 31 DECODED-STATE))
                  (APPEND
                   (FV-IF (F-NOR (NTH 7 DECODED-STATE)
                                 (NTH 16 DECODED-STATE))
                          (MAKE-LIST 4
                                     (THREEFIX (NTH 28 DECODED-STATE)))
                          SET-FLAGS)
                   (APPEND
                    (FV-IF (F-NAND (F-NOR3 (NTH 5 DECODED-STATE)
                                           (NTH 8 DECODED-STATE)
                                           (NTH 9 DECODED-STATE))
                                   (F-NOR3 (NTH 13 DECODED-STATE)
                                           (NTH 20 DECODED-STATE)
                                           (NTH 21 DECODED-STATE)))
                           RN-A
                           (FV-IF (F-NAND (F-NOR5 (NTH 6 DECODED-STATE)
                                                  (NTH 7 DECODED-STATE)
                                                  (NTH 10 DECODED-STATE)
                                                  (NTH 12 DECODED-STATE)
                                                  (NTH 14 DECODED-STATE))
                                          (F-NOR4 (NTH 16 DECODED-STATE)
                                                  (NTH 17 DECODED-STATE)
                                                  (NTH 22 DECODED-STATE)
                                                  (NTH 23 DECODED-STATE)))
                                  RN-B
                                  (F$V-IF-F-4 (F-OR (NTH 28 DECODED-STATE)
                                                    (NTH 29 DECODED-STATE))
                                              (FV-IF (NTH 30 DECODED-STATE)
                                                     (F$V-INC4$V REGS-ADDRESS)
                                                     PC-REG))))
                    (APPEND
                     (F$SELECT-OP-CODE
                                 (F-NOR4 (NTH 2 DECODED-STATE)
                                         (F-OR (NTH 9 DECODED-STATE)
                                               (NTH 21 DECODED-STATE))
                                         (F-OR3 (NTH 14 DECODED-STATE)
                                                (NTH 17 DECODED-STATE)
                                                (NTH 23 DECODED-STATE))
                                         (F-OR4 (NTH 0 DECODED-STATE)
                                                (NTH 28 DECODED-STATE)
                                                (NTH 29 DECODED-STATE)
                                                (NTH 30 DECODED-STATE)))
                                 (F-NAND (F-NAND (F-OR (NTH 9 DECODED-STATE)
                                                       (NTH 21 DECODED-STATE))
                                                 PRE-DEC-A)
                                         (F-NAND (F-OR3 (NTH 14 DECODED-STATE)
                                                        (NTH 17 DECODED-STATE)
                                                        (NTH 23 DECODED-STATE))
                                                 PRE-DEC-B))
                                 OP-CODE)
                     (F$MPG
                      (CONS
                       (F-OR4 (NTH 0 DECODED-STATE)
                              (NTH 28 DECODED-STATE)
                              (NTH 29 DECODED-STATE)
                              (NTH 30 DECODED-STATE))
                       (CONS
                        (F-OR3 (NTH 14 DECODED-STATE)
                               (NTH 17 DECODED-STATE)
                               (NTH 23 DECODED-STATE))
                        (F$SELECT-OP-CODE
                                 (F-NOR4 (NTH 2 DECODED-STATE)
                                         (F-OR (NTH 9 DECODED-STATE)
                                               (NTH 21 DECODED-STATE))
                                         (F-OR3 (NTH 14 DECODED-STATE)
                                                (NTH 17 DECODED-STATE)
                                                (NTH 23 DECODED-STATE))
                                         (F-OR4 (NTH 0 DECODED-STATE)
                                                (NTH 28 DECODED-STATE)
                                                (NTH 29 DECODED-STATE)
                                                (NTH 30 DECODED-STATE)))
                                 (F-NAND (F-NAND (F-OR (NTH 9 DECODED-STATE)
                                                       (NTH 21 DECODED-STATE))
                                                 PRE-DEC-A)
                                         (F-NAND (F-OR3 (NTH 14 DECODED-STATE)
                                                        (NTH 17 DECODED-STATE)
                                                        (NTH 23 DECODED-STATE))
                                                 PRE-DEC-B))
                                 OP-CODE)))))))))))))))))))))))))
\end{verbatim}



\noindent{\sc Event}:   Enable f\$cv; name this event `f\$cv-off'.\index{f\$cv-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  make-list-crock-for-f\$cv=cv \\ \index{make-list-crock-for-f\$cv=cv}
\=\+{\rm{boolp}}\,({\it{v\/}})\index{boolp} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{make-list}}\,({\tt{4}}, {\it{v\/}})\index{make-list} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{v\/}}$\;\;${\bf then }{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}) \\ 
{\bf else }{\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}})$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable make-list-crock-for-f\$cv=cv; name this event `make-list-crock-for-f\$cv=cv-off'.\index{make-list-crock-for-f\$cv=cv-of!f}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$cv=cv \\ \index{f\$cv=cv}
\=\+(\=\+{\rm{bvp}}\,({\it{decoded-state\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{decoded-state\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{rn-a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{rn-a\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{rn-b\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{rn-b\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{op-code\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{op-code\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{pc-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{pc-reg\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{regs-address\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{regs-address\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{set-flags\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{set-flags\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{store\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{c\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{a-immediate-p\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{direct-a\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{side-effect-a\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{side-effect-b\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{pre-dec-a\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{pre-dec-b\/}})\index{boolp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$cv}}\,(\=\+{\it{decoded-state\/}}, \\ 
{\it{rn-a\/}}, \\ 
{\it{rn-b\/}}, \\ 
{\it{op-code\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\it{store\/}}, \\ 
{\it{c\/}}, \\ 
{\it{a-immediate-p\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{direct-a\/}}, \\ 
{\it{side-effect-a\/}}, \\ 
{\it{side-effect-b\/}}, \\ 
{\it{pre-dec-a\/}}, \\ 
{\it{pre-dec-b\/}})\-\index{f\$cv} \\ 
$=$$\;\;\;\;${\rm{cv}}\,(\=\+{\it{decoded-state\/}}, \\ 
{\it{rn-a\/}}, \\ 
{\it{rn-b\/}}, \\ 
{\it{op-code\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\it{store\/}}, \\ 
{\it{c\/}}, \\ 
{\it{a-immediate-p\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{direct-a\/}}, \\ 
{\it{side-effect-a\/}}, \\ 
{\it{side-effect-b\/}}, \\ 
{\it{pre-dec-a\/}}, \\ 
{\it{pre-dec-b\/}})\-\index{cv})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-length-cv \\ \index{bvp-length-cv}
\=\+(\=\+(\=\+({\rm{length}}\,({\it{set-flags\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{rn-a\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{rn-b\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{op-code\/}})\index{length} $=$ {\tt{4}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{length}}\,({\rm{cv}}\,(\=\+{\it{decoded-state\/}}, \\ 
{\it{rn-a\/}}, \\ 
{\it{rn-b\/}}, \\ 
{\it{op-code\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\it{store\/}}, \\ 
{\it{c\/}}, \\ 
{\it{a-immediate-p\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{direct-a\/}}, \\ 
{\it{side-effect-a\/}}, \\ 
{\it{side-effect-b\/}}, \\ 
{\it{pre-dec-a\/}}, \\ 
{\it{pre-dec-b\/}})\-\index{cv})\index{length} \\ 
$=$$\;\;\;\;${\tt{40}})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{bvp}}\,({\it{decoded-state\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{decoded-state\/}})\index{length} $=$ {\tt{32}})) \\ 
$\rightarrow$$\;\;\;\;${\rm{bvp}}\,({\rm{cv}}\,(\=\+{\it{decoded-state\/}}, \\ 
{\it{rn-a\/}}, \\ 
{\it{rn-b\/}}, \\ 
{\it{op-code\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\it{store\/}}, \\ 
{\it{c\/}}, \\ 
{\it{a-immediate-p\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{direct-a\/}}, \\ 
{\it{side-effect-a\/}}, \\ 
{\it{side-effect-b\/}}, \\ 
{\it{pre-dec-a\/}}, \\ 
{\it{pre-dec-b\/}})\-\index{cv})\index{bvp})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-length-f\$cv \\ \index{properp-length-f\$cv}
\=\+(\=\+(\=\+({\rm{length}}\,({\it{set-flags\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{rn-a\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{rn-b\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{op-code\/}})\index{length} $=$ {\tt{4}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{length}}\,({\rm{f\$cv}}\,(\=\+{\it{decoded-state\/}}, \\ 
{\it{rn-a\/}}, \\ 
{\it{rn-b\/}}, \\ 
{\it{op-code\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\it{store\/}}, \\ 
{\it{c\/}}, \\ 
{\it{a-immediate-p\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{direct-a\/}}, \\ 
{\it{side-effect-a\/}}, \\ 
{\it{side-effect-b\/}}, \\ 
{\it{pre-dec-a\/}}, \\ 
{\it{pre-dec-b\/}})\-\index{f\$cv})\index{length} \\ 
$=$$\;\;\;\;${\tt{40}})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{properp}}\,({\it{decoded-state\/}})\index{properp} $\wedge$ ({\rm{length}}\,({\it{decoded-state\/}})\index{length} $=$ {\tt{32}})) \\ 
$\rightarrow$$\;\;\;\;${\rm{properp}}\,({\rm{f\$cv}}\,(\=\+{\it{decoded-state\/}}, \\ 
{\it{rn-a\/}}, \\ 
{\it{rn-b\/}}, \\ 
{\it{op-code\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\it{store\/}}, \\ 
{\it{c\/}}, \\ 
{\it{a-immediate-p\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{direct-a\/}}, \\ 
{\it{side-effect-a\/}}, \\ 
{\it{side-effect-b\/}}, \\ 
{\it{pre-dec-a\/}}, \\ 
{\it{pre-dec-b\/}})\-\index{f\$cv})\index{properp})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cv*} \\  
\=\+{\sc{cv*}}\index{cv*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\tt{'}}{\tt{cv}}, \\ 
{\rm{cons}}\,(\=\+{\rm{append8}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{0}}, {\tt{32}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{rn-a}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{rn-b}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{op-code}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{pc-reg}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{regs-address}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{set-flags}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{store}}{\tt{ }}{\tt{c}}{\tt{ }}{\tt{a-immediate-p}}{\tt{ }}{\tt{rw-}}{\tt{ }}{\tt{direct-a}} \\ 
{\tt{side-effect-a}}{\tt{ }}{\tt{side-effect-b}}{\tt{ }}{\tt{pre-dec-a}} \\ 
{\tt{pre-dec-b}}{\tt{)}}\-)\-\index{append8}, \\ 
{\rm{cons}}\,(\=\+{\rm{append6}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{new-rw-}}{\tt{ }}{\tt{strobe-}}{\tt{ }}{\tt{hdack-}}{\tt{ }}{\tt{we-regs}} \\ 
{\tt{we-a-reg}}{\tt{ }}{\tt{we-b-reg}}{\tt{ }}{\tt{we-i-reg}} \\ 
{\tt{we-data-out}}{\tt{ }}{\tt{we-addr-out}}{\tt{ }}{\tt{we-hold-}} \\ 
{\tt{we-pc-reg}}{\tt{ }}{\tt{data-in-select}} \\ 
{\tt{dec-addr-out}}{\tt{ }}{\tt{select-immediate}}{\tt{ }}{\tt{alu-c}} \\ 
{\tt{alu-zero}}{\tt{)}}\-, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{state}}, {\tt{0}}, {\tt{5}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{we-flags}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{new-regs-address}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{alu-op}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{alu-mpg}}, {\tt{0}}, {\tt{7}})\index{indices})\-\index{append6}, \\ 
{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-fetch0}}, \\ 
{\tt{'}}{\tt{(}}{\tt{fetch0}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{0}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-fetch1}}, \\ 
{\tt{'}}{\tt{(}}{\tt{fetch1}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{1}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-fetch2}}, \\ 
{\tt{'}}{\tt{(}}{\tt{fetch2}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{2}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-fetch3}}, \\ 
{\tt{'}}{\tt{(}}{\tt{fetch3}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{3}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-decode}}, \\ 
{\tt{'}}{\tt{(}}{\tt{decode}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{4}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-rega}}, \\ 
{\tt{'}}{\tt{(}}{\tt{rega}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{5}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-regb}}, \\ 
{\tt{'}}{\tt{(}}{\tt{regb}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{6}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-update}}, \\ 
{\tt{'}}{\tt{(}}{\tt{update}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{7}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-reada0}}, \\ 
{\tt{'}}{\tt{(}}{\tt{reada0}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{8}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-reada1}}, \\ 
{\tt{'}}{\tt{(}}{\tt{reada1}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{9}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-reada2}}, \\ 
{\tt{'}}{\tt{(}}{\tt{reada2}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{10}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-reada3}}, \\ 
{\tt{'}}{\tt{(}}{\tt{reada3}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{11}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-readb0}}, \\ 
{\tt{'}}{\tt{(}}{\tt{readb0}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{12}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-readb1}}, \\ 
{\tt{'}}{\tt{(}}{\tt{readb1}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{13}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-readb2}}, \\ 
{\tt{'}}{\tt{(}}{\tt{readb2}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{14}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-readb3}}, \\ 
{\tt{'}}{\tt{(}}{\tt{readb3}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{15}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-write0}}, \\ 
{\tt{'}}{\tt{(}}{\tt{write0}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{16}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-write1}}, \\ 
{\tt{'}}{\tt{(}}{\tt{write1}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{17}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-write2}}, \\ 
{\tt{'}}{\tt{(}}{\tt{write2}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{18}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-write3}}, \\ 
{\tt{'}}{\tt{(}}{\tt{write3}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{19}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-sefa0}}, \\ 
{\tt{'}}{\tt{(}}{\tt{sefa0}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{20}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-sefa1}}, \\ 
{\tt{'}}{\tt{(}}{\tt{sefa1}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{21}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-sefb0}}, \\ 
{\tt{'}}{\tt{(}}{\tt{sefb0}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{22}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-sefb1}}, \\ 
{\tt{'}}{\tt{(}}{\tt{sefb1}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{23}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-hold0}}, \\ 
{\tt{'}}{\tt{(}}{\tt{hold0}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{24}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-hold1}}, \\ 
{\tt{'}}{\tt{(}}{\tt{hold1}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{25}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-v11010}}, \\ 
{\tt{'}}{\tt{(}}{\tt{v11010}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{26}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-v11011}}, \\ 
{\tt{'}}{\tt{(}}{\tt{v11011}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{27}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-reset0}}, \\ 
{\tt{'}}{\tt{(}}{\tt{reset0}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{28}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-reset1}}, \\ 
{\tt{'}}{\tt{(}}{\tt{reset1}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{29}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-reset2}}, \\ 
{\tt{'}}{\tt{(}}{\tt{reset2}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{30}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g-v11111}}, \\ 
{\tt{'}}{\tt{(}}{\tt{v11111}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{31}})\index{index}))\-, \\ 
{\tt{'}}{\tt{(}}{\tt{g0}}{\tt{ }}{\tt{(}}{\tt{store-}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{store}}{\tt{)}}{\tt{)}}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g1}} \\ 
{\tt{(}}{\tt{alu-zero}}{\tt{)}} \\ 
{\tt{b-or4}} \\ 
{\tt{(}}{\tt{fetch0}}{\tt{ }}{\tt{reset0}}{\tt{ }}{\tt{reset1}}{\tt{ }}{\tt{reset2}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g2}} \\ 
{\tt{(}}{\tt{alu-swap}}{\tt{)}} \\ 
{\tt{b-or3}} \\ 
{\tt{(}}{\tt{readb2}}{\tt{ }}{\tt{write1}}{\tt{ }}{\tt{sefb1}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g3}} \\ 
{\tt{(}}{\tt{incdeca}}{\tt{)}} \\ 
{\tt{b-or}} \\ 
{\tt{(}}{\tt{reada1}}{\tt{ }}{\tt{sefa1}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g4}} \\ 
{\tt{(}}{\tt{s4}}{\tt{)}} \\ 
{\tt{b-nor4}} \\ 
{\tt{(}}\=\+{\tt{fetch2}}{\tt{ }}{\tt{incdeca}}{\tt{ }}{\tt{alu-swap}}{\tt{ }}{\tt{alu-zero}}{\tt{)}}\-{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g5}} \\ 
{\tt{(}}{\tt{s5}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{incdeca}}{\tt{ }}{\tt{pre-dec-a}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g6}} \\ 
{\tt{(}}{\tt{s6}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{alu-swap}}{\tt{ }}{\tt{pre-dec-b}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}{\tt{g7}}{\tt{ }}{\tt{(}}{\tt{s7}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{s5}}{\tt{ }}{\tt{s6}}{\tt{)}}{\tt{)}}, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g8}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{alu-op}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\tt{'}}{\tt{select-op-code}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{s4}}, \\ 
{\rm{cons}}\,({\tt{'}}{\tt{s7}}, {\rm{indices}}\,({\tt{'}}{\tt{op-code}}, {\tt{0}}, {\tt{4}})\index{indices}))\-)\-, \\ 
{\tt{'}}{\tt{(}}{\tt{g10}}{\tt{ }}{\tt{(}}{\tt{s10}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{rw-}}{\tt{)}}{\tt{)}}, \\ 
{\tt{'}}{\tt{(}}{\tt{g11}}{\tt{ }}{\tt{(}}{\tt{s11}}{\tt{)}}{\tt{ }}{\tt{b-nand}}{\tt{ }}{\tt{(}}{\tt{s10}}{\tt{ }}{\tt{fetch0}}{\tt{)}}{\tt{)}}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g12}} \\ 
{\tt{(}}{\tt{s12}}{\tt{)}} \\ 
{\tt{b-nor3}} \\ 
{\tt{(}}{\tt{write1}}{\tt{ }}{\tt{write2}}{\tt{ }}{\tt{write3}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}{\tt{g13}}{\tt{ }}{\tt{(}}{\tt{new-rw-}}{\tt{)}}{\tt{ }}{\tt{b-and}}{\tt{ }}{\tt{(}}{\tt{s11}}{\tt{ }}{\tt{s12}}{\tt{)}}{\tt{)}}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g14}} \\ 
{\tt{(}}{\tt{strobe-}}{\tt{)}} \\ 
{\tt{b-nor8}} \\ 
{\tt{(}}\=\+{\tt{fetch2}}{\tt{ }}{\tt{fetch3}}{\tt{ }}{\tt{reada2}}{\tt{ }}{\tt{reada3}} \\ 
{\tt{readb2}}{\tt{ }}{\tt{readb3}}{\tt{ }}{\tt{write2}}{\tt{ }}{\tt{write3}}{\tt{)}}\-{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}{\tt{g15}}{\tt{ }}{\tt{(}}{\tt{hdack-}}{\tt{)}}{\tt{ }}{\tt{b-not}}{\tt{ }}{\tt{(}}{\tt{hold0}}{\tt{)}}{\tt{)}}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g17}} \\ 
{\tt{(}}{\tt{s17}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{store}}{\tt{ }}{\tt{update}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g18}} \\ 
{\tt{(}}{\tt{s18}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{side-effect-a}}{\tt{ }}{\tt{reada1}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g19}} \\ 
{\tt{(}}{\tt{s19}}{\tt{)}} \\ 
{\tt{b-nand3}} \\ 
{\tt{(}}{\tt{store-}}{\tt{ }}{\tt{side-effect-b}}{\tt{ }}{\tt{readb2}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g20}} \\ 
{\tt{(}}{\tt{s20}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{side-effect-b}}{\tt{ }}{\tt{write1}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g21}} \\ 
{\tt{(}}{\tt{s21}}{\tt{)}} \\ 
{\tt{b-nor5}} \\ 
{\tt{(}}\=\+{\tt{fetch2}}{\tt{ }}{\tt{sefa1}}{\tt{ }}{\tt{sefb1}}{\tt{ }}{\tt{reset0}}{\tt{ }}{\tt{reset2}}{\tt{)}}\-{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g22}} \\ 
{\tt{(}}{\tt{we-regs}}{\tt{)}} \\ 
{\tt{b-nand5}} \\ 
{\tt{(}}{\tt{s17}}{\tt{ }}{\tt{s18}}{\tt{ }}{\tt{s19}}{\tt{ }}{\tt{s20}}{\tt{ }}{\tt{s21}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g23}} \\ 
{\tt{(}}{\tt{s23}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{direct-a}}{\tt{ }}{\tt{readb1}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g24}} \\ 
{\tt{(}}{\tt{s24}}{\tt{)}} \\ 
{\tt{b-nor6}} \\ 
{\tt{(}}\=\+{\tt{fetch0}}{\tt{ }}{\tt{rega}}{\tt{ }}{\tt{reada0}}{\tt{ }}{\tt{reada3}}{\tt{ }}{\tt{sefa0}} \\ 
{\tt{reset1}}{\tt{)}}\-{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g25}} \\ 
{\tt{(}}{\tt{we-a-reg}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{s23}}{\tt{ }}{\tt{s24}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g26}} \\ 
{\tt{(}}{\tt{s26}}{\tt{)}} \\ 
{\tt{b-nor4}} \\ 
{\tt{(}}{\tt{regb}}{\tt{ }}{\tt{update}}{\tt{ }}{\tt{reada2}}{\tt{ }}{\tt{readb0}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g27}} \\ 
{\tt{(}}{\tt{s27}}{\tt{)}} \\ 
{\tt{b-nor4}} \\ 
{\tt{(}}{\tt{readb3}}{\tt{ }}{\tt{write0}}{\tt{ }}{\tt{sefb0}}{\tt{ }}{\tt{reset1}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g28}} \\ 
{\tt{(}}{\tt{we-b-reg}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{s26}}{\tt{ }}{\tt{s27}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g29}} \\ 
{\tt{(}}{\tt{we-i-reg}}{\tt{)}} \\ 
{\tt{b-or}} \\ 
{\tt{(}}{\tt{fetch3}}{\tt{ }}{\tt{reset1}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g30}} \\ 
{\tt{(}}{\tt{we-data-out}}{\tt{)}} \\ 
{\tt{b-or}} \\ 
{\tt{(}}{\tt{write0}}{\tt{ }}{\tt{reset0}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g31}} \\ 
{\tt{(}}{\tt{s31}}{\tt{)}} \\ 
{\tt{b-nor3}} \\ 
{\tt{(}}{\tt{fetch0}}{\tt{ }}{\tt{reada0}}{\tt{ }}{\tt{readb0}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g32}} \\ 
{\tt{(}}{\tt{s32}}{\tt{)}} \\ 
{\tt{b-nor}} \\ 
{\tt{(}}{\tt{write0}}{\tt{ }}{\tt{reset1}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g33}} \\ 
{\tt{(}}{\tt{we-addr-out}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{s31}}{\tt{ }}{\tt{s32}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g34}} \\ 
{\tt{(}}{\tt{we-hold-}}{\tt{)}} \\ 
{\tt{b-or3}} \\ 
{\tt{(}}{\tt{fetch0}}{\tt{ }}{\tt{hold0}}{\tt{ }}{\tt{reset0}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g35}} \\ 
{\tt{(}}{\tt{we-pc-reg}}{\tt{)}} \\ 
{\tt{b-or}} \\ 
{\tt{(}}{\tt{hold0}}{\tt{ }}{\tt{reset0}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g36}} \\ 
{\tt{(}}{\tt{data-in-select}}{\tt{)}} \\ 
{\tt{b-or3}} \\ 
{\tt{(}}{\tt{fetch3}}{\tt{ }}{\tt{reada3}}{\tt{ }}{\tt{readb3}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g37}} \\ 
{\tt{(}}{\tt{s37}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{pre-dec-a}}{\tt{ }}{\tt{reada0}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}{\tt{g38}}{\tt{ }}{\tt{(}}{\tt{s38}}{\tt{)}}{\tt{ }}{\tt{b-or}}{\tt{ }}{\tt{(}}{\tt{readb0}}{\tt{ }}{\tt{write0}}{\tt{)}}{\tt{)}}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g39}} \\ 
{\tt{(}}{\tt{s39}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{pre-dec-b}}{\tt{ }}{\tt{s38}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g40}} \\ 
{\tt{(}}{\tt{dec-addr-out}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{s37}}{\tt{ }}{\tt{s39}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}{\tt{g41}}{\tt{ }}{\tt{(}}{\tt{s41}}{\tt{)}}{\tt{ }}{\tt{b-or}}{\tt{ }}{\tt{(}}{\tt{rega}}{\tt{ }}{\tt{readb1}}{\tt{)}}{\tt{)}}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g42}} \\ 
{\tt{(}}{\tt{select-immediate}}{\tt{)}} \\ 
{\tt{b-and}} \\ 
{\tt{(}}{\tt{a-immediate-p}}{\tt{ }}{\tt{s41}}{\tt{)}}{\tt{)}}\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g43}}, \\ 
{\tt{'}}{\tt{(}}{\tt{alu-c}}{\tt{)}}, \\ 
{\tt{'}}{\tt{carry-in-help}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{c}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{alu-zero}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{alu-op}}, {\tt{0}}, {\tt{4}})\index{indices})\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g44}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{state}}, {\tt{0}}, {\tt{5}})\index{indices}, \\ 
{\tt{'}}{\tt{encode-32}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{0}}, {\tt{32}})\index{indices})\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{g45}}, \\ 
{\rm{cons}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{fanout-reset0}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\tt{'}}{\tt{(}}{\tt{fanout-4}}{\tt{ }}{\tt{(}}{\tt{reset0}}{\tt{)}}{\tt{)}})\-)\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g46}} \\ 
{\tt{(}}{\tt{s46}}{\tt{)}} \\ 
{\tt{b-nor}} \\ 
{\tt{(}}{\tt{update}}{\tt{ }}{\tt{write0}}{\tt{)}}{\tt{)}}\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g47}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{we-flags}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-if}}, \\ 
{\rm{tree-number}}\,({\rm{make-tree}}\,({\tt{4}})\index{make-tree})\index{tree-number})\-\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{s46}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,(\=\+{\tt{'}}{\tt{fanout-reset0}}, \\ 
{\tt{0}}, \\ 
{\tt{4}})\-\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{set-flags}}, {\tt{0}}, {\tt{4}})\index{indices})\-)\-)\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g48}} \\ 
{\tt{(}}{\tt{s48}}{\tt{)}} \\ 
{\tt{b-nor3}} \\ 
{\tt{(}}{\tt{rega}}{\tt{ }}{\tt{reada0}}{\tt{ }}{\tt{reada1}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g49}} \\ 
{\tt{(}}{\tt{s49}}{\tt{)}} \\ 
{\tt{b-nor3}} \\ 
{\tt{(}}{\tt{readb1}}{\tt{ }}{\tt{sefa0}}{\tt{ }}{\tt{sefa1}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g50}} \\ 
{\tt{(}}{\tt{select-rn-a}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{s48}}{\tt{ }}{\tt{s49}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g51}} \\ 
{\tt{(}}{\tt{s51}}{\tt{)}} \\ 
{\tt{b-nor5}} \\ 
{\tt{(}}\=\+{\tt{regb}}{\tt{ }}{\tt{update}}{\tt{ }}{\tt{reada2}}{\tt{ }}{\tt{readb0}}{\tt{ }}{\tt{readb2}}{\tt{)}}\-{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g52}} \\ 
{\tt{(}}{\tt{s52}}{\tt{)}} \\ 
{\tt{b-nor4}} \\ 
{\tt{(}}{\tt{write0}}{\tt{ }}{\tt{write1}}{\tt{ }}{\tt{sefb0}}{\tt{ }}{\tt{sefb1}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g53}} \\ 
{\tt{(}}{\tt{select-rn-b}}{\tt{)}} \\ 
{\tt{b-nand}} \\ 
{\tt{(}}{\tt{s51}}{\tt{ }}{\tt{s52}}{\tt{)}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{g54}} \\ 
{\tt{(}}{\tt{select-all-f}}{\tt{)}} \\ 
{\tt{b-or}} \\ 
{\tt{(}}{\tt{reset0}}{\tt{ }}{\tt{reset1}}{\tt{)}}{\tt{)}}\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g55}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{v-inc-regs-address}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\tt{'}}{\tt{v-inc4}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{regs-address}}, {\tt{0}}, {\tt{4}})\index{indices})\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g56}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{s56}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-if}}, \\ 
{\rm{tree-number}}\,({\rm{make-tree}}\,({\tt{4}})\index{make-tree})\index{tree-number})\-\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{reset2}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,(\=\+{\tt{'}}{\tt{v-inc-regs-address}}, \\ 
{\tt{0}}, \\ 
{\tt{4}})\-\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{pc-reg}}, {\tt{0}}, {\tt{4}})\index{indices})\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g57}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{s57}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\tt{'}}{\tt{v-if-f-4}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{select-all-f}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{s56}}, {\tt{0}}, {\tt{4}})\index{indices})\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g58}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{s58}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-if}}, \\ 
{\rm{tree-number}}\,({\rm{make-tree}}\,({\tt{4}})\index{make-tree})\index{tree-number})\-\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{select-rn-b}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{rn-b}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{s57}}, {\tt{0}}, {\tt{4}})\index{indices})\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g59}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{new-regs-address}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-if}}, \\ 
{\rm{tree-number}}\,({\rm{make-tree}}\,({\tt{4}})\index{make-tree})\index{tree-number})\-\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{select-rn-a}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{rn-a}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{s58}}, {\tt{0}}, {\tt{4}})\index{indices})\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{g60}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{alu-mpg}}, {\tt{0}}, {\tt{7}})\index{indices}, \\ 
{\tt{'}}{\tt{mpg}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{alu-zero}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{alu-swap}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{alu-op}}, {\tt{0}}, {\tt{4}})\index{indices})\-)\-)\-)\-, \\ 
{\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}})\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cv\&} \\  
\=\+{\rm{cv\&}}\,({\it{netlist\/}})\index{cv\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{cv*}}\index{cv*}) \\ 
$\wedge$$\;\;\;\;${\rm{id\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{id\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-or\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{b-or\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-or3\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{b-or3\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-or4\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{b-or4\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{b-nand\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand3\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{b-nand3\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nand5\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{b-nand5\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nor\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{b-nor\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nor3\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{b-nor3\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nor4\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{b-nor4\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nor5\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{b-nor5\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nor6\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{b-nor6\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-nor8\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{b-nor8\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-and\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{b-and\&} \\ 
$\wedge$$\;\;\;\;${\rm{select-op-code\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{select-op-code\&} \\ 
$\wedge$$\;\;\;\;${\rm{tv-if\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module}, {\rm{make-tree}}\,({\tt{4}})\index{make-tree})\index{tv-if\&} \\ 
$\wedge$$\;\;\;\;${\rm{carry-in-help\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{carry-in-help\&} \\ 
$\wedge$$\;\;\;\;${\rm{encode-32\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{encode-32\&} \\ 
$\wedge$$\;\;\;\;${\rm{fanout-4\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{fanout-4\&} \\ 
$\wedge$$\;\;\;\;${\rm{v-inc4\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{v-inc4\&} \\ 
$\wedge$$\;\;\;\;${\rm{v-if-f-4\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{v-if-f-4\&} \\ 
$\wedge$$\;\;\;\;${\rm{mpg\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{cv}}, {\it{netlist\/}})\index{delete-module})\index{mpg\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\&; name this event `cv\&-off'.\index{cv\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{cv\$netlist} \\  
\=\+{\sc{cv\$netlist}}\index{cv\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{cv*}}\index{cv*}, \\ 
\=\+(\=\+(\=\+(\=\+({\sc{id\$netlist}}\index{id\$netlist} $\cup$ {\sc{b-not\$netlist}}\index{b-not\$netlist}) \\ 
$\cup$$\;\;\;\;$({\sc{b-or\$netlist}}\index{b-or\$netlist} $\cup$ ({\sc{b-or3\$netlist}}\index{b-or3\$netlist} $\cup$ {\sc{b-or4\$netlist}}\index{b-or4\$netlist})))\- \\ 
$\cup$$\;\;\;\;$(\=\+({\sc{b-nand\$netlist}}\index{b-nand\$netlist} $\cup$ {\sc{b-nand3\$netlist}}\index{b-nand3\$netlist}) \\ 
$\cup$$\;\;\;\;$({\sc{b-nor\$netlist}}\index{b-nor\$netlist} $\cup$ {\sc{b-nor3\$netlist}}\index{b-nor3\$netlist}))\-)\- \\ 
$\cup$$\;\;\;\;$(\=\+(\=\+({\sc{b-nor4\$netlist}}\index{b-nor4\$netlist} $\cup$ {\sc{b-nor5\$netlist}}\index{b-nor5\$netlist}) \\ 
$\cup$$\;\;\;\;$({\sc{b-nor6\$netlist}}\index{b-nor6\$netlist} $\cup$ {\sc{b-nor8\$netlist}}\index{b-nor8\$netlist}))\- \\ 
$\cup$$\;\;\;\;$(\=\+({\sc{b-and\$netlist}}\index{b-and\$netlist} $\cup$ {\sc{select-op-code\$netlist}}\index{select-op-code\$netlist}) \\ 
$\cup$$\;\;\;\;$(\=\+{\rm{tv-if\$netlist}}\,({\rm{make-tree}}\,({\tt{4}})\index{make-tree})\index{tv-if\$netlist} \\ 
$\cup$$\;\;\;\;${\sc{carry-in-help\$netlist}}\index{carry-in-help\$netlist})\-)\-)\-)\- \\ 
$\cup$$\;\;\;\;$(\=\+(\=\+({\sc{encode-32\$netlist}}\index{encode-32\$netlist} $\cup$ {\sc{fanout-4\$netlist}}\index{fanout-4\$netlist}) \\ 
$\cup$$\;\;\;\;$({\sc{v-inc4\$netlist}}\index{v-inc4\$netlist} $\cup$ {\sc{v-if-f-4\$netlist}}\index{v-if-f-4\$netlist}))\- \\ 
$\cup$$\;\;\;\;$({\sc{mpg\$netlist}}\index{mpg\$netlist} $\cup$ {\sc{b-nand5\$netlist}}\index{b-nand5\$netlist}))\-\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  check-cv\$netlist \\ \index{check-cv\$netlist}
{\rm{cv\&}}\,({\sc{cv\$netlist}}\index{cv\$netlist})\index{cv\&}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  cv\$value \\ \index{cv\$value}
\=\+(\=\+{\rm{cv\&}}\,({\it{netlist\/}})\index{cv\&} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{decoded-state\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{decoded-state\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{rn-a\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{rn-a\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{rn-b\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{rn-b\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{op-code\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{op-code\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{pc-reg\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{pc-reg\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{regs-address\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{regs-address\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{set-flags\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{set-flags\/}})\index{length} $=$ {\tt{4}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{cv}}, \\ 
{\rm{append}}\,(\=\+{\it{decoded-state\/}}, \\ 
{\rm{append}}\,(\=\+{\it{rn-a\/}}, \\ 
{\rm{append}}\,(\=\+{\it{rn-b\/}}, \\ 
{\rm{append}}\,(\=\+{\it{op-code\/}}, \\ 
{\rm{append}}\,(\=\+{\it{pc-reg\/}}, \\ 
{\rm{append}}\,(\=\+{\it{regs-address\/}}, \\ 
{\rm{append}}\,(\=\+{\it{set-flags\/}}, \\ 
{\rm{list}}\,(\=\+{\it{store\/}}, \\ 
{\it{c\/}}, \\ 
{\it{a-immediate-p\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{direct-a\/}}, \\ 
{\it{side-effect-a\/}}, \\ 
{\it{side-effect-b\/}}, \\ 
{\it{pre-dec-a\/}}, \\ 
{\it{pre-dec-b\/}})\-)\-)\-)\-)\-)\-)\-)\-, \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$cv}}\,(\=\+{\it{decoded-state\/}}, \\ 
{\it{rn-a\/}}, \\ 
{\it{rn-b\/}}, \\ 
{\it{op-code\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\it{store\/}}, \\ 
{\it{c\/}}, \\ 
{\it{a-immediate-p\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{direct-a\/}}, \\ 
{\it{side-effect-a\/}}, \\ 
{\it{side-effect-b\/}}, \\ 
{\it{pre-dec-a\/}}, \\ 
{\it{pre-dec-b\/}})\-\index{f\$cv})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable cv\$value; name this event `cv\$value-off'.\index{cv\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{next-cntl-state} \\  
\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{state\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv}}\,(\=\+{\rm{next-state}}\,(\=\+{\rm{decode-5}}\,({\rm{v-if}}\,({\it{reset-\/}}, {\it{state\/}}, {\sc{v\_v11111}}\index{v\_v11111})\index{v-if})\index{decode-5}, \\ 
{\rm{store-resultp}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, {\it{flags\/}})\index{store-resultp}, \\ 
{\rm{set-some-flags}}\,({\rm{set-flags}}\,({\it{i-reg\/}})\index{set-flags})\index{set-some-flags}, \\ 
{\rm{unary-op-code-p}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{unary-op-code-p}, \\ 
{\rm{or*}}\,({\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p}, {\rm{reg-direct-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{reg-direct-p})\index{or*}, \\ 
{\rm{reg-direct-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{reg-direct-p}, \\ 
{\rm{and*}}\,(\=\+{\rm{not*}}\,({\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p})\index{not*}, \\ 
{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{post-inc-p})\-\index{or*})\-\index{and*}, \\ 
{\rm{or*}}\,({\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, {\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{post-inc-p})\index{or*}, \\ 
{\it{regs-address\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}), \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}})\-\index{next-state}, \\ 
{\rm{rn-a}}\,({\it{i-reg\/}})\index{rn-a}, \\ 
{\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b}, \\ 
{\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\rm{set-flags}}\,({\it{i-reg\/}})\index{set-flags}, \\ 
{\rm{store-resultp}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, {\it{flags\/}})\index{store-resultp}, \\ 
{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p}, \\ 
{\it{rw-\/}}, \\ 
{\rm{or*}}\,({\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p}, {\rm{reg-direct-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{reg-direct-p})\index{or*}, \\ 
{\rm{and*}}\,(\=\+{\rm{not*}}\,({\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p})\index{not*}, \\ 
{\rm{or*}}\,({\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, {\rm{post-inc-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{post-inc-p})\index{or*})\-\index{and*}, \\ 
{\rm{or*}}\,({\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, {\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{post-inc-p})\index{or*}, \\ 
{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p})\-\index{cv}\-
\end{tabbing}


\noindent{\sc Event}:   Enable next-cntl-state; name this event `next-cntl-state-off'.\index{next-cntl-state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  bvp-length-next-cntl-state \\ \index{bvp-length-next-cntl-state}
\=\+(\=\+{\rm{length}}\,({\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{state\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state})\index{length} \\ 
$=$$\;\;\;\;${\tt{40}})\- \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{state\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state})\index{bvp}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$next-cntl-state} \\  
\=\+{\rm{f\$next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{state\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{f\$next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{f\$cv}}\,(\=\+{\rm{f\$next-state}}\,(\=\+{\rm{f\$decode-5}}\,({\rm{fv-or}}\,({\rm{make-list}}\,({\tt{5}}, {\rm{f-not}}\,({\it{reset-\/}})\index{f-not})\index{make-list}, {\it{state\/}})\index{fv-or})\index{f\$decode-5}, \\ 
{\rm{cadr}}\,({\rm{f\$control-let}}\,({\it{i-reg\/}}, {\it{flags\/}}, {\it{regs-address\/}})\index{f\$control-let}), \\ 
{\rm{caddr}}\,({\rm{f\$control-let}}\,({\it{i-reg\/}}, {\it{flags\/}}, {\it{regs-address\/}})\index{f\$control-let}), \\ 
{\rm{cadddddr}}\,({\rm{f\$control-let}}\,({\it{i-reg\/}}, {\it{flags\/}}, {\it{regs-address\/}})\index{f\$control-let}), \\ 
{\rm{cadddr}}\,({\rm{f\$control-let}}\,({\it{i-reg\/}}, {\it{flags\/}}, {\it{regs-address\/}})\index{f\$control-let}), \\ 
{\rm{caddddr}}\,({\rm{f\$control-let}}\,({\it{i-reg\/}}, {\it{flags\/}}, {\it{regs-address\/}})\index{f\$control-let}), \\ 
{\rm{caddddddddddr}}\,({\rm{f\$control-let}}\,(\=\+{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{regs-address\/}})\-\index{f\$control-let}), \\ 
{\rm{cadddddddddddr}}\,({\rm{f\$control-let}}\,(\=\+{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{regs-address\/}})\-\index{f\$control-let}), \\ 
{\rm{cadddddddddr}}\,({\rm{f\$control-let}}\,({\it{i-reg\/}}, {\it{flags\/}}, {\it{regs-address\/}})\index{f\$control-let}), \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}})\-\index{f\$next-state}, \\ 
{\rm{rn-a}}\,({\it{i-reg\/}})\index{rn-a}, \\ 
{\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b}, \\ 
{\rm{op-code}}\,({\it{i-reg\/}})\index{op-code}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\rm{set-flags}}\,({\it{i-reg\/}})\index{set-flags}, \\ 
{\rm{cadr}}\,({\rm{f\$control-let}}\,({\it{i-reg\/}}, {\it{flags\/}}, {\it{regs-address\/}})\index{f\$control-let}), \\ 
{\rm{caddddddddr}}\,({\rm{f\$control-let}}\,({\it{i-reg\/}}, {\it{flags\/}}, {\it{regs-address\/}})\index{f\$control-let}), \\ 
{\rm{car}}\,({\rm{f\$control-let}}\,({\it{i-reg\/}}, {\it{flags\/}}, {\it{regs-address\/}})\index{f\$control-let}), \\ 
{\it{rw-\/}}, \\ 
{\rm{cadddr}}\,({\rm{f\$control-let}}\,({\it{i-reg\/}}, {\it{flags\/}}, {\it{regs-address\/}})\index{f\$control-let}), \\ 
{\rm{caddddddddddr}}\,({\rm{f\$control-let}}\,({\it{i-reg\/}}, {\it{flags\/}}, {\it{regs-address\/}})\index{f\$control-let}), \\ 
{\rm{cadddddddddddr}}\,({\rm{f\$control-let}}\,({\it{i-reg\/}}, {\it{flags\/}}, {\it{regs-address\/}})\index{f\$control-let}), \\ 
{\rm{caddddddr}}\,({\rm{f\$control-let}}\,({\it{i-reg\/}}, {\it{flags\/}}, {\it{regs-address\/}})\index{f\$control-let}), \\ 
{\rm{cadddddddr}}\,({\rm{f\$control-let}}\,({\it{i-reg\/}}, {\it{flags\/}}, {\it{regs-address\/}})\index{f\$control-let}))\-\index{f\$cv}\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$next-cntl-state; name this event `f\$next-cntl-state-off'.\index{f\$next-cntl-state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  properp-length-f\$next-cntl-state \\ \index{properp-length-f\$next-cntl-state}
\=\+(\=\+{\rm{length}}\,({\rm{f\$next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{state\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{f\$next-cntl-state})\index{length} \\ 
$=$$\;\;\;\;${\tt{40}})\- \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{f\$next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{state\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{f\$next-cntl-state})\index{properp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-or-crock-for-f\$next-cntl-state \\ \index{v-or-crock-for-f\$next-cntl-state}
\=\+(({\rm{length}}\,({\it{state\/}})\index{length} $=$ {\tt{5}}) $\wedge$ {\rm{bvp}}\,({\it{state\/}})\index{bvp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{v-or}}\,({\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}}), {\it{state\/}})\index{v-or} $=$ {\it{state\/}}) \\ 
$\wedge$$\;\;\;\;$({\rm{v-or}}\,({\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}), {\it{state\/}})\index{v-or} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}})))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-or-crock-for-f\$next-cntl-state; name this event `v-or-crock-for-f\$next-cntl-state-off'.\index{v-or-crock-for-f\$next-cntl-state!-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f\$next-cntl-state=next-cntl-state \\ \index{f\$next-cntl-state=next-cntl-st!ate}
\=\+(\=\+{\rm{boolp}}\,({\it{reset-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{rw-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{state\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{state\/}})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{i-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{i-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{flags\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{flags\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{pc-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{pc-reg\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{regs-address\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{regs-address\/}})\index{length} $=$ {\tt{4}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{state\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{f\$next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{state\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{next-cntl-state*} \\  
\=\+{\sc{next-cntl-state*}}\index{next-cntl-state*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\tt{'}}{\tt{next-cntl-state}}, \\ 
{\rm{cons}}\,(\=\+{\rm{append6}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{reset-}}{\tt{ }}{\tt{dtack-}}{\tt{ }}{\tt{hold-}}{\tt{ }}{\tt{rw-}}{\tt{)}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{state}}, {\tt{0}}, {\tt{5}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{i-reg}}, {\tt{0}}, {\tt{32}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{flags}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{pc-reg}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{regs-address}}, {\tt{0}}, {\tt{4}})\index{indices})\-\index{append6}, \\ 
{\rm{cons}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{next-cntl-state}}, {\tt{0}}, {\tt{40}})\index{indices}, \\ 
{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{control-signals}}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{a-immediate-p}}{\tt{ }}{\tt{store}} \\ 
{\tt{set-some-flags}}{\tt{ }}{\tt{direct-a}} \\ 
{\tt{direct-b}}{\tt{ }}{\tt{unary}}{\tt{ }}{\tt{pre-dec-a}} \\ 
{\tt{pre-dec-b}}{\tt{ }}{\tt{c}}{\tt{ }}{\tt{all-t-regs-address}} \\ 
{\tt{side-effect-a}}{\tt{ }}{\tt{side-effect-b}}{\tt{)}}\-, \\ 
{\tt{'}}{\tt{control-let}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{i-reg}}, {\tt{0}}, {\tt{32}})\index{indices}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{flags}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{indices}}\,(\=\+{\tt{'}}{\tt{regs-address}}, \\ 
{\tt{0}}, \\ 
{\tt{4}})\-\index{indices})\-)\-)\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{not-reset}} \\ 
{\tt{(}}{\tt{reset}}{\tt{)}} \\ 
{\tt{b-not}} \\ 
{\tt{(}}{\tt{reset-}}{\tt{)}}{\tt{)}}\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{reset5x}}, \\ 
{\rm{cons}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{reset5x}}, {\tt{0}}, {\tt{5}})\index{indices}, \\ 
{\tt{'}}{\tt{(}}{\tt{fanout-5}}{\tt{ }}{\tt{(}}{\tt{reset}}{\tt{)}}{\tt{)}})\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{xstate}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{xstate}}, {\tt{0}}, {\tt{5}})\index{indices}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{v-or}}, {\tt{5}})\index{index}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{reset5x}}, {\tt{0}}, {\tt{5}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{state}}, {\tt{0}}, {\tt{5}})\index{indices})\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{dstate}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{decoded-state}}, {\tt{0}}, {\tt{32}})\index{indices}, \\ 
{\tt{'}}{\tt{decode-5}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{xstate}}, {\tt{0}}, {\tt{5}})\index{indices})\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{nxstate}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{next-state}}, {\tt{0}}, {\tt{32}})\index{indices}, \\ 
{\tt{'}}{\tt{next-state}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,(\=\+{\tt{'}}{\tt{decoded-state}}, \\ 
{\tt{0}}, \\ 
{\tt{32}})\-\index{indices}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{store}}{\tt{ }}{\tt{set-some-flags}} \\ 
{\tt{unary}}{\tt{ }}{\tt{direct-a}}{\tt{ }}{\tt{direct-b}} \\ 
{\tt{side-effect-a}} \\ 
{\tt{side-effect-b}} \\ 
{\tt{all-t-regs-address}} \\ 
{\tt{dtack-}}{\tt{ }}{\tt{hold-}}{\tt{)}}\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{cvector}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{next-cntl-state}}, {\tt{0}}, {\tt{40}})\index{indices}, \\ 
{\tt{'}}{\tt{cv}}, \\ 
{\rm{append8}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{next-state}}, {\tt{0}}, {\tt{32}})\index{indices}, \\ 
{\rm{rn-a}}\,({\rm{indices}}\,({\tt{'}}{\tt{i-reg}}, {\tt{0}}, {\tt{32}})\index{indices})\index{rn-a}, \\ 
{\rm{rn-b}}\,({\rm{indices}}\,({\tt{'}}{\tt{i-reg}}, {\tt{0}}, {\tt{32}})\index{indices})\index{rn-b}, \\ 
{\rm{op-code}}\,({\rm{indices}}\,({\tt{'}}{\tt{i-reg}}, {\tt{0}}, {\tt{32}})\index{indices})\index{op-code}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{pc-reg}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{regs-address}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{set-flags}}\,({\rm{indices}}\,(\=\+{\tt{'}}{\tt{i-reg}}, \\ 
{\tt{0}}, \\ 
{\tt{32}})\-\index{indices})\index{set-flags}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{store}}{\tt{ }}{\tt{c}}{\tt{ }}{\tt{a-immediate-p}} \\ 
{\tt{rw-}}{\tt{ }}{\tt{direct-a}} \\ 
{\tt{side-effect-a}} \\ 
{\tt{side-effect-b}}{\tt{ }}{\tt{pre-dec-a}} \\ 
{\tt{pre-dec-b}}{\tt{)}}\-)\-\index{append8})\-)\-, \\ 
{\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}})\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{next-cntl-state\&} \\  
\=\+{\rm{next-cntl-state\&}}\,({\it{netlist\/}})\index{next-cntl-state\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{next-cntl-state}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{next-cntl-state*}}\index{next-cntl-state*}) \\ 
$\wedge$$\;\;\;\;${\rm{control-let\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{next-cntl-state}}, {\it{netlist\/}})\index{delete-module})\index{control-let\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{next-cntl-state}}, {\it{netlist\/}})\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{fanout-5\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{next-cntl-state}}, {\it{netlist\/}})\index{delete-module})\index{fanout-5\&} \\ 
$\wedge$$\;\;\;\;${\rm{v-or\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{next-cntl-state}}, {\it{netlist\/}})\index{delete-module}, {\tt{5}})\index{v-or\&} \\ 
$\wedge$$\;\;\;\;${\rm{decode-5\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{next-cntl-state}}, {\it{netlist\/}})\index{delete-module})\index{decode-5\&} \\ 
$\wedge$$\;\;\;\;${\rm{next-state\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{next-cntl-state}}, {\it{netlist\/}})\index{delete-module})\index{next-state\&} \\ 
$\wedge$$\;\;\;\;${\rm{cv\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{next-cntl-state}}, {\it{netlist\/}})\index{delete-module})\index{cv\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable next-cntl-state\&; name this event `next-cntl-state\&-off'.\index{next-cntl-state\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{next-cntl-state\$netlist} \\  
\=\+{\sc{next-cntl-state\$netlist}}\index{next-cntl-state\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{next-cntl-state*}}\index{next-cntl-state*}, \\ 
\=\+(\=\+(\=\+({\sc{control-let\$netlist}}\index{control-let\$netlist} $\cup$ {\sc{b-not\$netlist}}\index{b-not\$netlist}) \\ 
$\cup$$\;\;\;\;$({\sc{fanout-5\$netlist}}\index{fanout-5\$netlist} $\cup$ {\rm{v-or\$netlist}}\,({\tt{5}})\index{v-or\$netlist}))\- \\ 
$\cup$$\;\;\;\;$({\sc{decode-5\$netlist}}\index{decode-5\$netlist} $\cup$ {\sc{next-state\$netlist}}\index{next-state\$netlist}))\- \\ 
$\cup$$\;\;\;\;${\sc{cv\$netlist}}\index{cv\$netlist}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  check-next-cntl-state\$netlist \\ \index{check-next-cntl-state\$netlist}
{\rm{next-cntl-state\&}}\,({\sc{next-cntl-state\$netlist}}\index{next-cntl-state\$netlist})\index{next-cntl-state\&}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$value \\ \index{next-cntl-state\$value}
\=\+(\=\+{\rm{next-cntl-state\&}}\,({\it{netlist\/}})\index{next-cntl-state\&} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{state\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{state\/}})\index{length} $=$ {\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{i-reg\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{i-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{flags\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{flags\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{pc-reg\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{pc-reg\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{regs-address\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{regs-address\/}})\index{length} $=$ {\tt{4}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{next-cntl-state}}, \\ 
{\rm{cons}}\,(\=\+{\it{reset-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{dtack-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{hold-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{rw-\/}}, \\ 
{\rm{append}}\,(\=\+{\it{state\/}}, \\ 
{\rm{append}}\,(\=\+{\it{i-reg\/}}, \\ 
{\rm{append}}\,(\=\+{\it{flags\/}}, \\ 
{\rm{append}}\,(\=\+{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-)\-)\-)\-)\-)\-)\-)\-, \\ 
{\it{dual-eval-state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{state\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{f\$next-cntl-state})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable next-cntl-state\$value; name this event `next-cntl-state\$value-off'.\index{next-cntl-state\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$fetch0 \\ \index{next-cntl-state\$fetch0}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_fetch0}}\index{v\_fetch0}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv\_fetch1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$fetch1 \\ \index{next-cntl-state\$fetch1}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_fetch1}}\index{v\_fetch1}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\it{hold-\/}}, \\ 
{\rm{cv\_fetch2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch2}, \\ 
{\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\-\index{if*})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$fetch2 \\ \index{next-cntl-state\$fetch2}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_fetch2}}\index{v\_fetch2}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$fetch3 \\ \index{next-cntl-state\$fetch3}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_fetch3}}\index{v\_fetch3}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\it{dtack-\/}}, \\ 
{\rm{cv\_fetch3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch3}, \\ 
{\rm{cv\_decode}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_decode})\-\index{if*})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$decode \\ \index{next-cntl-state\$decode}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_decode}}\index{v\_decode}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{store-resultp}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, {\it{flags\/}})\index{store-resultp}, \\ 
{\rm{set-some-flags}}\,({\rm{set-flags}}\,({\it{i-reg\/}})\index{set-flags})\index{set-some-flags})\-\index{or*}, \\ 
{\rm{if*}}\,(\=\+{\rm{or*}}\,({\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p}, {\rm{reg-direct-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{reg-direct-p})\index{or*}, \\ 
{\rm{if*}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{reg-direct-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{reg-direct-p}, \\ 
{\rm{unary-op-code-p}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{unary-op-code-p})\-\index{or*}, \\ 
{\rm{cv\_rega}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_rega}, \\ 
{\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\-\index{if*}, \\ 
{\rm{cv\_reada0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada0})\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{and*}}\,(\=\+{\rm{not*}}\,({\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p})\index{not*}, \\ 
{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{post-inc-p})\-\index{or*})\-\index{and*}, \\ 
{\rm{cv\_sefa0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa0}, \\ 
{\rm{if*}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{post-inc-p})\-\index{or*}, \\ 
{\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0}, \\ 
{\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\-\index{if*})\-\index{if*})\-\index{if*})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$rega \\ \index{next-cntl-state\$rega}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_rega}}\index{v\_rega}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\rm{reg-direct-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{reg-direct-p}, \\ 
{\rm{if*}}\,(\=\+{\rm{unary-op-code-p}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{unary-op-code-p}, \\ 
{\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update}, \\ 
{\rm{cv\_regb}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_regb})\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{store-resultp}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, {\it{flags\/}})\index{store-resultp}, \\ 
{\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0}, \\ 
{\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\-\index{if*})\-\index{if*})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$regb \\ \index{next-cntl-state\$regb}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_regb}}\index{v\_regb}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$update \\ \index{next-cntl-state\$update}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_update}}\index{v\_update}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\rm{and*}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{post-inc-p})\-\index{or*}, \\ 
{\rm{unary-op-code-p}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{unary-op-code-p})\-\index{and*}, \\ 
{\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1}, \\ 
{\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\-\index{if*})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$reada0 \\ \index{next-cntl-state\$reada0}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_reada0}}\index{v\_reada0}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv\_reada1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada1})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$reada1 \\ \index{next-cntl-state\$reada1}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_reada1}}\index{v\_reada1}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv\_reada2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada2})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$reada2 \\ \index{next-cntl-state\$reada2}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_reada2}}\index{v\_reada2}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$reada3 \\ \index{next-cntl-state\$reada3}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_reada3}}\index{v\_reada3}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\it{dtack-\/}}, \\ 
{\rm{cv\_reada3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3}, \\ 
{\rm{if*}}\,(\=\+{\rm{reg-direct-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{reg-direct-p}, \\ 
{\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update}, \\ 
{\rm{if*}}\,(\=\+{\rm{unary-op-code-p}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{unary-op-code-p}, \\ 
{\rm{if*}}\,(\=\+{\rm{store-resultp}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, {\it{flags\/}})\index{store-resultp}, \\ 
{\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0}, \\ 
{\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\-\index{if*}, \\ 
{\rm{cv\_readb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\-\index{if*})\-\index{if*})\-\index{if*})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$readb0 \\ \index{next-cntl-state\$readb0}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_readb0}}\index{v\_readb0}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv\_readb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb1})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$readb1 \\ \index{next-cntl-state\$readb1}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_readb1}}\index{v\_readb1}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv\_readb2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb2})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$readb2 \\ \index{next-cntl-state\$readb2}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_readb2}}\index{v\_readb2}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$readb3 \\ \index{next-cntl-state\$readb3}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_readb3}}\index{v\_readb3}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\it{dtack-\/}}, \\ 
{\rm{cv\_readb3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3}, \\ 
{\rm{if*}}\,(\=\+{\rm{store-resultp}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, {\it{flags\/}})\index{store-resultp}, \\ 
{\rm{cv\_write0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0}, \\ 
{\rm{cv\_update}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\-\index{if*})\-\index{if*})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$write0 \\ \index{next-cntl-state\$write0}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_write0}}\index{v\_write0}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv\_write1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write1})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$write1 \\ \index{next-cntl-state\$write1}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_write1}}\index{v\_write1}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv\_write2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write2})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$write2 \\ \index{next-cntl-state\$write2}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_write2}}\index{v\_write2}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$write3 \\ \index{next-cntl-state\$write3}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_write3}}\index{v\_write3}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\it{dtack-\/}}, \\ 
{\rm{cv\_write3}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3}, \\ 
{\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\-\index{if*})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$sefa0 \\ \index{next-cntl-state\$sefa0}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_sefa0}}\index{v\_sefa0}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv\_sefa1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefa1})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$sefa1 \\ \index{next-cntl-state\$sefa1}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_sefa1}}\index{v\_sefa1}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\rm{or*}}\,({\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, {\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{post-inc-p})\index{or*}, \\ 
{\rm{cv\_sefb0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0}, \\ 
{\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\-\index{if*})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$sefb0 \\ \index{next-cntl-state\$sefb0}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_sefb0}}\index{v\_sefb0}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv\_sefb1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$sefb1 \\ \index{next-cntl-state\$sefb1}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_sefb1}}\index{v\_sefb1}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$hold0 \\ \index{next-cntl-state\$hold0}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_hold0}}\index{v\_hold0}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\it{hold-\/}}, \\ 
{\rm{cv\_hold1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold1}, \\ 
{\rm{cv\_hold0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_hold0})\-\index{if*})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$hold1 \\ \index{next-cntl-state\$hold1}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_hold1}}\index{v\_hold1}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$v11010 \\ \index{next-cntl-state\$v11010}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_v11010}}\index{v\_v11010}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$v11011 \\ \index{next-cntl-state\$v11011}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_v11011}}\index{v\_v11011}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$reset0 \\ \index{next-cntl-state\$reset0}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_reset0}}\index{v\_reset0}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv\_reset1}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset1})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$reset1 \\ \index{next-cntl-state\$reset1}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_reset1}}\index{v\_reset1}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$reset2 \\ \index{next-cntl-state\$reset2}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_reset2}}\index{v\_reset2}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{if*}}\,(\=\+{\it{regs-address\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}), \\ 
{\rm{cv\_fetch0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0}, \\ 
{\rm{cv\_reset2}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset2})\-\index{if*})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  next-cntl-state\$v11111 \\ \index{next-cntl-state\$v11111}
\=\+(({\it{reset-\/}} $=$ {\bf{t}}) $\wedge$ {\rm{cv-hyps}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{next-cntl-state}}\,(\=\+{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\sc{v\_v11111}}\index{v\_v11111}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{regs-address\/}})\-\index{next-cntl-state} \\ 
$=$$\;\;\;\;${\rm{cv\_reset0}}\,({\it{rw-\/}}, {\it{regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reset0})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{read-regs} \\  
\=\+{\rm{read-regs}}\,({\it{address\/}}, {\it{regs\/}})\index{read-regs} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{cadr}}\,({\it{regs\/}}) $\wedge$ {\rm{v-iff}}\,({\it{address\/}}, {\rm{cadddr}}\,({\it{regs\/}}))\index{v-iff}$\;\;${\bf then }{\rm{caddr}}\,({\it{regs\/}}) \\ 
{\bf else }{\rm{read-mem}}\,({\it{address\/}}, {\rm{car}}\,({\it{regs\/}}))\index{read-mem}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable read-regs; name this event `read-regs-off'.\index{read-regs-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{write-regs} \\  
\=\+{\rm{write-regs}}\,({\it{we\/}}, {\it{address\/}}, {\it{regs\/}}, {\it{data\/}})\index{write-regs} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+\=\+{\bf if }{\rm{cadr}}\,({\it{regs\/}})$\;\;${\bf then }{\rm{write-mem}}\,({\rm{cadddr}}\,({\it{regs\/}}), {\rm{car}}\,({\it{regs\/}}), {\rm{caddr}}\,({\it{regs\/}}))\index{write-mem} \\ 
{\bf else }{\rm{car}}\,({\it{regs\/}})$\;${\bf  endif}\-, \\ 
{\it{we\/}}, \\ 
\=\+{\bf if }{\it{we\/}}$\;\;${\bf then }{\it{data\/}} \\ 
{\bf else }{\rm{caddr}}\,({\it{regs\/}})$\;${\bf  endif}\-, \\ 
\=\+{\bf if }{\it{we\/}}$\;\;${\bf then }{\it{address\/}} \\ 
{\bf else }{\rm{cadddr}}\,({\it{regs\/}})$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable write-regs; name this event `write-regs-off'.\index{write-regs-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  write-regs-f-write-regs-f \\ \index{write-regs-f-write-regs-f}
\=\+{\rm{write-regs}}\,({\bf{f}}, {\it{addr1\/}}, {\rm{write-regs}}\,({\bf{f}}, {\it{addr2\/}}, {\it{regs\/}}, {\it{data2\/}})\index{write-regs}, {\it{data1\/}})\index{write-regs} \\ 
$=$$\;\;\;\;${\rm{write-regs}}\,({\bf{f}}, {\it{addr1\/}}, {\it{regs\/}}, {\it{data1\/}})\index{write-regs}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  write-regs-f-bv-crock \\ \index{write-regs-f-bv-crock}
{\rm{write-regs}}\,({\bf{f}}, {\it{addr\/}}, {\it{regs\/}}, {\rm{bv}}\,({\it{x\/}})\index{bv})\index{write-regs} $=$ {\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-length-write-regs \\ \index{properp-length-write-regs}
\=\+{\rm{properp}}\,({\rm{write-regs}}\,({\it{we\/}}, {\it{address\/}}, {\it{regs\/}}, {\it{data\/}})\index{write-regs})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{write-regs}}\,({\it{we\/}}, {\it{address\/}}, {\it{regs\/}}, {\it{data\/}})\index{write-regs})\index{length} $=$ {\tt{4}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  write-regs-if \\ \index{write-regs-if}
\=\+{\rm{write-regs}}\,(\=\+\=\+{\bf if }{\it{c\/}}$\;\;${\bf then }{\it{a\/}} \\ 
{\bf else }{\it{b\/}}$\;${\bf  endif}\-, \\ 
{\it{address\/}}, \\ 
{\it{regs\/}}, \\ 
{\it{data\/}})\-\index{write-regs} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{c\/}}$\;\;${\bf then }{\rm{write-regs}}\,({\it{a\/}}, {\it{address\/}}, {\it{regs\/}}, {\it{data\/}})\index{write-regs} \\ 
{\bf else }{\rm{write-regs}}\,({\it{b\/}}, {\it{address\/}}, {\it{regs\/}}, {\it{data\/}})\index{write-regs}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  write-regs-ok \\ \index{write-regs-ok}
\=\+(\=\+{\rm{memory-okp}}\,({\it{n\/}}, {\it{m\/}}, {\rm{car}}\,({\rm{write-regs}}\,({\it{we\/}}, {\it{address\/}}, {\it{regs\/}}, {\it{data\/}})\index{write-regs}))\index{memory-okp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{cadr}}\,({\it{regs\/}}) \\ 
{\bf then }{\rm{memory-okp}}\,({\it{n\/}}, {\it{m\/}}, {\rm{write-mem}}\,({\rm{cadddr}}\,({\it{regs\/}}), {\rm{car}}\,({\it{regs\/}}), {\rm{caddr}}\,({\it{regs\/}}))\index{write-mem})\index{memory-okp} \\ 
{\bf else }{\rm{memory-okp}}\,({\it{n\/}}, {\it{m\/}}, {\rm{car}}\,({\it{regs\/}}))\index{memory-okp}$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{boolp}}\,({\rm{cadr}}\,({\rm{write-regs}}\,({\it{we\/}}, {\it{address\/}}, {\it{regs\/}}, {\it{data\/}})\index{write-regs}))\index{boolp} $=$ {\rm{boolp}}\,({\it{we\/}})\index{boolp}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{bvp}}\,({\rm{caddr}}\,({\rm{write-regs}}\,({\it{we\/}}, {\it{address\/}}, {\it{regs\/}}, {\it{data\/}})\index{write-regs}))\index{bvp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{we\/}}$\;\;${\bf then }{\rm{bvp}}\,({\it{data\/}})\index{bvp} \\ 
{\bf else }{\rm{bvp}}\,({\rm{caddr}}\,({\it{regs\/}}))\index{bvp}$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{length}}\,({\rm{caddr}}\,({\rm{write-regs}}\,({\it{we\/}}, {\it{address\/}}, {\it{regs\/}}, {\it{data\/}})\index{write-regs}))\index{length} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{we\/}}$\;\;${\bf then }{\rm{length}}\,({\it{data\/}})\index{length} \\ 
{\bf else }{\rm{length}}\,({\rm{caddr}}\,({\it{regs\/}}))\index{length}$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{bvp}}\,({\rm{cadddr}}\,({\rm{write-regs}}\,({\it{we\/}}, {\it{address\/}}, {\it{regs\/}}, {\it{data\/}})\index{write-regs}))\index{bvp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{we\/}}$\;\;${\bf then }{\rm{bvp}}\,({\it{address\/}})\index{bvp} \\ 
{\bf else }{\rm{bvp}}\,({\rm{cadddr}}\,({\it{regs\/}}))\index{bvp}$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{length}}\,({\rm{cadddr}}\,({\rm{write-regs}}\,({\it{we\/}}, {\it{address\/}}, {\it{regs\/}}, {\it{data\/}})\index{write-regs}))\index{length} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{we\/}}$\;\;${\bf then }{\rm{length}}\,({\it{address\/}})\index{length} \\ 
{\bf else }{\rm{length}}\,({\rm{cadddr}}\,({\it{regs\/}}))\index{length}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  read-regs-write-regs-f \\ \index{read-regs-write-regs-f}
\=\+(\=\+{\rm{all-ramp-mem}}\,({\rm{length}}\,({\it{addr\/}})\index{length}, {\rm{car}}\,({\it{regs\/}}))\index{all-ramp-mem} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr\/}})\index{length} $=$ {\rm{length}}\,({\rm{cadddr}}\,({\it{regs\/}}))\index{length}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr\/}})\index{bvp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{read-regs}}\,({\it{addr\/}}, {\rm{write-regs}}\,({\bf{f}}, {\it{address\/}}, {\it{regs\/}}, {\it{value\/}})\index{write-regs})\index{read-regs} \\ 
$=$$\;\;\;\;${\rm{read-regs}}\,({\it{addr\/}}, {\it{regs\/}})\index{read-regs})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  all-ramp-mem-after-write-regs \\ \index{all-ramp-mem-after-write-regs}
\=\+({\rm{all-ramp-mem}}\,({\it{n\/}}, {\rm{car}}\,({\it{regs\/}}))\index{all-ramp-mem} $\wedge$ ({\rm{length}}\,({\rm{cadddr}}\,({\it{regs\/}}))\index{length} $=$ {\it{n\/}})) \\ 
$\rightarrow$$\;\;\;\;${\rm{all-ramp-mem}}\,({\it{n\/}}, {\rm{car}}\,({\rm{write-regs}}\,({\it{we\/}}, {\it{address\/}}, {\it{regs\/}}, {\it{data\/}})\index{write-regs}))\index{all-ramp-mem}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  read-regs=read-mem \\ \index{read-regs=read-mem}
\=\+($\neg$ {\rm{cadr}}\,({\it{regs\/}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{read-regs}}\,({\it{v-addr\/}}, {\it{regs\/}})\index{read-regs} $=$ {\rm{read-mem}}\,({\it{v-addr\/}}, {\rm{car}}\,({\it{regs\/}}))\index{read-mem})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  read-regs=read-mem-write-mem \\ \index{read-regs=read-mem-write-mem}
\=\+(\=\+{\rm{all-ramp-mem}}\,({\rm{length}}\,({\it{v-addr1\/}})\index{length}, {\rm{car}}\,({\it{regs\/}}))\index{all-ramp-mem} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{v-addr1\/}})\index{length} $=$ {\rm{length}}\,({\rm{cadddr}}\,({\it{regs\/}}))\index{length}) \\ 
$\wedge$$\;\;\;\;${\rm{cadr}}\,({\it{regs\/}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{read-regs}}\,({\it{v-addr1\/}}, {\it{regs\/}})\index{read-regs} \\ 
$=$$\;\;\;\;${\rm{read-mem}}\,(\=\+{\it{v-addr1\/}}, \\ 
{\rm{write-mem}}\,({\rm{cadddr}}\,({\it{regs\/}}), {\rm{car}}\,({\it{regs\/}}), {\rm{caddr}}\,({\it{regs\/}}))\index{write-mem})\-\index{read-mem})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-length-read-regs-32 \\ \index{bvp-length-read-regs-32}
\=\+(\=\+{\rm{memory-okp}}\,({\rm{length}}\,({\it{v-addr\/}})\index{length}, {\tt{32}}, {\rm{car}}\,({\it{regs\/}}))\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{caddr}}\,({\it{regs\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{caddr}}\,({\it{regs\/}}))\index{length} $=$ {\tt{32}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{bvp}}\,({\rm{read-regs}}\,({\it{v-addr\/}}, {\it{regs\/}})\index{read-regs})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{read-regs}}\,({\it{v-addr\/}}, {\it{regs\/}})\index{read-regs})\index{length} $=$ {\tt{32}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{regfile*} \\  
\=\+{\sc{regfile*}}\index{regfile*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\tt{'}}{\tt{regfile}}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{clk}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{te}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{ti}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{we}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{disable-regfile-}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{test-regfile-}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,(\=\+{\tt{'}}{\tt{address}}, \\ 
{\tt{0}}, \\ 
{\tt{4}})\-\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{data}}, {\tt{0}}, {\tt{32}})\index{indices})\-)\-)\-)\-)\-)\-)\-, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,({\tt{'}}{\tt{to}}, {\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\tt{32}})\index{indices}), \\ 
{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{we-latch}} \\ 
{\tt{(}}{\tt{we-dp-ram}}{\tt{ }}{\tt{we-dp-ram-}}{\tt{)}} \\ 
{\tt{fd1s}} \\ 
{\tt{(}}{\tt{we}}{\tt{ }}{\tt{clk}}{\tt{ }}{\tt{ti}}{\tt{ }}{\tt{te}}{\tt{)}}{\tt{)}}\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{address-latch}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{address-dp-ram}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{we-reg}}, {\tt{4}})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{clk}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{we}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{te}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{we-dp-ram}}, \\ 
{\rm{indices}}\,(\=\+{\tt{'}}{\tt{address}}, \\ 
{\tt{0}}, \\ 
{\tt{4}})\-\index{indices})\-)\-)\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{data-latch}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{data-dp-ram}}, {\tt{0}}, {\tt{32}})\index{indices}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{we-reg}}, {\tt{32}})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{clk}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{we}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{te}}, \\ 
{\rm{cons}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{address-dp-ram}}, \\ 
{\tt{3}})\-\index{index}, \\ 
{\rm{indices}}\,(\=\+{\tt{'}}{\tt{data}}, \\ 
{\tt{0}}, \\ 
{\tt{32}})\-\index{indices})\-)\-)\-)\-)\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{reg-en-circuit}} \\ 
{\tt{(}}{\tt{we-}}{\tt{)}} \\ 
{\tt{ram-enable-circuit}} \\ 
{\tt{(}}\=\+{\tt{clk}}{\tt{ }}{\tt{test-regfile-}}{\tt{ }}{\tt{disable-regfile-}} \\ 
{\tt{we-dp-ram}}{\tt{)}}\-{\tt{)}}\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{ram}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{ramout}}, {\tt{0}}, {\tt{32}})\index{indices}, \\ 
{\tt{'}}{\tt{dp-ram-16x32}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{address}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,(\=\+{\tt{'}}{\tt{address-dp-ram}}, \\ 
{\tt{0}}, \\ 
{\tt{4}})\-\index{indices}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{we-}}, \\ 
{\rm{indices}}\,(\=\+{\tt{'}}{\tt{data-dp-ram}}, \\ 
{\tt{0}}, \\ 
{\tt{32}})\-\index{indices})\-)\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{compare}}, \\ 
{\tt{'}}{\tt{(}}{\tt{read-equal-write}}{\tt{)}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{v-equal}}, {\tt{4}})\index{index}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{address}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{indices}}\,(\=\+{\tt{'}}{\tt{address-dp-ram}}, \\ 
{\tt{0}}, \\ 
{\tt{4}})\-\index{indices})\-)\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{mux-control}} \\ 
{\tt{(}}{\tt{s}}{\tt{)}} \\ 
{\tt{b-and3}} \\ 
{\tt{(}}\=\+{\tt{we-dp-ram}}{\tt{ }}{\tt{read-equal-write}} \\ 
{\tt{test-regfile-}}{\tt{)}}\-{\tt{)}}\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{mux}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\tt{32}})\index{indices}, \\ 
{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-if}}, \\ 
{\rm{tree-number}}\,({\rm{make-tree}}\,({\tt{32}})\index{make-tree})\index{tree-number})\-\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{s}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,(\=\+{\tt{'}}{\tt{data-dp-ram}}, \\ 
{\tt{0}}, \\ 
{\tt{32}})\-\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{ramout}}, {\tt{0}}, {\tt{32}})\index{indices})\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{scanout}}, \\ 
{\tt{'}}{\tt{(}}{\tt{to}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{data-dp-ram}}, {\tt{31}})\index{index}))\-)\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{(}}\=\+{\tt{ram}}{\tt{ }}{\tt{we-latch}}{\tt{ }}{\tt{data-latch}}{\tt{ }}{\tt{address-latch}}{\tt{)}}\-{\tt{)}}\-)\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  regfile*\$destructure \\ \index{regfile*\$destructure}
\=\+({\rm{car}}\,({\sc{regfile*}}\index{regfile*}) $=$ {\tt{'}}{\tt{regfile}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadr}}\,({\sc{regfile*}}\index{regfile*}) \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\tt{'}}{\tt{clk}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{te}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{ti}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{we}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{disable-regfile-}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{test-regfile-}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{address}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{data}}, {\tt{0}}, {\tt{32}})\index{indices})\-)\-)\-)\-)\-)\-)\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\sc{regfile*}}\index{regfile*}) $=$ {\rm{cons}}\,({\tt{'}}{\tt{to}}, {\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\tt{32}})\index{indices})) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadddr}}\,({\sc{regfile*}}\index{regfile*}) \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{we-latch}} \\ 
{\tt{(}}{\tt{we-dp-ram}}{\tt{ }}{\tt{we-dp-ram-}}{\tt{)}} \\ 
{\tt{fd1s}} \\ 
{\tt{(}}{\tt{we}}{\tt{ }}{\tt{clk}}{\tt{ }}{\tt{ti}}{\tt{ }}{\tt{te}}{\tt{)}}{\tt{)}}\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{address-latch}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{address-dp-ram}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{we-reg}}, {\tt{4}})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{clk}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{we}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{te}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{we-dp-ram}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{address}}, {\tt{0}}, {\tt{4}})\index{indices})\-)\-)\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{data-latch}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{data-dp-ram}}, {\tt{0}}, {\tt{32}})\index{indices}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{we-reg}}, {\tt{32}})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{clk}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{we}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{te}}, \\ 
{\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{address-dp-ram}}, {\tt{3}})\index{index}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{data}}, {\tt{0}}, {\tt{32}})\index{indices})\-)\-)\-)\-)\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{reg-en-circuit}} \\ 
{\tt{(}}{\tt{we-}}{\tt{)}} \\ 
{\tt{ram-enable-circuit}} \\ 
{\tt{(}}\=\+{\tt{clk}}{\tt{ }}{\tt{test-regfile-}}{\tt{ }}{\tt{disable-regfile-}} \\ 
{\tt{we-dp-ram}}{\tt{)}}\-{\tt{)}}\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{ram}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{ramout}}, {\tt{0}}, {\tt{32}})\index{indices}, \\ 
{\tt{'}}{\tt{dp-ram-16x32}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{address}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{address-dp-ram}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{we-}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{data-dp-ram}}, {\tt{0}}, {\tt{32}})\index{indices})\-)\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{compare}}, \\ 
{\tt{'}}{\tt{(}}{\tt{read-equal-write}}{\tt{)}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{v-equal}}, {\tt{4}})\index{index}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{address}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{address-dp-ram}}, {\tt{0}}, {\tt{4}})\index{indices})\-)\-, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{mux-control}} \\ 
{\tt{(}}{\tt{s}}{\tt{)}} \\ 
{\tt{b-and3}} \\ 
{\tt{(}}\=\+{\tt{we-dp-ram}}{\tt{ }}{\tt{read-equal-write}}{\tt{ }}{\tt{test-regfile-}}{\tt{)}}\-{\tt{)}}\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{mux}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\tt{32}})\index{indices}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{tv-if}}, {\rm{tree-number}}\,({\rm{make-tree}}\,({\tt{32}})\index{make-tree})\index{tree-number})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{s}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{data-dp-ram}}, {\tt{0}}, {\tt{32}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{ramout}}, {\tt{0}}, {\tt{32}})\index{indices})\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{scanout}}, \\ 
{\tt{'}}{\tt{(}}{\tt{to}}{\tt{)}}, \\ 
{\tt{'}}{\tt{id}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{data-dp-ram}}, {\tt{31}})\index{index}))\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{caddddr}}\,({\sc{regfile*}}\index{regfile*}) \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{ram}}{\tt{ }}{\tt{we-latch}}{\tt{ }}{\tt{data-latch}}{\tt{ }}{\tt{address-latch}}{\tt{)}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable regfile*; name this event `regfile*-off'.\index{regfile*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable regfile*\$destructure; name this event `regfile*\$destructure-off'.\index{regfile*\$destructure-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*regfile*; name this event `g*1*regfile*-off'.\index{g*1*regfile*-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{regfile\&} \\  
\=\+{\rm{regfile\&}}\,({\it{netlist\/}})\index{regfile\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{regfile}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{regfile*}}\index{regfile*}) \\ 
$\wedge$$\;\;\;\;${\rm{fd1s\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{regfile}}, {\it{netlist\/}})\index{delete-module})\index{fd1s\&} \\ 
$\wedge$$\;\;\;\;${\rm{we-reg\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{regfile}}, {\it{netlist\/}})\index{delete-module}, {\tt{4}})\index{we-reg\&} \\ 
$\wedge$$\;\;\;\;${\rm{we-reg\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{regfile}}, {\it{netlist\/}})\index{delete-module}, {\tt{32}})\index{we-reg\&} \\ 
$\wedge$$\;\;\;\;${\rm{ram-enable-circuit\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{regfile}}, {\it{netlist\/}})\index{delete-module})\index{ram-enable-circuit\&} \\ 
$\wedge$$\;\;\;\;${\rm{dp-ram-16x32\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{regfile}}, {\it{netlist\/}})\index{delete-module})\index{dp-ram-16x32\&} \\ 
$\wedge$$\;\;\;\;${\rm{v-equal\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{regfile}}, {\it{netlist\/}})\index{delete-module}, {\tt{4}})\index{v-equal\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-and3\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{regfile}}, {\it{netlist\/}})\index{delete-module})\index{b-and3\&} \\ 
$\wedge$$\;\;\;\;${\rm{tv-if\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{regfile}}, {\it{netlist\/}})\index{delete-module}, {\rm{make-tree}}\,({\tt{32}})\index{make-tree})\index{tv-if\&} \\ 
$\wedge$$\;\;\;\;${\rm{id\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{regfile}}, {\it{netlist\/}})\index{delete-module})\index{id\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable regfile\&; name this event `regfile\&-off'.\index{regfile\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{regfile\$netlist} \\  
\=\+{\sc{regfile\$netlist}}\index{regfile\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{regfile*}}\index{regfile*}, \\ 
\=\+(\=\+(\=\+({\sc{fd1s\$netlist}}\index{fd1s\$netlist} $\cup$ {\rm{we-reg\$netlist}}\,({\tt{4}})\index{we-reg\$netlist}) \\ 
$\cup$$\;\;\;\;$({\rm{we-reg\$netlist}}\,({\tt{32}})\index{we-reg\$netlist} $\cup$ {\sc{ram-enable-circuit\$netlist}}\index{ram-enable-circuit\$netlist}))\- \\ 
$\cup$$\;\;\;\;$(\=\+{\sc{dp-ram-16x32\$netlist}}\index{dp-ram-16x32\$netlist} \\ 
$\cup$$\;\;\;\;$({\rm{v-equal\$netlist}}\,({\tt{4}})\index{v-equal\$netlist} $\cup$ {\sc{b-and3\$netlist}}\index{b-and3\$netlist}))\-)\- \\ 
$\cup$$\;\;\;\;$({\rm{tv-if\$netlist}}\,({\rm{make-tree}}\,({\tt{32}})\index{make-tree})\index{tv-if\$netlist} $\cup$ {\sc{id\$netlist}}\index{id\$netlist})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  check-regfile\$netlist \\ \index{check-regfile\$netlist}
{\rm{regfile\&}}\,({\sc{regfile\$netlist}}\index{regfile\$netlist})\index{regfile\&}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$read-regs} \\  
\=\+{\rm{f\$read-regs}}\,({\it{address\/}}, {\it{regs\/}})\index{f\$read-regs} \\ 
$=$$\;\;\;\;${\rm{fv-if}}\,(\=\+{\rm{f-and3}}\,(\=\+{\rm{f-buf}}\,({\rm{cadr}}\,({\it{regs\/}}))\index{f-buf}, \\ 
{\rm{f\$v-equal}}\,({\it{address\/}}, {\rm{v-threefix}}\,({\rm{cadddr}}\,({\it{regs\/}}))\index{v-threefix})\index{f\$v-equal}, \\ 
{\bf{t}})\-\index{f-and3}, \\ 
{\rm{v-threefix}}\,({\rm{caddr}}\,({\it{regs\/}}))\index{v-threefix}, \\ 
{\rm{dual-port-ram-value}}\,(\=\+{\tt{32}}, \\ 
{\tt{4}}, \\ 
{\rm{append}}\,(\=\+{\it{address\/}}, \\ 
{\rm{append}}\,(\=\+{\rm{v-threefix}}\,({\rm{cadddr}}\,({\it{regs\/}}))\index{v-threefix}, \\ 
{\rm{cons}}\,(\=\+{\rm{f-nand}}\,(\=\+{\bf{t}}, \\ 
{\rm{f-buf}}\,({\rm{cadr}}\,({\it{regs\/}}))\index{f-buf})\-\index{f-nand}, \\ 
{\rm{v-threefix}}\,({\rm{caddr}}\,({\it{regs\/}}))\index{v-threefix})\-)\-)\-, \\ 
{\rm{car}}\,({\it{regs\/}}))\-\index{dual-port-ram-value})\-\index{fv-if}\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$read-regs; name this event `f\$read-regs-off'.\index{f\$read-regs-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  properp-length-f\$read-regs \\ \index{properp-length-f\$read-regs}
\=\+{\rm{properp}}\,({\rm{f\$read-regs}}\,({\it{address\/}}, {\it{mem\/}})\index{f\$read-regs})\index{properp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\rm{caddr}}\,({\it{mem\/}}))\index{length} $=$ {\tt{32}}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{length}}\,({\rm{f\$read-regs}}\,({\it{address\/}}, {\it{mem\/}})\index{f\$read-regs})\index{length} $=$ {\tt{32}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f\$read-regs=read-regs \\ \index{f\$read-regs=read-regs}
\=\+(\=\+{\rm{memory-okp}}\,({\tt{4}}, {\tt{32}}, {\rm{car}}\,({\it{regs\/}}))\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{cadr}}\,({\it{regs\/}}))\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{caddr}}\,({\it{regs\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{caddr}}\,({\it{regs\/}}))\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cadddr}}\,({\it{regs\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cadddr}}\,({\it{regs\/}}))\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{address\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{address\/}})\index{length} $=$ {\tt{4}}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{f\$read-regs}}\,({\it{address\/}}, {\it{regs\/}})\index{f\$read-regs} $=$ {\rm{read-regs}}\,({\it{address\/}}, {\it{regs\/}})\index{read-regs})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  regfile\$value \\ \index{regfile\$value}
\=\+(\=\+{\rm{regfile\&}}\,({\it{netlist\/}})\index{regfile\&} \\ 
$\wedge$$\;\;\;\;$({\it{test-regfile-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\it{disable-regfile-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\rm{memory-properp}}\,({\tt{4}}, {\tt{32}}, {\it{mem\/}})\index{memory-properp} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{last-data\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{last-data\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{address\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{address\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{last-address\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{last-address\/}})\index{length} $=$ {\tt{4}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{cdr}}\,({\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{regfile}}, \\ 
{\rm{cons}}\,(\=\+{\it{clk\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{te\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{ti\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{we\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{disable-regfile-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{test-regfile-\/}}, \\ 
{\rm{append}}\,({\it{address\/}}, {\it{data\/}}))\-)\-)\-)\-)\-)\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\it{last-we\/}}, {\it{last-data\/}}, {\it{last-address\/}}), \\ 
{\it{netlist\/}})\-\index{dual-eval}) \\ 
$=$$\;\;\;\;${\rm{f\$read-regs}}\,({\it{address\/}}, {\rm{list}}\,({\it{mem\/}}, {\it{last-we\/}}, {\it{last-data\/}}, {\it{last-address\/}}))\index{f\$read-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable regfile\$value; name this event `regfile\$value-off'.\index{regfile\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{f\$write-regs} \\  
\=\+{\rm{f\$write-regs}}\,({\it{we\/}}, {\it{address\/}}, {\it{regs\/}}, {\it{data\/}})\index{f\$write-regs} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{dual-port-ram-state}}\,(\=\+{\tt{32}}, \\ 
{\tt{4}}, \\ 
{\rm{append}}\,(\=\+{\it{address\/}}, \\ 
{\rm{append}}\,(\=\+{\rm{v-threefix}}\,({\rm{cadddr}}\,({\it{regs\/}}))\index{v-threefix}, \\ 
{\rm{cons}}\,(\=\+{\rm{f-nand}}\,(\=\+{\bf{t}}, \\ 
{\rm{f-buf}}\,({\rm{cadr}}\,({\it{regs\/}}))\index{f-buf})\-\index{f-nand}, \\ 
{\rm{v-threefix}}\,({\rm{caddr}}\,({\it{regs\/}}))\index{v-threefix})\-)\-)\-, \\ 
{\rm{car}}\,({\it{regs\/}}))\-\index{dual-port-ram-state}, \\ 
{\rm{threefix}}\,({\it{we\/}})\index{threefix}, \\ 
{\rm{fv-if}}\,({\it{we\/}}, {\it{data\/}}, {\rm{caddr}}\,({\it{regs\/}}))\index{fv-if}, \\ 
{\rm{fv-if}}\,({\it{we\/}}, {\it{address\/}}, {\rm{cadddr}}\,({\it{regs\/}}))\index{fv-if})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$write-regs; name this event `f\$write-regs-off'.\index{f\$write-regs-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  properp-length-f\$write-regs \\ \index{properp-length-f\$write-regs}
\=\+{\rm{properp}}\,({\rm{f\$write-regs}}\,({\it{we\/}}, {\it{address\/}}, {\it{regs\/}}, {\it{data\/}})\index{f\$write-regs})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{f\$write-regs}}\,({\it{we\/}}, {\it{address\/}}, {\it{regs\/}}, {\it{data\/}})\index{f\$write-regs})\index{length} $=$ {\tt{4}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f\$write-regs=write-regs \\ \index{f\$write-regs=write-regs}
\=\+(\=\+{\rm{boolp}}\,({\it{we\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{cadr}}\,({\it{regs\/}}))\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{caddr}}\,({\it{regs\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{caddr}}\,({\it{regs\/}}))\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cadddr}}\,({\it{regs\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cadddr}}\,({\it{regs\/}}))\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{address\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{address\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data\/}})\index{length} $=$ {\tt{32}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$write-regs}}\,({\it{we\/}}, {\it{address\/}}, {\it{regs\/}}, {\it{data\/}})\index{f\$write-regs} \\ 
$=$$\;\;\;\;${\rm{write-regs}}\,({\it{we\/}}, {\it{address\/}}, {\it{regs\/}}, {\it{data\/}})\index{write-regs})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  regfile\$state \\ \index{regfile\$state}
\=\+(\=\+{\rm{regfile\&}}\,({\it{netlist\/}})\index{regfile\&} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\it{te\/}}) \\ 
$\wedge$$\;\;\;\;$({\it{test-regfile-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\it{disable-regfile-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{data\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{last-data\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{last-data\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{address\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{address\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{last-address\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{last-address\/}})\index{length} $=$ {\tt{4}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\tt{'}}{\tt{regfile}}, \\ 
{\rm{cons}}\,(\=\+{\it{clk\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{te\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{ti\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{we\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{disable-regfile-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{test-regfile-\/}}, \\ 
{\rm{append}}\,({\it{address\/}}, {\it{data\/}}))\-)\-)\-)\-)\-)\-, \\ 
{\rm{list}}\,({\it{regfile\/}}, {\it{last-we\/}}, {\it{last-data\/}}, {\it{last-address\/}}), \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$write-regs}}\,(\=\+{\it{we\/}}, \\ 
{\it{address\/}}, \\ 
{\rm{list}}\,({\it{regfile\/}}, {\it{last-we\/}}, {\it{last-data\/}}, {\it{last-address\/}}), \\ 
{\it{data\/}})\-\index{f\$write-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable regfile\$state; name this event `regfile\$state-off'.\index{regfile\$state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{flags*} \\  
\=\+{\sc{flags*}}\index{flags*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\tt{'}}{\tt{flags}}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{clk}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{te}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{ti}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{set-flags}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{cvzbv}}, {\tt{0}}, {\tt{35}})\index{indices})\-)\-)\-)\-, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{z}}{\tt{ }}{\tt{n}}{\tt{ }}{\tt{v}}{\tt{ }}{\tt{c}}{\tt{)}}, \\ 
{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{z-latch}}, \\ 
{\tt{'}}{\tt{(}}{\tt{z}}{\tt{ }}{\tt{zb}}{\tt{)}}, \\ 
{\tt{'}}{\tt{fd1slp}}, \\ 
{\rm{cons}}\,(\=\+{\rm{zb}}\,({\rm{indices}}\,({\tt{'}}{\tt{cvzbv}}, {\tt{0}}, {\tt{35}})\index{indices})\index{zb}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{clk}}, \\ 
{\rm{cons}}\,(\=\+{\rm{z-set}}\,({\rm{indices}}\,(\=\+{\tt{'}}{\tt{set-flags}}, \\ 
{\tt{0}}, \\ 
{\tt{4}})\-\index{indices})\index{z-set}, \\ 
{\tt{'}}{\tt{(}}{\tt{ti}}{\tt{ }}{\tt{te}}{\tt{)}})\-)\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{n-latch}}, \\ 
{\tt{'}}{\tt{(}}{\tt{n}}{\tt{ }}{\tt{nb}}{\tt{)}}, \\ 
{\tt{'}}{\tt{fd1slp}}, \\ 
{\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{cvzbv}}, {\tt{34}})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{clk}}, \\ 
{\rm{cons}}\,(\=\+{\rm{n-set}}\,({\rm{indices}}\,(\=\+{\tt{'}}{\tt{set-flags}}, \\ 
{\tt{0}}, \\ 
{\tt{4}})\-\index{indices})\index{n-set}, \\ 
{\tt{'}}{\tt{(}}{\tt{z}}{\tt{ }}{\tt{te}}{\tt{)}})\-)\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{v-latch}}, \\ 
{\tt{'}}{\tt{(}}{\tt{v}}{\tt{ }}{\tt{vb}}{\tt{)}}, \\ 
{\tt{'}}{\tt{fd1slp}}, \\ 
{\rm{cons}}\,(\=\+{\rm{v}}\,({\rm{indices}}\,({\tt{'}}{\tt{cvzbv}}, {\tt{0}}, {\tt{35}})\index{indices})\index{v}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{clk}}, \\ 
{\rm{cons}}\,(\=\+{\rm{v-set}}\,({\rm{indices}}\,(\=\+{\tt{'}}{\tt{set-flags}}, \\ 
{\tt{0}}, \\ 
{\tt{4}})\-\index{indices})\index{v-set}, \\ 
{\tt{'}}{\tt{(}}{\tt{n}}{\tt{ }}{\tt{te}}{\tt{)}})\-)\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{c-latch}}, \\ 
{\tt{'}}{\tt{(}}{\tt{c}}{\tt{ }}{\tt{cb}}{\tt{)}}, \\ 
{\tt{'}}{\tt{fd1slp}}, \\ 
{\rm{cons}}\,(\=\+{\rm{c}}\,({\rm{indices}}\,({\tt{'}}{\tt{cvzbv}}, {\tt{0}}, {\tt{35}})\index{indices})\index{c}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{clk}}, \\ 
{\rm{cons}}\,(\=\+{\rm{c-set}}\,({\rm{indices}}\,(\=\+{\tt{'}}{\tt{set-flags}}, \\ 
{\tt{0}}, \\ 
{\tt{4}})\-\index{indices})\index{c-set}, \\ 
{\tt{'}}{\tt{(}}{\tt{v}}{\tt{ }}{\tt{te}}{\tt{)}})\-)\-)\-)\-)\-, \\ 
{\tt{'}}{\tt{(}}{\tt{(}}{\tt{z-latch}}{\tt{ }}{\tt{n-latch}}{\tt{ }}{\tt{v-latch}}{\tt{ }}{\tt{c-latch}}{\tt{)}}{\tt{)}})\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags*\$destructure \\ \index{flags*\$destructure}
\=\+({\rm{car}}\,({\sc{flags*}}\index{flags*}) $=$ {\tt{'}}{\tt{flags}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadr}}\,({\sc{flags*}}\index{flags*}) \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\tt{'}}{\tt{clk}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{te}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{ti}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{set-flags}}, {\tt{0}}, {\tt{4}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{cvzbv}}, {\tt{0}}, {\tt{35}})\index{indices})\-)\-)\-)\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\sc{flags*}}\index{flags*}) $=$ {\tt{'}}{\tt{(}}{\tt{z}}{\tt{ }}{\tt{n}}{\tt{ }}{\tt{v}}{\tt{ }}{\tt{c}}{\tt{)}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadddr}}\,({\sc{flags*}}\index{flags*}) \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{z-latch}}, \\ 
{\tt{'}}{\tt{(}}{\tt{z}}{\tt{ }}{\tt{zb}}{\tt{)}}, \\ 
{\tt{'}}{\tt{fd1slp}}, \\ 
{\rm{cons}}\,(\=\+{\rm{zb}}\,({\rm{indices}}\,({\tt{'}}{\tt{cvzbv}}, {\tt{0}}, {\tt{35}})\index{indices})\index{zb}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{clk}}, \\ 
{\rm{cons}}\,(\=\+{\rm{z-set}}\,({\rm{indices}}\,({\tt{'}}{\tt{set-flags}}, {\tt{0}}, {\tt{4}})\index{indices})\index{z-set}, \\ 
{\tt{'}}{\tt{(}}{\tt{ti}}{\tt{ }}{\tt{te}}{\tt{)}})\-)\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{n-latch}}, \\ 
{\tt{'}}{\tt{(}}{\tt{n}}{\tt{ }}{\tt{nb}}{\tt{)}}, \\ 
{\tt{'}}{\tt{fd1slp}}, \\ 
{\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{cvzbv}}, {\tt{34}})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{clk}}, \\ 
{\rm{cons}}\,(\=\+{\rm{n-set}}\,({\rm{indices}}\,({\tt{'}}{\tt{set-flags}}, {\tt{0}}, {\tt{4}})\index{indices})\index{n-set}, \\ 
{\tt{'}}{\tt{(}}{\tt{z}}{\tt{ }}{\tt{te}}{\tt{)}})\-)\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{v-latch}}, \\ 
{\tt{'}}{\tt{(}}{\tt{v}}{\tt{ }}{\tt{vb}}{\tt{)}}, \\ 
{\tt{'}}{\tt{fd1slp}}, \\ 
{\rm{cons}}\,(\=\+{\rm{v}}\,({\rm{indices}}\,({\tt{'}}{\tt{cvzbv}}, {\tt{0}}, {\tt{35}})\index{indices})\index{v}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{clk}}, \\ 
{\rm{cons}}\,(\=\+{\rm{v-set}}\,({\rm{indices}}\,({\tt{'}}{\tt{set-flags}}, {\tt{0}}, {\tt{4}})\index{indices})\index{v-set}, \\ 
{\tt{'}}{\tt{(}}{\tt{n}}{\tt{ }}{\tt{te}}{\tt{)}})\-)\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{c-latch}}, \\ 
{\tt{'}}{\tt{(}}{\tt{c}}{\tt{ }}{\tt{cb}}{\tt{)}}, \\ 
{\tt{'}}{\tt{fd1slp}}, \\ 
{\rm{cons}}\,(\=\+{\rm{c}}\,({\rm{indices}}\,({\tt{'}}{\tt{cvzbv}}, {\tt{0}}, {\tt{35}})\index{indices})\index{c}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{clk}}, \\ 
{\rm{cons}}\,(\=\+{\rm{c-set}}\,({\rm{indices}}\,({\tt{'}}{\tt{set-flags}}, {\tt{0}}, {\tt{4}})\index{indices})\index{c-set}, \\ 
{\tt{'}}{\tt{(}}{\tt{v}}{\tt{ }}{\tt{te}}{\tt{)}})\-)\-)\-)\-)\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\sc{flags*}}\index{flags*}) $=$ {\tt{'}}{\tt{(}}{\tt{z-latch}}{\tt{ }}{\tt{n-latch}}{\tt{ }}{\tt{v-latch}}{\tt{ }}{\tt{c-latch}}{\tt{)}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable flags*; name this event `flags*-off'.\index{flags*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable flags*\$destructure; name this event `flags*\$destructure-off'.\index{flags*\$destructure-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*flags*; name this event `g*1*flags*-off'.\index{g*1*flags*-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{flags\&} \\  
\=\+{\rm{flags\&}}\,({\it{netlist\/}})\index{flags\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{flags}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{flags*}}\index{flags*}) \\ 
$\wedge$$\;\;\;\;${\rm{fd1slp\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{flags}}, {\it{netlist\/}})\index{delete-module})\index{fd1slp\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable flags\&; name this event `flags\&-off'.\index{flags\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{flags\$netlist}$\;\;$
{\sc{flags\$netlist}}\index{flags\$netlist} $=$ {\rm{cons}}\,({\sc{flags*}}\index{flags*}, {\sc{fd1slp\$netlist}}\index{fd1slp\$netlist})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  check-flags\$netlist \\ \index{check-flags\$netlist}
{\rm{flags\&}}\,({\sc{flags\$netlist}}\index{flags\$netlist})\index{flags\&}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags\$value \\ \index{flags\$value}
\=\+({\rm{flags\&}}\,({\it{netlist\/}})\index{flags\&} $\wedge$ {\rm{properp}}\,({\it{flags\/}})\index{properp} $\wedge$ ({\rm{length}}\,({\it{flags\/}})\index{length} $=$ {\tt{4}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{flags}}, \\ 
{\rm{cons}}\,({\it{clk\/}}, {\rm{cons}}\,({\it{te\/}}, {\rm{cons}}\,({\it{ti\/}}, {\rm{append}}\,({\it{set-flags\/}}, {\it{cvzbv\/}})))), \\ 
{\it{flags\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{v-threefix}}\,({\it{flags\/}})\index{v-threefix})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable flags\$value; name this event `flags\$value-off'.\index{flags\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{f\$update-flags} \\  
\=\+{\rm{f\$update-flags}}\,({\it{flags\/}}, {\it{set-flags\/}}, {\it{cvzbv\/}})\index{f\$update-flags} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{f-if}}\,({\rm{z-set}}\,({\it{set-flags\/}})\index{z-set}, {\rm{zb}}\,({\it{cvzbv\/}})\index{zb}, {\rm{z-flag}}\,({\it{flags\/}})\index{z-flag})\index{f-if}, \\ 
{\rm{f-if}}\,({\rm{n-set}}\,({\it{set-flags\/}})\index{n-set}, {\rm{n}}\,({\it{cvzbv\/}})\index{n}, {\rm{n-flag}}\,({\it{flags\/}})\index{n-flag})\index{f-if}, \\ 
{\rm{f-if}}\,({\rm{v-set}}\,({\it{set-flags\/}})\index{v-set}, {\rm{v}}\,({\it{cvzbv\/}})\index{v}, {\rm{v-flag}}\,({\it{flags\/}})\index{v-flag})\index{f-if}, \\ 
{\rm{f-if}}\,({\rm{c-set}}\,({\it{set-flags\/}})\index{c-set}, {\rm{c}}\,({\it{cvzbv\/}})\index{c}, {\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{f-if})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$update-flags; name this event `f\$update-flags-off'.\index{f\$update-flags-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  properp-length-f\$update-flags \\ \index{properp-length-f\$update-flags}
\=\+{\rm{properp}}\,({\rm{f\$update-flags}}\,({\it{flags\/}}, {\it{set-flags\/}}, {\it{cvzbv\/}})\index{f\$update-flags})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{f\$update-flags}}\,({\it{flags\/}}, {\it{set-flags\/}}, {\it{cvzbv\/}})\index{f\$update-flags})\index{length} $=$ {\tt{4}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f\$update-flags=update-flags \\ \index{f\$update-flags=update-flags}
\=\+(\=\+{\rm{bvp}}\,({\it{flags\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{flags\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{set-flags\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{set-flags\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{cvzbv\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{cvzbv\/}})\index{length} $=$ {\tt{35}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$update-flags}}\,({\it{flags\/}}, {\it{set-flags\/}}, {\it{cvzbv\/}})\index{f\$update-flags} \\ 
$=$$\;\;\;\;${\rm{update-flags}}\,({\it{flags\/}}, {\it{set-flags\/}}, {\it{cvzbv\/}})\index{update-flags})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags\$state-help \\ \index{flags\$state-help}
\=\+(\=\+{\rm{flags\&}}\,({\it{netlist\/}})\index{flags\&} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{flags\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{flags\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;$({\it{set-flags\/}} $=$ {\rm{list}}\,({\it{set-z\/}}, {\it{set-n\/}}, {\it{set-v\/}}, {\it{set-c\/}})) \\ 
$\wedge$$\;\;\;\;$({\it{cvzbv\/}} $=$ {\rm{cons}}\,({\it{c\/}}, {\rm{cons}}\,({\it{v\/}}, {\rm{cons}}\,({\it{z\/}}, {\it{bv\/}})))) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{cvzbv\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{cvzbv\/}})\index{length} $=$ {\tt{35}}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\it{te\/}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\tt{'}}{\tt{flags}}, \\ 
{\rm{cons}}\,({\it{clk\/}}, {\rm{cons}}\,({\it{te\/}}, {\rm{cons}}\,({\it{ti\/}}, {\rm{append}}\,({\it{set-flags\/}}, {\it{cvzbv\/}})))), \\ 
{\it{flags\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$update-flags}}\,({\it{flags\/}}, {\it{set-flags\/}}, {\it{cvzbv\/}})\index{f\$update-flags})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable flags\$state-help; name this event `flags\$state-help-off'.\index{flags\$state-help-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  flags\$state \\ \index{flags\$state}
\=\+(\=\+{\rm{flags\&}}\,({\it{netlist\/}})\index{flags\&} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{flags\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{flags\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{set-flags\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{set-flags\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{cvzbv\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{cvzbv\/}})\index{length} $=$ {\tt{35}}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\it{te\/}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\tt{'}}{\tt{flags}}, \\ 
{\rm{cons}}\,({\it{clk\/}}, {\rm{cons}}\,({\it{te\/}}, {\rm{cons}}\,({\it{ti\/}}, {\rm{append}}\,({\it{set-flags\/}}, {\it{cvzbv\/}})))), \\ 
{\it{flags\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$update-flags}}\,({\it{flags\/}}, {\it{set-flags\/}}, {\it{cvzbv\/}})\index{f\$update-flags})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable flags\$state; name this event `flags\$state-off'.\index{flags\$state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  flags\$partial-state-help \\ \index{flags\$partial-state-help}
\=\+(\=\+{\rm{flags\&}}\,({\it{netlist\/}})\index{flags\&} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{flags\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{flags\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;$({\it{set-flags\/}} $=$ {\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list}) \\ 
$\wedge$$\;\;\;\;$({\it{cvzbv\/}} $=$ {\rm{cons}}\,({\it{c\/}}, {\rm{cons}}\,({\it{v\/}}, {\rm{cons}}\,({\it{z\/}}, {\it{bv\/}})))) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{cvzbv\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{cvzbv\/}})\index{length} $=$ {\tt{35}}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\it{te\/}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\tt{'}}{\tt{flags}}, \\ 
{\rm{cons}}\,({\it{clk\/}}, {\rm{cons}}\,({\it{te\/}}, {\rm{cons}}\,({\it{ti\/}}, {\rm{append}}\,({\it{set-flags\/}}, {\it{cvzbv\/}})))), \\ 
{\it{flags\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{update-flags}}\,({\it{flags\/}}, {\it{set-flags\/}}, {\it{cvzbv\/}})\index{update-flags})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable flags\$partial-state-help; name this event `flags\$partial-state-help-off'.\index{flags\$partial-state-help-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  flags\$partial-state \\ \index{flags\$partial-state}
\=\+(\=\+{\rm{flags\&}}\,({\it{netlist\/}})\index{flags\&} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{flags\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{flags\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;$({\it{set-flags\/}} $=$ {\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{cvzbv\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{cvzbv\/}})\index{length} $=$ {\tt{35}}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\it{te\/}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\tt{'}}{\tt{flags}}, \\ 
{\rm{cons}}\,({\it{clk\/}}, {\rm{cons}}\,({\it{te\/}}, {\rm{cons}}\,({\it{ti\/}}, {\rm{append}}\,({\it{set-flags\/}}, {\it{cvzbv\/}})))), \\ 
{\it{flags\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{update-flags}}\,({\it{flags\/}}, {\it{set-flags\/}}, {\it{cvzbv\/}})\index{update-flags})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable flags\$partial-state; name this event `flags\$partial-state-off'.\index{flags\$partial-state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{extend-immediate*} \\  
\=\+{\sc{extend-immediate*}}\index{extend-immediate*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\tt{'}}{\tt{extend-immediate}}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{select-immediate}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{immediate}}, {\tt{0}}, {\tt{9}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{reg-data}}, {\tt{0}}, {\tt{32}})\index{indices})\-)\-, \\ 
{\rm{cons}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\tt{32}})\index{indices}, \\ 
{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{buffer}}, \\ 
{\tt{'}}{\tt{(}}{\tt{sign-bit}}{\tt{)}}, \\ 
{\tt{'}}{\tt{b-buf-pwr}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{immediate}}, {\tt{8}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{mux}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\tt{32}})\index{indices}, \\ 
{\rm{index}}\,(\=\+{\tt{'}}{\tt{tv-if}}, \\ 
{\rm{tree-number}}\,({\rm{make-tree}}\,({\tt{32}})\index{make-tree})\index{tree-number})\-\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{select-immediate}}, \\ 
{\rm{append}}\,(\=\+{\rm{append}}\,(\=\+{\rm{indices}}\,(\=\+{\tt{'}}{\tt{immediate}}, \\ 
{\tt{0}}, \\ 
{\tt{9}})\-\index{indices}, \\ 
{\rm{make-list}}\,(\=\+{\tt{23}}, \\ 
{\tt{'}}{\tt{sign-bit}})\-\index{make-list})\-, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{reg-data}}, {\tt{0}}, {\tt{32}})\index{indices})\-)\-)\-)\-, \\ 
{\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}})\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  extend-immediate*\$destructure \\ \index{extend-immediate*\$destructure}
\=\+({\rm{car}}\,({\sc{extend-immediate*}}\index{extend-immediate*}) $=$ {\tt{'}}{\tt{extend-immediate}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadr}}\,({\sc{extend-immediate*}}\index{extend-immediate*}) \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\tt{'}}{\tt{select-immediate}}, \\ 
{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{immediate}}, {\tt{0}}, {\tt{9}})\index{indices}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{reg-data}}, {\tt{0}}, {\tt{32}})\index{indices})\-)\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\sc{extend-immediate*}}\index{extend-immediate*}) $=$ {\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\tt{32}})\index{indices}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadddr}}\,({\sc{extend-immediate*}}\index{extend-immediate*}) \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\tt{'}}{\tt{buffer}}, \\ 
{\tt{'}}{\tt{(}}{\tt{sign-bit}}{\tt{)}}, \\ 
{\tt{'}}{\tt{b-buf-pwr}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{immediate}}, {\tt{8}})\index{index}))\-, \\ 
{\rm{list}}\,(\=\+{\tt{'}}{\tt{mux}}, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{z}}, {\tt{0}}, {\tt{32}})\index{indices}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{tv-if}}, {\rm{tree-number}}\,({\rm{make-tree}}\,({\tt{32}})\index{make-tree})\index{tree-number})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{select-immediate}}, \\ 
{\rm{append}}\,(\=\+{\rm{append}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{immediate}}, {\tt{0}}, {\tt{9}})\index{indices}, \\ 
{\rm{make-list}}\,({\tt{23}}, {\tt{'}}{\tt{sign-bit}})\index{make-list})\-, \\ 
{\rm{indices}}\,({\tt{'}}{\tt{reg-data}}, {\tt{0}}, {\tt{32}})\index{indices})\-)\-)\-)\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\sc{extend-immediate*}}\index{extend-immediate*}) $=$ {\bf{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable extend-immediate*; name this event `extend-immediate*-off'.\index{extend-immediate*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable extend-immediate*\$destructure; name this event `extend-immediate*\$destructure-off'.\index{extend-immediate*\$destructure-!off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*extend-immediate*; name this event `g*1*extend-immediate*-off'.\index{g*1*extend-immediate*-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{extend-immediate\&} \\  
\=\+{\rm{extend-immediate\&}}\,({\it{netlist\/}})\index{extend-immediate\&} \\ 
$=$$\;\;\;\;$(\=\+(\=\+{\rm{lookup-module}}\,({\tt{'}}{\tt{extend-immediate}}, {\it{netlist\/}})\index{lookup-module} \\ 
$=$$\;\;\;\;${\sc{extend-immediate*}}\index{extend-immediate*})\- \\ 
$\wedge$$\;\;\;\;${\rm{b-buf-pwr\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{extend-immediate}}, {\it{netlist\/}})\index{delete-module})\index{b-buf-pwr\&} \\ 
$\wedge$$\;\;\;\;${\rm{tv-if\&}}\,(\=\+{\rm{delete-module}}\,({\tt{'}}{\tt{extend-immediate}}, {\it{netlist\/}})\index{delete-module}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{tv-if\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable extend-immediate\&; name this event `extend-immediate\&-off'.\index{extend-immediate\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{extend-immediate\$netlist} \\  
\=\+{\sc{extend-immediate\$netlist}}\index{extend-immediate\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{extend-immediate*}}\index{extend-immediate*}, \\ 
{\sc{b-buf-pwr\$netlist}}\index{b-buf-pwr\$netlist} $\cup$ {\rm{tv-if\$netlist}}\,({\rm{make-tree}}\,({\tt{32}})\index{make-tree})\index{tv-if\$netlist})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  check-extend-immediate\$netlist \\ \index{check-extend-immediate\$netlist}
{\rm{extend-immediate\&}}\,({\sc{extend-immediate\$netlist}}\index{extend-immediate\$netlist})\index{extend-immediate\&}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{f\$extend-immediate} \\  
\=\+{\rm{f\$extend-immediate}}\,({\it{select-immediate\/}}, {\it{immediate\/}}, {\it{reg-data\/}})\index{f\$extend-immediate} \\ 
$=$$\;\;\;\;${\rm{fv-if}}\,(\=\+{\it{select-immediate\/}}, \\ 
{\rm{append}}\,(\=\+{\it{immediate\/}}, \\ 
\=\+{\bf if }{\rm{boolp}}\,({\rm{nth}}\,({\tt{8}}, {\it{immediate\/}})\index{nth})\index{boolp} \\ 
{\bf then }{\rm{make-list}}\,({\tt{23}}, {\rm{nth}}\,({\tt{8}}, {\it{immediate\/}})\index{nth})\index{make-list} \\ 
{\bf else }{\rm{make-list}}\,({\tt{23}}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\-, \\ 
{\it{reg-data\/}})\-\index{fv-if}\-
\end{tabbing}


\noindent{\sc Event}:   Enable f\$extend-immediate; name this event `f\$extend-immediate-off'.\index{f\$extend-immediate-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  properp-length-f\$extend-immediate \\ \index{properp-length-f\$extend-immedi!ate}
\=\+{\rm{properp}}\,({\rm{f\$extend-immediate}}\,({\it{select-immediate\/}}, {\it{immediate\/}}, {\it{reg-bus\/}})\index{f\$extend-immediate})\index{properp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\it{immediate\/}})\index{length} $=$ {\tt{9}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{length}}\,({\rm{f\$extend-immediate}}\,({\it{select-immediate\/}}, {\it{immediate\/}}, {\it{reg-bus\/}})\index{f\$extend-immediate})\index{length} \\ 
$=$$\;\;\;\;${\tt{32}})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f\$extend-immediate=extend-immediate \\ \index{f\$extend-immediate=extend-imme!diate}
\=\+(\=\+{\rm{bvp}}\,({\it{immediate\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{immediate\/}})\index{length} $=$ {\tt{9}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{reg-data\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{reg-data\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{select-immediate\/}})\index{boolp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{f\$extend-immediate}}\,({\it{select-immediate\/}}, {\it{immediate\/}}, {\it{reg-data\/}})\index{f\$extend-immediate} \\ 
$=$$\;\;\;\;${\rm{if*}}\,({\it{select-immediate\/}}, {\rm{sign-extend}}\,({\it{immediate\/}}, {\tt{32}})\index{sign-extend}, {\it{reg-data\/}})\index{if*})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  extend-immediate\$value \\ \index{extend-immediate\$value}
\=\+(\=\+{\rm{extend-immediate\&}}\,({\it{netlist\/}})\index{extend-immediate\&} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{immediate\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{immediate\/}})\index{length} $=$ {\tt{9}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{reg-data\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{reg-data\/}})\index{length} $=$ {\tt{32}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{extend-immediate}}, \\ 
{\rm{cons}}\,({\it{select-immediate\/}}, {\rm{append}}\,({\it{immediate\/}}, {\it{reg-data\/}})), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f\$extend-immediate}}\,({\it{select-immediate\/}}, {\it{immediate\/}}, {\it{reg-data\/}})\index{f\$extend-immediate})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable extend-immediate\$value; name this event `extend-immediate\$value-off'.\index{extend-immediate\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-input-pads-body} \\  
\=\+{\rm{ttl-input-pads-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{pi\/}})\index{ttl-input-pads-body} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{g}}, {\it{m\/}})\index{index}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{out}}, {\it{m\/}})\index{index}, {\rm{index}}\,({\tt{'}}{\tt{po}}, {\it{m\/}})\index{index}), \\ 
{\tt{'}}{\tt{ttl-input}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{in}}, {\it{m\/}})\index{index}, {\it{pi\/}}))\-, \\ 
{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{b}}, {\it{m\/}})\index{index}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{b-out}}, {\it{m\/}})\index{index}), \\ 
{\tt{'}}{\tt{b-buf}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{out}}, {\it{m\/}})\index{index}))\-, \\ 
{\rm{ttl-input-pads-body}}\,($1\;+$ {\it{m\/}}, {\it{n\/}} $-\;1$, {\rm{index}}\,({\tt{'}}{\tt{po}}, {\it{m\/}})\index{index})\index{ttl-input-pads-body})\-)\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-input-pads-body; name this event `ttl-input-pads-body-off'.\index{ttl-input-pads-body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-input-pads-body\$induction} \\  
\=\+{\rm{ttl-input-pads-body\$induction}}\,({\it{m\/}}, {\it{n\/}}, {\it{pi\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{ttl-input-pads-body\$induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{ttl-input-pads-body\$induction}}\,(\=\+$1\;+$ {\it{m\/}}, \\ 
{\it{n\/}} $-\;1$, \\ 
{\rm{index}}\,({\tt{'}}{\tt{po}}, {\it{m\/}})\index{index}, \\ 
{\rm{dual-eval-body-bindings}}\,(\=\+{\tt{2}}, \\ 
{\rm{ttl-input-pads-body}}\,(\=\+{\it{m\/}}, \\ 
{\it{n\/}}, \\ 
{\it{pi\/}})\-\index{ttl-input-pads-body}, \\ 
{\it{bindings\/}}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval-body-bindings}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{ttl-input-pads-body\$induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ttl-input-pads*} \\  
\=\+{\rm{ttl-input-pads*}}\,({\it{n\/}})\index{ttl-input-pads*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{ttl-input-pads}}, {\it{n\/}})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,({\tt{'}}{\tt{pi}}, {\rm{indices}}\,({\tt{'}}{\tt{in}}, {\tt{0}}, {\it{n\/}})\index{indices}), \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,({\rm{index}}\,({\tt{'}}{\tt{po}}, {\it{n\/}} $-\;1$)\index{index}, {\rm{indices}}\,({\tt{'}}{\tt{b-out}}, {\tt{0}}, {\it{n\/}})\index{indices}), \\ 
{\rm{cons}}\,({\rm{ttl-input-pads-body}}\,({\tt{0}}, {\it{n\/}}, {\tt{'}}{\tt{pi}})\index{ttl-input-pads-body}, {\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}}))\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-input-pads*\$destructure \\ \index{ttl-input-pads*\$destructure}
\=\+({\rm{car}}\,({\rm{ttl-input-pads*}}\,({\it{n\/}})\index{ttl-input-pads*}) $=$ {\rm{index}}\,({\tt{'}}{\tt{ttl-input-pads}}, {\it{n\/}})\index{index}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadr}}\,({\rm{ttl-input-pads*}}\,({\it{n\/}})\index{ttl-input-pads*}) $=$ {\rm{cons}}\,({\tt{'}}{\tt{pi}}, {\rm{indices}}\,({\tt{'}}{\tt{in}}, {\tt{0}}, {\it{n\/}})\index{indices})) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{caddr}}\,({\rm{ttl-input-pads*}}\,({\it{n\/}})\index{ttl-input-pads*}) \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\rm{index}}\,({\tt{'}}{\tt{po}}, {\it{n\/}} $-\;1$)\index{index}, {\rm{indices}}\,({\tt{'}}{\tt{b-out}}, {\tt{0}}, {\it{n\/}})\index{indices}))\- \\ 
$\wedge$$\;\;\;\;$({\rm{cadddr}}\,({\rm{ttl-input-pads*}}\,({\it{n\/}})\index{ttl-input-pads*}) $=$ {\rm{ttl-input-pads-body}}\,({\tt{0}}, {\it{n\/}}, {\tt{'}}{\tt{pi}})\index{ttl-input-pads-body}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{ttl-input-pads*}}\,({\it{n\/}})\index{ttl-input-pads*}) $=$ {\bf{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-input-pads*; name this event `ttl-input-pads*-off'.\index{ttl-input-pads*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ttl-input-pads*\$destructure; name this event `ttl-input-pads*\$destructure-off'.\index{ttl-input-pads*\$destructure-of!f}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-input-pads\&} \\  
\=\+{\rm{ttl-input-pads\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{ttl-input-pads\&} \\ 
$=$$\;\;\;\;$(\=\+(\=\+{\rm{lookup-module}}\,({\rm{index}}\,({\tt{'}}{\tt{ttl-input-pads}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{lookup-module} \\ 
$=$$\;\;\;\;${\rm{ttl-input-pads*}}\,({\it{n\/}})\index{ttl-input-pads*})\- \\ 
$\wedge$$\;\;\;\;${\rm{ttl-input\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{ttl-input-pads}}, {\it{n\/}})\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{ttl-input\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-buf\&}}\,({\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{ttl-input-pads}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{delete-module})\index{b-buf\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-input-pads\&; name this event `ttl-input-pads\&-off'.\index{ttl-input-pads\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-input-pads\$netlist} \\  
\=\+{\rm{ttl-input-pads\$netlist}}\,({\it{n\/}})\index{ttl-input-pads\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\rm{ttl-input-pads*}}\,({\it{n\/}})\index{ttl-input-pads*}, {\sc{ttl-input\$netlist}}\index{ttl-input\$netlist} $\cup$ {\sc{b-buf\$netlist}}\index{b-buf\$netlist})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-input-pads-body\$unbound-in-body \\ \index{ttl-input-pads-body\$unbound-in!-body}
\=\+({\it{l\/}} $<$ {\it{m\/}}) \\ 
$\rightarrow$$\;\;\;\;${\rm{unbound-in-body}}\,({\rm{index}}\,({\tt{'}}{\tt{b-out}}, {\it{l\/}})\index{index}, {\rm{ttl-input-pads-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{pi\/}})\index{ttl-input-pads-body})\index{unbound-in-body}\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-input-pads-body\$unbound-in-body; name this event `ttl-input-pads-body\$unbound-in-body-off'.\index{ttl-input-pads-body\$unbound-in!-body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ttl-input-pads-body\$value \\ \index{ttl-input-pads-body\$value}
\=\+({\rm{ttl-input\&}}\,({\it{netlist\/}})\index{ttl-input\&} $\wedge$ {\rm{b-buf\&}}\,({\it{netlist\/}})\index{b-buf\&}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{b-out}}, {\it{m\/}}, {\it{n\/}})\index{indices}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{1}}, \\ 
{\rm{ttl-input-pads-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{pi\/}})\index{ttl-input-pads-body}, \\ 
{\it{bindings\/}}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{v-threefix}}\,({\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{in}}, {\it{m\/}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value})\index{v-threefix})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-input-pads-body\$value; name this event `ttl-input-pads-body\$value-off'.\index{ttl-input-pads-body\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ttl-input-pads\$value \\ \index{ttl-input-pads\$value}
\=\+({\rm{ttl-input-pads\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{ttl-input-pads\&} $\wedge$ ({\rm{length}}\,({\it{inputs\/}})\index{length} $=$ {\it{n\/}}) $\wedge$ {\rm{properp}}\,({\it{inputs\/}})\index{properp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{cdr}}\,({\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{ttl-input-pads}}, {\it{n\/}})\index{index}, \\ 
{\rm{cons}}\,({\it{pi\/}}, {\it{inputs\/}}), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval}) \\ 
$=$$\;\;\;\;${\rm{v-threefix}}\,({\it{inputs\/}})\index{v-threefix})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-input-pads\$value; name this event `ttl-input-pads\$value-off'.\index{ttl-input-pads\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-output-pads-body} \\  
\=\+{\rm{ttl-output-pads-body}}\,({\it{m\/}}, {\it{n\/}})\index{ttl-output-pads-body} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{b}}, {\it{m\/}})\index{index}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{b-in}}, {\it{m\/}})\index{index}), \\ 
{\tt{'}}{\tt{b-buf}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{in}}, {\it{m\/}})\index{index}))\-, \\ 
{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{g}}, {\it{m\/}})\index{index}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{out}}, {\it{m\/}})\index{index}), \\ 
{\tt{'}}{\tt{ttl-output}}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{b-in}}, {\it{m\/}})\index{index}))\-, \\ 
{\rm{ttl-output-pads-body}}\,($1\;+$ {\it{m\/}}, {\it{n\/}} $-\;1$)\index{ttl-output-pads-body})\-)\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-output-pads-body; name this event `ttl-output-pads-body-off'.\index{ttl-output-pads-body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-output-pads-body\$induction} \\  
\=\+{\rm{ttl-output-pads-body\$induction}}\,({\it{m\/}}, {\it{n\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{ttl-output-pads-body\$induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{ttl-output-pads-body\$induction}}\,(\=\+$1\;+$ {\it{m\/}}, \\ 
{\it{n\/}} $-\;1$, \\ 
{\rm{dual-eval-body-bindings}}\,(\=\+{\tt{2}}, \\ 
{\rm{ttl-output-pads-body}}\,(\=\+{\it{m\/}}, \\ 
{\it{n\/}})\-\index{ttl-output-pads-body}, \\ 
{\it{bindings\/}}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval-body-bindings}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{ttl-output-pads-body\$induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ttl-output-pads*} \\  
\=\+{\rm{ttl-output-pads*}}\,({\it{n\/}})\index{ttl-output-pads*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{ttl-output-pads}}, {\it{n\/}})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{in}}, {\tt{0}}, {\it{n\/}})\index{indices}, \\ 
{\rm{cons}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\it{n\/}})\index{indices}, \\ 
{\rm{cons}}\,({\rm{ttl-output-pads-body}}\,({\tt{0}}, {\it{n\/}})\index{ttl-output-pads-body}, {\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}}))\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-output-pads*\$destructure \\ \index{ttl-output-pads*\$destructure}
\=\+({\rm{car}}\,({\rm{ttl-output-pads*}}\,({\it{n\/}})\index{ttl-output-pads*}) $=$ {\rm{index}}\,({\tt{'}}{\tt{ttl-output-pads}}, {\it{n\/}})\index{index}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadr}}\,({\rm{ttl-output-pads*}}\,({\it{n\/}})\index{ttl-output-pads*}) $=$ {\rm{indices}}\,({\tt{'}}{\tt{in}}, {\tt{0}}, {\it{n\/}})\index{indices}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\rm{ttl-output-pads*}}\,({\it{n\/}})\index{ttl-output-pads*}) $=$ {\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\it{n\/}})\index{indices}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadddr}}\,({\rm{ttl-output-pads*}}\,({\it{n\/}})\index{ttl-output-pads*}) $=$ {\rm{ttl-output-pads-body}}\,({\tt{0}}, {\it{n\/}})\index{ttl-output-pads-body}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{ttl-output-pads*}}\,({\it{n\/}})\index{ttl-output-pads*}) $=$ {\bf{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-output-pads*; name this event `ttl-output-pads*-off'.\index{ttl-output-pads*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ttl-output-pads*\$destructure; name this event `ttl-output-pads*\$destructure-off'.\index{ttl-output-pads*\$destructure-o!ff}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-output-pads\&} \\  
\=\+{\rm{ttl-output-pads\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{ttl-output-pads\&} \\ 
$=$$\;\;\;\;$(\=\+(\=\+{\rm{lookup-module}}\,({\rm{index}}\,({\tt{'}}{\tt{ttl-output-pads}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{lookup-module} \\ 
$=$$\;\;\;\;${\rm{ttl-output-pads*}}\,({\it{n\/}})\index{ttl-output-pads*})\- \\ 
$\wedge$$\;\;\;\;${\rm{ttl-output\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{ttl-output-pads}}, {\it{n\/}})\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{ttl-output\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-buf\&}}\,({\rm{delete-module}}\,({\rm{index}}\,({\tt{'}}{\tt{ttl-output-pads}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{delete-module})\index{b-buf\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-output-pads\&; name this event `ttl-output-pads\&-off'.\index{ttl-output-pads\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-output-pads\$netlist} \\  
\=\+{\rm{ttl-output-pads\$netlist}}\,({\it{n\/}})\index{ttl-output-pads\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\rm{ttl-output-pads*}}\,({\it{n\/}})\index{ttl-output-pads*}, {\sc{ttl-output\$netlist}}\index{ttl-output\$netlist} $\cup$ {\sc{b-buf\$netlist}}\index{b-buf\$netlist})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-output-pads-body\$unbound-in-body \\ \index{ttl-output-pads-body\$unbound-i!n-body}
({\it{l\/}} $<$ {\it{m\/}}) $\rightarrow$ {\rm{unbound-in-body}}\,({\rm{index}}\,({\tt{'}}{\tt{out}}, {\it{l\/}})\index{index}, {\rm{ttl-output-pads-body}}\,({\it{m\/}}, {\it{n\/}})\index{ttl-output-pads-body})\index{unbound-in-body}
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-output-pads-body\$unbound-in-body; name this event `ttl-output-pads-body\$unbound-in-body-off'.\index{ttl-output-pads-body\$unbound-i!n-body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ttl-output-pads-body\$value \\ \index{ttl-output-pads-body\$value}
\=\+({\rm{ttl-output\&}}\,({\it{netlist\/}})\index{ttl-output\&} $\wedge$ {\rm{b-buf\&}}\,({\it{netlist\/}})\index{b-buf\&}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\it{m\/}}, {\it{n\/}})\index{indices}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{1}}, \\ 
{\rm{ttl-output-pads-body}}\,({\it{m\/}}, {\it{n\/}})\index{ttl-output-pads-body}, \\ 
{\it{bindings\/}}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{v-threefix}}\,({\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{in}}, {\it{m\/}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value})\index{v-threefix})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-output-pads-body\$value; name this event `ttl-output-pads-body\$value-off'.\index{ttl-output-pads-body\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ttl-output-pads\$value \\ \index{ttl-output-pads\$value}
\=\+({\rm{ttl-output-pads\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{ttl-output-pads\&} $\wedge$ ({\rm{length}}\,({\it{inputs\/}})\index{length} $=$ {\it{n\/}}) $\wedge$ {\rm{properp}}\,({\it{inputs\/}})\index{properp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\rm{index}}\,({\tt{'}}{\tt{ttl-output-pads}}, {\it{n\/}})\index{index}, {\it{inputs\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{v-threefix}}\,({\it{inputs\/}})\index{v-threefix})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ttl-tri-output-pads-body} \\  
\=\+{\rm{ttl-tri-output-pads-body}}\,({\it{m\/}}, {\it{n\/}})\index{ttl-tri-output-pads-body} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{g}}, {\it{m\/}})\index{index}, \\ 
{\rm{list}}\,({\rm{index}}\,({\tt{'}}{\tt{out}}, {\it{m\/}})\index{index}), \\ 
{\tt{'}}{\tt{ttl-tri-output}}, \\ 
{\rm{cons}}\,({\rm{index}}\,({\tt{'}}{\tt{in}}, {\it{m\/}})\index{index}, {\tt{'}}{\tt{(}}{\tt{enable-buf}}{\tt{)}}))\-, \\ 
{\rm{ttl-tri-output-pads-body}}\,($1\;+$ {\it{m\/}}, {\it{n\/}} $-\;1$)\index{ttl-tri-output-pads-body})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-tri-output-pads-body; name this event `ttl-tri-output-pads-body-off'.\index{ttl-tri-output-pads-body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-tri-output-pads-body\$inducti!on} \\  
\=\+{\rm{ttl-tri-output-pads-body\$induction}}\,({\it{m\/}}, {\it{n\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{ttl-tri-output-pads-body\$inducti!on} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{ttl-tri-output-pads-body\$induction}}\,(\=\+$1\;+$ {\it{m\/}}, \\ 
{\it{n\/}} $-\;1$, \\ 
{\rm{dual-eval-body-bindings}}\,(\=\+{\tt{1}}, \\ 
{\rm{ttl-tri-output-pads-body}}\,(\=\+{\it{m\/}}, \\ 
{\it{n\/}})\-\index{ttl-tri-output-pads-body}, \\ 
{\it{bindings\/}}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval-body-bindings}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{ttl-tri-output-pads-body\$inducti!on}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ttl-tri-output-pads*} \\  
\=\+{\rm{ttl-tri-output-pads*}}\,({\it{n\/}})\index{ttl-tri-output-pads*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{ttl-tri-output-pads}}, {\it{n\/}})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,({\tt{'}}{\tt{enable}}, {\rm{indices}}\,({\tt{'}}{\tt{in}}, {\tt{0}}, {\it{n\/}})\index{indices}), \\ 
{\rm{cons}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\it{n\/}})\index{indices}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{enable-buffer}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{enable-buf}}{\tt{)}}, \\ 
{\rm{cons}}\,(\=\+\=\+{\bf if }{\it{n\/}} $<$ {\tt{8}}$\;\;${\bf then }{\tt{'}}{\tt{b-buf}} \\ 
{\bf else }{\tt{'}}{\tt{b-buf-pwr}}$\;${\bf  endif}\-, \\ 
{\tt{'}}{\tt{(}}{\tt{(}}{\tt{enable}}{\tt{)}}{\tt{)}})\-)\-)\-, \\ 
{\rm{ttl-tri-output-pads-body}}\,({\tt{0}}, {\it{n\/}})\index{ttl-tri-output-pads-body})\-, \\ 
{\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}})\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-tri-output-pads*\$destructure \\ \index{ttl-tri-output-pads*\$destructu!re}
\=\+({\rm{car}}\,({\rm{ttl-tri-output-pads*}}\,({\it{n\/}})\index{ttl-tri-output-pads*}) $=$ {\rm{index}}\,({\tt{'}}{\tt{ttl-tri-output-pads}}, {\it{n\/}})\index{index}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadr}}\,({\rm{ttl-tri-output-pads*}}\,({\it{n\/}})\index{ttl-tri-output-pads*}) $=$ {\rm{cons}}\,({\tt{'}}{\tt{enable}}, {\rm{indices}}\,({\tt{'}}{\tt{in}}, {\tt{0}}, {\it{n\/}})\index{indices})) \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\rm{ttl-tri-output-pads*}}\,({\it{n\/}})\index{ttl-tri-output-pads*}) $=$ {\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\it{n\/}})\index{indices}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadddr}}\,({\rm{ttl-tri-output-pads*}}\,({\it{n\/}})\index{ttl-tri-output-pads*}) \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{enable-buffer}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{enable-buf}}{\tt{)}}, \\ 
{\rm{cons}}\,(\=\+\=\+{\bf if }{\it{n\/}} $<$ {\tt{8}}$\;\;${\bf then }{\tt{'}}{\tt{b-buf}} \\ 
{\bf else }{\tt{'}}{\tt{b-buf-pwr}}$\;${\bf  endif}\-, \\ 
{\tt{'}}{\tt{(}}{\tt{(}}{\tt{enable}}{\tt{)}}{\tt{)}})\-)\-)\-, \\ 
{\rm{ttl-tri-output-pads-body}}\,({\tt{0}}, {\it{n\/}})\index{ttl-tri-output-pads-body})\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{ttl-tri-output-pads*}}\,({\it{n\/}})\index{ttl-tri-output-pads*}) $=$ {\bf{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-tri-output-pads*; name this event `ttl-tri-output-pads*-off'.\index{ttl-tri-output-pads*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ttl-tri-output-pads*\$destructure; name this event `ttl-tri-output-pads*\$destructure-off'.\index{ttl-tri-output-pads*\$destructu!re-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-tri-output-pads\&} \\  
\=\+{\rm{ttl-tri-output-pads\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{ttl-tri-output-pads\&} \\ 
$=$$\;\;\;\;$(\=\+(\=\+{\rm{lookup-module}}\,({\rm{index}}\,({\tt{'}}{\tt{ttl-tri-output-pads}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{lookup-module} \\ 
$=$$\;\;\;\;${\rm{ttl-tri-output-pads*}}\,({\it{n\/}})\index{ttl-tri-output-pads*})\- \\ 
$\wedge$$\;\;\;\;${\rm{ttl-tri-output\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{ttl-tri-output-pads}}, \\ 
{\it{n\/}})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{ttl-tri-output\&} \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $<$ {\tt{8}} \\ 
{\bf then }{\rm{b-buf\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{ttl-tri-output-pads}}, {\it{n\/}})\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{b-buf\&} \\ 
{\bf else }{\rm{b-buf-pwr\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{ttl-tri-output-pads}}, \\ 
{\it{n\/}})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{b-buf-pwr\&}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-tri-output-pads\&; name this event `ttl-tri-output-pads\&-off'.\index{ttl-tri-output-pads\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-tri-output-pads\$netlist} \\  
\=\+{\rm{ttl-tri-output-pads\$netlist}}\,({\it{n\/}})\index{ttl-tri-output-pads\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{ttl-tri-output-pads*}}\,({\it{n\/}})\index{ttl-tri-output-pads*}, \\ 
\=\+\=\+{\bf if }{\it{n\/}} $<$ {\tt{8}}$\;\;${\bf then }{\sc{b-buf\$netlist}}\index{b-buf\$netlist} \\ 
{\bf else }{\sc{b-buf-pwr\$netlist}}\index{b-buf-pwr\$netlist}$\;${\bf  endif}\- \\ 
$\cup$$\;\;\;\;${\sc{ttl-tri-output\$netlist}}\index{ttl-tri-output\$netlist}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-tri-output-pads-body\$unbound-in-body \\ \index{ttl-tri-output-pads-body\$unbou!nd-in-body}
\=\+({\it{l\/}} $<$ {\it{m\/}}) \\ 
$\rightarrow$$\;\;\;\;${\rm{unbound-in-body}}\,({\rm{index}}\,({\tt{'}}{\tt{out}}, {\it{l\/}})\index{index}, {\rm{ttl-tri-output-pads-body}}\,({\it{m\/}}, {\it{n\/}})\index{ttl-tri-output-pads-body})\index{unbound-in-body}\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-tri-output-pads-body\$unbound-in-body; name this event `ttl-tri-output-pads-body\$unbound-in-body-off'.\index{ttl-tri-output-pads-body\$unbou!nd-in-body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ttl-tri-output-pads-body\$value \\ \index{ttl-tri-output-pads-body\$value}
\=\+{\rm{ttl-tri-output\&}}\,({\it{netlist\/}})\index{ttl-tri-output\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{collect-value}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\it{m\/}}, {\it{n\/}})\index{indices}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{1}}, \\ 
{\rm{ttl-tri-output-pads-body}}\,({\it{m\/}}, {\it{n\/}})\index{ttl-tri-output-pads-body}, \\ 
{\it{bindings\/}}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-\index{collect-value} \\ 
$=$$\;\;\;\;${\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{value}}\,({\tt{'}}{\tt{enable-buf}}, {\it{bindings\/}})\index{value})\index{f-not}, \\ 
{\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{in}}, {\it{m\/}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value})\-\index{vft-buf})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-tri-output-pads-body\$value; name this event `ttl-tri-output-pads-body\$value-off'.\index{ttl-tri-output-pads-body\$value!-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ttl-tri-output-pads\$value \\ \index{ttl-tri-output-pads\$value}
\=\+(\=\+{\rm{ttl-tri-output-pads\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{ttl-tri-output-pads\&} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{inputs\/}})\index{length} $=$ {\it{n\/}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{inputs\/}})\index{properp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{ttl-tri-output-pads}}, {\it{n\/}})\index{index}, \\ 
{\rm{cons}}\,({\it{enable\/}}, {\it{inputs\/}}), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{vft-buf}}\,({\rm{f-not}}\,({\it{enable\/}})\index{f-not}, {\it{inputs\/}})\index{vft-buf})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-tri-output-pads\$value; name this event `ttl-tri-output-pads\$value-off'.\index{ttl-tri-output-pads\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-bidirect-pads-body} \\  
\=\+{\rm{ttl-bidirect-pads-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{pi\/}})\index{ttl-bidirect-pads-body} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{g}}, {\it{m\/}})\index{index}, \\ 
{\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{data}}, {\it{m\/}})\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{out}}, {\it{m\/}})\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{po}}, {\it{m\/}})\index{index})\-, \\ 
{\tt{'}}{\tt{ttl-bidirect}}, \\ 
{\rm{list}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{data}}, {\it{m\/}})\index{index}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{in}}, {\it{m\/}})\index{index}, \\ 
{\tt{'}}{\tt{buf-enable}}, \\ 
{\it{pi\/}})\-)\-, \\ 
{\rm{ttl-bidirect-pads-body}}\,($1\;+$ {\it{m\/}}, {\it{n\/}} $-\;1$, {\rm{index}}\,({\tt{'}}{\tt{po}}, {\it{m\/}})\index{index})\index{ttl-bidirect-pads-body})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-bidirect-pads-body; name this event `ttl-bidirect-pads-body-off'.\index{ttl-bidirect-pads-body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-bidirect-pads-body\$inducti!on} \\  
\=\+{\rm{ttl-bidirect-pads-body\$induction}}\,({\it{m\/}}, {\it{n\/}}, {\it{pi\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{ttl-bidirect-pads-body\$inducti!on} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{ttl-bidirect-pads-body\$induction}}\,(\=\+$1\;+$ {\it{m\/}}, \\ 
{\it{n\/}} $-\;1$, \\ 
{\rm{index}}\,({\tt{'}}{\tt{po}}, {\it{m\/}})\index{index}, \\ 
{\rm{dual-eval-body-bindings}}\,(\=\+{\tt{1}}, \\ 
{\rm{ttl-bidirect-pads-body}}\,(\=\+{\it{m\/}}, \\ 
{\it{n\/}}, \\ 
{\it{pi\/}})\-\index{ttl-bidirect-pads-body}, \\ 
{\it{bindings\/}}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval-body-bindings}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{ttl-bidirect-pads-body\$inducti!on}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ttl-bidirect-pads*} \\  
\=\+{\rm{ttl-bidirect-pads*}}\,({\it{n\/}})\index{ttl-bidirect-pads*} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{ttl-bidirect-pads}}, {\it{n\/}})\index{index}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{enable}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{pi}}, \\ 
{\rm{append}}\,({\rm{indices}}\,({\tt{'}}{\tt{data}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{indices}}\,({\tt{'}}{\tt{in}}, {\tt{0}}, {\it{n\/}})\index{indices}))\-)\-, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{po}}, {\it{n\/}} $-\;1$)\index{index}, \\ 
{\rm{append}}\,({\rm{indices}}\,({\tt{'}}{\tt{data}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\it{n\/}})\index{indices}))\-, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{enable-buf}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{buf-enable}}{\tt{)}}, \\ 
{\rm{cons}}\,(\=\+\=\+{\bf if }{\it{n\/}} $<$ {\tt{8}}$\;\;${\bf then }{\tt{'}}{\tt{b-buf}} \\ 
{\bf else }{\tt{'}}{\tt{b-buf-pwr}}$\;${\bf  endif}\-, \\ 
{\tt{'}}{\tt{(}}{\tt{(}}{\tt{enable}}{\tt{)}}{\tt{)}})\-)\-)\-, \\ 
{\rm{ttl-bidirect-pads-body}}\,({\tt{0}}, {\it{n\/}}, {\tt{'}}{\tt{pi}})\index{ttl-bidirect-pads-body})\-, \\ 
{\tt{'}}{\tt{(}}{\tt{nil}}{\tt{)}})\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-bidirect-pads*\$destructure \\ \index{ttl-bidirect-pads*\$destructure}
\=\+({\rm{car}}\,({\rm{ttl-bidirect-pads*}}\,({\it{n\/}})\index{ttl-bidirect-pads*}) $=$ {\rm{index}}\,({\tt{'}}{\tt{ttl-bidirect-pads}}, {\it{n\/}})\index{index}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadr}}\,({\rm{ttl-bidirect-pads*}}\,({\it{n\/}})\index{ttl-bidirect-pads*}) \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\tt{'}}{\tt{enable}}, \\ 
{\rm{cons}}\,({\tt{'}}{\tt{pi}}, {\rm{append}}\,({\rm{indices}}\,({\tt{'}}{\tt{data}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{indices}}\,({\tt{'}}{\tt{in}}, {\tt{0}}, {\it{n\/}})\index{indices})))\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{caddr}}\,({\rm{ttl-bidirect-pads*}}\,({\it{n\/}})\index{ttl-bidirect-pads*}) \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{po}}, {\it{n\/}} $-\;1$)\index{index}, \\ 
{\rm{append}}\,({\rm{indices}}\,({\tt{'}}{\tt{data}}, {\tt{0}}, {\it{n\/}})\index{indices}, {\rm{indices}}\,({\tt{'}}{\tt{out}}, {\tt{0}}, {\it{n\/}})\index{indices}))\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadddr}}\,({\rm{ttl-bidirect-pads*}}\,({\it{n\/}})\index{ttl-bidirect-pads*}) \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{enable-buf}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{buf-enable}}{\tt{)}}, \\ 
{\rm{cons}}\,(\=\+\=\+{\bf if }{\it{n\/}} $<$ {\tt{8}}$\;\;${\bf then }{\tt{'}}{\tt{b-buf}} \\ 
{\bf else }{\tt{'}}{\tt{b-buf-pwr}}$\;${\bf  endif}\-, \\ 
{\tt{'}}{\tt{(}}{\tt{(}}{\tt{enable}}{\tt{)}}{\tt{)}})\-)\-)\-, \\ 
{\rm{ttl-bidirect-pads-body}}\,({\tt{0}}, {\it{n\/}}, {\tt{'}}{\tt{pi}})\index{ttl-bidirect-pads-body})\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{caddddr}}\,({\rm{ttl-bidirect-pads*}}\,({\it{n\/}})\index{ttl-bidirect-pads*}) $=$ {\bf{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-bidirect-pads*; name this event `ttl-bidirect-pads*-off'.\index{ttl-bidirect-pads*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ttl-bidirect-pads*\$destructure; name this event `ttl-bidirect-pads*\$destructure-off'.\index{ttl-bidirect-pads*\$destructure!-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-bidirect-pads\&} \\  
\=\+{\rm{ttl-bidirect-pads\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{ttl-bidirect-pads\&} \\ 
$=$$\;\;\;\;$(\=\+(\=\+{\rm{lookup-module}}\,({\rm{index}}\,({\tt{'}}{\tt{ttl-bidirect-pads}}, {\it{n\/}})\index{index}, {\it{netlist\/}})\index{lookup-module} \\ 
$=$$\;\;\;\;${\rm{ttl-bidirect-pads*}}\,({\it{n\/}})\index{ttl-bidirect-pads*})\- \\ 
$\wedge$$\;\;\;\;${\rm{ttl-bidirect\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{ttl-bidirect-pads}}, {\it{n\/}})\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{ttl-bidirect\&} \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $<$ {\tt{8}} \\ 
{\bf then }{\rm{b-buf\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{ttl-bidirect-pads}}, {\it{n\/}})\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{b-buf\&} \\ 
{\bf else }{\rm{b-buf-pwr\&}}\,({\rm{delete-module}}\,(\=\+{\rm{index}}\,(\=\+{\tt{'}}{\tt{ttl-bidirect-pads}}, \\ 
{\it{n\/}})\-\index{index}, \\ 
{\it{netlist\/}})\-\index{delete-module})\index{b-buf-pwr\&}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-bidirect-pads\&; name this event `ttl-bidirect-pads\&-off'.\index{ttl-bidirect-pads\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ttl-bidirect-pads\$netlist} \\  
\=\+{\rm{ttl-bidirect-pads\$netlist}}\,({\it{n\/}})\index{ttl-bidirect-pads\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{ttl-bidirect-pads*}}\,({\it{n\/}})\index{ttl-bidirect-pads*}, \\ 
\=\+{\sc{ttl-bidirect\$netlist}}\index{ttl-bidirect\$netlist} \\ 
$\cup$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $<$ {\tt{8}}$\;\;${\bf then }{\sc{b-buf\$netlist}}\index{b-buf\$netlist} \\ 
{\bf else }{\sc{b-buf-pwr\$netlist}}\index{b-buf-pwr\$netlist}$\;${\bf  endif}\-\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-bidirect-pads-body\$unbound-in-body \\ \index{ttl-bidirect-pads-body\$unbound!-in-body}
\=\+({\it{l\/}} $<$ {\it{m\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{unbound-in-body}}\,({\rm{index}}\,({\tt{'}}{\tt{data}}, {\it{l\/}})\index{index}, {\rm{ttl-bidirect-pads-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{pi\/}})\index{ttl-bidirect-pads-body})\index{unbound-in-body} \\ 
$\wedge$$\;\;\;\;${\rm{unbound-in-body}}\,(\=\+{\rm{index}}\,({\tt{'}}{\tt{out}}, {\it{l\/}})\index{index}, \\ 
{\rm{ttl-bidirect-pads-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{pi\/}})\index{ttl-bidirect-pads-body})\-\index{unbound-in-body} \\ 
$\wedge$$\;\;\;\;${\rm{unbound-in-body}}\,({\rm{index}}\,({\tt{'}}{\tt{po}}, {\it{l\/}})\index{index}, {\rm{ttl-bidirect-pads-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{pi\/}})\index{ttl-bidirect-pads-body})\index{unbound-in-body} \\ 
$\wedge$$\;\;\;\;${\rm{unbound-in-body}}\,({\rm{index}}\,({\tt{'}}{\tt{in}}, {\it{l\/}})\index{index}, {\rm{ttl-bidirect-pads-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{pi\/}})\index{ttl-bidirect-pads-body})\index{unbound-in-body})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-bidirect-pads-body\$unbound-in-body; name this event `ttl-bidirect-pads-body\$unbound-in-body-off'.\index{ttl-bidirect-pads-body\$unbound!-in-body-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ttl-bidirect-pads-body\$value \\ \index{ttl-bidirect-pads-body\$value}
\=\+{\rm{ttl-bidirect\&}}\,({\it{netlist\/}})\index{ttl-bidirect\&} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{collect-value}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{data}}, {\it{m\/}}, {\it{n\/}})\index{indices}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{1}}, \\ 
{\rm{ttl-bidirect-pads-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{pi\/}})\index{ttl-bidirect-pads-body}, \\ 
{\it{bindings\/}}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-\index{collect-value} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{value}}\,({\tt{'}}{\tt{buf-enable}}, {\it{bindings\/}})\index{value} $=$ {\bf{f}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{collect-value}}\,({\rm{indices}}\,({\tt{'}}{\tt{in}}, {\it{m\/}}, {\it{n\/}})\index{indices}, {\it{bindings\/}})\index{collect-value})\index{v-threefix} \\ 
{\bf elseif }{\rm{value}}\,({\tt{'}}{\tt{buf-enable}}, {\it{bindings\/}})\index{value} $=$ {\bf{t}} \\ 
{\bf then }{\rm{make-list}}\,({\it{n\/}}, {\sc{z}}\index{z})\index{make-list} \\ 
{\bf else }{\rm{make-list}}\,({\it{n\/}}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{collect-value}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{out}}, {\it{m\/}}, {\it{n\/}})\index{indices}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{1}}, \\ 
{\rm{ttl-bidirect-pads-body}}\,({\it{m\/}}, {\it{n\/}}, {\it{pi\/}})\index{ttl-bidirect-pads-body}, \\ 
{\it{bindings\/}}, \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-\index{collect-value} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{value}}\,({\tt{'}}{\tt{buf-enable}}, {\it{bindings\/}})\index{value} $=$ {\bf{f}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{v-wire}}\,(\=\+{\rm{collect-value}}\,(\=\+{\rm{indices}}\,(\=\+{\tt{'}}{\tt{data}}, \\ 
{\it{m\/}}, \\ 
{\it{n\/}})\-\index{indices}, \\ 
{\it{bindings\/}})\-\index{collect-value}, \\ 
{\rm{v-threefix}}\,({\rm{collect-value}}\,(\=\+{\rm{indices}}\,(\=\+{\tt{'}}{\tt{in}}, \\ 
{\it{m\/}}, \\ 
{\it{n\/}})\-\index{indices}, \\ 
{\it{bindings\/}})\-\index{collect-value})\index{v-threefix})\-\index{v-wire})\index{v-threefix} \\ 
{\bf elseif }{\rm{value}}\,({\tt{'}}{\tt{buf-enable}}, {\it{bindings\/}})\index{value} $=$ {\bf{t}} \\ 
{\bf then }{\rm{v-threefix}}\,({\rm{collect-value}}\,(\=\+{\rm{indices}}\,({\tt{'}}{\tt{data}}, {\it{m\/}}, {\it{n\/}})\index{indices}, \\ 
{\it{bindings\/}})\-\index{collect-value})\index{v-threefix} \\ 
{\bf else }{\rm{make-list}}\,({\it{n\/}}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-bidirect-pads-body\$value; name this event `ttl-bidirect-pads-body\$value-off'.\index{ttl-bidirect-pads-body\$value-o!ff}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ttl-bidirect-pads\$value \\ \index{ttl-bidirect-pads\$value}
\=\+(\=\+{\rm{ttl-bidirect-pads\&}}\,({\it{netlist\/}}, {\it{n\/}})\index{ttl-bidirect-pads\&} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data\/}})\index{length} $=$ {\it{n\/}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{data\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{inputs\/}})\index{length} $=$ {\it{n\/}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{inputs\/}})\index{properp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{cdr}}\,({\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\rm{index}}\,({\tt{'}}{\tt{ttl-bidirect-pads}}, {\it{n\/}})\index{index}, \\ 
{\rm{cons}}\,({\it{enable\/}}, {\rm{cons}}\,({\it{pi\/}}, {\rm{append}}\,({\it{data\/}}, {\it{inputs\/}}))), \\ 
{\it{state-bindings\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval}) \\ 
$=$$\;\;\;\;${\rm{append}}\,(\=\+{\rm{vft-buf}}\,({\rm{f-not}}\,({\it{enable\/}})\index{f-not}, {\it{inputs\/}})\index{vft-buf}, \\ 
{\rm{v-threefix}}\,({\rm{v-wire}}\,({\it{data\/}}, {\rm{vft-buf}}\,({\rm{f-not}}\,({\it{enable\/}})\index{f-not}, {\it{inputs\/}})\index{vft-buf})\index{v-wire})\index{v-threefix})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable ttl-bidirect-pads\$value; name this event `ttl-bidirect-pads\$value-off'.\index{ttl-bidirect-pads\$value-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{a-reg}$\;\;$
{\rm{a-reg}}\,({\it{state\/}})\index{a-reg} $=$ {\rm{nth}}\,({\tt{2}}, {\it{state\/}})\index{nth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-reg}$\;\;$
{\rm{b-reg}}\,({\it{state\/}})\index{b-reg} $=$ {\rm{nth}}\,({\tt{3}}, {\it{state\/}})\index{nth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{i-reg}$\;\;$
{\rm{i-reg}}\,({\it{state\/}})\index{i-reg} $=$ {\rm{nth}}\,({\tt{4}}, {\it{state\/}})\index{nth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{data-out}$\;\;$
{\rm{data-out}}\,({\it{state\/}})\index{data-out} $=$ {\rm{nth}}\,({\tt{5}}, {\it{state\/}})\index{nth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{addr-out}$\;\;$
{\rm{addr-out}}\,({\it{state\/}})\index{addr-out} $=$ {\rm{nth}}\,({\tt{6}}, {\it{state\/}})\index{nth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{reset-}$\;\;$
{\rm{reset-}}\,({\it{state\/}})\index{reset-} $=$ {\rm{nth}}\,({\tt{7}}, {\it{state\/}})\index{nth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{dtack-}$\;\;$
{\rm{dtack-}}\,({\it{state\/}})\index{dtack-} $=$ {\rm{nth}}\,({\tt{8}}, {\it{state\/}})\index{nth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{hold-}$\;\;$
{\rm{hold-}}\,({\it{state\/}})\index{hold-} $=$ {\rm{nth}}\,({\tt{9}}, {\it{state\/}})\index{nth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{pc-reg}$\;\;$
{\rm{pc-reg}}\,({\it{state\/}})\index{pc-reg} $=$ {\rm{nth}}\,({\tt{10}}, {\it{state\/}})\index{nth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cntl-state}$\;\;$
{\rm{cntl-state}}\,({\it{state\/}})\index{cntl-state} $=$ {\rm{nth}}\,({\tt{11}}, {\it{state\/}})\index{nth}
\end{tabbing}


\noindent{\sc Event}:   Enable a-reg; name this event `a-reg-off'.\index{a-reg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-reg; name this event `b-reg-off'.\index{b-reg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable i-reg; name this event `i-reg-off'.\index{i-reg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable data-out; name this event `data-out-off'.\index{data-out-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable addr-out; name this event `addr-out-off'.\index{addr-out-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable reset-; name this event `reset--off'.\index{reset--off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dtack-; name this event `dtack--off'.\index{dtack--off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable hold-; name this event `hold--off'.\index{hold--off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable pc-reg; name this event `pc-reg-off'.\index{pc-reg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cntl-state; name this event `cntl-state-off'.\index{cntl-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{fm9001-hardware-state-accessors}} to consist of the following events: regs,
flags,
a-reg,
b-reg,
i-reg,
data-out,
addr-out,
reset-,
dtack-,
hold-,
pc-reg,
cntl-state.\index{fm9001-hardware-state-accessors}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{reset--input}$\;\;$
{\rm{reset--input}}\,({\it{ext-in\/}})\index{reset--input} $=$ {\rm{nth}}\,({\tt{0}}, {\it{ext-in\/}})\index{nth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{hold--input}$\;\;$
{\rm{hold--input}}\,({\it{ext-in\/}})\index{hold--input} $=$ {\rm{nth}}\,({\tt{1}}, {\it{ext-in\/}})\index{nth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{pc-reg-input}$\;\;$
{\rm{pc-reg-input}}\,({\it{ext-in\/}})\index{pc-reg-input} $=$ {\rm{subrange}}\,({\it{ext-in\/}}, {\tt{2}}, {\tt{5}})\index{subrange}
\end{tabbing}


\noindent{\sc Event}:   Enable reset--input; name this event `reset--input-off'.\index{reset--input-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable hold--input; name this event `hold--input-off'.\index{hold--input-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable pc-reg-input; name this event `pc-reg-input-off'.\index{pc-reg-input-off}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{fm9001-external-input-accessors}} to consist of the following events: reset--input,
hold--input,
pc-reg-input.\index{fm9001-external-input-accessors}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{fm9001-next-state} \\  
\=\+{\rm{fm9001-next-state}}\,({\it{total-state\/}}, {\it{external-inputs\/}})\index{fm9001-next-state} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{f\$write-regs}}\,(\=\+{\rm{we-regs}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{we-regs}, \\ 
{\rm{regs-address}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{regs-address}, \\ 
{\rm{regs}}\,({\rm{car}}\,({\it{total-state\/}}))\index{regs}, \\ 
{\rm{bv}}\,({\rm{f\$core-alu}}\,(\=\+{\rm{alu-c}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{alu-c}, \\ 
{\rm{v-threefix}}\,({\rm{a-reg}}\,({\rm{car}}\,({\it{total-state\/}}))\index{a-reg})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\rm{b-reg}}\,({\rm{car}}\,({\it{total-state\/}}))\index{b-reg})\index{v-threefix}, \\ 
{\rm{alu-zero}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{alu-zero}, \\ 
{\rm{alu-mpg}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{alu-mpg}, \\ 
{\rm{alu-op}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{alu-op}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{f\$core-alu})\index{bv})\-\index{f\$write-regs}, \\ 
{\rm{f\$update-flags}}\,(\=\+{\rm{flags}}\,({\rm{car}}\,({\it{total-state\/}}))\index{flags}, \\ 
{\rm{we-flags}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{we-flags}, \\ 
{\rm{f\$core-alu}}\,(\=\+{\rm{alu-c}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{alu-c}, \\ 
{\rm{v-threefix}}\,({\rm{a-reg}}\,({\rm{car}}\,({\it{total-state\/}}))\index{a-reg})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\rm{b-reg}}\,({\rm{car}}\,({\it{total-state\/}}))\index{b-reg})\index{v-threefix}, \\ 
{\rm{alu-zero}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{alu-zero}, \\ 
{\rm{alu-mpg}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{alu-mpg}, \\ 
{\rm{alu-op}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{alu-op}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{f\$core-alu})\-\index{f\$update-flags}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-a-reg}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{we-a-reg}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{f-nand}}\,(\=\+{\rm{data-in-select}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{data-in-select}, \\ 
{\rm{f-not}}\,({\rm{dtack-}}\,({\rm{car}}\,({\it{total-state\/}}))\index{dtack-})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f\$extend-immediate}}\,(\=\+{\rm{select-immediate}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{select-immediate}, \\ 
{\rm{a-immediate}}\,({\rm{v-threefix}}\,({\rm{i-reg}}\,({\rm{car}}\,({\it{total-state\/}}))\index{i-reg})\index{v-threefix})\index{a-immediate}, \\ 
{\rm{f\$read-regs}}\,(\=\+{\rm{regs-address}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{regs-address}, \\ 
{\rm{regs}}\,({\rm{car}}\,({\it{total-state\/}}))\index{regs})\-\index{f\$read-regs})\-\index{f\$extend-immediate}, \\ 
{\rm{v-threefix}}\,({\rm{v-wire}}\,(\=\+{\rm{v-pullup}}\,({\rm{v-wire}}\,(\=\+{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\rm{v-threefix}}\,({\rm{data-out}}\,({\rm{car}}\,({\it{total-state\/}}))\index{data-out})\index{v-threefix})\-\index{vft-buf}, \\ 
{\rm{cdr}}\,({\rm{memory-value}}\,(\=\+{\rm{cadr}}\,({\it{total-state\/}}), \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{strobe-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{strobe-})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{rw-})\index{f-buf})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{v-pullup}}\,({\rm{vft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{v-threefix}}\,({\rm{addr-out}}\,({\rm{car}}\,({\it{total-state\/}}))\index{addr-out})\index{v-threefix})\-\index{vft-buf})\index{v-pullup}, \\ 
{\rm{make-list}}\,(\=\+{\tt{32}}, \\ 
{\sc{x}}\index{x})\-\index{make-list})\-\index{memory-value}))\-\index{v-wire})\index{v-pullup}, \\ 
{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\rm{v-threefix}}\,({\rm{data-out}}\,({\rm{car}}\,({\it{total-state\/}}))\index{data-out})\index{v-threefix})\-\index{vft-buf})\-\index{v-wire})\index{v-threefix})\-\index{fv-if}, \\ 
{\rm{a-reg}}\,({\rm{car}}\,({\it{total-state\/}}))\index{a-reg})\-\index{fv-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-b-reg}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{we-b-reg}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{f-nand}}\,(\=\+{\rm{data-in-select}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{data-in-select}, \\ 
{\rm{f-not}}\,({\rm{dtack-}}\,({\rm{car}}\,({\it{total-state\/}}))\index{dtack-})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f\$extend-immediate}}\,(\=\+{\rm{select-immediate}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{select-immediate}, \\ 
{\rm{a-immediate}}\,({\rm{v-threefix}}\,({\rm{i-reg}}\,({\rm{car}}\,({\it{total-state\/}}))\index{i-reg})\index{v-threefix})\index{a-immediate}, \\ 
{\rm{f\$read-regs}}\,(\=\+{\rm{regs-address}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{regs-address}, \\ 
{\rm{regs}}\,({\rm{car}}\,({\it{total-state\/}}))\index{regs})\-\index{f\$read-regs})\-\index{f\$extend-immediate}, \\ 
{\rm{v-threefix}}\,({\rm{v-wire}}\,(\=\+{\rm{v-pullup}}\,({\rm{v-wire}}\,(\=\+{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\rm{v-threefix}}\,({\rm{data-out}}\,({\rm{car}}\,({\it{total-state\/}}))\index{data-out})\index{v-threefix})\-\index{vft-buf}, \\ 
{\rm{cdr}}\,({\rm{memory-value}}\,(\=\+{\rm{cadr}}\,({\it{total-state\/}}), \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{strobe-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{strobe-})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{rw-})\index{f-buf})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{v-pullup}}\,({\rm{vft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{v-threefix}}\,({\rm{addr-out}}\,({\rm{car}}\,({\it{total-state\/}}))\index{addr-out})\index{v-threefix})\-\index{vft-buf})\index{v-pullup}, \\ 
{\rm{make-list}}\,(\=\+{\tt{32}}, \\ 
{\sc{x}}\index{x})\-\index{make-list})\-\index{memory-value}))\-\index{v-wire})\index{v-pullup}, \\ 
{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\rm{v-threefix}}\,({\rm{data-out}}\,({\rm{car}}\,({\it{total-state\/}}))\index{data-out})\index{v-threefix})\-\index{vft-buf})\-\index{v-wire})\index{v-threefix})\-\index{fv-if}, \\ 
{\rm{b-reg}}\,({\rm{car}}\,({\it{total-state\/}}))\index{b-reg})\-\index{fv-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-i-reg}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{we-i-reg}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{f-nand}}\,(\=\+{\rm{data-in-select}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{data-in-select}, \\ 
{\rm{f-not}}\,({\rm{dtack-}}\,({\rm{car}}\,({\it{total-state\/}}))\index{dtack-})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f\$extend-immediate}}\,(\=\+{\rm{select-immediate}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{select-immediate}, \\ 
{\rm{a-immediate}}\,({\rm{v-threefix}}\,({\rm{i-reg}}\,({\rm{car}}\,({\it{total-state\/}}))\index{i-reg})\index{v-threefix})\index{a-immediate}, \\ 
{\rm{f\$read-regs}}\,(\=\+{\rm{regs-address}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{regs-address}, \\ 
{\rm{regs}}\,({\rm{car}}\,({\it{total-state\/}}))\index{regs})\-\index{f\$read-regs})\-\index{f\$extend-immediate}, \\ 
{\rm{v-threefix}}\,({\rm{v-wire}}\,(\=\+{\rm{v-pullup}}\,({\rm{v-wire}}\,(\=\+{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\rm{v-threefix}}\,({\rm{data-out}}\,({\rm{car}}\,({\it{total-state\/}}))\index{data-out})\index{v-threefix})\-\index{vft-buf}, \\ 
{\rm{cdr}}\,({\rm{memory-value}}\,(\=\+{\rm{cadr}}\,({\it{total-state\/}}), \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{strobe-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{strobe-})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{rw-})\index{f-buf})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{v-pullup}}\,({\rm{vft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{v-threefix}}\,({\rm{addr-out}}\,({\rm{car}}\,({\it{total-state\/}}))\index{addr-out})\index{v-threefix})\-\index{vft-buf})\index{v-pullup}, \\ 
{\rm{make-list}}\,(\=\+{\tt{32}}, \\ 
{\sc{x}}\index{x})\-\index{make-list})\-\index{memory-value}))\-\index{v-wire})\index{v-pullup}, \\ 
{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\rm{v-threefix}}\,({\rm{data-out}}\,({\rm{car}}\,({\it{total-state\/}}))\index{data-out})\index{v-threefix})\-\index{vft-buf})\-\index{v-wire})\index{v-threefix})\-\index{fv-if}, \\ 
{\rm{i-reg}}\,({\rm{car}}\,({\it{total-state\/}}))\index{i-reg})\-\index{fv-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-data-out}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{we-data-out}, \\ 
{\rm{bv}}\,({\rm{f\$core-alu}}\,(\=\+{\rm{alu-c}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{alu-c}, \\ 
{\rm{v-threefix}}\,({\rm{a-reg}}\,({\rm{car}}\,({\it{total-state\/}}))\index{a-reg})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\rm{b-reg}}\,({\rm{car}}\,({\it{total-state\/}}))\index{b-reg})\index{v-threefix}, \\ 
{\rm{alu-zero}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{alu-zero}, \\ 
{\rm{alu-mpg}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{alu-mpg}, \\ 
{\rm{alu-op}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{alu-op}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{f\$core-alu})\index{bv}, \\ 
{\rm{data-out}}\,({\rm{car}}\,({\it{total-state\/}}))\index{data-out})\-\index{fv-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-addr-out}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{we-addr-out}, \\ 
{\rm{f\$dec-pass}}\,(\=\+{\rm{dec-addr-out}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{dec-addr-out}, \\ 
{\rm{f\$extend-immediate}}\,(\=\+{\rm{select-immediate}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{select-immediate}, \\ 
{\rm{a-immediate}}\,({\rm{v-threefix}}\,({\rm{i-reg}}\,({\rm{car}}\,({\it{total-state\/}}))\index{i-reg})\index{v-threefix})\index{a-immediate}, \\ 
{\rm{f\$read-regs}}\,(\=\+{\rm{regs-address}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{regs-address}, \\ 
{\rm{regs}}\,({\rm{car}}\,({\it{total-state\/}}))\index{regs})\-\index{f\$read-regs})\-\index{f\$extend-immediate})\-\index{f\$dec-pass}, \\ 
{\rm{addr-out}}\,({\rm{car}}\,({\it{total-state\/}}))\index{addr-out})\-\index{fv-if}, \\ 
{\rm{f-buf}}\,({\rm{reset--input}}\,({\it{external-inputs\/}})\index{reset--input})\index{f-buf}, \\ 
{\rm{f-or}}\,(\=\+{\rm{strobe-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{strobe-}, \\ 
{\rm{f-buf}}\,({\rm{car}}\,({\rm{memory-value}}\,(\=\+{\rm{cadr}}\,({\it{total-state\/}}), \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{strobe-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{strobe-})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{rw-})\index{f-buf})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{v-pullup}}\,({\rm{vft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{v-threefix}}\,({\rm{addr-out}}\,({\rm{car}}\,({\it{total-state\/}}))\index{addr-out})\index{v-threefix})\-\index{vft-buf})\index{v-pullup}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-\index{memory-value}))\index{f-buf})\-\index{f-or}, \\ 
{\rm{f-if}}\,(\=\+{\rm{we-hold-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{we-hold-}, \\ 
{\rm{f-buf}}\,({\rm{hold--input}}\,({\it{external-inputs\/}})\index{hold--input})\index{f-buf}, \\ 
{\rm{hold-}}\,({\rm{car}}\,({\it{total-state\/}}))\index{hold-})\-\index{f-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-pc-reg}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{we-pc-reg}, \\ 
{\rm{pc-reg-input}}\,({\it{external-inputs\/}})\index{pc-reg-input}, \\ 
{\rm{pc-reg}}\,({\rm{car}}\,({\it{total-state\/}}))\index{pc-reg})\-\index{fv-if}, \\ 
{\rm{v-threefix}}\,({\rm{f\$next-cntl-state}}\,(\=\+{\rm{f-buf}}\,({\rm{reset-}}\,({\rm{car}}\,({\it{total-state\/}}))\index{reset-})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\rm{dtack-}}\,({\rm{car}}\,({\it{total-state\/}}))\index{dtack-})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\rm{hold-}}\,({\rm{car}}\,({\it{total-state\/}}))\index{hold-})\index{f-buf}, \\ 
{\rm{rw-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{rw-}, \\ 
{\rm{state}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{state}, \\ 
{\rm{v-threefix}}\,({\rm{i-reg}}\,({\rm{car}}\,({\it{total-state\/}}))\index{i-reg})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\rm{flags}}\,({\rm{car}}\,({\it{total-state\/}}))\index{flags})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\rm{pc-reg}}\,({\rm{car}}\,({\it{total-state\/}}))\index{pc-reg})\index{v-threefix}, \\ 
{\rm{regs-address}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{regs-address})\-\index{f\$next-cntl-state})\index{v-threefix})\-, \\ 
{\rm{next-memory-state}}\,(\=\+{\rm{cadr}}\,({\it{total-state\/}}), \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{strobe-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{strobe-})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{rw-})\index{f-buf})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{v-pullup}}\,({\rm{vft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{v-threefix}}\,({\rm{addr-out}}\,({\rm{car}}\,({\it{total-state\/}}))\index{addr-out})\index{v-threefix})\-\index{vft-buf})\index{v-pullup}, \\ 
{\rm{v-pullup}}\,({\rm{v-wire}}\,(\=\+{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\rm{v-threefix}}\,({\rm{data-out}}\,({\rm{car}}\,({\it{total-state\/}}))\index{data-out})\index{v-threefix})\-\index{vft-buf}, \\ 
{\rm{cdr}}\,({\rm{memory-value}}\,(\=\+{\rm{cadr}}\,({\it{total-state\/}}), \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{strobe-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{strobe-})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{rw-})\index{f-buf})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{v-pullup}}\,({\rm{vft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\rm{cntl-state}}\,({\rm{car}}\,({\it{total-state\/}}))\index{cntl-state})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{v-threefix}}\,({\rm{addr-out}}\,({\rm{car}}\,({\it{total-state\/}}))\index{addr-out})\index{v-threefix})\-\index{vft-buf})\index{v-pullup}, \\ 
{\rm{make-list}}\,(\=\+{\tt{32}}, \\ 
{\sc{x}}\index{x})\-\index{make-list})\-\index{memory-value}))\-\index{v-wire})\index{v-pullup})\-\index{next-memory-state})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable fm9001-next-state; name this event `fm9001-next-state-off'.\index{fm9001-next-state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{run-fm9001} \\  
\=\+{\rm{run-fm9001}}\,({\it{state\/}}, {\it{inputs\/}}, {\it{n\/}})\index{run-fm9001} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\it{state\/}} \\ 
{\bf else }{\rm{run-fm9001}}\,(\=\+{\rm{fm9001-next-state}}\,({\it{state\/}}, {\rm{car}}\,({\it{inputs\/}}))\index{fm9001-next-state}, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable run-fm9001; name this event `run-fm9001-off'.\index{run-fm9001-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  run-fm9001-base-case \\ \index{run-fm9001-base-case}
({\it{n\/}} $\simeq {\tt{0}}$) $\rightarrow$ ({\rm{run-fm9001}}\,({\it{state\/}}, {\it{inputs\/}}, {\it{n\/}})\index{run-fm9001} $=$ {\it{state\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  run-fm9001-step-case \\ \index{run-fm9001-step-case}
\=\+({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,({\it{state\/}}, {\it{inputs\/}}, {\it{n\/}})\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{fm9001-next-state}}\,({\it{state\/}}, {\rm{car}}\,({\it{inputs\/}}))\index{fm9001-next-state}, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable run-fm9001-step-case; name this event `run-fm9001-step-case-off'.\index{run-fm9001-step-case-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  run-fm9001-plus \\ \index{run-fm9001-plus}
\=\+{\rm{run-fm9001}}\,({\it{state\/}}, {\it{inputs\/}}, {\it{n\/}} $+$ {\it{m\/}})\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,({\rm{run-fm9001}}\,({\it{state\/}}, {\it{inputs\/}}, {\it{n\/}})\index{run-fm9001}, {\rm{nthcdr}}\,({\it{n\/}}, {\it{inputs\/}})\index{nthcdr}, {\it{m\/}})\index{run-fm9001}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fm9001-state-structure} \\  
\=\+{\rm{fm9001-state-structure}}\,({\it{state\/}})\index{fm9001-state-structure} \\ 
$=$$\;\;\;\;$(\=\+({\rm{length}}\,({\it{state\/}})\index{length} $=$ {\tt{2}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{state\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{car}}\,({\it{state\/}}))\index{length} $=$ {\tt{12}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{car}}\,({\it{state\/}}))\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cadr}}\,({\it{state\/}}))\index{length} $=$ {\tt{8}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{cadr}}\,({\it{state\/}}))\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{caar}}\,({\it{state\/}}))\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{caar}}\,({\it{state\/}}))\index{properp})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fm9001-state-structure\$step \\ \index{fm9001-state-structure\$step}
\=\+{\rm{fm9001-state-structure}}\,({\it{state\/}})\index{fm9001-state-structure} \\ 
$\rightarrow$$\;\;\;\;${\rm{fm9001-state-structure}}\,({\rm{fm9001-next-state}}\,({\it{state\/}}, {\it{external-inputs\/}})\index{fm9001-next-state})\index{fm9001-state-structure}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fm9001-state-structure\$induction \\ \index{fm9001-state-structure\$inducti!on}
\=\+{\rm{fm9001-state-structure}}\,({\it{state\/}})\index{fm9001-state-structure} \\ 
$\rightarrow$$\;\;\;\;${\rm{fm9001-state-structure}}\,({\rm{run-fm9001}}\,({\it{state\/}}, {\it{inputs\/}}, {\it{steps\/}})\index{run-fm9001})\index{fm9001-state-structure}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fm9001-state-as-a-list \\ \index{fm9001-state-as-a-list}
\=\+{\rm{fm9001-state-structure}}\,({\it{state\/}})\index{fm9001-state-structure} \\ 
$\rightarrow$$\;\;\;\;$({\it{state\/}} $=$ {\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{caaar}}\,({\it{state\/}}), \\ 
{\rm{cadaar}}\,({\it{state\/}}), \\ 
{\rm{caddaar}}\,({\it{state\/}}), \\ 
{\rm{cadddaar}}\,({\it{state\/}}))\-, \\ 
{\rm{cadar}}\,({\it{state\/}}), \\ 
{\rm{caddar}}\,({\it{state\/}}), \\ 
{\rm{cadddar}}\,({\it{state\/}}), \\ 
{\rm{caddddar}}\,({\it{state\/}}), \\ 
{\rm{cadddddar}}\,({\it{state\/}}), \\ 
{\rm{caddddddar}}\,({\it{state\/}}), \\ 
{\rm{cadddddddar}}\,({\it{state\/}}), \\ 
{\rm{caddddddddar}}\,({\it{state\/}}), \\ 
{\rm{cadddddddddar}}\,({\it{state\/}}), \\ 
{\rm{caddddddddddar}}\,({\it{state\/}}), \\ 
{\rm{cadddddddddddar}}\,({\it{state\/}}))\-, \\ 
{\rm{list}}\,(\=\+{\rm{caadr}}\,({\it{state\/}}), \\ 
{\rm{cadadr}}\,({\it{state\/}}), \\ 
{\rm{caddadr}}\,({\it{state\/}}), \\ 
{\rm{cadddadr}}\,({\it{state\/}}), \\ 
{\rm{caddddadr}}\,({\it{state\/}}), \\ 
{\rm{cadddddadr}}\,({\it{state\/}}), \\ 
{\rm{caddddddadr}}\,({\it{state\/}}), \\ 
{\rm{cadddddddadr}}\,({\it{state\/}}))\-)\-)\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN CHIP-MODULE* NIL
 (CONS 'CHIP-MODULE
  (CONS
   (CONS 'CLK
    (CONS 'TI
     (CONS 'TE
        (CONS 'DTACK-
              (CONS 'RESET-
                    (CONS 'HOLD-
                          (CONS 'DISABLE-REGFILE-
                                (CONS 'TEST-REGFILE-
                                      (APPEND (INDICES 'PC-REG-IN 0 4)
                                              (INDICES 'DATA-IN 0 32))))))))))
   (CONS
    (CONS 'TO
     (CONS 'TIMING
      (CONS 'HDACK-
       (CONS 'EN-ADDR-OUT-
        (CONS 'RW-
         (CONS 'STROBE-
               (APPEND (INDICES 'ADDR-OUT 0 32)
                       (APPEND (INDICES 'DATA-OUT 0 32)
                               (APPEND (INDICES 'FLAGS 0 4)
                                       (APPEND (INDICES 'CNTL-STATE 0 5)
                                               (SUBRANGE (INDICES 'I-REG 0 32)
                                                         28 31)))))))))))
    (CONS
     (LIST
      (LIST 'CNTL-STATE
       (CONS 'RW-SIG-
        (CONS 'STROBE-
         (CONS 'HDACK-
          (CONS 'WE-REGS
           (CONS 'WE-A-REG
            (CONS 'WE-B-REG
             (CONS 'WE-I-REG
              (CONS 'WE-DATA-OUT
               (CONS 'WE-ADDR-OUT
                (CONS 'WE-HOLD-
                 (CONS 'WE-PC-REG
                  (CONS 'DATA-IN-SELECT
                   (CONS 'DEC-ADDR-OUT
                    (CONS 'SELECT-IMMEDIATE
                     (CONS 'ALU-C
                      (CONS 'ALU-ZERO
                       (APPEND
                        (INDICES 'CNTL-STATE 0 5)
                        (APPEND (INDICES 'WE-FLAGS 0 4)
                                (APPEND (INDICES 'REGS-ADDRESS 0 4)
                                        (APPEND (INDICES 'ALU-OP 0 4)
                                                (INDICES 'ALU-MPG
                                                         0
                                                         7)))))))))))))))))))))
       (INDEX 'REG 40)
       (CONS 'CLK
             (CONS 'TE-SIG
                   (CONS 'TI
                         (INDICES 'NEXT-STATE 0 40)))))
      (LIST 'REGS
       (CONS 'REGFILE-TO
             (INDICES 'REGFILE-OUT 0 32))
       'REGFILE
       (CONS 'CLK
        (CONS 'TE-SIG
          (CONS (INDEX 'ALU-MPG 6)
                (CONS 'WE-REGS
                      (CONS 'DISABLE-REGFILE-
                            (CONS 'TEST-REGFILE-
                                  (APPEND (INDICES 'REGS-ADDRESS 0 4)
                                          (BV (INDICES 'ALU-BUS 0 35))))))))))
      (LIST 'CVNZ-FLAGS
            (INDICES 'FLAGS 0 4)
            'FLAGS
            (CONS 'CLK
                  (CONS 'TE-SIG
                        (CONS 'REGFILE-TO
                              (APPEND (INDICES 'WE-FLAGS 0 4)
                                      (INDICES 'ALU-BUS 0 35))))))
      (LIST 'A-REG
            (INDICES 'A-REG 0 32)
            (INDEX 'WE-REG 32)
            (CONS 'CLK
                  (CONS 'WE-A-REG
                        (CONS 'TE-SIG
                              (CONS (INDEX 'FLAGS 3)
                                    (INDICES 'ABI-BUS 0 32))))))
      (LIST 'B-REG
            (INDICES 'B-REG 0 32)
            (INDEX 'WE-REG 32)
            (CONS 'CLK
                  (CONS 'WE-B-REG
                        (CONS 'TE-SIG
                              (CONS (INDEX 'A-REG 31)
                                    (INDICES 'ABI-BUS 0 32))))))
      (LIST 'I-REG
            (INDICES 'I-REG 0 32)
            (INDEX 'WE-REG 32)
            (CONS 'CLK
                  (CONS 'WE-I-REG
                        (CONS 'TE-SIG
                              (CONS (INDEX 'B-REG 31)
                                    (INDICES 'ABI-BUS 0 32))))))
      (LIST 'DATA-OUT
            (INDICES 'DATA-OUT 0 32)
            (INDEX 'WE-REG 32)
            (CONS 'CLK
                  (CONS 'WE-DATA-OUT
                        (CONS 'TE-SIG
                              (CONS (INDEX 'I-REG 31)
                                    (BV (INDICES 'ALU-BUS 0 35)))))))
      (LIST 'ADDR-OUT
            (INDICES 'ADDR-OUT 0 32)
            (INDEX 'WE-REG 32)
            (CONS 'CLK
                  (CONS 'WE-ADDR-OUT
                        (CONS 'TE-SIG
                              (CONS (INDEX 'DATA-OUT 31)
                                    (INDICES 'ADDR-OUT-BUS 0 32))))))
      (LIST 'RESET-LATCH
            '(LAST-RESET- LAST-RESET-INV)
            'FD1S
            (LIST 'RESET-
                  'CLK
                  (INDEX 'ADDR-OUT 31)
                  'TE-SIG))
      '(DTACK--OR (DTACK--OR-STROBE-)
                  B-OR
                  (STROBE- DTACK-))
      '(DTACK-LATCH (LAST-DTACK- LAST-DTACK-INV)
                    FD1S
                    (DTACK--OR-STROBE- CLK LAST-RESET- TE-SIG))
      '(HOLD-LATCH (LAST-HOLD- LAST-HOLD-INV)
                   FD1SLP
                   (HOLD- CLK WE-HOLD- LAST-DTACK- TE-SIG))
      (LIST 'PC-REG
            (INDICES 'PC-REG 0 4)
            (INDEX 'WE-REG 4)
            (CONS 'CLK
                  (CONS 'WE-PC-REG
                        (CONS 'TE-SIG
                              (CONS 'LAST-HOLD-
                                    (INDICES 'PC-REG-IN 0 4))))))
      (LIST 'IMMEDIATE-PASS
            (INDICES 'REG-BUS 0 32)
            'EXTEND-IMMEDIATE
            (CONS 'SELECT-IMMEDIATE
                  (APPEND (A-IMMEDIATE (INDICES 'I-REG 0 32))
                          (INDICES 'REGFILE-OUT 0 32))))
      (LIST 'DEC-PASS
            (INDICES 'ADDR-OUT-BUS 0 32)
            (INDEX 'DEC-PASS 32)
            (CONS 'DEC-ADDR-OUT
                  (INDICES 'REG-BUS 0 32)))
      '(MUX-CNTL (ABI-CNTL)
                 B-NAND
                 (DATA-IN-SELECT LAST-DTACK-INV))
      (LIST 'DATA-IN-MUX
            (INDICES 'ABI-BUS 0 32)
            (INDEX 'TV-IF
                   (TREE-NUMBER (MAKE-TREE 32)))
            (CONS 'ABI-CNTL
                  (APPEND (INDICES 'REG-BUS 0 32)
                          (INDICES 'DATA-IN 0 32))))
      (LIST 'ALU
            (INDICES 'ALU-BUS 0 35)
            (INDEX 'CORE-ALU
                   (TREE-NUMBER (MAKE-TREE 32)))
            (CONS 'ALU-C
                  (APPEND (INDICES 'A-REG 0 32)
                          (APPEND (INDICES 'B-REG 0 32)
                                  (CONS 'ALU-ZERO
                                        (APPEND (INDICES 'ALU-MPG 0 7)
                                                (INDICES 'ALU-OP 0 4)))))))
      (LIST 'NEXT-STATE
       (INDICES 'NEXT-STATE 0 40)
       'NEXT-CNTL-STATE
       (CONS 'LAST-RESET-
        (CONS 'LAST-DTACK-
         (CONS 'LAST-HOLD-
          (CONS 'RW-SIG-
           (APPEND
                  (INDICES 'CNTL-STATE 0 5)
                  (APPEND (INDICES 'I-REG 0 32)
                          (APPEND (INDICES 'FLAGS 0 4)
                                  (APPEND (INDICES 'PC-REG 0 4)
                                          (INDICES 'REGS-ADDRESS 0 4))))))))))
      '(TE-BUFFER (TE-SIG) B-BUF-PWR (TE))
      '(RW-BUFFER (RW-) B-BUF (RW-SIG-))
      '(EN-ADDR-OUT-GATE (EN-ADDR-OUT-)
                         B-NOT
                         (HDACK-))
      (LIST 'TIMING-GATE
            '(TIMING)
            'ID
            (LIST (INDEX 'ALU-BUS 2)))
      (LIST 'SCANOUT
            '(TO)
            'ID
            (LIST (INDEX 'PC-REG 3))))
     '((REGS CVNZ-FLAGS A-REG B-REG I-REG DATA-OUT ADDR-OUT RESET-LATCH
             DTACK-LATCH HOLD-LATCH PC-REG CNTL-STATE)))))))
\end{verbatim}


%\item 
\begin{verbatim}


(PROVE-LEMMA CHIP-MODULE*$DESTRUCTURE
 (REWRITE)
 (AND
  (EQUAL (CAR (CHIP-MODULE*))
         'CHIP-MODULE)
  (EQUAL
   (CADR (CHIP-MODULE*))
   (CONS 'CLK
    (CONS 'TI
     (CONS 'TE
       (CONS 'DTACK-
             (CONS 'RESET-
                   (CONS 'HOLD-
                         (CONS 'DISABLE-REGFILE-
                               (CONS 'TEST-REGFILE-
                                     (APPEND (INDICES 'PC-REG-IN 0 4)
                                             (INDICES 'DATA-IN 0 32)))))))))))
  (EQUAL
   (CADDR (CHIP-MODULE*))
   (CONS 'TO
    (CONS 'TIMING
     (CONS 'HDACK-
      (CONS 'EN-ADDR-OUT-
       (CONS 'RW-
         (CONS 'STROBE-
               (APPEND (INDICES 'ADDR-OUT 0 32)
                       (APPEND (INDICES 'DATA-OUT 0 32)
                               (APPEND (INDICES 'FLAGS 0 4)
                                       (APPEND (INDICES 'CNTL-STATE 0 5)
                                               (SUBRANGE (INDICES 'I-REG 0 32)
                                                         28 31))))))))))))
  (EQUAL
   (CADDDR (CHIP-MODULE*))
   (LIST
    (LIST 'CNTL-STATE
     (CONS 'RW-SIG-
      (CONS 'STROBE-
       (CONS 'HDACK-
        (CONS 'WE-REGS
         (CONS 'WE-A-REG
          (CONS 'WE-B-REG
           (CONS 'WE-I-REG
            (CONS 'WE-DATA-OUT
             (CONS 'WE-ADDR-OUT
              (CONS 'WE-HOLD-
               (CONS 'WE-PC-REG
                (CONS 'DATA-IN-SELECT
                 (CONS 'DEC-ADDR-OUT
                  (CONS 'SELECT-IMMEDIATE
                   (CONS 'ALU-C
                    (CONS 'ALU-ZERO
                     (APPEND
                        (INDICES 'CNTL-STATE 0 5)
                        (APPEND (INDICES 'WE-FLAGS 0 4)
                                (APPEND (INDICES 'REGS-ADDRESS 0 4)
                                        (APPEND (INDICES 'ALU-OP 0 4)
                                                (INDICES 'ALU-MPG
                                                         0
                                                         7)))))))))))))))))))))
     (INDEX 'REG 40)
     (CONS 'CLK
           (CONS 'TE-SIG
                 (CONS 'TI
                       (INDICES 'NEXT-STATE 0 40)))))
    (LIST 'REGS
     (CONS 'REGFILE-TO
           (INDICES 'REGFILE-OUT 0 32))
     'REGFILE
     (CONS 'CLK
      (CONS 'TE-SIG
          (CONS (INDEX 'ALU-MPG 6)
                (CONS 'WE-REGS
                      (CONS 'DISABLE-REGFILE-
                            (CONS 'TEST-REGFILE-
                                  (APPEND (INDICES 'REGS-ADDRESS 0 4)
                                          (BV (INDICES 'ALU-BUS 0 35))))))))))
    (LIST 'CVNZ-FLAGS
          (INDICES 'FLAGS 0 4)
          'FLAGS
          (CONS 'CLK
                (CONS 'TE-SIG
                      (CONS 'REGFILE-TO
                            (APPEND (INDICES 'WE-FLAGS 0 4)
                                    (INDICES 'ALU-BUS 0 35))))))
    (LIST 'A-REG
          (INDICES 'A-REG 0 32)
          (INDEX 'WE-REG 32)
          (CONS 'CLK
                (CONS 'WE-A-REG
                      (CONS 'TE-SIG
                            (CONS (INDEX 'FLAGS 3)
                                  (INDICES 'ABI-BUS 0 32))))))
    (LIST 'B-REG
          (INDICES 'B-REG 0 32)
          (INDEX 'WE-REG 32)
          (CONS 'CLK
                (CONS 'WE-B-REG
                      (CONS 'TE-SIG
                            (CONS (INDEX 'A-REG 31)
                                  (INDICES 'ABI-BUS 0 32))))))
    (LIST 'I-REG
          (INDICES 'I-REG 0 32)
          (INDEX 'WE-REG 32)
          (CONS 'CLK
                (CONS 'WE-I-REG
                      (CONS 'TE-SIG
                            (CONS (INDEX 'B-REG 31)
                                  (INDICES 'ABI-BUS 0 32))))))
    (LIST 'DATA-OUT
          (INDICES 'DATA-OUT 0 32)
          (INDEX 'WE-REG 32)
          (CONS 'CLK
                (CONS 'WE-DATA-OUT
                      (CONS 'TE-SIG
                            (CONS (INDEX 'I-REG 31)
                                  (BV (INDICES 'ALU-BUS 0 35)))))))
    (LIST 'ADDR-OUT
          (INDICES 'ADDR-OUT 0 32)
          (INDEX 'WE-REG 32)
          (CONS 'CLK
                (CONS 'WE-ADDR-OUT
                      (CONS 'TE-SIG
                            (CONS (INDEX 'DATA-OUT 31)
                                  (INDICES 'ADDR-OUT-BUS 0 32))))))
    (LIST 'RESET-LATCH
          '(LAST-RESET- LAST-RESET-INV)
          'FD1S
          (LIST 'RESET-
                'CLK
                (INDEX 'ADDR-OUT 31)
                'TE-SIG))
    '(DTACK--OR (DTACK--OR-STROBE-)
                B-OR
                (STROBE- DTACK-))
    '(DTACK-LATCH (LAST-DTACK- LAST-DTACK-INV)
                  FD1S
                  (DTACK--OR-STROBE- CLK LAST-RESET- TE-SIG))
    '(HOLD-LATCH (LAST-HOLD- LAST-HOLD-INV)
                 FD1SLP
                 (HOLD- CLK WE-HOLD- LAST-DTACK- TE-SIG))
    (LIST 'PC-REG
          (INDICES 'PC-REG 0 4)
          (INDEX 'WE-REG 4)
          (CONS 'CLK
                (CONS 'WE-PC-REG
                      (CONS 'TE-SIG
                            (CONS 'LAST-HOLD-
                                  (INDICES 'PC-REG-IN 0 4))))))
    (LIST 'IMMEDIATE-PASS
          (INDICES 'REG-BUS 0 32)
          'EXTEND-IMMEDIATE
          (CONS 'SELECT-IMMEDIATE
                (APPEND (A-IMMEDIATE (INDICES 'I-REG 0 32))
                        (INDICES 'REGFILE-OUT 0 32))))
    (LIST 'DEC-PASS
          (INDICES 'ADDR-OUT-BUS 0 32)
          (INDEX 'DEC-PASS 32)
          (CONS 'DEC-ADDR-OUT
                (INDICES 'REG-BUS 0 32)))
    '(MUX-CNTL (ABI-CNTL)
               B-NAND
               (DATA-IN-SELECT LAST-DTACK-INV))
    (LIST 'DATA-IN-MUX
          (INDICES 'ABI-BUS 0 32)
          (INDEX 'TV-IF
                 (TREE-NUMBER (MAKE-TREE 32)))
          (CONS 'ABI-CNTL
                (APPEND (INDICES 'REG-BUS 0 32)
                        (INDICES 'DATA-IN 0 32))))
    (LIST 'ALU
          (INDICES 'ALU-BUS 0 35)
          (INDEX 'CORE-ALU
                 (TREE-NUMBER (MAKE-TREE 32)))
          (CONS 'ALU-C
                (APPEND (INDICES 'A-REG 0 32)
                        (APPEND (INDICES 'B-REG 0 32)
                                (CONS 'ALU-ZERO
                                      (APPEND (INDICES 'ALU-MPG 0 7)
                                              (INDICES 'ALU-OP 0 4)))))))
    (LIST 'NEXT-STATE
     (INDICES 'NEXT-STATE 0 40)
     'NEXT-CNTL-STATE
     (CONS 'LAST-RESET-
      (CONS 'LAST-DTACK-
       (CONS 'LAST-HOLD-
        (CONS 'RW-SIG-
          (APPEND (INDICES 'CNTL-STATE 0 5)
                  (APPEND (INDICES 'I-REG 0 32)
                          (APPEND (INDICES 'FLAGS 0 4)
                                  (APPEND (INDICES 'PC-REG 0 4)
                                          (INDICES 'REGS-ADDRESS 0 4))))))))))
    '(TE-BUFFER (TE-SIG) B-BUF-PWR (TE))
    '(RW-BUFFER (RW-) B-BUF (RW-SIG-))
    '(EN-ADDR-OUT-GATE (EN-ADDR-OUT-)
                       B-NOT
                       (HDACK-))
    (LIST 'TIMING-GATE
          '(TIMING)
          'ID
          (LIST (INDEX 'ALU-BUS 2)))
    (LIST 'SCANOUT
          '(TO)
          'ID
          (LIST (INDEX 'PC-REG 3)))))
  (EQUAL (CADDDDR (CHIP-MODULE*))
         '(REGS CVNZ-FLAGS A-REG B-REG I-REG DATA-OUT ADDR-OUT RESET-LATCH
                DTACK-LATCH HOLD-LATCH PC-REG CNTL-STATE))))
\end{verbatim}



\noindent{\sc Event}:   Enable chip-module*; name this event `chip-module*-off'.\index{chip-module*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable chip-module*\$destructure; name this event `chip-module*\$destructure-off'.\index{chip-module*\$destructure-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*chip-module*; name this event `g*1*chip-module*-off'.\index{g*1*chip-module*-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{chip-module\&} \\  
\=\+{\rm{chip-module\&}}\,({\it{netlist\/}})\index{chip-module\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{chip-module}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{chip-module*}}\index{chip-module*}) \\ 
$\wedge$$\;\;\;\;${\rm{regfile\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip-module}}, {\it{netlist\/}})\index{delete-module})\index{regfile\&} \\ 
$\wedge$$\;\;\;\;${\rm{flags\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip-module}}, {\it{netlist\/}})\index{delete-module})\index{flags\&} \\ 
$\wedge$$\;\;\;\;${\rm{we-reg\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip-module}}, {\it{netlist\/}})\index{delete-module}, {\tt{32}})\index{we-reg\&} \\ 
$\wedge$$\;\;\;\;${\rm{fd1s\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip-module}}, {\it{netlist\/}})\index{delete-module})\index{fd1s\&} \\ 
$\wedge$$\;\;\;\;${\rm{fd1slp\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip-module}}, {\it{netlist\/}})\index{delete-module})\index{fd1slp\&} \\ 
$\wedge$$\;\;\;\;${\rm{we-reg\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip-module}}, {\it{netlist\/}})\index{delete-module}, {\tt{4}})\index{we-reg\&} \\ 
$\wedge$$\;\;\;\;${\rm{reg\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip-module}}, {\it{netlist\/}})\index{delete-module}, {\tt{40}})\index{reg\&} \\ 
$\wedge$$\;\;\;\;${\rm{id\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip-module}}, {\it{netlist\/}})\index{delete-module})\index{id\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-buf-pwr\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip-module}}, {\it{netlist\/}})\index{delete-module})\index{b-buf-pwr\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-buf\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip-module}}, {\it{netlist\/}})\index{delete-module})\index{b-buf\&} \\ 
$\wedge$$\;\;\;\;${\rm{b-not\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip-module}}, {\it{netlist\/}})\index{delete-module})\index{b-not\&} \\ 
$\wedge$$\;\;\;\;${\rm{extend-immediate\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip-module}}, {\it{netlist\/}})\index{delete-module})\index{extend-immediate\&} \\ 
$\wedge$$\;\;\;\;${\rm{dec-pass\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip-module}}, {\it{netlist\/}})\index{delete-module}, {\tt{32}})\index{dec-pass\&} \\ 
$\wedge$$\;\;\;\;${\rm{tv-if\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip-module}}, {\it{netlist\/}})\index{delete-module}, {\rm{make-tree}}\,({\tt{32}})\index{make-tree})\index{tv-if\&} \\ 
$\wedge$$\;\;\;\;${\rm{core-alu\&}}\,(\=\+{\rm{delete-module}}\,({\tt{'}}{\tt{chip-module}}, {\it{netlist\/}})\index{delete-module}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{core-alu\&} \\ 
$\wedge$$\;\;\;\;${\rm{next-cntl-state\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip-module}}, {\it{netlist\/}})\index{delete-module})\index{next-cntl-state\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable chip-module\&; name this event `chip-module\&-off'.\index{chip-module\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{chip-module\$netlist} \\  
\=\+{\sc{chip-module\$netlist}}\index{chip-module\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{chip-module*}}\index{chip-module*}, \\ 
\=\+{\sc{regfile\$netlist}}\index{regfile\$netlist} \\ 
$\cup$$\;\;\;\;$(\=\+(\=\+(\=\+({\sc{flags\$netlist}}\index{flags\$netlist} $\cup$ {\rm{we-reg\$netlist}}\,({\tt{32}})\index{we-reg\$netlist}) \\ 
$\cup$$\;\;\;\;$({\sc{fd1s\$netlist}}\index{fd1s\$netlist} $\cup$ {\sc{fd1slp\$netlist}}\index{fd1slp\$netlist}))\- \\ 
$\cup$$\;\;\;\;$(\=\+(\=\+({\rm{we-reg\$netlist}}\,({\tt{4}})\index{we-reg\$netlist} $\cup$ {\rm{reg\$netlist}}\,({\tt{40}})\index{reg\$netlist}) \\ 
$\cup$$\;\;\;\;$(\=\+{\sc{id\$netlist}}\index{id\$netlist} \\ 
$\cup$$\;\;\;\;${\sc{extend-immediate\$netlist}}\index{extend-immediate\$netlist})\-)\- \\ 
$\cup$$\;\;\;\;$(\=\+(\=\+{\rm{dec-pass\$netlist}}\,({\tt{32}})\index{dec-pass\$netlist} \\ 
$\cup$$\;\;\;\;${\rm{tv-if\$netlist}}\,({\rm{make-tree}}\,({\tt{32}})\index{make-tree})\index{tv-if\$netlist})\- \\ 
$\cup$$\;\;\;\;$(\=\+{\rm{core-alu\$netlist}}\,({\rm{make-tree}}\,({\tt{32}})\index{make-tree})\index{core-alu\$netlist} \\ 
$\cup$$\;\;\;\;${\sc{next-cntl-state\$netlist}}\index{next-cntl-state\$netlist})\-)\-)\-)\- \\ 
$\cup$$\;\;\;\;$(\=\+{\sc{b-buf-pwr\$netlist}}\index{b-buf-pwr\$netlist} \\ 
$\cup$$\;\;\;\;$({\sc{b-buf\$netlist}}\index{b-buf\$netlist} $\cup$ {\sc{b-not\$netlist}}\index{b-not\$netlist}))\-)\-\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-length-40-as-collected-nth+subrange \\ \index{equal-length-40-as-collected-nt!h+subrange}
\=\+(({\rm{length}}\,({\it{l\/}})\index{length} $=$ {\tt{40}}) $\wedge$ {\rm{properp}}\,({\it{l\/}})\index{properp}) \\ 
$\rightarrow$$\;\;\;\;$({\it{l\/}} $=$ {\rm{append}}\,({\rm{list-as-collected-nth}}\,({\it{l\/}}, {\tt{16}}, {\tt{0}})\index{list-as-collected-nth}, {\rm{subrange}}\,({\it{l\/}}, {\tt{16}}, {\tt{39}})\index{subrange}))\-
\end{tabbing}

%\item 
\begin{verbatim}


(PROVE-LEMMA LIST-AS-CNTL-STATE-CROCK NIL
 (IMPLIES
  (AND (PROPERP LIST)
       (EQUAL (LENGTH LIST) 40))
  (EQUAL LIST
   (CONS
    (RW- LIST)
    (CONS
     (STROBE- LIST)
     (CONS
      (HDACK- LIST)
      (CONS
       (WE-REGS LIST)
       (CONS
        (WE-A-REG LIST)
        (CONS
         (WE-B-REG LIST)
         (CONS
          (WE-I-REG LIST)
          (CONS
           (WE-DATA-OUT LIST)
           (CONS
            (WE-ADDR-OUT LIST)
            (CONS
             (WE-HOLD- LIST)
             (CONS
              (WE-PC-REG LIST)
              (CONS
               (DATA-IN-SELECT LIST)
               (CONS
                (DEC-ADDR-OUT LIST)
                (CONS
                 (SELECT-IMMEDIATE LIST)
                 (CONS
                  (ALU-C LIST)
                  (CONS
                   (ALU-ZERO LIST)
                   (APPEND
                    (STATE LIST)
                    (APPEND
                           (WE-FLAGS LIST)
                           (APPEND (REGS-ADDRESS LIST)
                                   (APPEND (ALU-OP LIST)
                                           (ALU-MPG LIST)))))))))))))))))))))))
 ((ENABLE-THEORY CONTROL-STATE-ACCESSOR-THEORY)
  (ENABLE OPEN-SUBRANGE)
  (USE (EQUAL-LENGTH-40-AS-COLLECTED-NTH+SUBRANGE (L LIST)))))
\end{verbatim}


%\item 
\begin{verbatim}


(PROVE-LEMMA REG-40$VALUE-AS-CNTL-STATE
 (REWRITE)
 (IMPLIES
  (AND (REG& NETLIST 40)
       (PROPERP STATE)
       (EQUAL (LENGTH STATE) 40))
  (EQUAL
   (DUAL-EVAL 0
              (INDEX 'REG 40)
              ARGS STATE NETLIST)
   (CONS
    (RW- (V-THREEFIX STATE))
    (CONS
     (STROBE- (V-THREEFIX STATE))
     (CONS
      (HDACK- (V-THREEFIX STATE))
      (CONS
       (WE-REGS (V-THREEFIX STATE))
       (CONS
        (WE-A-REG (V-THREEFIX STATE))
        (CONS
         (WE-B-REG (V-THREEFIX STATE))
         (CONS
          (WE-I-REG (V-THREEFIX STATE))
          (CONS
           (WE-DATA-OUT (V-THREEFIX STATE))
           (CONS
            (WE-ADDR-OUT (V-THREEFIX STATE))
            (CONS
             (WE-HOLD- (V-THREEFIX STATE))
             (CONS
              (WE-PC-REG (V-THREEFIX STATE))
              (CONS
               (DATA-IN-SELECT (V-THREEFIX STATE))
               (CONS
                (DEC-ADDR-OUT (V-THREEFIX STATE))
                (CONS
                 (SELECT-IMMEDIATE (V-THREEFIX STATE))
                 (CONS
                  (ALU-C (V-THREEFIX STATE))
                  (CONS
                   (ALU-ZERO (V-THREEFIX STATE))
                   (APPEND
                    (STATE (V-THREEFIX STATE))
                    (APPEND
                     (WE-FLAGS (V-THREEFIX STATE))
                     (APPEND
                      (REGS-ADDRESS (V-THREEFIX STATE))
                      (APPEND
                             (ALU-OP (V-THREEFIX STATE))
                             (ALU-MPG (V-THREEFIX STATE))))))))))))))))))))))))
 ((ENABLE REG$VALUE)
  (USE (LIST-AS-CNTL-STATE-CROCK (LIST (V-THREEFIX STATE))))))
\end{verbatim}



\noindent{\sc Event}:   Enable reg-40\$value-as-cntl-state; name this event `reg-40\$value-as-cntl-state-off'.\index{reg-40\$value-as-cntl-state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  bv-as-subrange \\ \index{bv-as-subrange}
\=\+(\=\+\=\+{\bf if }{\rm{length}}\,({\it{x\/}})\index{length} $<$ {\tt{3}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{x\/}})\index{properp})\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{bv}}\,({\it{x\/}})\index{bv} $=$ {\rm{subrange}}\,({\it{x\/}}, {\tt{3}}, {\rm{length}}\,({\it{x\/}})\index{length} $-\;1$)\index{subrange})\-
\end{tabbing}


\noindent{\sc Event}:   Enable bv-as-subrange; name this event `bv-as-subrange-off'.\index{bv-as-subrange-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{machine-state-invariant} \\  
\=\+{\rm{machine-state-invariant}}\,({\it{machine-state\/}})\index{machine-state-invariant} \\ 
$=$$\;\;\;\;$(\=\+{\rm{all-ramp-mem}}\,({\tt{4}}, {\rm{caar}}\,({\it{machine-state\/}}))\index{all-ramp-mem} \\ 
$\wedge$$\;\;\;\;${\rm{memory-properp}}\,({\tt{4}}, {\tt{32}}, {\rm{caar}}\,({\it{machine-state\/}}))\index{memory-properp} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{caddar}}\,({\it{machine-state\/}}))\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{caddar}}\,({\it{machine-state\/}}))\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{cadddar}}\,({\it{machine-state\/}}))\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cadddar}}\,({\it{machine-state\/}}))\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{cadr}}\,({\it{machine-state\/}}))\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cadr}}\,({\it{machine-state\/}}))\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{caddr}}\,({\it{machine-state\/}}))\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{caddr}}\,({\it{machine-state\/}}))\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{cadddr}}\,({\it{machine-state\/}}))\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cadddr}}\,({\it{machine-state\/}}))\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{caddddr}}\,({\it{machine-state\/}}))\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{caddddr}}\,({\it{machine-state\/}}))\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{cadddddr}}\,({\it{machine-state\/}}))\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cadddddr}}\,({\it{machine-state\/}}))\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{caddddddr}}\,({\it{machine-state\/}}))\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{caddddddr}}\,({\it{machine-state\/}}))\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{caddddddddddr}}\,({\it{machine-state\/}}))\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{caddddddddddr}}\,({\it{machine-state\/}}))\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{cadddddddddddr}}\,({\it{machine-state\/}}))\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cadddddddddddr}}\,({\it{machine-state\/}}))\index{length} $=$ {\tt{40}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  chip-module\$state \\ \index{chip-module\$state}
\=\+(\=\+{\rm{chip-module\&}}\,({\it{netlist\/}})\index{chip-module\&} \\ 
$\wedge$$\;\;\;\;${\rm{machine-state-invariant}}\,({\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-addr\/}})\-, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-)\index{machine-state-invariant} \\ 
$\wedge$$\;\;\;\;$({\it{te\/}} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$({\it{disable-regfile-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\it{test-regfile-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{pc-reg-in\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{pc-reg-in\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{data-in\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-in\/}})\index{length} $=$ {\tt{32}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\tt{'}}{\tt{chip-module}}, \\ 
{\rm{cons}}\,(\=\+{\it{clk\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{ti\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{te\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{dtack-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{reset-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{hold-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{disable-regfile-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{test-regfile-\/}}, \\ 
{\rm{append}}\,(\=\+{\it{pc-reg-in\/}}, \\ 
{\it{data-in\/}})\-)\-)\-)\-)\-)\-)\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,({\it{regs-regs\/}}, {\it{regs-we\/}}, {\it{regs-data\/}}, {\it{regs-addr\/}}), \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{f\$write-regs}}\,(\=\+{\rm{we-regs}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-regs}, \\ 
{\rm{regs-address}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{regs-address}, \\ 
{\rm{list}}\,({\it{regs-regs\/}}, {\it{regs-we\/}}, {\it{regs-data\/}}, {\it{regs-addr\/}}), \\ 
{\rm{bv}}\,({\rm{f\$core-alu}}\,(\=\+{\rm{alu-c}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-c}, \\ 
{\rm{v-threefix}}\,({\it{a-reg\/}})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\it{b-reg\/}})\index{v-threefix}, \\ 
{\rm{alu-zero}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-zero}, \\ 
{\rm{alu-mpg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-mpg}, \\ 
{\rm{alu-op}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-op}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{f\$core-alu})\index{bv})\-\index{f\$write-regs}, \\ 
{\rm{f\$update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\rm{we-flags}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-flags}, \\ 
{\rm{f\$core-alu}}\,(\=\+{\rm{alu-c}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-c}, \\ 
{\rm{v-threefix}}\,({\it{a-reg\/}})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\it{b-reg\/}})\index{v-threefix}, \\ 
{\rm{alu-zero}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-zero}, \\ 
{\rm{alu-mpg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-mpg}, \\ 
{\rm{alu-op}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-op}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{f\$core-alu})\-\index{f\$update-flags}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-a-reg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-a-reg}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{f-nand}}\,(\=\+{\rm{data-in-select}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{data-in-select}, \\ 
{\rm{f-not}}\,({\it{last-dtack-\/}})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f\$extend-immediate}}\,(\=\+{\rm{select-immediate}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{select-immediate}, \\ 
{\rm{a-immediate}}\,({\rm{v-threefix}}\,({\it{i-reg\/}})\index{v-threefix})\index{a-immediate}, \\ 
{\rm{f\$read-regs}}\,(\=\+{\rm{regs-address}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{regs-address}, \\ 
{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-addr\/}})\-)\-\index{f\$read-regs})\-\index{f\$extend-immediate}, \\ 
{\it{data-in\/}})\-\index{fv-if}, \\ 
{\it{a-reg\/}})\-\index{fv-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-b-reg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-b-reg}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{f-nand}}\,(\=\+{\rm{data-in-select}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{data-in-select}, \\ 
{\rm{f-not}}\,({\it{last-dtack-\/}})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f\$extend-immediate}}\,(\=\+{\rm{select-immediate}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{select-immediate}, \\ 
{\rm{a-immediate}}\,({\rm{v-threefix}}\,({\it{i-reg\/}})\index{v-threefix})\index{a-immediate}, \\ 
{\rm{f\$read-regs}}\,(\=\+{\rm{regs-address}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{regs-address}, \\ 
{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-addr\/}})\-)\-\index{f\$read-regs})\-\index{f\$extend-immediate}, \\ 
{\it{data-in\/}})\-\index{fv-if}, \\ 
{\it{b-reg\/}})\-\index{fv-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-i-reg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-i-reg}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{f-nand}}\,(\=\+{\rm{data-in-select}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{data-in-select}, \\ 
{\rm{f-not}}\,({\it{last-dtack-\/}})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f\$extend-immediate}}\,(\=\+{\rm{select-immediate}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{select-immediate}, \\ 
{\rm{a-immediate}}\,({\rm{v-threefix}}\,({\it{i-reg\/}})\index{v-threefix})\index{a-immediate}, \\ 
{\rm{f\$read-regs}}\,(\=\+{\rm{regs-address}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{regs-address}, \\ 
{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-addr\/}})\-)\-\index{f\$read-regs})\-\index{f\$extend-immediate}, \\ 
{\it{data-in\/}})\-\index{fv-if}, \\ 
{\it{i-reg\/}})\-\index{fv-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-data-out}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-data-out}, \\ 
{\rm{bv}}\,({\rm{f\$core-alu}}\,(\=\+{\rm{alu-c}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-c}, \\ 
{\rm{v-threefix}}\,({\it{a-reg\/}})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\it{b-reg\/}})\index{v-threefix}, \\ 
{\rm{alu-zero}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-zero}, \\ 
{\rm{alu-mpg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-mpg}, \\ 
{\rm{alu-op}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-op}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{f\$core-alu})\index{bv}, \\ 
{\it{data-out\/}})\-\index{fv-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-addr-out}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-addr-out}, \\ 
{\rm{f\$dec-pass}}\,(\=\+{\rm{dec-addr-out}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{dec-addr-out}, \\ 
{\rm{f\$extend-immediate}}\,(\=\+{\rm{select-immediate}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{select-immediate}, \\ 
{\rm{a-immediate}}\,({\rm{v-threefix}}\,({\it{i-reg\/}})\index{v-threefix})\index{a-immediate}, \\ 
{\rm{f\$read-regs}}\,(\=\+{\rm{regs-address}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{regs-address}, \\ 
{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-addr\/}})\-)\-\index{f\$read-regs})\-\index{f\$extend-immediate})\-\index{f\$dec-pass}, \\ 
{\it{addr-out\/}})\-\index{fv-if}, \\ 
{\rm{f-buf}}\,({\it{reset-\/}})\index{f-buf}, \\ 
{\rm{f-or}}\,({\rm{strobe-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{strobe-}, {\it{dtack-\/}})\index{f-or}, \\ 
{\rm{f-if}}\,({\rm{we-hold-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-hold-}, {\it{hold-\/}}, {\it{last-hold-\/}})\index{f-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-pc-reg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-pc-reg}, \\ 
{\it{pc-reg-in\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{fv-if}, \\ 
{\rm{v-threefix}}\,({\rm{f\$next-cntl-state}}\,(\=\+{\rm{f-buf}}\,({\it{last-reset-\/}})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\it{last-dtack-\/}})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\it{last-hold-\/}})\index{f-buf}, \\ 
{\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-}, \\ 
{\rm{state}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{state}, \\ 
{\rm{v-threefix}}\,({\it{i-reg\/}})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\it{flags\/}})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\it{last-pc-reg\/}})\index{v-threefix}, \\ 
{\rm{regs-address}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{regs-address})\-\index{f\$next-cntl-state})\index{v-threefix})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  chip-module\$value \\ \index{chip-module\$value}
\=\+(\=\+{\rm{chip-module\&}}\,({\it{netlist\/}})\index{chip-module\&} \\ 
$\wedge$$\;\;\;\;${\rm{machine-state-invariant}}\,({\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-addr\/}})\-, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-)\index{machine-state-invariant} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{pc-reg-in\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{pc-reg-in\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{data-in\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-in\/}})\index{length} $=$ {\tt{32}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{chip-module}}, \\ 
{\rm{cons}}\,(\=\+{\it{clk\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{ti\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{te\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{dtack-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{reset-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{hold-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{disable-regfile-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{test-regfile-\/}}, \\ 
{\rm{append}}\,(\=\+{\it{pc-reg-in\/}}, \\ 
{\it{data-in\/}})\-)\-)\-)\-)\-)\-)\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,({\it{regs-regs\/}}, {\it{regs-we\/}}, {\it{regs-data\/}}, {\it{regs-addr\/}}), \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{nth}}\,({\tt{3}}, {\rm{v-threefix}}\,({\it{last-pc-reg\/}})\index{v-threefix})\index{nth}, \\ 
{\rm{cons}}\,(\=\+{\rm{nth}}\,(\=\+{\tt{2}}, \\ 
{\rm{f\$core-alu}}\,(\=\+{\rm{alu-c}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-c}, \\ 
{\rm{v-threefix}}\,({\it{a-reg\/}})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\it{b-reg\/}})\index{v-threefix}, \\ 
{\rm{alu-zero}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-zero}, \\ 
{\rm{alu-mpg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-mpg}, \\ 
{\rm{alu-op}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-op}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{f\$core-alu})\-\index{nth}, \\ 
{\rm{cons}}\,(\=\+{\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-}, \\ 
{\rm{cons}}\,(\=\+{\rm{f-not}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-not}, \\ 
{\rm{cons}}\,(\=\+{\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-})\index{f-buf}, \\ 
{\rm{cons}}\,(\=\+{\rm{strobe-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{strobe-}, \\ 
{\rm{append5}}\,(\=\+{\rm{v-threefix}}\,({\it{addr-out\/}})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\it{data-out\/}})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\it{flags\/}})\index{v-threefix}, \\ 
{\rm{state}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{state}, \\ 
{\rm{subrange}}\,(\=\+{\rm{v-threefix}}\,({\it{i-reg\/}})\index{v-threefix}, \\ 
{\tt{28}}, \\ 
{\tt{31}})\-\index{subrange})\-\index{append5})\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN CHIP* NIL
 (CONS 'CHIP
  (CONS
   (CONS 'CLK
    (CONS 'TI
     (CONS 'TE
       (CONS 'DTACK-
             (CONS 'RESET-
                   (CONS 'HOLD-
                         (CONS 'DISABLE-REGFILE-
                               (CONS 'TEST-REGFILE-
                                     (APPEND (INDICES 'PC-REG-IN 0 4)
                                             (INDICES 'DATA-BUS 0 32))))))))))
   (CONS
    (CONS 'PO
     (CONS 'TO
      (CONS 'TIMING
       (CONS 'HDACK-
        (CONS 'RW-
         (CONS 'STROBE-
               (APPEND (INDICES 'ADDR-OUT 0 32)
                       (APPEND (INDICES 'DATA-BUS 0 32)
                               (APPEND (INDICES 'FLAGS 0 4)
                                       (APPEND (INDICES 'CNTL-STATE 0 5)
                                               (INDICES 'I-REG 28 4)))))))))))
    (CONS
     (LIST
      (LIST 'BODY
       (CONS 'I-TO
        (CONS 'I-TIMING
         (CONS 'I-HDACK-
          (CONS 'I-EN-ADDR-OUT-
           (CONS 'I-RW-
            (CONS 'I-STROBE-
             (APPEND (INDICES 'I-ADDR-OUT 0 32)
                     (APPEND (INDICES 'I-DATA-OUT 0 32)
                             (APPEND (INDICES 'I-FLAGS 0 4)
                                     (APPEND (INDICES 'I-CNTL-STATE 0 5)
                                             (INDICES 'I-I-REG 28 4)))))))))))
       'CHIP-MODULE
       (CONS 'I-CLK
        (CONS 'I-TI
         (CONS 'I-TE
          (CONS 'I-DTACK-
           (CONS 'I-RESET-
                 (CONS 'I-HOLD-
                       (CONS 'I-DISABLE-REGFILE-
                             (CONS 'I-TEST-REGFILE-
                                   (APPEND (INDICES 'I-PC-REG 0 4)
                                           (INDICES 'I-DATA-IN 0 32)))))))))))
      '(PLUS-5 (B-TRUE-P) VDD-PARAMETRIC NIL)
      '(CLOCK-PAD (I-CLK CLK-PO)
                  TTL-CLK-INPUT
                  (CLK B-TRUE-P))
      '(TI-PAD (I-TI TI-PO)
               TTL-INPUT
               (TI B-TRUE-P))
      '(TE-PAD (I-TE TE-PO)
               TTL-INPUT
               (TE TI-PO))
      '(DTACK-PAD (I-DTACK- DTACK-PO)
                  TTL-INPUT
                  (DTACK- TE-PO))
      '(RESET-PAD (I-RESET- RESET-PO)
                  TTL-INPUT
                  (RESET- DTACK-PO))
      '(HOLD-PAD (I-HOLD- HOLD-PO)
                 TTL-INPUT
                 (HOLD- RESET-PO))
      '(DISABLE-REGFILE-PAD (I-DISABLE-REGFILE- DISABLE-REGFILE-PO)
                            TTL-INPUT
                            (DISABLE-REGFILE- HOLD-PO))
      '(TEST-REGFILE-PAD (I-TEST-REGFILE- TEST-REGFILE-PO)
                         TTL-INPUT
                         (TEST-REGFILE- DISABLE-REGFILE-PO))
      (LIST 'DATA-BUS-PADS
            (CONS 'DATA-BUS-PO
                  (APPEND (INDICES 'DATA-BUS 0 32)
                          (INDICES 'I-DATA-IN 0 32)))
            (INDEX 'TTL-BIDIRECT-PADS 32)
            (CONS 'I-RW-
                  (CONS 'TEST-REGFILE-PO
                        (APPEND (INDICES 'DATA-BUS 0 32)
                                (INDICES 'I-DATA-OUT 0 32)))))
      (LIST 'PC-REG-PADS
            (CONS 'PC-REG-PO
                  (INDICES 'I-PC-REG 0 4))
            (INDEX 'TTL-INPUT-PADS 4)
            (CONS 'DATA-BUS-PO
                  (INDICES 'PC-REG-IN 0 4)))
      '(MONITOR (I-PO)
                PROCMON
                (PC-REG-PO CLK-PO B-TRUE-P B-TRUE-P))
      '(PO-PAD (PO)
               TTL-OUTPUT-PARAMETRIC
               (I-PO))
      '(TO-PAD (TO) TTL-OUTPUT (I-TO))
      '(TIMING-PAD (TIMING)
                   TTL-OUTPUT-FAST
                   (I-TIMING))
      '(HDACK-PAD (HDACK-)
                  TTL-OUTPUT-FAST
                  (I-HDACK-))
      '(RW-PAD (RW-)
               TTL-TRI-OUTPUT-FAST
               (I-RW- I-EN-ADDR-OUT-))
      '(STROBE-PAD (STROBE-)
                   TTL-TRI-OUTPUT-FAST
                   (I-STROBE- I-EN-ADDR-OUT-))
      (LIST 'ADDR-OUT-PADS
            (INDICES 'ADDR-OUT 0 32)
            (INDEX 'TTL-TRI-OUTPUT-PADS 32)
            (CONS 'I-EN-ADDR-OUT-
                  (INDICES 'I-ADDR-OUT 0 32)))
      (LIST 'FLAGS-PADS
            (INDICES 'FLAGS 0 4)
            (INDEX 'TTL-OUTPUT-PADS 4)
            (INDICES 'I-FLAGS 0 4))
      (LIST 'CNTL-STATE-PADS
            (INDICES 'CNTL-STATE 0 5)
            (INDEX 'TTL-OUTPUT-PADS 5)
            (INDICES 'I-CNTL-STATE 0 5))
      (LIST 'I-REG-PADS
            (INDICES 'I-REG 28 4)
            (INDEX 'TTL-OUTPUT-PADS 4)
            (INDICES 'I-I-REG 28 4)))
     '(BODY))))))
\end{verbatim}


%\item 
\begin{verbatim}


(PROVE-LEMMA CHIP*$DESTRUCTURE
 (REWRITE)
 (AND
  (EQUAL (CAR (CHIP*)) 'CHIP)
  (EQUAL
   (CADR (CHIP*))
   (CONS 'CLK
    (CONS 'TI
     (CONS 'TE
      (CONS 'DTACK-
            (CONS 'RESET-
                  (CONS 'HOLD-
                        (CONS 'DISABLE-REGFILE-
                              (CONS 'TEST-REGFILE-
                                    (APPEND (INDICES 'PC-REG-IN 0 4)
                                            (INDICES 'DATA-BUS 0 32)))))))))))
  (EQUAL
   (CADDR (CHIP*))
   (CONS 'PO
    (CONS 'TO
     (CONS 'TIMING
      (CONS 'HDACK-
       (CONS 'RW-
        (CONS 'STROBE-
              (APPEND (INDICES 'ADDR-OUT 0 32)
                      (APPEND (INDICES 'DATA-BUS 0 32)
                              (APPEND (INDICES 'FLAGS 0 4)
                                      (APPEND (INDICES 'CNTL-STATE 0 5)
                                              (INDICES 'I-REG 28 4))))))))))))
  (EQUAL
   (CADDDR (CHIP*))
   (LIST
    (LIST 'BODY
     (CONS 'I-TO
      (CONS 'I-TIMING
       (CONS 'I-HDACK-
        (CONS 'I-EN-ADDR-OUT-
         (CONS 'I-RW-
          (CONS 'I-STROBE-
             (APPEND (INDICES 'I-ADDR-OUT 0 32)
                     (APPEND (INDICES 'I-DATA-OUT 0 32)
                             (APPEND (INDICES 'I-FLAGS 0 4)
                                     (APPEND (INDICES 'I-CNTL-STATE 0 5)
                                             (INDICES 'I-I-REG 28 4)))))))))))
     'CHIP-MODULE
     (CONS 'I-CLK
      (CONS 'I-TI
       (CONS 'I-TE
        (CONS 'I-DTACK-
           (CONS 'I-RESET-
                 (CONS 'I-HOLD-
                       (CONS 'I-DISABLE-REGFILE-
                             (CONS 'I-TEST-REGFILE-
                                   (APPEND (INDICES 'I-PC-REG 0 4)
                                           (INDICES 'I-DATA-IN 0 32)))))))))))
    '(PLUS-5 (B-TRUE-P) VDD-PARAMETRIC NIL)
    '(CLOCK-PAD (I-CLK CLK-PO)
                TTL-CLK-INPUT
                (CLK B-TRUE-P))
    '(TI-PAD (I-TI TI-PO)
             TTL-INPUT
             (TI B-TRUE-P))
    '(TE-PAD (I-TE TE-PO)
             TTL-INPUT
             (TE TI-PO))
    '(DTACK-PAD (I-DTACK- DTACK-PO)
                TTL-INPUT
                (DTACK- TE-PO))
    '(RESET-PAD (I-RESET- RESET-PO)
                TTL-INPUT
                (RESET- DTACK-PO))
    '(HOLD-PAD (I-HOLD- HOLD-PO)
               TTL-INPUT
               (HOLD- RESET-PO))
    '(DISABLE-REGFILE-PAD (I-DISABLE-REGFILE- DISABLE-REGFILE-PO)
                          TTL-INPUT
                          (DISABLE-REGFILE- HOLD-PO))
    '(TEST-REGFILE-PAD (I-TEST-REGFILE- TEST-REGFILE-PO)
                       TTL-INPUT
                       (TEST-REGFILE- DISABLE-REGFILE-PO))
    (LIST 'DATA-BUS-PADS
          (CONS 'DATA-BUS-PO
                (APPEND (INDICES 'DATA-BUS 0 32)
                        (INDICES 'I-DATA-IN 0 32)))
          (INDEX 'TTL-BIDIRECT-PADS 32)
          (CONS 'I-RW-
                (CONS 'TEST-REGFILE-PO
                      (APPEND (INDICES 'DATA-BUS 0 32)
                              (INDICES 'I-DATA-OUT 0 32)))))
    (LIST 'PC-REG-PADS
          (CONS 'PC-REG-PO
                (INDICES 'I-PC-REG 0 4))
          (INDEX 'TTL-INPUT-PADS 4)
          (CONS 'DATA-BUS-PO
                (INDICES 'PC-REG-IN 0 4)))
    '(MONITOR (I-PO)
              PROCMON
              (PC-REG-PO CLK-PO B-TRUE-P B-TRUE-P))
    '(PO-PAD (PO)
             TTL-OUTPUT-PARAMETRIC
             (I-PO))
    '(TO-PAD (TO) TTL-OUTPUT (I-TO))
    '(TIMING-PAD (TIMING)
                 TTL-OUTPUT-FAST
                 (I-TIMING))
    '(HDACK-PAD (HDACK-)
                TTL-OUTPUT-FAST
                (I-HDACK-))
    '(RW-PAD (RW-)
             TTL-TRI-OUTPUT-FAST
             (I-RW- I-EN-ADDR-OUT-))
    '(STROBE-PAD (STROBE-)
                 TTL-TRI-OUTPUT-FAST
                 (I-STROBE- I-EN-ADDR-OUT-))
    (LIST 'ADDR-OUT-PADS
          (INDICES 'ADDR-OUT 0 32)
          (INDEX 'TTL-TRI-OUTPUT-PADS 32)
          (CONS 'I-EN-ADDR-OUT-
                (INDICES 'I-ADDR-OUT 0 32)))
    (LIST 'FLAGS-PADS
          (INDICES 'FLAGS 0 4)
          (INDEX 'TTL-OUTPUT-PADS 4)
          (INDICES 'I-FLAGS 0 4))
    (LIST 'CNTL-STATE-PADS
          (INDICES 'CNTL-STATE 0 5)
          (INDEX 'TTL-OUTPUT-PADS 5)
          (INDICES 'I-CNTL-STATE 0 5))
    (LIST 'I-REG-PADS
          (INDICES 'I-REG 28 4)
          (INDEX 'TTL-OUTPUT-PADS 4)
          (INDICES 'I-I-REG 28 4))))
  (EQUAL (CADDDDR (CHIP*)) 'BODY)))
\end{verbatim}



\noindent{\sc Event}:   Enable chip*; name this event `chip*-off'.\index{chip*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable chip*\$destructure; name this event `chip*\$destructure-off'.\index{chip*\$destructure-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*chip*; name this event `g*1*chip*-off'.\index{g*1*chip*-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{chip\&} \\  
\=\+{\rm{chip\&}}\,({\it{netlist\/}})\index{chip\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{chip}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{chip*}}\index{chip*}) \\ 
$\wedge$$\;\;\;\;${\rm{vdd-parametric\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip}}, {\it{netlist\/}})\index{delete-module})\index{vdd-parametric\&} \\ 
$\wedge$$\;\;\;\;${\rm{ttl-clk-input\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip}}, {\it{netlist\/}})\index{delete-module})\index{ttl-clk-input\&} \\ 
$\wedge$$\;\;\;\;${\rm{ttl-input\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip}}, {\it{netlist\/}})\index{delete-module})\index{ttl-input\&} \\ 
$\wedge$$\;\;\;\;${\rm{ttl-input-pads\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip}}, {\it{netlist\/}})\index{delete-module}, {\tt{4}})\index{ttl-input-pads\&} \\ 
$\wedge$$\;\;\;\;${\rm{chip-module\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip}}, {\it{netlist\/}})\index{delete-module})\index{chip-module\&} \\ 
$\wedge$$\;\;\;\;${\rm{ttl-bidirect-pads\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip}}, {\it{netlist\/}})\index{delete-module}, {\tt{32}})\index{ttl-bidirect-pads\&} \\ 
$\wedge$$\;\;\;\;${\rm{ttl-output-parametric\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip}}, {\it{netlist\/}})\index{delete-module})\index{ttl-output-parametric\&} \\ 
$\wedge$$\;\;\;\;${\rm{ttl-output\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip}}, {\it{netlist\/}})\index{delete-module})\index{ttl-output\&} \\ 
$\wedge$$\;\;\;\;${\rm{ttl-output-fast\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip}}, {\it{netlist\/}})\index{delete-module})\index{ttl-output-fast\&} \\ 
$\wedge$$\;\;\;\;${\rm{ttl-tri-output-fast\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip}}, {\it{netlist\/}})\index{delete-module})\index{ttl-tri-output-fast\&} \\ 
$\wedge$$\;\;\;\;${\rm{ttl-tri-output-pads\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip}}, {\it{netlist\/}})\index{delete-module}, {\tt{32}})\index{ttl-tri-output-pads\&} \\ 
$\wedge$$\;\;\;\;${\rm{ttl-output-pads\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip}}, {\it{netlist\/}})\index{delete-module}, {\tt{4}})\index{ttl-output-pads\&} \\ 
$\wedge$$\;\;\;\;${\rm{ttl-output-pads\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip}}, {\it{netlist\/}})\index{delete-module}, {\tt{5}})\index{ttl-output-pads\&} \\ 
$\wedge$$\;\;\;\;${\rm{procmon\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip}}, {\it{netlist\/}})\index{delete-module})\index{procmon\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable chip\&; name this event `chip\&-off'.\index{chip\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{chip\$netlist} \\  
\=\+{\sc{chip\$netlist}}\index{chip\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{chip*}}\index{chip*}, \\ 
\=\+(\=\+(\=\+({\rm{ttl-bidirect-pads\$netlist}}\,({\tt{32}})\index{ttl-bidirect-pads\$netlist} $\cup$ {\sc{chip-module\$netlist}}\index{chip-module\$netlist}) \\ 
$\cup$$\;\;\;\;$({\sc{ttl-input\$netlist}}\index{ttl-input\$netlist} $\cup$ {\rm{ttl-input-pads\$netlist}}\,({\tt{4}})\index{ttl-input-pads\$netlist}))\- \\ 
$\cup$$\;\;\;\;$(\=\+({\sc{ttl-clk-input\$netlist}}\index{ttl-clk-input\$netlist} $\cup$ {\sc{vdd-parametric\$netlist}}\index{vdd-parametric\$netlist}) \\ 
$\cup$$\;\;\;\;$(\=\+{\sc{ttl-output-parametric\$netlist}}\index{ttl-output-parametric\$netlist} \\ 
$\cup$$\;\;\;\;${\sc{ttl-output\$netlist}}\index{ttl-output\$netlist})\-)\-)\- \\ 
$\cup$$\;\;\;\;$(\=\+(\=\+(\=\+{\sc{ttl-output-fast\$netlist}}\index{ttl-output-fast\$netlist} \\ 
$\cup$$\;\;\;\;${\sc{ttl-tri-output-fast\$netlist}}\index{ttl-tri-output-fast\$netlist})\- \\ 
$\cup$$\;\;\;\;$(\=\+{\rm{ttl-tri-output-pads\$netlist}}\,({\tt{32}})\index{ttl-tri-output-pads\$netlist} \\ 
$\cup$$\;\;\;\;${\rm{ttl-output-pads\$netlist}}\,({\tt{4}})\index{ttl-output-pads\$netlist})\-)\- \\ 
$\cup$$\;\;\;\;$({\rm{ttl-output-pads\$netlist}}\,({\tt{5}})\index{ttl-output-pads\$netlist} $\cup$ {\sc{procmon\$netlist}}\index{procmon\$netlist}))\-\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  chip\$state \\ \index{chip\$state}
\=\+(\=\+{\rm{chip\&}}\,({\it{netlist\/}})\index{chip\&} \\ 
$\wedge$$\;\;\;\;${\rm{machine-state-invariant}}\,({\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-addr\/}})\-, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-)\index{machine-state-invariant} \\ 
$\wedge$$\;\;\;\;$({\it{te\/}} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$({\it{disable-regfile-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\it{test-regfile-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{pc-reg-in\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{pc-reg-in\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{data-in\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-in\/}})\index{length} $=$ {\tt{32}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\tt{'}}{\tt{chip}}, \\ 
{\rm{cons}}\,(\=\+{\it{clk\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{ti\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{te\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{dtack-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{reset-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{hold-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{disable-regfile-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{test-regfile-\/}}, \\ 
{\rm{append}}\,(\=\+{\it{pc-reg-in\/}}, \\ 
{\it{data-in\/}})\-)\-)\-)\-)\-)\-)\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,({\it{regs-regs\/}}, {\it{regs-we\/}}, {\it{regs-data\/}}, {\it{regs-addr\/}}), \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{f\$write-regs}}\,(\=\+{\rm{we-regs}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-regs}, \\ 
{\rm{regs-address}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{regs-address}, \\ 
{\rm{list}}\,({\it{regs-regs\/}}, {\it{regs-we\/}}, {\it{regs-data\/}}, {\it{regs-addr\/}}), \\ 
{\rm{bv}}\,({\rm{f\$core-alu}}\,(\=\+{\rm{alu-c}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-c}, \\ 
{\rm{v-threefix}}\,({\it{a-reg\/}})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\it{b-reg\/}})\index{v-threefix}, \\ 
{\rm{alu-zero}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-zero}, \\ 
{\rm{alu-mpg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-mpg}, \\ 
{\rm{alu-op}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-op}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{f\$core-alu})\index{bv})\-\index{f\$write-regs}, \\ 
{\rm{f\$update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\rm{we-flags}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-flags}, \\ 
{\rm{f\$core-alu}}\,(\=\+{\rm{alu-c}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-c}, \\ 
{\rm{v-threefix}}\,({\it{a-reg\/}})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\it{b-reg\/}})\index{v-threefix}, \\ 
{\rm{alu-zero}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-zero}, \\ 
{\rm{alu-mpg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-mpg}, \\ 
{\rm{alu-op}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-op}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{f\$core-alu})\-\index{f\$update-flags}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-a-reg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-a-reg}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{f-nand}}\,(\=\+{\rm{data-in-select}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{data-in-select}, \\ 
{\rm{f-not}}\,({\it{last-dtack-\/}})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f\$extend-immediate}}\,(\=\+{\rm{select-immediate}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{select-immediate}, \\ 
{\rm{a-immediate}}\,({\rm{v-threefix}}\,({\it{i-reg\/}})\index{v-threefix})\index{a-immediate}, \\ 
{\rm{f\$read-regs}}\,(\=\+{\rm{regs-address}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{regs-address}, \\ 
{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-addr\/}})\-)\-\index{f\$read-regs})\-\index{f\$extend-immediate}, \\ 
{\rm{v-wire}}\,(\=\+{\it{data-in\/}}, \\ 
{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\rm{v-threefix}}\,({\it{data-out\/}})\index{v-threefix})\-\index{vft-buf})\-\index{v-wire})\-\index{fv-if}, \\ 
{\it{a-reg\/}})\-\index{fv-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-b-reg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-b-reg}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{f-nand}}\,(\=\+{\rm{data-in-select}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{data-in-select}, \\ 
{\rm{f-not}}\,({\it{last-dtack-\/}})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f\$extend-immediate}}\,(\=\+{\rm{select-immediate}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{select-immediate}, \\ 
{\rm{a-immediate}}\,({\rm{v-threefix}}\,({\it{i-reg\/}})\index{v-threefix})\index{a-immediate}, \\ 
{\rm{f\$read-regs}}\,(\=\+{\rm{regs-address}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{regs-address}, \\ 
{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-addr\/}})\-)\-\index{f\$read-regs})\-\index{f\$extend-immediate}, \\ 
{\rm{v-wire}}\,(\=\+{\it{data-in\/}}, \\ 
{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\rm{v-threefix}}\,({\it{data-out\/}})\index{v-threefix})\-\index{vft-buf})\-\index{v-wire})\-\index{fv-if}, \\ 
{\it{b-reg\/}})\-\index{fv-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-i-reg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-i-reg}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{f-nand}}\,(\=\+{\rm{data-in-select}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{data-in-select}, \\ 
{\rm{f-not}}\,({\it{last-dtack-\/}})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f\$extend-immediate}}\,(\=\+{\rm{select-immediate}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{select-immediate}, \\ 
{\rm{a-immediate}}\,({\rm{v-threefix}}\,({\it{i-reg\/}})\index{v-threefix})\index{a-immediate}, \\ 
{\rm{f\$read-regs}}\,(\=\+{\rm{regs-address}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{regs-address}, \\ 
{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-addr\/}})\-)\-\index{f\$read-regs})\-\index{f\$extend-immediate}, \\ 
{\rm{v-wire}}\,(\=\+{\it{data-in\/}}, \\ 
{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\rm{v-threefix}}\,({\it{data-out\/}})\index{v-threefix})\-\index{vft-buf})\-\index{v-wire})\-\index{fv-if}, \\ 
{\it{i-reg\/}})\-\index{fv-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-data-out}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-data-out}, \\ 
{\rm{bv}}\,({\rm{f\$core-alu}}\,(\=\+{\rm{alu-c}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-c}, \\ 
{\rm{v-threefix}}\,({\it{a-reg\/}})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\it{b-reg\/}})\index{v-threefix}, \\ 
{\rm{alu-zero}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-zero}, \\ 
{\rm{alu-mpg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-mpg}, \\ 
{\rm{alu-op}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-op}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{f\$core-alu})\index{bv}, \\ 
{\it{data-out\/}})\-\index{fv-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-addr-out}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-addr-out}, \\ 
{\rm{f\$dec-pass}}\,(\=\+{\rm{dec-addr-out}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{dec-addr-out}, \\ 
{\rm{f\$extend-immediate}}\,(\=\+{\rm{select-immediate}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{select-immediate}, \\ 
{\rm{a-immediate}}\,({\rm{v-threefix}}\,({\it{i-reg\/}})\index{v-threefix})\index{a-immediate}, \\ 
{\rm{f\$read-regs}}\,(\=\+{\rm{regs-address}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{regs-address}, \\ 
{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-addr\/}})\-)\-\index{f\$read-regs})\-\index{f\$extend-immediate})\-\index{f\$dec-pass}, \\ 
{\it{addr-out\/}})\-\index{fv-if}, \\ 
{\rm{f-buf}}\,({\it{reset-\/}})\index{f-buf}, \\ 
{\rm{f-or}}\,({\rm{strobe-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{strobe-}, {\rm{f-buf}}\,({\it{dtack-\/}})\index{f-buf})\index{f-or}, \\ 
{\rm{f-if}}\,(\=\+{\rm{we-hold-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-hold-}, \\ 
{\rm{f-buf}}\,({\it{hold-\/}})\index{f-buf}, \\ 
{\it{last-hold-\/}})\-\index{f-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-pc-reg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-pc-reg}, \\ 
{\it{pc-reg-in\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{fv-if}, \\ 
{\rm{v-threefix}}\,({\rm{f\$next-cntl-state}}\,(\=\+{\rm{f-buf}}\,({\it{last-reset-\/}})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\it{last-dtack-\/}})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\it{last-hold-\/}})\index{f-buf}, \\ 
{\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-}, \\ 
{\rm{state}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{state}, \\ 
{\rm{v-threefix}}\,({\it{i-reg\/}})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\it{flags\/}})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\it{last-pc-reg\/}})\index{v-threefix}, \\ 
{\rm{regs-address}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{regs-address})\-\index{f\$next-cntl-state})\index{v-threefix})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  chip\$value \\ \index{chip\$value}
\=\+(\=\+{\rm{chip\&}}\,({\it{netlist\/}})\index{chip\&} \\ 
$\wedge$$\;\;\;\;${\rm{machine-state-invariant}}\,({\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-addr\/}})\-, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-)\index{machine-state-invariant} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{pc-reg-in\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{pc-reg-in\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{data-in\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-in\/}})\index{length} $=$ {\tt{32}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{cdr}}\,({\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\tt{'}}{\tt{chip}}, \\ 
{\rm{cons}}\,(\=\+{\it{clk\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{ti\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{te\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{dtack-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{reset-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{hold-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{disable-regfile-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{test-regfile-\/}}, \\ 
{\rm{append}}\,(\=\+{\it{pc-reg-in\/}}, \\ 
{\it{data-in\/}})\-)\-)\-)\-)\-)\-)\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,({\it{regs-regs\/}}, {\it{regs-we\/}}, {\it{regs-data\/}}, {\it{regs-addr\/}}), \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-, \\ 
{\it{netlist\/}})\-\index{dual-eval}) \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{f-buf}}\,({\rm{nth}}\,({\tt{3}}, {\rm{v-threefix}}\,({\it{last-pc-reg\/}})\index{v-threefix})\index{nth})\index{f-buf}, \\ 
{\rm{cons}}\,(\=\+{\rm{f-buf}}\,({\rm{nth}}\,(\=\+{\tt{2}}, \\ 
{\rm{f\$core-alu}}\,(\=\+{\rm{alu-c}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-c}, \\ 
{\rm{v-threefix}}\,({\it{a-reg\/}})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\it{b-reg\/}})\index{v-threefix}, \\ 
{\rm{alu-zero}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-zero}, \\ 
{\rm{alu-mpg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-mpg}, \\ 
{\rm{alu-op}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-op}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{f\$core-alu})\-\index{nth})\index{f-buf}, \\ 
{\rm{cons}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{cons}}\,(\=\+{\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-})\index{f-buf})\-\index{ft-buf}, \\ 
{\rm{cons}}\,(\=\+{\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{strobe-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{strobe-})\-\index{ft-buf}, \\ 
{\rm{append5}}\,(\=\+{\rm{vft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{v-threefix}}\,({\it{addr-out\/}})\index{v-threefix})\-\index{vft-buf}, \\ 
{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\rm{v-threefix}}\,({\it{data-out\/}})\index{v-threefix})\-\index{vft-buf}, \\ 
{\rm{v-threefix}}\,({\it{flags\/}})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\rm{state}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{state})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\rm{subrange}}\,(\=\+{\rm{v-threefix}}\,({\it{i-reg\/}})\index{v-threefix}, \\ 
{\tt{28}}, \\ 
{\tt{31}})\-\index{subrange})\index{v-threefix})\-\index{append5})\-)\-)\-)\-)\-)\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN CHIP-SYSTEM* NIL
 (CONS 'CHIP-SYSTEM
  (CONS
   (CONS 'CLK
         (CONS 'TI
               (CONS 'TE
                     (CONS 'RESET-
                           (CONS 'HOLD-
                                 (CONS 'DISABLE-REGFILE-
                                       (CONS 'TEST-REGFILE-
                                             (INDICES 'PC-REG 0 4))))))))
   (CONS NIL
    (CONS
     (LIST
      (LIST 'FM9001
       (CONS 'PO
        (CONS 'TO
         (CONS 'TIMING
          (CONS 'HDACK-
           (CONS 'RW-
            (CONS 'STROBE-
               (APPEND (INDICES 'ADDR-OUT 0 32)
                       (APPEND (INDICES 'FM9001-DATA 0 32)
                               (APPEND (INDICES 'FLAGS 0 4)
                                       (APPEND (INDICES 'CNTL-STATE 0 5)
                                               (INDICES 'I-REG 28 4)))))))))))
       'CHIP
       (CONS 'CLK
        (CONS 'TI
         (CONS 'TE
          (CONS 'DTACK-
            (CONS 'RESET-
                  (CONS 'HOLD-
                        (CONS 'DISABLE-REGFILE-
                              (CONS 'TEST-REGFILE-
                                    (APPEND (INDICES 'PC-REG 0 4)
                                            (INDICES 'DATA-BUS 0 32)))))))))))
      '(PULLUP-RW- (RW-BUS) PULLUP (RW-))
      '(PULLUP-STROBE- (STROBE-BUS)
                       PULLUP
                       (STROBE-))
      (LIST 'ADDRESS
            (INDICES 'ADDR-BUS 0 32)
            (INDEX 'V-PULLUP 32)
            (INDICES 'ADDR-OUT 0 32))
      (LIST 'MEM
            (CONS 'DTACK-
                  (INDICES 'MEM-DATA 0 32))
            'MEM-32X32
            (CONS 'RW-BUS
                  (CONS 'STROBE-BUS
                        (APPEND (INDICES 'ADDR-BUS 0 32)
                                (INDICES 'DATA-BUS 0 32)))))
      (LIST 'DATA-WIRE
            (INDICES 'DATA-WIRE 0 32)
            (INDEX 'V-WIRE 32)
            (APPEND (INDICES 'FM9001-DATA 0 32)
                    (INDICES 'MEM-DATA 0 32)))
      (LIST 'DATA
            (INDICES 'DATA-BUS 0 32)
            (INDEX 'V-PULLUP 32)
            (INDICES 'DATA-WIRE 0 32)))
     '((FM9001 MEM)))))))
\end{verbatim}


%\item 
\begin{verbatim}


(PROVE-LEMMA CHIP-SYSTEM*$DESTRUCTURE
 (REWRITE)
 (AND
  (EQUAL (CAR (CHIP-SYSTEM*))
         'CHIP-SYSTEM)
  (EQUAL
       (CADR (CHIP-SYSTEM*))
       (CONS 'CLK
             (CONS 'TI
                   (CONS 'TE
                         (CONS 'RESET-
                               (CONS 'HOLD-
                                     (CONS 'DISABLE-REGFILE-
                                           (CONS 'TEST-REGFILE-
                                                 (INDICES 'PC-REG 0 4)))))))))
  (EQUAL (CADDR (CHIP-SYSTEM*)) NIL)
  (EQUAL
   (CADDDR (CHIP-SYSTEM*))
   (LIST
    (LIST 'FM9001
     (CONS 'PO
      (CONS 'TO
       (CONS 'TIMING
        (CONS 'HDACK-
         (CONS 'RW-
          (CONS 'STROBE-
               (APPEND (INDICES 'ADDR-OUT 0 32)
                       (APPEND (INDICES 'FM9001-DATA 0 32)
                               (APPEND (INDICES 'FLAGS 0 4)
                                       (APPEND (INDICES 'CNTL-STATE 0 5)
                                               (INDICES 'I-REG 28 4)))))))))))
     'CHIP
     (CONS 'CLK
      (CONS 'TI
       (CONS 'TE
        (CONS 'DTACK-
            (CONS 'RESET-
                  (CONS 'HOLD-
                        (CONS 'DISABLE-REGFILE-
                              (CONS 'TEST-REGFILE-
                                    (APPEND (INDICES 'PC-REG 0 4)
                                            (INDICES 'DATA-BUS 0 32)))))))))))
    '(PULLUP-RW- (RW-BUS) PULLUP (RW-))
    '(PULLUP-STROBE- (STROBE-BUS)
                     PULLUP
                     (STROBE-))
    (LIST 'ADDRESS
          (INDICES 'ADDR-BUS 0 32)
          (INDEX 'V-PULLUP 32)
          (INDICES 'ADDR-OUT 0 32))
    (LIST 'MEM
          (CONS 'DTACK-
                (INDICES 'MEM-DATA 0 32))
          'MEM-32X32
          (CONS 'RW-BUS
                (CONS 'STROBE-BUS
                      (APPEND (INDICES 'ADDR-BUS 0 32)
                              (INDICES 'DATA-BUS 0 32)))))
    (LIST 'DATA-WIRE
          (INDICES 'DATA-WIRE 0 32)
          (INDEX 'V-WIRE 32)
          (APPEND (INDICES 'FM9001-DATA 0 32)
                  (INDICES 'MEM-DATA 0 32)))
    (LIST 'DATA
          (INDICES 'DATA-BUS 0 32)
          (INDEX 'V-PULLUP 32)
          (INDICES 'DATA-WIRE 0 32))))
  (EQUAL (CADDDDR (CHIP-SYSTEM*))
         '(FM9001 MEM))))
\end{verbatim}



\noindent{\sc Event}:   Enable chip-system*; name this event `chip-system*-off'.\index{chip-system*-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable chip-system*\$destructure; name this event `chip-system*\$destructure-off'.\index{chip-system*\$destructure-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*chip-system*; name this event `g*1*chip-system*-off'.\index{g*1*chip-system*-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{chip-system\&} \\  
\=\+{\rm{chip-system\&}}\,({\it{netlist\/}})\index{chip-system\&} \\ 
$=$$\;\;\;\;$(\=\+({\rm{lookup-module}}\,({\tt{'}}{\tt{chip-system}}, {\it{netlist\/}})\index{lookup-module} $=$ {\sc{chip-system*}}\index{chip-system*}) \\ 
$\wedge$$\;\;\;\;${\rm{chip\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip-system}}, {\it{netlist\/}})\index{delete-module})\index{chip\&} \\ 
$\wedge$$\;\;\;\;${\rm{pullup\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip-system}}, {\it{netlist\/}})\index{delete-module})\index{pullup\&} \\ 
$\wedge$$\;\;\;\;${\rm{v-pullup\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip-system}}, {\it{netlist\/}})\index{delete-module}, {\tt{32}})\index{v-pullup\&} \\ 
$\wedge$$\;\;\;\;${\rm{mem-32x32\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip-system}}, {\it{netlist\/}})\index{delete-module})\index{mem-32x32\&} \\ 
$\wedge$$\;\;\;\;${\rm{v-wire\&}}\,({\rm{delete-module}}\,({\tt{'}}{\tt{chip-system}}, {\it{netlist\/}})\index{delete-module}, {\tt{32}})\index{v-wire\&})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable chip-system\&; name this event `chip-system\&-off'.\index{chip-system\&-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{chip-system\$netlist} \\  
\=\+{\sc{chip-system\$netlist}}\index{chip-system\$netlist} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{chip-system*}}\index{chip-system*}, \\ 
\=\+{\sc{pullup\$netlist}}\index{pullup\$netlist} \\ 
$\cup$$\;\;\;\;$(\=\+{\rm{v-pullup\$netlist}}\,({\tt{32}})\index{v-pullup\$netlist} \\ 
$\cup$$\;\;\;\;$(\=\+{\sc{mem-32x32\$netlist}}\index{mem-32x32\$netlist} \\ 
$\cup$$\;\;\;\;$({\rm{v-wire\$netlist}}\,({\tt{32}})\index{v-wire\$netlist} $\cup$ {\sc{chip\$netlist}}\index{chip\$netlist}))\-)\-\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{memory-state-invariant} \\  
\=\+{\rm{memory-state-invariant}}\,({\it{mem-state\/}})\index{memory-state-invariant} \\ 
$=$$\;\;\;\;$(\=\+{\rm{memory-properp}}\,({\tt{32}}, {\tt{32}}, {\rm{car}}\,({\it{mem-state\/}}))\index{memory-properp} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{caddddddr}}\,({\it{mem-state\/}}))\index{properp} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{cadddddddr}}\,({\it{mem-state\/}}))\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cadddddddr}}\,({\it{mem-state\/}}))\index{length} $=$ {\tt{32}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{chip-system-invariant} \\  
\=\+{\rm{chip-system-invariant}}\,({\it{state\/}})\index{chip-system-invariant} \\ 
$=$$\;\;\;\;$(\=\+{\rm{machine-state-invariant}}\,({\rm{car}}\,({\it{state\/}}))\index{machine-state-invariant} \\ 
$\wedge$$\;\;\;\;${\rm{memory-state-invariant}}\,({\rm{cadr}}\,({\it{state\/}}))\index{memory-state-invariant})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-memory-value-for-chip-system\$state \\ \index{equal-memory-value-for-chip-syste!m\$state}
\=\+{\rm{memory-value}}\,({\it{state\/}}, {\it{strobe\/}}, {\it{rw-\/}}, {\it{address\/}}, {\rm{collect-value}}\,({\it{args\/}}, {\it{alist\/}})\index{collect-value})\index{memory-value} \\ 
$=$$\;\;\;\;${\rm{memory-value}}\,({\it{state\/}}, {\it{strobe\/}}, {\it{rw-\/}}, {\it{address\/}}, {\rm{make-list}}\,({\rm{length}}\,({\it{args\/}})\index{length}, {\sc{x}}\index{x})\index{make-list})\index{memory-value}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  chip-system\$state-help \\ \index{chip-system\$state-help}
\=\+(\=\+{\rm{chip-system\&}}\,({\it{netlist\/}})\index{chip-system\&} \\ 
$\wedge$$\;\;\;\;${\rm{chip-system-invariant}}\,({\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-addr\/}})\-, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-, \\ 
{\it{mem-state\/}})\-)\index{chip-system-invariant} \\ 
$\wedge$$\;\;\;\;$({\it{te\/}} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$({\it{disable-regfile-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\it{test-regfile-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{pc-reg-in\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{pc-reg-in\/}})\index{length} $=$ {\tt{4}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\tt{'}}{\tt{chip-system}}, \\ 
{\rm{cons}}\,(\=\+{\it{clk\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{ti\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{te\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{reset-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{hold-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{disable-regfile-\/}}, \\ 
{\rm{cons}}\,({\it{test-regfile-\/}}, {\it{pc-reg-in\/}}))\-)\-)\-)\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,({\it{regs-regs\/}}, {\it{regs-we\/}}, {\it{regs-data\/}}, {\it{regs-addr\/}}), \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-, \\ 
{\it{mem-state\/}})\-, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{f\$write-regs}}\,(\=\+{\rm{we-regs}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-regs}, \\ 
{\rm{regs-address}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{regs-address}, \\ 
{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-addr\/}})\-, \\ 
{\rm{bv}}\,({\rm{f\$core-alu}}\,(\=\+{\rm{alu-c}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-c}, \\ 
{\rm{v-threefix}}\,({\it{a-reg\/}})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\it{b-reg\/}})\index{v-threefix}, \\ 
{\rm{alu-zero}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-zero}, \\ 
{\rm{alu-mpg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-mpg}, \\ 
{\rm{alu-op}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-op}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{f\$core-alu})\index{bv})\-\index{f\$write-regs}, \\ 
{\rm{f\$update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\rm{we-flags}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-flags}, \\ 
{\rm{f\$core-alu}}\,(\=\+{\rm{alu-c}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-c}, \\ 
{\rm{v-threefix}}\,({\it{a-reg\/}})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\it{b-reg\/}})\index{v-threefix}, \\ 
{\rm{alu-zero}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-zero}, \\ 
{\rm{alu-mpg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-mpg}, \\ 
{\rm{alu-op}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-op}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{f\$core-alu})\-\index{f\$update-flags}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-a-reg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-a-reg}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{f-nand}}\,(\=\+{\rm{data-in-select}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{data-in-select}, \\ 
{\rm{f-not}}\,({\it{last-dtack-\/}})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f\$extend-immediate}}\,(\=\+{\rm{select-immediate}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{select-immediate}, \\ 
{\rm{a-immediate}}\,({\rm{v-threefix}}\,({\it{i-reg\/}})\index{v-threefix})\index{a-immediate}, \\ 
{\rm{f\$read-regs}}\,(\=\+{\rm{regs-address}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{regs-address}, \\ 
{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-addr\/}})\-)\-\index{f\$read-regs})\-\index{f\$extend-immediate}, \\ 
{\rm{v-threefix}}\,({\rm{v-wire}}\,(\=\+{\rm{v-pullup}}\,({\rm{v-wire}}\,(\=\+{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\rm{v-threefix}}\,({\it{data-out\/}})\index{v-threefix})\-\index{vft-buf}, \\ 
{\rm{cdr}}\,({\rm{memory-value}}\,(\=\+{\it{mem-state\/}}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{strobe-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{strobe-})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-})\index{f-buf})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{v-pullup}}\,({\rm{vft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{v-threefix}}\,({\it{addr-out\/}})\index{v-threefix})\-\index{vft-buf})\index{v-pullup}, \\ 
{\rm{make-list}}\,(\=\+{\tt{32}}, \\ 
{\sc{x}}\index{x})\-\index{make-list})\-\index{memory-value}))\-\index{v-wire})\index{v-pullup}, \\ 
{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\rm{v-threefix}}\,({\it{data-out\/}})\index{v-threefix})\-\index{vft-buf})\-\index{v-wire})\index{v-threefix})\-\index{fv-if}, \\ 
{\it{a-reg\/}})\-\index{fv-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-b-reg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-b-reg}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{f-nand}}\,(\=\+{\rm{data-in-select}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{data-in-select}, \\ 
{\rm{f-not}}\,({\it{last-dtack-\/}})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f\$extend-immediate}}\,(\=\+{\rm{select-immediate}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{select-immediate}, \\ 
{\rm{a-immediate}}\,({\rm{v-threefix}}\,({\it{i-reg\/}})\index{v-threefix})\index{a-immediate}, \\ 
{\rm{f\$read-regs}}\,(\=\+{\rm{regs-address}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{regs-address}, \\ 
{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-addr\/}})\-)\-\index{f\$read-regs})\-\index{f\$extend-immediate}, \\ 
{\rm{v-threefix}}\,({\rm{v-wire}}\,(\=\+{\rm{v-pullup}}\,({\rm{v-wire}}\,(\=\+{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\rm{v-threefix}}\,({\it{data-out\/}})\index{v-threefix})\-\index{vft-buf}, \\ 
{\rm{cdr}}\,({\rm{memory-value}}\,(\=\+{\it{mem-state\/}}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{strobe-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{strobe-})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-})\index{f-buf})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{v-pullup}}\,({\rm{vft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{v-threefix}}\,({\it{addr-out\/}})\index{v-threefix})\-\index{vft-buf})\index{v-pullup}, \\ 
{\rm{make-list}}\,(\=\+{\tt{32}}, \\ 
{\sc{x}}\index{x})\-\index{make-list})\-\index{memory-value}))\-\index{v-wire})\index{v-pullup}, \\ 
{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\rm{v-threefix}}\,({\it{data-out\/}})\index{v-threefix})\-\index{vft-buf})\-\index{v-wire})\index{v-threefix})\-\index{fv-if}, \\ 
{\it{b-reg\/}})\-\index{fv-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-i-reg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-i-reg}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{f-nand}}\,(\=\+{\rm{data-in-select}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{data-in-select}, \\ 
{\rm{f-not}}\,({\it{last-dtack-\/}})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f\$extend-immediate}}\,(\=\+{\rm{select-immediate}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{select-immediate}, \\ 
{\rm{a-immediate}}\,({\rm{v-threefix}}\,({\it{i-reg\/}})\index{v-threefix})\index{a-immediate}, \\ 
{\rm{f\$read-regs}}\,(\=\+{\rm{regs-address}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{regs-address}, \\ 
{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-addr\/}})\-)\-\index{f\$read-regs})\-\index{f\$extend-immediate}, \\ 
{\rm{v-threefix}}\,({\rm{v-wire}}\,(\=\+{\rm{v-pullup}}\,({\rm{v-wire}}\,(\=\+{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\rm{v-threefix}}\,({\it{data-out\/}})\index{v-threefix})\-\index{vft-buf}, \\ 
{\rm{cdr}}\,({\rm{memory-value}}\,(\=\+{\it{mem-state\/}}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{strobe-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{strobe-})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-})\index{f-buf})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{v-pullup}}\,({\rm{vft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{v-threefix}}\,({\it{addr-out\/}})\index{v-threefix})\-\index{vft-buf})\index{v-pullup}, \\ 
{\rm{make-list}}\,(\=\+{\tt{32}}, \\ 
{\sc{x}}\index{x})\-\index{make-list})\-\index{memory-value}))\-\index{v-wire})\index{v-pullup}, \\ 
{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\rm{v-threefix}}\,({\it{data-out\/}})\index{v-threefix})\-\index{vft-buf})\-\index{v-wire})\index{v-threefix})\-\index{fv-if}, \\ 
{\it{i-reg\/}})\-\index{fv-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-data-out}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-data-out}, \\ 
{\rm{bv}}\,({\rm{f\$core-alu}}\,(\=\+{\rm{alu-c}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-c}, \\ 
{\rm{v-threefix}}\,({\it{a-reg\/}})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\it{b-reg\/}})\index{v-threefix}, \\ 
{\rm{alu-zero}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-zero}, \\ 
{\rm{alu-mpg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-mpg}, \\ 
{\rm{alu-op}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{alu-op}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{f\$core-alu})\index{bv}, \\ 
{\it{data-out\/}})\-\index{fv-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-addr-out}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-addr-out}, \\ 
{\rm{f\$dec-pass}}\,(\=\+{\rm{dec-addr-out}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{dec-addr-out}, \\ 
{\rm{f\$extend-immediate}}\,(\=\+{\rm{select-immediate}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{select-immediate}, \\ 
{\rm{a-immediate}}\,({\rm{v-threefix}}\,({\it{i-reg\/}})\index{v-threefix})\index{a-immediate}, \\ 
{\rm{f\$read-regs}}\,(\=\+{\rm{regs-address}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{regs-address}, \\ 
{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-addr\/}})\-)\-\index{f\$read-regs})\-\index{f\$extend-immediate})\-\index{f\$dec-pass}, \\ 
{\it{addr-out\/}})\-\index{fv-if}, \\ 
{\rm{f-buf}}\,({\it{reset-\/}})\index{f-buf}, \\ 
{\rm{f-or}}\,(\=\+{\rm{strobe-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{strobe-}, \\ 
{\rm{f-buf}}\,({\rm{car}}\,({\rm{memory-value}}\,(\=\+{\it{mem-state\/}}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{strobe-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{strobe-})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-})\index{f-buf})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{v-pullup}}\,({\rm{vft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{v-threefix}}\,({\it{addr-out\/}})\index{v-threefix})\-\index{vft-buf})\index{v-pullup}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-\index{memory-value}))\index{f-buf})\-\index{f-or}, \\ 
{\rm{f-if}}\,(\=\+{\rm{we-hold-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-hold-}, \\ 
{\rm{f-buf}}\,({\it{hold-\/}})\index{f-buf}, \\ 
{\it{last-hold-\/}})\-\index{f-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-pc-reg}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{we-pc-reg}, \\ 
{\it{pc-reg-in\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{fv-if}, \\ 
{\rm{v-threefix}}\,({\rm{f\$next-cntl-state}}\,(\=\+{\rm{f-buf}}\,({\it{last-reset-\/}})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\it{last-dtack-\/}})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\it{last-hold-\/}})\index{f-buf}, \\ 
{\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-}, \\ 
{\rm{state}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{state}, \\ 
{\rm{v-threefix}}\,({\it{i-reg\/}})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\it{flags\/}})\index{v-threefix}, \\ 
{\rm{v-threefix}}\,({\it{last-pc-reg\/}})\index{v-threefix}, \\ 
{\rm{regs-address}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{regs-address})\-\index{f\$next-cntl-state})\index{v-threefix})\-, \\ 
{\rm{next-memory-state}}\,(\=\+{\it{mem-state\/}}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{strobe-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{strobe-})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-})\index{f-buf})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{v-pullup}}\,({\rm{vft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{v-threefix}}\,({\it{addr-out\/}})\index{v-threefix})\-\index{vft-buf})\index{v-pullup}, \\ 
{\rm{v-pullup}}\,({\rm{v-wire}}\,(\=\+{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\rm{v-threefix}}\,({\it{data-out\/}})\index{v-threefix})\-\index{vft-buf}, \\ 
{\rm{cdr}}\,({\rm{memory-value}}\,(\=\+{\it{mem-state\/}}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{strobe-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{strobe-})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\rm{rw-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{rw-})\index{f-buf})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{v-pullup}}\,({\rm{vft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\rm{v-threefix}}\,({\it{cntl-state\/}})\index{v-threefix})\index{hdack-})\index{f-buf}, \\ 
{\rm{v-threefix}}\,({\it{addr-out\/}})\index{v-threefix})\-\index{vft-buf})\index{v-pullup}, \\ 
{\rm{make-list}}\,(\=\+{\tt{32}}, \\ 
{\sc{x}}\index{x})\-\index{make-list})\-\index{memory-value}))\-\index{v-wire})\index{v-pullup})\-\index{next-memory-state})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable chip-system\$state-help; name this event `chip-system\$state-help-off'.\index{chip-system\$state-help-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  chip-system\$state \\ \index{chip-system\$state}
\=\+(\=\+{\rm{chip-system\&}}\,({\it{netlist\/}})\index{chip-system\&} \\ 
$\wedge$$\;\;\;\;${\rm{chip-system-invariant}}\,({\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-addr\/}})\-, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-, \\ 
{\it{mem-state\/}})\-)\index{chip-system-invariant} \\ 
$\wedge$$\;\;\;\;$({\it{te\/}} $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$({\it{disable-regfile-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\it{test-regfile-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{pc-reg-in\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{pc-reg-in\/}})\index{length} $=$ {\tt{4}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\tt{'}}{\tt{chip-system}}, \\ 
{\rm{cons}}\,(\=\+{\it{clk\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{ti\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{te\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{reset-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{hold-\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{disable-regfile-\/}}, \\ 
{\rm{cons}}\,({\it{test-regfile-\/}}, {\it{pc-reg-in\/}}))\-)\-)\-)\-)\-)\-, \\ 
{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,({\it{regs-regs\/}}, {\it{regs-we\/}}, {\it{regs-data\/}}, {\it{regs-addr\/}}), \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-, \\ 
{\it{mem-state\/}})\-, \\ 
{\it{netlist\/}})\-\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{fm9001-next-state}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-addr\/}})\-, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-, \\ 
{\it{mem-state\/}})\-, \\ 
{\rm{cons}}\,({\it{reset-\/}}, {\rm{cons}}\,({\it{hold-\/}}, {\it{pc-reg-in\/}})))\-\index{fm9001-next-state})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable chip-system\$state; name this event `chip-system\$state-off'.\index{chip-system\$state-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  next-memory-state-preserves-memory-invariant \\ \index{next-memory-state-preserves-mem!ory-invariant}
\=\+(\=\+{\rm{memory-state-invariant}}\,({\it{mem-state\/}})\index{memory-state-invariant} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{data\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{address\/}})\index{length} $=$ {\tt{32}}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{memory-state-invariant}}\,({\rm{next-memory-state}}\,(\=\+{\it{mem-state\/}}, \\ 
{\it{strobe-\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{address\/}}, \\ 
{\it{data\/}})\-\index{next-memory-state})\index{memory-state-invariant}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  memory-properp-dual-port-ram-state-crock \\ \index{memory-properp-dual-port-ram-st!ate-crock}
\=\+(\=\+{\rm{memory-properp}}\,({\tt{4}}, {\tt{32}}, {\it{regs\/}})\index{memory-properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-address\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-address\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{data\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data\/}})\index{length} $=$ {\tt{32}}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{memory-properp}}\,(\=\+{\tt{4}}, \\ 
{\tt{32}}, \\ 
{\rm{dual-port-ram-state}}\,(\=\+{\tt{32}}, \\ 
{\tt{4}}, \\ 
{\rm{append}}\,(\=\+{\it{a-address\/}}, \\ 
{\rm{append}}\,(\=\+{\it{b-address\/}}, \\ 
{\rm{cons}}\,({\it{we\/}}, {\it{data\/}}))\-)\-, \\ 
{\it{regs\/}})\-\index{dual-port-ram-state})\-\index{memory-properp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  all-ramp-mem-dual-port-ram-state-crock \\ \index{all-ramp-mem-dual-port-ram-state!-crock}
\=\+(\=\+{\rm{all-ramp-mem}}\,({\tt{4}}, {\it{regs\/}})\index{all-ramp-mem} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-address\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-address\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{data\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data\/}})\index{length} $=$ {\tt{32}}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{all-ramp-mem}}\,(\=\+{\tt{4}}, \\ 
{\rm{dual-port-ram-state}}\,(\=\+{\tt{32}}, \\ 
{\tt{4}}, \\ 
{\rm{append}}\,(\=\+{\it{a-address\/}}, \\ 
{\rm{append}}\,(\=\+{\it{b-address\/}}, \\ 
{\rm{cons}}\,({\it{we\/}}, {\it{data\/}}))\-)\-, \\ 
{\it{regs\/}})\-\index{dual-port-ram-state})\-\index{all-ramp-mem}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fm9001-preserves-chip-system-invariant \\ \index{fm9001-preserves-chip-system-inv!ariant}
\=\+(\=\+{\rm{chip-system-invariant}}\,({\it{state\/}})\index{chip-system-invariant} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{pc-reg-input}}\,({\it{inputs\/}})\index{pc-reg-input})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{pc-reg-input}}\,({\it{inputs\/}})\index{pc-reg-input})\index{length} $=$ {\tt{4}}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{chip-system-invariant}}\,({\rm{fm9001-next-state}}\,({\it{state\/}}, {\it{inputs\/}})\index{fm9001-next-state})\index{chip-system-invariant}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{chip-system-input-invariant} \\  
\=\+{\rm{chip-system-input-invariant}}\,({\it{inputs\/}})\index{chip-system-input-invariant} \\ 
$=$$\;\;\;\;$(\=\+({\rm{caddr}}\,({\it{inputs\/}}) $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadddddr}}\,({\it{inputs\/}}) $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddddddr}}\,({\it{inputs\/}}) $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{cdddddddr}}\,({\it{inputs\/}}))\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cdddddddr}}\,({\it{inputs\/}}))\index{length} $=$ {\tt{4}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-chip-system-input-invariant \\ \index{rewrite-chip-system-input-invari!ant}
\=\+{\rm{chip-system-input-invariant}}\,({\it{inputs\/}})\index{chip-system-input-invariant} \\ 
$=$$\;\;\;\;$(\=\+({\it{inputs\/}} $=$ {\rm{cons}}\,(\=\+{\rm{car}}\,({\it{inputs\/}}), \\ 
{\rm{cons}}\,(\=\+{\rm{cadr}}\,({\it{inputs\/}}), \\ 
{\rm{cons}}\,(\=\+{\rm{caddr}}\,({\it{inputs\/}}), \\ 
{\rm{cons}}\,(\=\+{\rm{cadddr}}\,({\it{inputs\/}}), \\ 
{\rm{cons}}\,(\=\+{\rm{caddddr}}\,({\it{inputs\/}}), \\ 
{\rm{cons}}\,(\=\+{\rm{cadddddr}}\,({\it{inputs\/}}), \\ 
{\rm{cons}}\,(\=\+{\rm{caddddddr}}\,({\it{inputs\/}}), \\ 
{\rm{cdddddddr}}\,({\it{inputs\/}}))\-)\-)\-)\-)\-)\-)\-) \\ 
$\wedge$$\;\;\;\;$({\rm{caddr}}\,({\it{inputs\/}}) $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadddddr}}\,({\it{inputs\/}}) $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddddddr}}\,({\it{inputs\/}}) $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{cdddddddr}}\,({\it{inputs\/}}))\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cdddddddr}}\,({\it{inputs\/}}))\index{length} $=$ {\tt{4}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{chip-system-operating-inputs-p} \\  
\=\+{\rm{chip-system-operating-inputs-p}}\,({\it{inputs\/}}, {\it{n\/}})\index{chip-system-operating-inputs-p} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }\=\+{\rm{chip-system-input-invariant}}\,({\rm{car}}\,({\it{inputs\/}}))\index{chip-system-input-invariant} \\ 
$\wedge$$\;\;\;\;${\rm{chip-system-operating-inputs-p}}\,({\rm{cdr}}\,({\it{inputs\/}}), {\it{n\/}} $-\;1$)\index{chip-system-operating-inputs-p}\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable chip-system-operating-inputs-p; name this event `chip-system-operating-inputs-p-off'.\index{chip-system-operating-inputs-p-!off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-chip-system-operating-inputs-p \\ \index{open-chip-system-operating-input!s-p}
\=\+(({\it{n\/}} $\simeq {\tt{0}}$) $\rightarrow$ ({\rm{chip-system-operating-inputs-p}}\,({\it{inputs\/}}, {\it{n\/}})\index{chip-system-operating-inputs-p} $=$ {\bf{t}})) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{chip-system-operating-inputs-p}}\,({\it{inputs\/}}, {\it{n\/}})\index{chip-system-operating-inputs-p} \\ 
$=$$\;\;\;\;$(\=\+{\rm{chip-system-input-invariant}}\,({\rm{car}}\,({\it{inputs\/}}))\index{chip-system-input-invariant} \\ 
$\wedge$$\;\;\;\;${\rm{chip-system-operating-inputs-p}}\,(\=\+{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{chip-system-operating-inputs-p})\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{map-up-1-input} \\  
\=\+{\rm{map-up-1-input}}\,({\it{inputs\/}})\index{map-up-1-input} \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\rm{cadddr}}\,({\it{inputs\/}}), {\rm{cons}}\,({\rm{caddddr}}\,({\it{inputs\/}}), {\rm{cdddddddr}}\,({\it{inputs\/}})))\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{map-up-inputs} \\  
\=\+{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{inputs\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{nil}} \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{map-up-1-input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{map-up-1-input}, \\ 
{\rm{map-up-inputs}}\,({\rm{cdr}}\,({\it{inputs\/}}))\index{map-up-inputs})\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable map-up-inputs; name this event `map-up-inputs-off'.\index{map-up-inputs-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-map-up-inputs \\ \index{open-map-up-inputs}
\=\+(({\it{inputs\/}} $\simeq\;${{\bf{nil}}}${}$) $\rightarrow$ ({\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs} $=$ {\bf{nil}})) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{listp}}\,({\it{inputs\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{map-up-1-input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{map-up-1-input}, \\ 
{\rm{map-up-inputs}}\,({\rm{cdr}}\,({\it{inputs\/}}))\index{map-up-inputs})\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  chip-system=fm9001\$step \\ \index{chip-system=fm9001\$step}
\=\+(\=\+{\rm{chip-system\&}}\,({\it{netlist\/}})\index{chip-system\&} \\ 
$\wedge$$\;\;\;\;${\rm{fm9001-state-structure}}\,({\it{state\/}})\index{fm9001-state-structure} \\ 
$\wedge$$\;\;\;\;${\rm{chip-system-invariant}}\,({\it{state\/}})\index{chip-system-invariant} \\ 
$\wedge$$\;\;\;\;${\rm{chip-system-input-invariant}}\,({\it{inputs\/}})\index{chip-system-input-invariant})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{chip-system}}, {\it{inputs\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{fm9001-next-state}}\,({\it{state\/}}, {\rm{map-up-1-input}}\,({\it{inputs\/}})\index{map-up-1-input})\index{fm9001-next-state})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable chip-system=fm9001\$step; name this event `chip-system=fm9001\$step-off'.\index{chip-system=fm9001\$step-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{chip-system=run-fm9001\$inducti!on} \\  
\=\+{\rm{chip-system=run-fm9001\$induction}}\,({\it{state\/}}, {\it{inputs\/}}, {\it{fm9001-inputs\/}}, {\it{n\/}})\index{chip-system=run-fm9001\$inducti!on} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{chip-system=run-fm9001\$induction}}\,(\=\+{\rm{fm9001-next-state}}\,(\=\+{\it{state\/}}, \\ 
{\rm{car}}\,({\it{fm9001-inputs\/}}))\-\index{fm9001-next-state}, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\rm{cdr}}\,({\it{fm9001-inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{chip-system=run-fm9001\$inducti!on}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  chip-system=run-fm9001 \\ \index{chip-system=run-fm9001}
\=\+(\=\+{\rm{chip-system\&}}\,({\it{netlist\/}})\index{chip-system\&} \\ 
$\wedge$$\;\;\;\;${\rm{fm9001-state-structure}}\,({\it{state\/}})\index{fm9001-state-structure} \\ 
$\wedge$$\;\;\;\;${\rm{chip-system-invariant}}\,({\it{state\/}})\index{chip-system-invariant} \\ 
$\wedge$$\;\;\;\;${\rm{chip-system-operating-inputs-p}}\,({\it{inputs\/}}, {\it{n\/}})\index{chip-system-operating-inputs-p} \\ 
$\wedge$$\;\;\;\;$({\it{fm9001-inputs\/}} $=$ {\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{simulate-dual-eval-2}}\,({\tt{'}}{\tt{chip-system}}, {\it{inputs\/}}, {\it{state\/}}, {\it{netlist\/}}, {\it{n\/}})\index{simulate-dual-eval-2} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,({\it{state\/}}, {\it{fm9001-inputs\/}}, {\it{n\/}})\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{run-inputs-p} \\  
\=\+{\rm{run-inputs-p}}\,({\it{inputs\/}}, {\it{n\/}})\index{run-inputs-p} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }\=\+({\rm{reset--input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{reset--input} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{pc-reg-input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{pc-reg-input})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{pc-reg-input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{pc-reg-input})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\rm{cdr}}\,({\it{inputs\/}}), {\it{n\/}} $-\;1$)\index{run-inputs-p}\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable run-inputs-p; name this event `run-inputs-p-off'.\index{run-inputs-p-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-run-inputs-p \\ \index{open-run-inputs-p}
\=\+(({\it{n\/}} $\simeq {\tt{0}}$) $\rightarrow$ ({\rm{run-inputs-p}}\,({\it{inputs\/}}, {\it{n\/}})\index{run-inputs-p} $=$ {\bf{t}})) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-inputs-p}}\,({\it{inputs\/}}, {\it{n\/}})\index{run-inputs-p} \\ 
$=$$\;\;\;\;$(\=\+({\rm{reset--input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{reset--input} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{pc-reg-input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{pc-reg-input})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{pc-reg-input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{pc-reg-input})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\rm{cdr}}\,({\it{inputs\/}}), {\it{n\/}} $-\;1$)\index{run-inputs-p})\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  run-inputs-p-plus \\ \index{run-inputs-p-plus}
\=\+{\rm{run-inputs-p}}\,({\it{inputs\/}}, {\it{n\/}} $+$ {\it{m\/}})\index{run-inputs-p} \\ 
$=$$\;\;\;\;$({\rm{run-inputs-p}}\,({\it{inputs\/}}, {\it{n\/}})\index{run-inputs-p} $\wedge$ {\rm{run-inputs-p}}\,({\rm{nthcdr}}\,({\it{n\/}}, {\it{inputs\/}})\index{nthcdr}, {\it{m\/}})\index{run-inputs-p})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  run-inputs-p-1 \\ \index{run-inputs-p-1}
({\rm{run-inputs-p}}\,({\it{inputs\/}}, {\it{n\/}})\index{run-inputs-p} $\wedge$ ({\it{n\/}} $\not\simeq {\tt{0}}$)) $\rightarrow$ {\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  open-run-inputs-p-add1 \\ \index{open-run-inputs-p-add1}
\=\+{\rm{run-inputs-p}}\,({\it{inputs\/}}, $1\;+$ {\it{n\/}})\index{run-inputs-p} \\ 
$=$$\;\;\;\;$(\=\+({\rm{reset--input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{reset--input} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{pc-reg-input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{pc-reg-input})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{pc-reg-input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{pc-reg-input})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\rm{cdr}}\,({\it{inputs\/}}), {\it{n\/}})\index{run-inputs-p})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{regfile-okp} \\  
\=\+{\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$=$$\;\;\;\;$(\=\+({\rm{length}}\,({\it{regs\/}})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{4}}, {\tt{32}}, {\rm{car}}\,({\it{regs\/}}))\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{all-ramp-mem}}\,({\tt{4}}, {\rm{car}}\,({\it{regs\/}}))\index{all-ramp-mem} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{cadr}}\,({\it{regs\/}}))\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\rm{bvp}}\,({\rm{caddr}}\,({\it{regs\/}}))\index{bvp} $\wedge$ ({\rm{length}}\,({\rm{caddr}}\,({\it{regs\/}}))\index{length} $=$ {\tt{32}})) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cadddr}}\,({\it{regs\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cadddr}}\,({\it{regs\/}}))\index{length} $=$ {\tt{4}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-fm9001-next-state-for-step-lemmas \\ \index{rewrite-fm9001-next-state-for-step!-lemmas}
\=\+(\=\+{\rm{bvp}}\,({\it{flags\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{i-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{last-reset-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{last-dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{last-hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{last-pc-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{cntl-state\/}})\index{bvp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{fm9001-next-state}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-, \\ 
{\it{mem-state\/}})\-, \\ 
{\it{external-inputs\/}})\-\index{fm9001-next-state} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{f\$write-regs}}\,(\=\+{\rm{we-regs}}\,({\it{cntl-state\/}})\index{we-regs}, \\ 
{\rm{regs-address}}\,({\it{cntl-state\/}})\index{regs-address}, \\ 
{\it{regs\/}}, \\ 
{\rm{bv}}\,({\rm{f\$core-alu}}\,(\=\+{\rm{alu-c}}\,({\it{cntl-state\/}})\index{alu-c}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\rm{alu-zero}}\,({\it{cntl-state\/}})\index{alu-zero}, \\ 
{\rm{alu-mpg}}\,({\it{cntl-state\/}})\index{alu-mpg}, \\ 
{\rm{alu-op}}\,({\it{cntl-state\/}})\index{alu-op}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{f\$core-alu})\index{bv})\-\index{f\$write-regs}, \\ 
{\rm{f\$update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\rm{we-flags}}\,({\it{cntl-state\/}})\index{we-flags}, \\ 
{\rm{f\$core-alu}}\,(\=\+{\rm{alu-c}}\,({\it{cntl-state\/}})\index{alu-c}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\rm{alu-zero}}\,({\it{cntl-state\/}})\index{alu-zero}, \\ 
{\rm{alu-mpg}}\,({\it{cntl-state\/}})\index{alu-mpg}, \\ 
{\rm{alu-op}}\,({\it{cntl-state\/}})\index{alu-op}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{f\$core-alu})\-\index{f\$update-flags}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-a-reg}}\,({\it{cntl-state\/}})\index{we-a-reg}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{f-nand}}\,(\=\+{\rm{data-in-select}}\,({\it{cntl-state\/}})\index{data-in-select}, \\ 
{\rm{f-not}}\,({\it{last-dtack-\/}})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f\$extend-immediate}}\,(\=\+{\rm{select-immediate}}\,({\it{cntl-state\/}})\index{select-immediate}, \\ 
{\rm{a-immediate}}\,({\it{i-reg\/}})\index{a-immediate}, \\ 
{\rm{f\$read-regs}}\,(\=\+{\rm{regs-address}}\,({\it{cntl-state\/}})\index{regs-address}, \\ 
{\it{regs\/}})\-\index{f\$read-regs})\-\index{f\$extend-immediate}, \\ 
{\rm{v-threefix}}\,({\rm{v-wire}}\,(\=\+{\rm{v-pullup}}\,({\rm{v-wire}}\,(\=\+{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\it{cntl-state\/}})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\it{data-out\/}})\-\index{vft-buf}, \\ 
{\rm{cdr}}\,({\rm{memory-value}}\,(\=\+{\it{mem-state\/}}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\it{cntl-state\/}})\index{hdack-})\index{f-buf}, \\ 
{\rm{strobe-}}\,({\it{cntl-state\/}})\index{strobe-})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\it{cntl-state\/}})\index{hdack-})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\rm{rw-}}\,({\it{cntl-state\/}})\index{rw-})\index{f-buf})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{v-pullup}}\,({\rm{vft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\it{cntl-state\/}})\index{hdack-})\index{f-buf}, \\ 
{\it{addr-out\/}})\-\index{vft-buf})\index{v-pullup}, \\ 
{\rm{make-list}}\,(\=\+{\tt{32}}, \\ 
{\sc{x}}\index{x})\-\index{make-list})\-\index{memory-value}))\-\index{v-wire})\index{v-pullup}, \\ 
{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\it{cntl-state\/}})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\it{data-out\/}})\-\index{vft-buf})\-\index{v-wire})\index{v-threefix})\-\index{fv-if}, \\ 
{\it{a-reg\/}})\-\index{fv-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-b-reg}}\,({\it{cntl-state\/}})\index{we-b-reg}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{f-nand}}\,(\=\+{\rm{data-in-select}}\,({\it{cntl-state\/}})\index{data-in-select}, \\ 
{\rm{f-not}}\,({\it{last-dtack-\/}})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f\$extend-immediate}}\,(\=\+{\rm{select-immediate}}\,({\it{cntl-state\/}})\index{select-immediate}, \\ 
{\rm{a-immediate}}\,({\it{i-reg\/}})\index{a-immediate}, \\ 
{\rm{f\$read-regs}}\,(\=\+{\rm{regs-address}}\,({\it{cntl-state\/}})\index{regs-address}, \\ 
{\it{regs\/}})\-\index{f\$read-regs})\-\index{f\$extend-immediate}, \\ 
{\rm{v-threefix}}\,({\rm{v-wire}}\,(\=\+{\rm{v-pullup}}\,({\rm{v-wire}}\,(\=\+{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\it{cntl-state\/}})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\it{data-out\/}})\-\index{vft-buf}, \\ 
{\rm{cdr}}\,({\rm{memory-value}}\,(\=\+{\it{mem-state\/}}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\it{cntl-state\/}})\index{hdack-})\index{f-buf}, \\ 
{\rm{strobe-}}\,({\it{cntl-state\/}})\index{strobe-})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\it{cntl-state\/}})\index{hdack-})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\rm{rw-}}\,({\it{cntl-state\/}})\index{rw-})\index{f-buf})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{v-pullup}}\,({\rm{vft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\it{cntl-state\/}})\index{hdack-})\index{f-buf}, \\ 
{\it{addr-out\/}})\-\index{vft-buf})\index{v-pullup}, \\ 
{\rm{make-list}}\,(\=\+{\tt{32}}, \\ 
{\sc{x}}\index{x})\-\index{make-list})\-\index{memory-value}))\-\index{v-wire})\index{v-pullup}, \\ 
{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\it{cntl-state\/}})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\it{data-out\/}})\-\index{vft-buf})\-\index{v-wire})\index{v-threefix})\-\index{fv-if}, \\ 
{\it{b-reg\/}})\-\index{fv-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-i-reg}}\,({\it{cntl-state\/}})\index{we-i-reg}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{f-nand}}\,(\=\+{\rm{data-in-select}}\,({\it{cntl-state\/}})\index{data-in-select}, \\ 
{\rm{f-not}}\,({\it{last-dtack-\/}})\index{f-not})\-\index{f-nand}, \\ 
{\rm{f\$extend-immediate}}\,(\=\+{\rm{select-immediate}}\,({\it{cntl-state\/}})\index{select-immediate}, \\ 
{\rm{a-immediate}}\,({\it{i-reg\/}})\index{a-immediate}, \\ 
{\rm{f\$read-regs}}\,(\=\+{\rm{regs-address}}\,({\it{cntl-state\/}})\index{regs-address}, \\ 
{\it{regs\/}})\-\index{f\$read-regs})\-\index{f\$extend-immediate}, \\ 
{\rm{v-threefix}}\,({\rm{v-wire}}\,(\=\+{\rm{v-pullup}}\,({\rm{v-wire}}\,(\=\+{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\it{cntl-state\/}})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\it{data-out\/}})\-\index{vft-buf}, \\ 
{\rm{cdr}}\,({\rm{memory-value}}\,(\=\+{\it{mem-state\/}}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\it{cntl-state\/}})\index{hdack-})\index{f-buf}, \\ 
{\rm{strobe-}}\,({\it{cntl-state\/}})\index{strobe-})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\it{cntl-state\/}})\index{hdack-})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\rm{rw-}}\,({\it{cntl-state\/}})\index{rw-})\index{f-buf})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{v-pullup}}\,({\rm{vft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\it{cntl-state\/}})\index{hdack-})\index{f-buf}, \\ 
{\it{addr-out\/}})\-\index{vft-buf})\index{v-pullup}, \\ 
{\rm{make-list}}\,(\=\+{\tt{32}}, \\ 
{\sc{x}}\index{x})\-\index{make-list})\-\index{memory-value}))\-\index{v-wire})\index{v-pullup}, \\ 
{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\it{cntl-state\/}})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\it{data-out\/}})\-\index{vft-buf})\-\index{v-wire})\index{v-threefix})\-\index{fv-if}, \\ 
{\it{i-reg\/}})\-\index{fv-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-data-out}}\,({\it{cntl-state\/}})\index{we-data-out}, \\ 
{\rm{bv}}\,({\rm{f\$core-alu}}\,(\=\+{\rm{alu-c}}\,({\it{cntl-state\/}})\index{alu-c}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\rm{alu-zero}}\,({\it{cntl-state\/}})\index{alu-zero}, \\ 
{\rm{alu-mpg}}\,({\it{cntl-state\/}})\index{alu-mpg}, \\ 
{\rm{alu-op}}\,({\it{cntl-state\/}})\index{alu-op}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{f\$core-alu})\index{bv}, \\ 
{\it{data-out\/}})\-\index{fv-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-addr-out}}\,({\it{cntl-state\/}})\index{we-addr-out}, \\ 
{\rm{f\$dec-pass}}\,(\=\+{\rm{dec-addr-out}}\,({\it{cntl-state\/}})\index{dec-addr-out}, \\ 
{\rm{f\$extend-immediate}}\,(\=\+{\rm{select-immediate}}\,({\it{cntl-state\/}})\index{select-immediate}, \\ 
{\rm{a-immediate}}\,({\it{i-reg\/}})\index{a-immediate}, \\ 
{\rm{f\$read-regs}}\,(\=\+{\rm{regs-address}}\,({\it{cntl-state\/}})\index{regs-address}, \\ 
{\it{regs\/}})\-\index{f\$read-regs})\-\index{f\$extend-immediate})\-\index{f\$dec-pass}, \\ 
{\it{addr-out\/}})\-\index{fv-if}, \\ 
{\rm{f-buf}}\,({\rm{reset--input}}\,({\it{external-inputs\/}})\index{reset--input})\index{f-buf}, \\ 
{\rm{f-or}}\,(\=\+{\rm{strobe-}}\,({\it{cntl-state\/}})\index{strobe-}, \\ 
{\rm{f-buf}}\,({\rm{car}}\,({\rm{memory-value}}\,(\=\+{\it{mem-state\/}}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\it{cntl-state\/}})\index{hdack-})\index{f-buf}, \\ 
{\rm{strobe-}}\,({\it{cntl-state\/}})\index{strobe-})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\it{cntl-state\/}})\index{hdack-})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\rm{rw-}}\,({\it{cntl-state\/}})\index{rw-})\index{f-buf})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{v-pullup}}\,({\rm{vft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\it{cntl-state\/}})\index{hdack-})\index{f-buf}, \\ 
{\it{addr-out\/}})\-\index{vft-buf})\index{v-pullup}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-\index{memory-value}))\index{f-buf})\-\index{f-or}, \\ 
{\rm{f-if}}\,(\=\+{\rm{we-hold-}}\,({\it{cntl-state\/}})\index{we-hold-}, \\ 
{\rm{f-buf}}\,({\rm{hold--input}}\,({\it{external-inputs\/}})\index{hold--input})\index{f-buf}, \\ 
{\it{last-hold-\/}})\-\index{f-if}, \\ 
{\rm{fv-if}}\,(\=\+{\rm{we-pc-reg}}\,({\it{cntl-state\/}})\index{we-pc-reg}, \\ 
{\rm{pc-reg-input}}\,({\it{external-inputs\/}})\index{pc-reg-input}, \\ 
{\it{last-pc-reg\/}})\-\index{fv-if}, \\ 
{\rm{v-threefix}}\,({\rm{f\$next-cntl-state}}\,(\=\+{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\rm{rw-}}\,({\it{cntl-state\/}})\index{rw-}, \\ 
{\rm{state}}\,({\it{cntl-state\/}})\index{state}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\rm{regs-address}}\,({\it{cntl-state\/}})\index{regs-address})\-\index{f\$next-cntl-state})\index{v-threefix})\-, \\ 
{\rm{next-memory-state}}\,(\=\+{\it{mem-state\/}}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\it{cntl-state\/}})\index{hdack-})\index{f-buf}, \\ 
{\rm{strobe-}}\,({\it{cntl-state\/}})\index{strobe-})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\it{cntl-state\/}})\index{hdack-})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\rm{rw-}}\,({\it{cntl-state\/}})\index{rw-})\index{f-buf})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{v-pullup}}\,({\rm{vft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\it{cntl-state\/}})\index{hdack-})\index{f-buf}, \\ 
{\it{addr-out\/}})\-\index{vft-buf})\index{v-pullup}, \\ 
{\rm{v-pullup}}\,({\rm{v-wire}}\,(\=\+{\rm{vft-buf}}\,(\=\+{\rm{f-not}}\,({\rm{f-buf}}\,({\rm{rw-}}\,({\it{cntl-state\/}})\index{rw-})\index{f-buf})\index{f-not}, \\ 
{\it{data-out\/}})\-\index{vft-buf}, \\ 
{\rm{cdr}}\,({\rm{memory-value}}\,(\=\+{\it{mem-state\/}}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\it{cntl-state\/}})\index{hdack-})\index{f-buf}, \\ 
{\rm{strobe-}}\,({\it{cntl-state\/}})\index{strobe-})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{f-pullup}}\,({\rm{ft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\it{cntl-state\/}})\index{hdack-})\index{f-buf}, \\ 
{\rm{f-buf}}\,({\rm{rw-}}\,({\it{cntl-state\/}})\index{rw-})\index{f-buf})\-\index{ft-buf})\index{f-pullup}, \\ 
{\rm{v-pullup}}\,({\rm{vft-buf}}\,(\=\+{\rm{f-buf}}\,({\rm{hdack-}}\,({\it{cntl-state\/}})\index{hdack-})\index{f-buf}, \\ 
{\it{addr-out\/}})\-\index{vft-buf})\index{v-pullup}, \\ 
{\rm{make-list}}\,(\=\+{\tt{32}}, \\ 
{\sc{x}}\index{x})\-\index{make-list})\-\index{memory-value}))\-\index{v-wire})\index{v-pullup})\-\index{next-memory-state})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fetch0\$step0 \\ \index{fetch0\$step0}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_fetch0})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\rm{read-regs}}\,({\it{last-pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\rm{read-regs}}\,({\it{last-pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\rm{f-buf}}\,({\rm{f-buf}}\,({\rm{hold--input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{hold--input})\index{f-buf})\index{f-buf}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch1}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch1})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fetch0\$step1 \\ \index{fetch0\$step1}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_fetch0})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\rm{read-regs}}\,({\it{last-pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\rm{read-regs}}\,({\it{last-pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\rm{f-buf}}\,({\rm{f-buf}}\,({\rm{hold--input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{hold--input})\index{f-buf})\index{f-buf}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch1}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch1})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fetch0\$step2 \\ \index{fetch0\$step2}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{f}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\it{mem-count\/}} $\simeq {\tt{0}}$))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch0}}\,(\=\+{\bf{f}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_fetch0})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{2}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{f}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{data-out\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\rm{read-regs}}\,({\it{last-pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\rm{read-regs}}\,({\it{last-pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\rm{f-buf}}\,({\rm{f-buf}}\,({\rm{hold--input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{hold--input})\index{f-buf})\index{f-buf}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch1}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch1})\-, \\ 
{\rm{list}}\,(\=\+{\rm{write-mem}}\,({\it{addr-out\/}}, {\it{mem\/}}, {\it{data-out\/}})\index{write-mem}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{data-out\/}})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fetch1\$step \\ \index{fetch1\$step}
\=\+(\=\+{\rm{cv-hyps}}\,({\it{last-rw-\/}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{last-rw-\/}})\index{boolp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch1}}\,(\=\+{\it{last-rw-\/}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_fetch1})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\it{last-rw-\/}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{if*}}\,(\=\+{\it{hold-\/}}, \\ 
{\rm{cv\_fetch2}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch2}, \\ 
{\rm{cv\_hold0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_hold0})\-\index{if*})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fetch2\$step \\ \index{fetch2\$step}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch2}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_fetch2})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{car}}\,({\it{clock\/}}) $\simeq {\tt{0}}$ \\ 
{\bf then }{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{regs\/}}, \\ 
{\rm{v-inc}}\,({\it{a-reg\/}})\index{v-inc})\-\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch3}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch3})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\rm{cdr}}\,({\it{clock\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001} \\ 
{\bf else }{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{regs\/}}, \\ 
{\rm{v-inc}}\,({\it{a-reg\/}})\index{v-inc})\-\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch3}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch3})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\rm{cdr}}\,({\it{clock\/}}), \\ 
{\rm{car}}\,({\it{clock\/}}) $-\;1$, \\ 
{\bf{f}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fetch3\$step0 \\ \index{fetch3\$step0}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\bf{f}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\it{mem-count\/}} $\simeq {\tt{0}}$))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch3}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_fetch3})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{1}}, {\it{clock\/}}, {\it{mem-count\/}}, {\bf{t}}, {\bf{t}}, {\it{addr-out\/}}, {\it{last-data\/}}))\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\rm{read-mem}}\,({\it{addr-out\/}}, {\it{mem\/}})\index{read-mem}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_decode}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_decode})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fetch3\$step1 \\ \index{fetch3\$step1}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\bf{t}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch3}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_fetch3})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{1}}, {\it{clock\/}}, {\it{mem-count\/}}, {\bf{f}}, {\bf{t}}, {\it{addr-out\/}}, {\it{last-data\/}}))\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{mem-count\/}} $\simeq {\tt{0}}$ \\ 
{\bf then }{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\rm{read-regs}}\,({\it{last-pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch3}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch3})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001} \\ 
{\bf else }{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\rm{read-regs}}\,({\it{last-pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch3}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch3})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}} $-\;1$, \\ 
{\bf{f}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  decode\$step \\ \index{decode\$step}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_decode}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_decode})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{store-resultp}}\,(\=\+{\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, \\ 
{\it{flags\/}})\-\index{store-resultp}, \\ 
{\rm{set-some-flags}}\,({\rm{set-flags}}\,({\it{i-reg\/}})\index{set-flags})\index{set-some-flags})\-\index{or*}, \\ 
{\rm{if*}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p}, \\ 
{\rm{reg-direct-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{reg-direct-p})\-\index{or*}, \\ 
{\rm{if*}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{reg-direct-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{reg-direct-p}, \\ 
{\rm{unary-op-code-p}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{unary-op-code-p})\-\index{or*}, \\ 
{\rm{cv\_rega}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_rega}, \\ 
{\rm{cv\_readb0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_readb0})\-\index{if*}, \\ 
{\rm{cv\_reada0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_reada0})\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{and*}}\,(\=\+{\rm{not*}}\,({\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p})\index{not*}, \\ 
{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{post-inc-p})\-\index{or*})\-\index{and*}, \\ 
{\rm{cv\_sefa0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_sefa0}, \\ 
{\rm{if*}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{post-inc-p})\-\index{or*}, \\ 
{\rm{cv\_sefb0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_sefb0}, \\ 
{\rm{cv\_fetch0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch0})\-\index{if*})\-\index{if*})\-\index{if*})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rega\$step \\ \index{rega\$step}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_rega}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_rega})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{a-immediate-p}}\,({\it{last-i-reg\/}})\index{a-immediate-p}, \\ 
{\rm{sign-extend}}\,({\rm{a-immediate}}\,({\it{i-reg\/}})\index{a-immediate}, {\tt{32}})\index{sign-extend}, \\ 
{\rm{read-regs}}\,({\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, {\it{regs\/}})\index{read-regs})\-\index{if*}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{reg-direct-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{reg-direct-p}, \\ 
{\rm{if*}}\,(\=\+{\rm{unary-op-code-p}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{unary-op-code-p}, \\ 
{\rm{cv\_update}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_update}, \\ 
{\rm{cv\_regb}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_regb})\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{store-resultp}}\,(\=\+{\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, \\ 
{\it{flags\/}})\-\index{store-resultp}, \\ 
{\rm{cv\_write0}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_write0}, \\ 
{\rm{cv\_update}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_update})\-\index{if*})\-\index{if*})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  regb\$step \\ \index{regb\$step}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_regb}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_regb})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_update}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_update})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  update\$step \\ \index{update\$step}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(({\it{mem-state\/}} $=$ {\tt{0}}) $\vee$ ({\it{mem-state\/}} $=$ {\tt{1}})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_update}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_update})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\it{mem-state\/}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,(\=\+{\rm{store-resultp}}\,(\=\+{\rm{store-cc}}\,({\it{last-i-reg\/}})\index{store-cc}, \\ 
{\it{last-flags\/}})\-\index{store-resultp}, \\ 
{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{regs\/}}, \\ 
{\rm{bv}}\,({\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\rm{op-code}}\,({\it{last-i-reg\/}})\index{op-code})\-\index{v-alu})\index{bv})\-\index{write-regs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\rm{set-flags}}\,({\it{last-i-reg\/}})\index{set-flags}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\rm{op-code}}\,({\it{last-i-reg\/}})\index{op-code})\-\index{v-alu})\-\index{update-flags}, \\ 
{\it{a-reg\/}}, \\ 
{\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{and*}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{post-inc-p})\-\index{or*}, \\ 
{\rm{unary-op-code-p}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{unary-op-code-p})\-\index{and*}, \\ 
{\rm{cv\_sefb1}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_sefb1}, \\ 
{\rm{cv\_fetch0}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch0})\-\index{if*})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  reada0\$step \\ \index{reada0\$step}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_reada0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_reada0})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\rm{read-regs}}\,({\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{last-i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{v-dec}}\,({\rm{read-regs}}\,(\=\+{\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, \\ 
{\it{regs\/}})\-\index{read-regs})\index{v-dec}, \\ 
{\rm{read-regs}}\,({\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, {\it{regs\/}})\index{read-regs})\-\index{if*}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_reada1}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_reada1})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  reada1\$step \\ \index{reada1\$step}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_reada1}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_reada1})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,(\=\+{\rm{and*}}\,(\=\+{\rm{not*}}\,({\rm{a-immediate-p}}\,({\it{last-i-reg\/}})\index{a-immediate-p})\index{not*}, \\ 
{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{last-i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-a}}\,({\it{last-i-reg\/}})\index{mode-a})\index{post-inc-p})\-\index{or*})\-\index{and*}, \\ 
{\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, \\ 
{\it{regs\/}}, \\ 
{\rm{bv}}\,({\rm{core-alu}}\,(\=\+{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{last-i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{carry-in-help}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{carry-in-help})\-\index{if*}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\bf{f}}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{last-i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{mpg}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{mpg})\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{last-i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-\index{if*}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{core-alu})\index{bv})\-\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_reada2}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_reada2})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  reada2\$step \\ \index{reada2\$step}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_reada2}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_reada2})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{car}}\,({\it{clock\/}}) $\simeq {\tt{0}}$ \\ 
{\bf then }{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_reada3}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_reada3})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\rm{cdr}}\,({\it{clock\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001} \\ 
{\bf else }{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\rm{read-regs}}\,(\=\+{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{regs\/}})\-\index{read-regs}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_reada3}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_reada3})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\rm{cdr}}\,({\it{clock\/}}), \\ 
{\rm{car}}\,({\it{clock\/}}) $-\;1$, \\ 
{\bf{f}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  reada3\$step0 \\ \index{reada3\$step0}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\bf{f}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\it{mem-count\/}} $\simeq {\tt{0}}$))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_reada3}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_reada3})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{1}}, {\it{clock\/}}, {\it{mem-count\/}}, {\bf{t}}, {\bf{t}}, {\it{addr-out\/}}, {\it{last-data\/}}))\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\rm{read-mem}}\,({\it{addr-out\/}}, {\it{mem\/}})\index{read-mem}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{reg-direct-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{reg-direct-p}, \\ 
{\rm{cv\_update}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_update}, \\ 
{\rm{if*}}\,(\=\+{\rm{unary-op-code-p}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{unary-op-code-p}, \\ 
{\rm{if*}}\,(\=\+{\rm{store-resultp}}\,(\=\+{\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, \\ 
{\it{flags\/}})\-\index{store-resultp}, \\ 
{\rm{cv\_write0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_write0}, \\ 
{\rm{cv\_update}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_update})\-\index{if*}, \\ 
{\rm{cv\_readb0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_readb0})\-\index{if*})\-\index{if*})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  reada3\$step1 \\ \index{reada3\$step1}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\bf{t}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_reada3}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_reada3})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{1}}, {\it{clock\/}}, {\it{mem-count\/}}, {\bf{f}}, {\bf{t}}, {\it{addr-out\/}}, {\it{last-data\/}}))\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{mem-count\/}} $\simeq {\tt{0}}$ \\ 
{\bf then }{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\rm{read-regs}}\,({\it{last-pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_reada3}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_reada3})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001} \\ 
{\bf else }{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\rm{read-regs}}\,({\it{last-pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_reada3}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_reada3})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}} $-\;1$, \\ 
{\bf{f}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  readb0\$step \\ \index{readb0\$step}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(({\it{mem-state\/}} $=$ {\tt{0}}) $\vee$ ({\it{mem-state\/}} $=$ {\tt{1}})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_readb0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_readb0})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\it{mem-state\/}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{v-dec}}\,({\rm{read-regs}}\,(\=\+{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{regs\/}})\-\index{read-regs})\index{v-dec}, \\ 
{\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs})\-\index{if*}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_readb1}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_readb1})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  readb1\$step \\ \index{readb1\$step}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_readb1}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_readb1})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{a-immediate-p}}\,({\it{last-i-reg\/}})\index{a-immediate-p}, \\ 
{\rm{reg-direct-p}}\,({\rm{mode-a}}\,({\it{last-i-reg\/}})\index{mode-a})\index{reg-direct-p})\-\index{or*}, \\ 
{\rm{if*}}\,(\=\+{\rm{a-immediate-p}}\,({\it{last-i-reg\/}})\index{a-immediate-p}, \\ 
{\rm{sign-extend}}\,(\=\+{\rm{a-immediate}}\,({\it{i-reg\/}})\index{a-immediate}, \\ 
{\tt{32}})\-\index{sign-extend}, \\ 
{\rm{read-regs}}\,({\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, {\it{regs\/}})\index{read-regs})\-\index{if*}, \\ 
{\it{a-reg\/}})\-\index{if*}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_readb2}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_readb2})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  readb2\$step \\ \index{readb2\$step}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_readb2}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_readb2})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{car}}\,({\it{clock\/}}) $\simeq {\tt{0}}$ \\ 
{\bf then }{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,(\=\+{\rm{and*}}\,(\=\+{\rm{not*}}\,({\rm{store-resultp}}\,(\=\+{\rm{store-cc}}\,({\it{last-i-reg\/}})\index{store-cc}, \\ 
{\it{last-flags\/}})\-\index{store-resultp})\index{not*}, \\ 
{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{post-inc-p})\-\index{or*})\-\index{and*}, \\ 
{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{regs\/}}, \\ 
{\rm{bv}}\,({\rm{core-alu}}\,(\=\+{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{carry-in-help}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{carry-in-help})\-\index{if*}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\bf{f}}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{mpg}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{mpg})\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-\index{if*}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{core-alu})\index{bv})\-\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_readb3}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_readb3})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\rm{cdr}}\,({\it{clock\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001} \\ 
{\bf else }{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,(\=\+{\rm{and*}}\,(\=\+{\rm{not*}}\,({\rm{store-resultp}}\,(\=\+{\rm{store-cc}}\,({\it{last-i-reg\/}})\index{store-cc}, \\ 
{\it{last-flags\/}})\-\index{store-resultp})\index{not*}, \\ 
{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{post-inc-p})\-\index{or*})\-\index{and*}, \\ 
{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{regs\/}}, \\ 
{\rm{bv}}\,({\rm{core-alu}}\,(\=\+{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{carry-in-help}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{carry-in-help})\-\index{if*}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\bf{f}}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{mpg}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{mpg})\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-\index{if*}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{core-alu})\index{bv})\-\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_readb3}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_readb3})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\rm{cdr}}\,({\it{clock\/}}), \\ 
{\rm{car}}\,({\it{clock\/}}) $-\;1$, \\ 
{\bf{f}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  readb3\$step0 \\ \index{readb3\$step0}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\bf{f}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\it{mem-count\/}} $\simeq {\tt{0}}$))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_readb3}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_readb3})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{1}}, {\it{clock\/}}, {\it{mem-count\/}}, {\bf{t}}, {\bf{t}}, {\it{addr-out\/}}, {\it{last-data\/}}))\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\rm{read-mem}}\,({\it{addr-out\/}}, {\it{mem\/}})\index{read-mem}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{store-resultp}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, {\it{flags\/}})\index{store-resultp}, \\ 
{\rm{cv\_write0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_write0}, \\ 
{\rm{cv\_update}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_update})\-\index{if*})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  readb3\$step1 \\ \index{readb3\$step1}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\bf{t}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_readb3}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_readb3})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{1}}, {\it{clock\/}}, {\it{mem-count\/}}, {\bf{f}}, {\bf{t}}, {\it{addr-out\/}}, {\it{last-data\/}}))\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{mem-count\/}} $\simeq {\tt{0}}$ \\ 
{\bf then }{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\rm{read-regs}}\,({\it{last-pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_readb3}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_readb3})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001} \\ 
{\bf else }{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\rm{read-regs}}\,({\it{last-pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_readb3}}\,(\=\+{\bf{t}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_readb3})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}} $-\;1$, \\ 
{\bf{f}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  write0\$step \\ \index{write0\$step}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(({\it{mem-state\/}} $=$ {\tt{0}}) $\vee$ ({\it{mem-state\/}} $=$ {\tt{1}})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_write0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_write0})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\it{mem-state\/}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\rm{set-flags}}\,({\it{last-i-reg\/}})\index{set-flags}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\rm{op-code}}\,({\it{last-i-reg\/}})\index{op-code})\-\index{v-alu})\-\index{update-flags}, \\ 
{\it{a-reg\/}}, \\ 
{\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{i-reg\/}}, \\ 
{\rm{bv}}\,({\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\rm{op-code}}\,({\it{last-i-reg\/}})\index{op-code})\-\index{v-alu})\index{bv}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{v-dec}}\,({\rm{read-regs}}\,(\=\+{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{regs\/}})\-\index{read-regs})\index{v-dec}, \\ 
{\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs})\-\index{if*}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_write1}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_write1})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  write1\$step \\ \index{write1\$step}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_write1}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_write1})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{post-inc-p})\-\index{or*}, \\ 
{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{regs\/}}, \\ 
{\rm{bv}}\,({\rm{core-alu}}\,(\=\+{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{carry-in-help}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{carry-in-help})\-\index{if*}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\bf{f}}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{mpg}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{mpg})\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-\index{if*}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{core-alu})\index{bv})\-\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_write2}}\,(\=\+{\bf{f}}, \\ 
{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_write2})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{0}}, {\it{clock\/}}, {\tt{0}}, {\bf{t}}, {\bf{f}}, {\it{addr-out\/}}, {\it{data-out\/}}))\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  write2\$step \\ \index{write2\$step}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{f}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_write2}}\,(\=\+{\bf{f}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_write2})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{f}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{data-out\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{car}}\,({\it{clock\/}}) $\simeq {\tt{0}}$ \\ 
{\bf then }{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_write3}}\,(\=\+{\bf{f}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_write3})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{2}}, \\ 
{\rm{cdr}}\,({\it{clock\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{data-out\/}})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001} \\ 
{\bf else }{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_write3}}\,(\=\+{\bf{f}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_write3})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{2}}, \\ 
{\rm{cdr}}\,({\it{clock\/}}), \\ 
{\rm{car}}\,({\it{clock\/}}) $-\;1$, \\ 
{\bf{f}}, \\ 
{\bf{f}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{data-out\/}})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  write3\$step0 \\ \index{write3\$step0}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{f}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\bf{f}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\it{mem-count\/}} $\simeq {\tt{0}}$))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_write3}}\,(\=\+{\bf{f}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_write3})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{2}}, {\it{clock\/}}, {\it{mem-count\/}}, {\bf{t}}, {\bf{f}}, {\it{addr-out\/}}, {\it{data-out\/}}))\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch0}}\,(\=\+{\bf{f}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch0})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{2}}, {\it{clock\/}}, {\tt{0}}, {\bf{t}}, {\bf{f}}, {\it{addr-out\/}}, {\it{data-out\/}}))\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  write3\$step1 \\ \index{write3\$step1}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{f}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\bf{t}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_write3}}\,(\=\+{\bf{f}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_write3})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{2}}, {\it{clock\/}}, {\it{mem-count\/}}, {\bf{f}}, {\bf{f}}, {\it{addr-out\/}}, {\it{data-out\/}}))\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{mem-count\/}} $\simeq {\tt{0}}$ \\ 
{\bf then }{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_write3}}\,(\=\+{\bf{f}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_write3})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{2}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{data-out\/}})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001} \\ 
{\bf else }{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_write3}}\,(\=\+{\bf{f}}, \\ 
{\it{last-pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_write3})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{2}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}} $-\;1$, \\ 
{\bf{f}}, \\ 
{\bf{f}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{data-out\/}})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  sefa0\$step \\ \index{sefa0\$step}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_sefa0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_sefa0})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\rm{read-regs}}\,({\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_sefa1}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_sefa1})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  sefa1\$step \\ \index{sefa1\$step}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_sefa1}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_sefa1})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, \\ 
{\it{regs\/}}, \\ 
{\rm{bv}}\,({\rm{core-alu}}\,(\=\+{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{last-i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{carry-in-help}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{carry-in-help})\-\index{if*}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\bf{f}}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{last-i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{mpg}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{mpg})\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{last-i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-\index{if*}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{core-alu})\index{bv})\-\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{post-inc-p})\-\index{or*}, \\ 
{\rm{cv\_sefb0}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_sefb0}, \\ 
{\rm{cv\_fetch0}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch0})\-\index{if*})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  sefb0\$step \\ \index{sefb0\$step}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_sefb0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_sefb0})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_sefb1}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_sefb1})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  sefb1\$step \\ \index{sefb1\$step}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{last-pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_sefb1}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-pc-reg\/}})\-\index{cv\_sefb1})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{regs\/}}, \\ 
{\rm{bv}}\,({\rm{core-alu}}\,(\=\+{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{carry-in-help}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{carry-in-help})\-\index{if*}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\bf{f}}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{mpg}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{mpg})\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-\index{if*}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{core-alu})\index{bv})\-\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch0}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch0})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\it{n\/}} $-\;1$)\-\index{run-fm9001})\-\-
\end{tabbing}


\noindent{\sc Event}:   Let us define the theory {\it{fm9001-step-theory}} to consist of the following events: sefb1\$step,
sefb0\$step,
sefa1\$step,
sefa0\$step,
write3\$step1,
write3\$step0,
write2\$step,
write1\$step,
write0\$step,
readb3\$step1,
readb3\$step0,
readb2\$step,
readb1\$step,
readb0\$step,
reada3\$step1,
reada3\$step0,
reada2\$step,
reada1\$step,
reada0\$step,
update\$step,
regb\$step,
rega\$step,
decode\$step,
fetch3\$step1,
fetch3\$step0,
fetch2\$step,
fetch1\$step,
fetch0\$step2,
fetch0\$step1,
fetch0\$step0.\index{fm9001-step-theory}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{read-fn} \\  
\=\+{\rm{read-fn}}\,({\it{reg0\/}}, {\it{reg1\/}}, {\it{n\/}})\index{read-fn} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\it{reg0\/}} \\ 
{\bf else }{\rm{read-fn}}\,({\it{reg1\/}}, {\it{reg1\/}}, {\it{n\/}} $-\;1$)\index{read-fn}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable read-fn; name this event `read-fn-off'.\index{read-fn-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-read-fn \\ \index{open-read-fn}
\=\+(({\it{n\/}} $\simeq {\tt{0}}$) $\rightarrow$ ({\rm{read-fn}}\,({\it{reg0\/}}, {\it{reg1\/}}, {\it{n\/}})\index{read-fn} $=$ {\it{reg0\/}})) \\ 
$\wedge$$\;\;\;\;$(({\it{n\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ ({\rm{read-fn}}\,({\it{reg0\/}}, {\it{reg1\/}}, {\it{n\/}})\index{read-fn} $=$ {\rm{read-fn}}\,({\it{reg1\/}}, {\it{reg1\/}}, {\it{n\/}} $-\;1$)\index{read-fn}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-read-fn \\ \index{length-read-fn}
\=\+(({\rm{length}}\,({\it{reg0\/}})\index{length} $=$ {\tt{32}}) $\wedge$ ({\rm{length}}\,({\it{reg1\/}})\index{length} $=$ {\tt{32}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{length}}\,({\rm{read-fn}}\,({\it{reg0\/}}, {\it{reg1\/}}, {\it{n\/}})\index{read-fn})\index{length} $=$ {\tt{32}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  properp-read-fn \\ \index{properp-read-fn}
({\rm{properp}}\,({\it{reg0\/}})\index{properp} $\wedge$ {\rm{properp}}\,({\it{reg1\/}})\index{properp}) $\rightarrow$ {\rm{properp}}\,({\rm{read-fn}}\,({\it{reg0\/}}, {\it{reg1\/}}, {\it{n\/}})\index{read-fn})\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-read-fn \\ \index{bvp-read-fn}
({\rm{bvp}}\,({\it{reg0\/}})\index{bvp} $\wedge$ {\rm{bvp}}\,({\it{reg1\/}})\index{bvp}) $\rightarrow$ {\rm{bvp}}\,({\rm{read-fn}}\,({\it{reg0\/}}, {\it{reg1\/}}, {\it{n\/}})\index{read-fn})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fetch3\$induction} \\  
\=\+{\rm{fetch3\$induction}}\,(\=\+{\it{n\/}}, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{regs\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{last-rw-\/}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-data\/}})\-\index{fetch3\$induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{fetch3\$induction}}\,(\=\+{\it{n\/}} $-\;1$, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}} $-\;1$, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\bf{t}}, \\ 
{\it{regs-address\/}}, \\ 
{\rm{read-regs}}\,({\it{pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-\index{fetch3\$induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fetch3\$progress-help \\ \index{fetch3\$progress-help}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, $1\;+$ {\it{n\/}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{count\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch3}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch3})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{1}}, {\it{clock\/}}, {\it{count\/}}, {\bf{f}}, {\bf{t}}, {\it{addr-out\/}}, {\it{last-data\/}}))\-, \\ 
{\it{inputs\/}}, \\ 
$1\;+$ {\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\rm{read-fn}}\,({\it{i-reg\/}}, {\rm{read-regs}}\,({\it{pc-reg\/}}, {\it{regs\/}})\index{read-regs}, $1\;+$ {\it{n\/}})\index{read-fn}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
$\neg$ \=\+{\bf if }{\it{n\/}} $<$ {\it{count\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch3}}\,(\=\+{\bf{t}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{read-fn}}\,({\it{i-reg\/}}, {\rm{read-regs}}\,({\it{pc-reg\/}}, {\it{regs\/}})\index{read-regs}, {\it{n\/}})\index{read-fn}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch3})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}} $-$ ($1\;+$ {\it{n\/}}), \\ 
\=\+{\bf if }{\it{n\/}} $<$ {\it{count\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fetch3\$progress \\ \index{fetch3\$progress}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\it{count\/}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;$({\it{count\/}} $\not\simeq {\tt{0}}$))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch3}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch3})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{1}}, {\it{clock\/}}, {\it{count\/}} $-\;1$, {\bf{f}}, {\bf{t}}, {\it{addr-out\/}}, {\it{last-data\/}}))\-, \\ 
{\it{inputs\/}}, \\ 
{\it{count\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\rm{read-fn}}\,({\it{i-reg\/}}, {\rm{read-regs}}\,({\it{pc-reg\/}}, {\it{regs\/}})\index{read-regs}, {\it{count\/}})\index{read-fn}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch3}}\,(\=\+{\bf{t}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{read-fn}}\,(\=\+{\it{i-reg\/}}, \\ 
{\rm{read-regs}}\,({\it{pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{count\/}} $-\;1$)\-\index{read-fn}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch3})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{1}}, {\it{clock\/}}, {\tt{0}}, {\bf{t}}, {\bf{t}}, {\it{addr-out\/}}, {\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{reada3\$induction} \\  
\=\+{\rm{reada3\$induction}}\,(\=\+{\it{n\/}}, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{regs\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{last-rw-\/}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-data\/}})\-\index{reada3\$induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{reada3\$induction}}\,(\=\+{\it{n\/}} $-\;1$, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}} $-\;1$, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\rm{read-regs}}\,({\it{pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{b-reg\/}}, \\ 
{\bf{t}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-\index{reada3\$induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  reada3\$progress-help \\ \index{reada3\$progress-help}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, $1\;+$ {\it{n\/}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{count\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_reada3}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_reada3})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{1}}, {\it{clock\/}}, {\it{count\/}}, {\bf{f}}, {\bf{t}}, {\it{addr-out\/}}, {\it{last-data\/}}))\-, \\ 
{\it{inputs\/}}, \\ 
$1\;+$ {\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\rm{read-fn}}\,({\it{a-reg\/}}, {\rm{read-regs}}\,({\it{pc-reg\/}}, {\it{regs\/}})\index{read-regs}, $1\;+$ {\it{n\/}})\index{read-fn}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
$\neg$ \=\+{\bf if }{\it{n\/}} $<$ {\it{count\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_reada3}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}} $-$ ($1\;+$ {\it{n\/}}), \\ 
\=\+{\bf if }{\it{n\/}} $<$ {\it{count\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  reada3\$progress \\ \index{reada3\$progress}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\it{count\/}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;$({\it{count\/}} $\not\simeq {\tt{0}}$))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_reada3}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_reada3})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{1}}, {\it{clock\/}}, {\it{count\/}} $-\;1$, {\bf{f}}, {\bf{t}}, {\it{addr-out\/}}, {\it{last-data\/}}))\-, \\ 
{\it{inputs\/}}, \\ 
{\it{count\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\rm{read-fn}}\,({\it{a-reg\/}}, {\rm{read-regs}}\,({\it{pc-reg\/}}, {\it{regs\/}})\index{read-regs}, {\it{count\/}})\index{read-fn}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_reada3}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_reada3})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{1}}, {\it{clock\/}}, {\tt{0}}, {\bf{t}}, {\bf{t}}, {\it{addr-out\/}}, {\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{readb3\$induction} \\  
\=\+{\rm{readb3\$induction}}\,(\=\+{\it{n\/}}, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{regs\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{last-rw-\/}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-data\/}})\-\index{readb3\$induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{readb3\$induction}}\,(\=\+{\it{n\/}} $-\;1$, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}} $-\;1$, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{a-reg\/}}, \\ 
{\rm{read-regs}}\,({\it{pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\bf{t}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-\index{readb3\$induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  readb3\$progress-help \\ \index{readb3\$progress-help}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, $1\;+$ {\it{n\/}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{count\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_readb3}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_readb3})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{1}}, {\it{clock\/}}, {\it{count\/}}, {\bf{f}}, {\bf{t}}, {\it{addr-out\/}}, {\it{last-data\/}}))\-, \\ 
{\it{inputs\/}}, \\ 
$1\;+$ {\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\rm{read-fn}}\,({\it{b-reg\/}}, {\rm{read-regs}}\,({\it{pc-reg\/}}, {\it{regs\/}})\index{read-regs}, $1\;+$ {\it{n\/}})\index{read-fn}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
$\neg$ \=\+{\bf if }{\it{n\/}} $<$ {\it{count\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_readb3}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}} $-$ ($1\;+$ {\it{n\/}}), \\ 
\=\+{\bf if }{\it{n\/}} $<$ {\it{count\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  readb3\$progress \\ \index{readb3\$progress}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\it{count\/}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;$({\it{count\/}} $\not\simeq {\tt{0}}$))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_readb3}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_readb3})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{1}}, {\it{clock\/}}, {\it{count\/}} $-\;1$, {\bf{f}}, {\bf{t}}, {\it{addr-out\/}}, {\it{last-data\/}}))\-, \\ 
{\it{inputs\/}}, \\ 
{\it{count\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\rm{read-fn}}\,({\it{b-reg\/}}, {\rm{read-regs}}\,({\it{pc-reg\/}}, {\it{regs\/}})\index{read-regs}, {\it{count\/}})\index{read-fn}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_readb3}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb3})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{1}}, {\it{clock\/}}, {\tt{0}}, {\bf{t}}, {\bf{t}}, {\it{addr-out\/}}, {\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{write3\$induction} \\  
\=\+{\rm{write3\$induction}}\,(\=\+{\it{n\/}}, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}}, \\ 
{\it{inputs\/}}, \\ 
{\it{regs\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{last-rw-\/}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{last-data\/}})\-\index{write3\$induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{write3\$induction}}\,(\=\+{\it{n\/}} $-\;1$, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}} $-\;1$, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\bf{f}}, \\ 
{\it{regs-address\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{rw-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-\index{write3\$induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  write3\$progress-help \\ \index{write3\$progress-help}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, $1\;+$ {\it{n\/}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{count\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_write3}}\,(\=\+{\bf{f}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_write3})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{2}}, {\it{clock\/}}, {\it{count\/}}, {\bf{f}}, {\bf{f}}, {\it{addr-out\/}}, {\it{data-out\/}}))\-, \\ 
{\it{inputs\/}}, \\ 
$1\;+$ {\it{n\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
$\neg$ \=\+{\bf if }{\it{n\/}} $<$ {\it{count\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_write3}}\,({\bf{f}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{2}}, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}} $-$ ($1\;+$ {\it{n\/}}), \\ 
\=\+{\bf if }{\it{n\/}} $<$ {\it{count\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-, \\ 
{\bf{f}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{data-out\/}})\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  write3\$progress \\ \index{write3\$progress}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\it{count\/}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;$({\it{count\/}} $\not\simeq {\tt{0}}$))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_write3}}\,(\=\+{\bf{f}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_write3})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{2}}, {\it{clock\/}}, {\it{count\/}} $-\;1$, {\bf{f}}, {\bf{f}}, {\it{addr-out\/}}, {\it{data-out\/}}))\-, \\ 
{\it{inputs\/}}, \\ 
{\it{count\/}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_write3}}\,({\bf{f}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write3})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{2}}, {\it{clock\/}}, {\tt{0}}, {\bf{t}}, {\bf{f}}, {\it{addr-out\/}}, {\it{data-out\/}}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{zerop-not-zerop-cases} \\  
\=\+{\rm{zerop-not-zerop-cases}}\,({\it{n\/}})\index{zerop-not-zerop-cases} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\it{n\/}} $\not\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{zerop-not-zerop-cases}}\,({\it{n\/}})\index{zerop-not-zerop-cases}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fetch0-$>$fetch0\$sim0 \\ \index{fetch0-$>$fetch0\$sim0}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch0})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\tt{1}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\rm{read-regs}}\,({\it{pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\rm{read-regs}}\,({\it{pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\rm{f-buf}}\,({\rm{f-buf}}\,({\rm{hold--input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{hold--input})\index{f-buf})\index{f-buf}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch1}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{0}}, {\it{clock\/}}, {\tt{0}}, {\bf{t}}, {\bf{t}}, {\it{addr-out\/}}, {\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fetch0-$>$fetch0\$sim1 \\ \index{fetch0-$>$fetch0\$sim1}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch0})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\tt{1}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\rm{read-regs}}\,({\it{pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\rm{read-regs}}\,({\it{pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\rm{f-buf}}\,({\rm{f-buf}}\,({\rm{hold--input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{hold--input})\index{f-buf})\index{f-buf}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch1}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{0}}, {\it{clock\/}}, {\tt{0}}, {\bf{t}}, {\bf{t}}, {\it{addr-out\/}}, {\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fetch0-$>$fetch0\$sim2 \\ \index{fetch0-$>$fetch0\$sim2}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{f}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\it{mem-count\/}} $\simeq {\tt{0}}$))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch0}}\,(\=\+{\bf{f}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch0})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{2}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{f}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{data-out\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\tt{1}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\rm{read-regs}}\,({\it{pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\rm{read-regs}}\,({\it{pc-reg\/}}, {\it{regs\/}})\index{read-regs}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\rm{f-buf}}\,({\rm{f-buf}}\,({\rm{hold--input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{hold--input})\index{f-buf})\index{f-buf}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch1}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch1})\-, \\ 
{\rm{list}}\,(\=\+{\rm{write-mem}}\,({\it{addr-out\/}}, {\it{mem\/}}, {\it{data-out\/}})\index{write-mem}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{data-out\/}})\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fetch1-$>$decode\$sim \\ \index{fetch1-$>$decode\$sim}
\=\+(\=\+({\it{dtack-wait\/}} $=$ {\rm{car}}\,({\it{clock\/}})) \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\it{last-rw-\/}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, $1\;+$ ($1\;+$ ({\rm{car}}\,({\it{clock\/}}) $+$ {\tt{2}})))\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\it{hold-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{last-rw-\/}})\index{boolp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch1}}\,(\=\+{\it{last-rw-\/}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch1})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\it{last-rw-\/}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
$1\;+$ ($1\;+$ ({\rm{car}}\,({\it{clock\/}}) $+$ {\tt{2}})))\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,(\=\+{\bf{f}}, \\ 
{\tt{0}}, \\ 
{\rm{write-regs}}\,(\=\+{\bf{t}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\rm{v-inc}}\,({\it{a-reg\/}})\index{v-inc})\-\index{write-regs}, \\ 
{\tt{0}})\-\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\rm{read-mem}}\,({\it{addr-out\/}}, {\it{mem\/}})\index{read-mem}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{store-resultp}}\,(\=\+{\rm{store-cc}}\,({\rm{read-mem}}\,(\=\+{\it{addr-out\/}}, \\ 
{\it{mem\/}})\-\index{read-mem})\index{store-cc}, \\ 
{\it{flags\/}})\-\index{store-resultp}, \\ 
{\rm{set-some-flags}}\,({\rm{set-flags}}\,({\rm{read-mem}}\,(\=\+{\it{addr-out\/}}, \\ 
{\it{mem\/}})\-\index{read-mem})\index{set-flags})\index{set-some-flags})\-\index{or*}, \\ 
{\rm{if*}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{a-immediate-p}}\,({\rm{read-mem}}\,({\it{addr-out\/}}, {\it{mem\/}})\index{read-mem})\index{a-immediate-p}, \\ 
{\rm{reg-direct-p}}\,({\rm{mode-a}}\,({\rm{read-mem}}\,(\=\+{\it{addr-out\/}}, \\ 
{\it{mem\/}})\-\index{read-mem})\index{mode-a})\index{reg-direct-p})\-\index{or*}, \\ 
{\rm{if*}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{reg-direct-p}}\,({\rm{mode-b}}\,({\rm{read-mem}}\,(\=\+{\it{addr-out\/}}, \\ 
{\it{mem\/}})\-\index{read-mem})\index{mode-b})\index{reg-direct-p}, \\ 
{\rm{unary-op-code-p}}\,({\rm{op-code}}\,({\rm{read-mem}}\,(\=\+{\it{addr-out\/}}, \\ 
{\it{mem\/}})\-\index{read-mem})\index{op-code})\index{unary-op-code-p})\-\index{or*}, \\ 
{\rm{cv\_rega}}\,(\=\+{\bf{t}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{read-mem}}\,({\it{addr-out\/}}, {\it{mem\/}})\index{read-mem}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_rega}, \\ 
{\rm{cv\_readb0}}\,(\=\+{\bf{t}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{read-mem}}\,({\it{addr-out\/}}, {\it{mem\/}})\index{read-mem}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_readb0})\-\index{if*}, \\ 
{\rm{cv\_reada0}}\,(\=\+{\bf{t}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{read-mem}}\,({\it{addr-out\/}}, {\it{mem\/}})\index{read-mem}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_reada0})\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{and*}}\,(\=\+{\rm{not*}}\,({\rm{a-immediate-p}}\,({\rm{read-mem}}\,(\=\+{\it{addr-out\/}}, \\ 
{\it{mem\/}})\-\index{read-mem})\index{a-immediate-p})\index{not*}, \\ 
{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\rm{read-mem}}\,(\=\+{\it{addr-out\/}}, \\ 
{\it{mem\/}})\-\index{read-mem})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-a}}\,({\rm{read-mem}}\,(\=\+{\it{addr-out\/}}, \\ 
{\it{mem\/}})\-\index{read-mem})\index{mode-a})\index{post-inc-p})\-\index{or*})\-\index{and*}, \\ 
{\rm{cv\_sefa0}}\,(\=\+{\bf{t}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{read-mem}}\,({\it{addr-out\/}}, {\it{mem\/}})\index{read-mem}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_sefa0}, \\ 
{\rm{if*}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\rm{read-mem}}\,(\=\+{\it{addr-out\/}}, \\ 
{\it{mem\/}})\-\index{read-mem})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-b}}\,({\rm{read-mem}}\,(\=\+{\it{addr-out\/}}, \\ 
{\it{mem\/}})\-\index{read-mem})\index{mode-b})\index{post-inc-p})\-\index{or*}, \\ 
{\rm{cv\_sefb0}}\,(\=\+{\bf{t}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{read-mem}}\,({\it{addr-out\/}}, {\it{mem\/}})\index{read-mem}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_sefb0}, \\ 
{\rm{cv\_fetch0}}\,(\=\+{\bf{t}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{read-mem}}\,({\it{addr-out\/}}, {\it{mem\/}})\index{read-mem}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch0})\-\index{if*})\-\index{if*})\-\index{if*})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\rm{cdr}}\,({\it{clock\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{addr-out\/}}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rega-$>$rega\$sim \\ \index{rega-$>$rega\$sim}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_rega}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_rega})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\tt{1}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{a-immediate-p}}\,({\it{last-i-reg\/}})\index{a-immediate-p}, \\ 
{\rm{sign-extend}}\,({\rm{a-immediate}}\,({\it{i-reg\/}})\index{a-immediate}, {\tt{32}})\index{sign-extend}, \\ 
{\rm{read-regs}}\,({\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, {\it{regs\/}})\index{read-regs})\-\index{if*}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{reg-direct-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{reg-direct-p}, \\ 
{\rm{if*}}\,(\=\+{\rm{unary-op-code-p}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{unary-op-code-p}, \\ 
{\rm{cv\_update}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_update}, \\ 
{\rm{cv\_regb}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_regb})\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{store-resultp}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, {\it{flags\/}})\index{store-resultp}, \\ 
{\rm{cv\_write0}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_write0}, \\ 
{\rm{cv\_update}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, \\ 
{\it{i-reg\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_update})\-\index{if*})\-\index{if*})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{0}}, {\it{clock\/}}, {\tt{0}}, {\bf{t}}, {\bf{t}}, {\it{addr-out\/}}, {\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  regb-$>$update\$sim \\ \index{regb-$>$update\$sim}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{2}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_regb}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_regb})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\tt{2}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,(\=\+{\rm{store-resultp}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, {\it{flags\/}})\index{store-resultp}, \\ 
{\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b}, \\ 
{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\rm{bv}}\,({\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a-reg\/}}, \\ 
{\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs}, \\ 
{\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\-\index{v-alu})\index{bv})\-\index{write-regs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\rm{set-flags}}\,({\it{i-reg\/}})\index{set-flags}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a-reg\/}}, \\ 
{\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs}, \\ 
{\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\-\index{v-alu})\-\index{update-flags}, \\ 
{\it{a-reg\/}}, \\ 
{\rm{read-regs}}\,({\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{and*}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{post-inc-p})\-\index{or*}, \\ 
{\rm{unary-op-code-p}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{unary-op-code-p})\-\index{and*}, \\ 
{\rm{cv\_sefb1}}\,({\bf{t}}, {\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1}, \\ 
{\rm{cv\_fetch0}}\,({\bf{t}}, {\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\-\index{if*})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{0}}, {\it{clock\/}}, {\tt{0}}, {\bf{t}}, {\bf{t}}, {\it{addr-out\/}}, {\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  update-$>$update\$sim \\ \index{update-$>$update\$sim}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(({\it{mem-state\/}} $=$ {\tt{0}}) $\vee$ ({\it{mem-state\/}} $=$ {\tt{1}})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_update}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_update})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\it{mem-state\/}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\tt{1}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,(\=\+{\rm{store-resultp}}\,(\=\+{\rm{store-cc}}\,({\it{last-i-reg\/}})\index{store-cc}, \\ 
{\it{last-flags\/}})\-\index{store-resultp}, \\ 
{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{regs\/}}, \\ 
{\rm{bv}}\,({\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\rm{op-code}}\,({\it{last-i-reg\/}})\index{op-code})\-\index{v-alu})\index{bv})\-\index{write-regs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\rm{set-flags}}\,({\it{last-i-reg\/}})\index{set-flags}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\rm{op-code}}\,({\it{last-i-reg\/}})\index{op-code})\-\index{v-alu})\-\index{update-flags}, \\ 
{\it{a-reg\/}}, \\ 
{\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{and*}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{post-inc-p})\-\index{or*}, \\ 
{\rm{unary-op-code-p}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{unary-op-code-p})\-\index{and*}, \\ 
{\rm{cv\_sefb1}}\,({\bf{t}}, {\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb1}, \\ 
{\rm{cv\_fetch0}}\,({\bf{t}}, {\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\-\index{if*})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{0}}, {\it{clock\/}}, {\tt{0}}, {\bf{t}}, {\bf{t}}, {\it{addr-out\/}}, {\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  reada0-$>$reada3\$sim \\ \index{reada0-$>$reada3\$sim}
\=\+(\=\+({\it{dtack-wait\/}} $=$ {\rm{car}}\,({\it{clock\/}})) \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, $1\;+$ ($1\;+$ ($1\;+$ ({\rm{car}}\,({\it{clock\/}}) $+$ {\tt{1}}))))\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_reada0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_reada0})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
$1\;+$ ($1\;+$ ($1\;+$ ({\rm{car}}\,({\it{clock\/}}) $+$ {\tt{1}}))))\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,(\=\+{\bf{f}}, \\ 
{\tt{0}}, \\ 
{\rm{write-regs}}\,(\=\+{\rm{and*}}\,(\=\+{\rm{not*}}\,({\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p})\index{not*}, \\ 
{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{post-inc-p})\-\index{or*})\-\index{and*}, \\ 
{\rm{rn-a}}\,({\it{i-reg\/}})\index{rn-a}, \\ 
{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\rm{bv}}\,({\rm{core-alu}}\,(\=\+{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{carry-in-help}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{carry-in-help})\-\index{if*}, \\ 
{\rm{read-regs}}\,(\=\+{\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, \\ 
{\it{regs\/}})\-\index{read-regs}, \\ 
{\it{b-reg\/}}, \\ 
{\bf{f}}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{mpg}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{mpg})\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-\index{if*}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{core-alu})\index{bv})\-\index{write-regs}, \\ 
{\tt{0}})\-\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\rm{read-mem}}\,(\=\+{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{last-i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{v-dec}}\,({\rm{read-regs}}\,({\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, {\it{regs\/}})\index{read-regs})\index{v-dec}, \\ 
{\rm{read-regs}}\,({\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, {\it{regs\/}})\index{read-regs})\-\index{if*}, \\ 
{\it{mem\/}})\-\index{read-mem}, \\ 
{\rm{read-regs}}\,(\=\+{\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b}, \\ 
{\rm{write-regs}}\,(\=\+{\rm{and*}}\,(\=\+{\rm{not*}}\,({\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p})\index{not*}, \\ 
{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{post-inc-p})\-\index{or*})\-\index{and*}, \\ 
{\rm{rn-a}}\,({\it{i-reg\/}})\index{rn-a}, \\ 
{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\rm{bv}}\,({\rm{core-alu}}\,(\=\+{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{carry-in-help}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{carry-in-help})\-\index{if*}, \\ 
{\rm{read-regs}}\,(\=\+{\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, \\ 
{\it{regs\/}})\-\index{read-regs}, \\ 
{\it{b-reg\/}}, \\ 
{\bf{f}}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{mpg}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{mpg})\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-\index{if*}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{core-alu})\index{bv})\-\index{write-regs})\-\index{read-regs}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{last-i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{v-dec}}\,({\rm{read-regs}}\,({\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, {\it{regs\/}})\index{read-regs})\index{v-dec}, \\ 
{\rm{read-regs}}\,({\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, {\it{regs\/}})\index{read-regs})\-\index{if*}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{reg-direct-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{reg-direct-p}, \\ 
{\rm{cv\_update}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update}, \\ 
{\rm{if*}}\,(\=\+{\rm{unary-op-code-p}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{unary-op-code-p}, \\ 
{\rm{if*}}\,(\=\+{\rm{store-resultp}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, {\it{flags\/}})\index{store-resultp}, \\ 
{\rm{cv\_write0}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0}, \\ 
{\rm{cv\_update}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\-\index{if*}, \\ 
{\rm{cv\_readb0}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_readb0})\-\index{if*})\-\index{if*})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\rm{cdr}}\,({\it{clock\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{last-i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{v-dec}}\,({\rm{read-regs}}\,({\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, {\it{regs\/}})\index{read-regs})\index{v-dec}, \\ 
{\rm{read-regs}}\,({\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, {\it{regs\/}})\index{read-regs})\-\index{if*}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  readb0-$>$readb3\$sim \\ \index{readb0-$>$readb3\$sim}
\=\+(\=\+({\it{dtack-wait\/}} $=$ {\rm{car}}\,({\it{clock\/}})) \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, $1\;+$ ($1\;+$ ($1\;+$ ({\rm{car}}\,({\it{clock\/}}) $+$ {\tt{1}}))))\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(({\it{mem-state\/}} $=$ {\tt{0}}) $\vee$ ({\it{mem-state\/}} $=$ {\tt{1}})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_readb0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_readb0})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\it{mem-state\/}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
$1\;+$ ($1\;+$ ($1\;+$ ({\rm{car}}\,({\it{clock\/}}) $+$ {\tt{1}}))))\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,(\=\+{\bf{f}}, \\ 
{\tt{0}}, \\ 
{\rm{write-regs}}\,(\=\+{\rm{and*}}\,(\=\+{\rm{not*}}\,({\rm{store-resultp}}\,(\=\+{\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, \\ 
{\it{flags\/}})\-\index{store-resultp})\index{not*}, \\ 
{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{post-inc-p})\-\index{or*})\-\index{and*}, \\ 
{\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b}, \\ 
{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\rm{bv}}\,({\rm{core-alu}}\,(\=\+{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{carry-in-help}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{carry-in-help})\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p}, \\ 
{\rm{reg-direct-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{reg-direct-p})\-\index{or*}, \\ 
{\rm{if*}}\,(\=\+{\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p}, \\ 
{\rm{sign-extend}}\,(\=\+{\rm{a-immediate}}\,({\it{i-reg\/}})\index{a-immediate}, \\ 
{\tt{32}})\-\index{sign-extend}, \\ 
{\rm{read-regs}}\,(\=\+{\rm{rn-a}}\,({\it{i-reg\/}})\index{rn-a}, \\ 
{\it{regs\/}})\-\index{read-regs})\-\index{if*}, \\ 
{\it{a-reg\/}})\-\index{if*}, \\ 
{\rm{read-regs}}\,(\=\+{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{regs\/}})\-\index{read-regs}, \\ 
{\bf{f}}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{mpg}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{mpg})\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-\index{if*}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{core-alu})\index{bv})\-\index{write-regs}, \\ 
{\tt{0}})\-\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p}, \\ 
{\rm{reg-direct-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{reg-direct-p})\-\index{or*}, \\ 
{\rm{if*}}\,(\=\+{\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p}, \\ 
{\rm{sign-extend}}\,({\rm{a-immediate}}\,({\it{i-reg\/}})\index{a-immediate}, {\tt{32}})\index{sign-extend}, \\ 
{\rm{read-regs}}\,({\rm{rn-a}}\,({\it{i-reg\/}})\index{rn-a}, {\it{regs\/}})\index{read-regs})\-\index{if*}, \\ 
{\it{a-reg\/}})\-\index{if*}, \\ 
{\rm{read-mem}}\,(\=\+{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{v-dec}}\,({\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs})\index{v-dec}, \\ 
{\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs})\-\index{if*}, \\ 
{\it{mem\/}})\-\index{read-mem}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{v-dec}}\,({\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs})\index{v-dec}, \\ 
{\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs})\-\index{if*}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{store-resultp}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, {\it{flags\/}})\index{store-resultp}, \\ 
{\rm{cv\_write0}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_write0}, \\ 
{\rm{cv\_update}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_update})\-\index{if*})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{1}}, \\ 
{\rm{cdr}}\,({\it{clock\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{v-dec}}\,({\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs})\index{v-dec}, \\ 
{\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs})\-\index{if*}, \\ 
{\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix})\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  write0-$>$write3\$sim \\ \index{write0-$>$write3\$sim}
\=\+(\=\+({\it{dtack-wait\/}} $=$ {\rm{car}}\,({\it{clock\/}})) \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, $1\;+$ ($1\;+$ ($1\;+$ ({\rm{car}}\,({\it{clock\/}}) $+$ {\tt{1}}))))\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(({\it{mem-state\/}} $=$ {\tt{0}}) $\vee$ ({\it{mem-state\/}} $=$ {\tt{1}})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_write0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_write0})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\it{mem-state\/}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
$1\;+$ ($1\;+$ ($1\;+$ ({\rm{car}}\,({\it{clock\/}}) $+$ {\tt{1}}))))\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,(\=\+{\bf{f}}, \\ 
{\tt{0}}, \\ 
{\rm{write-regs}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{post-inc-p})\-\index{or*}, \\ 
{\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b}, \\ 
{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\rm{bv}}\,({\rm{core-alu}}\,(\=\+{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{carry-in-help}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{carry-in-help})\-\index{if*}, \\ 
{\it{a-reg\/}}, \\ 
{\rm{read-regs}}\,(\=\+{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{regs\/}})\-\index{read-regs}, \\ 
{\bf{f}}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{mpg}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{mpg})\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-\index{if*}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{core-alu})\index{bv})\-\index{write-regs}, \\ 
{\tt{0}})\-\index{write-regs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\rm{set-flags}}\,({\it{last-i-reg\/}})\index{set-flags}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\rm{op-code}}\,({\it{last-i-reg\/}})\index{op-code})\-\index{v-alu})\-\index{update-flags}, \\ 
{\it{a-reg\/}}, \\ 
{\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{i-reg\/}}, \\ 
{\rm{bv}}\,({\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\rm{op-code}}\,({\it{last-i-reg\/}})\index{op-code})\-\index{v-alu})\index{bv}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{v-dec}}\,({\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs})\index{v-dec}, \\ 
{\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs})\-\index{if*}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch0}}\,(\=\+{\bf{f}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\rm{set-flags}}\,({\it{last-i-reg\/}})\index{set-flags}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\rm{op-code}}\,({\it{last-i-reg\/}})\index{op-code})\-\index{v-alu})\-\index{update-flags}, \\ 
{\it{pc-reg\/}})\-\index{cv\_fetch0})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{2}}, \\ 
{\rm{cdr}}\,({\it{clock\/}}), \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{f}}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{v-dec}}\,({\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs})\index{v-dec}, \\ 
{\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs})\-\index{if*}, \\ 
{\rm{bv}}\,({\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\rm{op-code}}\,({\it{last-i-reg\/}})\index{op-code})\-\index{v-alu})\index{bv})\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  sefa0-$>$sefa1\$sim \\ \index{sefa0-$>$sefa1\$sim}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{2}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_sefa0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_sefa0})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\tt{2}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-a}}\,({\it{i-reg\/}})\index{rn-a}, \\ 
{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\rm{bv}}\,({\rm{core-alu}}\,(\=\+{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{carry-in-help}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{carry-in-help})\-\index{if*}, \\ 
{\rm{read-regs}}\,(\=\+{\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, \\ 
{\it{regs\/}})\-\index{read-regs}, \\ 
{\it{b-reg\/}}, \\ 
{\bf{f}}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{mpg}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{mpg})\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-\index{if*}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{core-alu})\index{bv})\-\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\rm{read-regs}}\,({\rm{rn-a}}\,({\it{last-i-reg\/}})\index{rn-a}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{if*}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{post-inc-p})\-\index{or*}, \\ 
{\rm{cv\_sefb0}}\,({\bf{t}}, {\rm{rn-a}}\,({\it{i-reg\/}})\index{rn-a}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_sefb0}, \\ 
{\rm{cv\_fetch0}}\,({\bf{t}}, {\rm{rn-a}}\,({\it{i-reg\/}})\index{rn-a}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\-\index{if*})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{0}}, {\it{clock\/}}, {\tt{0}}, {\bf{t}}, {\bf{t}}, {\it{addr-out\/}}, {\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  sefb0-$>$sefb1\$sim \\ \index{sefb0-$>$sefb1\$sim}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{2}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_sefb0}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_sefb0})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\tt{2}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b}, \\ 
{\rm{write-regs}}\,({\bf{f}}, {\tt{0}}, {\it{regs\/}}, {\tt{0}})\index{write-regs}, \\ 
{\rm{bv}}\,({\rm{core-alu}}\,(\=\+{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{carry-in-help}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{carry-in-help})\-\index{if*}, \\ 
{\it{a-reg\/}}, \\ 
{\rm{read-regs}}\,(\=\+{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{regs\/}})\-\index{read-regs}, \\ 
{\bf{f}}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{mpg}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{mpg})\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-\index{if*}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{core-alu})\index{bv})\-\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\rm{read-regs}}\,({\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{regs\/}})\index{read-regs}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch0}}\,({\bf{t}}, {\rm{rn-b}}\,({\it{i-reg\/}})\index{rn-b}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{0}}, {\it{clock\/}}, {\tt{0}}, {\bf{t}}, {\bf{t}}, {\it{addr-out\/}}, {\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  sefb1-$>$sefb1\$sim \\ \index{sefb1-$>$sefb1\$sim}
\=\+(\=\+{\rm{cv-hyps}}\,({\bf{t}}, {\it{last-regs-address\/}}, {\it{last-i-reg\/}}, {\it{last-flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{cv-hyps}}\,({\bf{t}}, {\it{pc-reg\/}}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv-hyps} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{mem\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{regfile-okp}}\,({\it{regs\/}})\index{regfile-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{a-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{b-reg\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{b-reg\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{addr-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{addr-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\it{data-out\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data-out\/}})\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{dtack-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\it{hold-\/}})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{run-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{run-inputs-p} \\ 
$\wedge$$\;\;\;\;$({\it{reset-\/}} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\bf{nil}})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs\/}}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{reset-\/}}, \\ 
{\it{dtack-\/}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_sefb1}}\,(\=\+{\bf{t}}, \\ 
{\it{last-regs-address\/}}, \\ 
{\it{last-i-reg\/}}, \\ 
{\it{last-flags\/}}, \\ 
{\it{pc-reg\/}})\-\index{cv\_sefb1})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\it{mem-count\/}}, \\ 
{\it{mem-dtack\/}}, \\ 
{\bf{t}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\tt{1}})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{write-regs}}\,(\=\+{\bf{t}}, \\ 
{\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, \\ 
{\it{regs\/}}, \\ 
{\rm{bv}}\,({\rm{core-alu}}\,(\=\+{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{carry-in-help}, \\ 
{\rm{carry-in-help}}\,({\rm{cons}}\,(\=\+{\rm{c-flag}}\,({\it{last-flags\/}})\index{c-flag}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{carry-in-help})\-\index{if*}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\bf{f}}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op})\-)\-)\index{mpg}, \\ 
{\rm{mpg}}\,({\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-)\-)\index{mpg})\-\index{if*}, \\ 
{\rm{if*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{last-i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\sc{alu-dec-op}}\index{alu-dec-op}, \\ 
{\sc{alu-inc-op}}\index{alu-inc-op})\-\index{if*}, \\ 
{\rm{make-tree}}\,({\tt{32}})\index{make-tree})\-\index{core-alu})\index{bv})\-\index{write-regs}, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\it{hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\rm{cv\_fetch0}}\,({\bf{t}}, {\rm{rn-b}}\,({\it{last-i-reg\/}})\index{rn-b}, {\it{i-reg\/}}, {\it{flags\/}}, {\it{pc-reg\/}})\index{cv\_fetch0})\-, \\ 
{\rm{list}}\,({\it{mem\/}}, {\tt{0}}, {\it{clock\/}}, {\tt{0}}, {\bf{t}}, {\bf{t}}, {\it{addr-out\/}}, {\rm{v-threefix}}\,({\it{last-data\/}})\index{v-threefix}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{t\_fetch0}$\;\;$
{\rm{t\_fetch0}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_fetch0} $=$ {\tt{1}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{t\_sefb1} \\  
{\rm{t\_sefb1}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_sefb1} $=$ ({\tt{1}} $+$ {\rm{t\_fetch0}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_fetch0})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{t\_sefb0} \\  
{\rm{t\_sefb0}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_sefb0} $=$ ({\tt{2}} $+$ {\rm{t\_fetch0}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_fetch0})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{t\_sefa0} \\  
\=\+{\rm{t\_sefa0}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_sefa0} \\ 
$=$$\;\;\;\;$({\tt{2}} $+$ \=\+{\bf if }{\rm{or*}}\,({\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, {\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{post-inc-p})\index{or*} \\ 
{\bf then }{\rm{t\_sefb0}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_sefb0} \\ 
{\bf else }{\rm{t\_fetch0}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_fetch0}$\;${\bf  endif}\-)\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{t\_write0} \\  
\=\+{\rm{t\_write0}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_write0} \\ 
$=$$\;\;\;\;$(\=\+($1\;+$ ($1\;+$ ($1\;+$ ({\rm{car}}\,({\it{clock\/}}) $+$ {\tt{1}})))) \\ 
$+$$\;\;\;\;${\rm{t\_fetch0}}\,({\rm{cdr}}\,({\it{clock\/}}), {\it{i-reg\/}}, {\it{flags\/}})\index{t\_fetch0})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{t\_update} \\  
\=\+{\rm{t\_update}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_update} \\ 
$=$$\;\;\;\;$({\tt{1}} $+$ \=\+{\bf if }{\rm{b-and}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{post-inc-p})\-\index{or*}, \\ 
{\rm{unary-op-code-p}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{unary-op-code-p})\-\index{b-and} \\ 
{\bf then }{\rm{t\_sefb1}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_sefb1} \\ 
{\bf else }{\rm{t\_fetch0}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_fetch0}$\;${\bf  endif}\-)\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{t\_readb0} \\  
\=\+{\rm{t\_readb0}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_readb0} \\ 
$=$$\;\;\;\;$(\=\+($1\;+$ ($1\;+$ ($1\;+$ ({\rm{car}}\,({\it{clock\/}}) $+$ {\tt{1}})))) \\ 
$+$$\;\;\;\;$\=\+{\bf if }{\rm{store-resultp}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, {\it{flags\/}})\index{store-resultp} \\ 
{\bf then }{\rm{t\_write0}}\,({\rm{cdr}}\,({\it{clock\/}}), {\it{i-reg\/}}, {\it{flags\/}})\index{t\_write0} \\ 
{\bf else }{\rm{t\_update}}\,({\rm{cdr}}\,({\it{clock\/}}), {\it{i-reg\/}}, {\it{flags\/}})\index{t\_update}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{t\_reada0} \\  
\=\+{\rm{t\_reada0}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_reada0} \\ 
$=$$\;\;\;\;$(\=\+($1\;+$ ($1\;+$ ($1\;+$ ({\rm{car}}\,({\it{clock\/}}) $+$ {\tt{1}})))) \\ 
$+$$\;\;\;\;$\=\+{\bf if }{\rm{reg-direct-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{reg-direct-p} \\ 
{\bf then }{\rm{t\_update}}\,({\rm{cdr}}\,({\it{clock\/}}), {\it{i-reg\/}}, {\it{flags\/}})\index{t\_update} \\ 
{\bf elseif }{\rm{unary-op-code-p}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{unary-op-code-p} \\ 
{\bf then }\=\+{\bf if }{\rm{store-resultp}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, {\it{flags\/}})\index{store-resultp} \\ 
{\bf then }{\rm{t\_write0}}\,({\rm{cdr}}\,({\it{clock\/}}), {\it{i-reg\/}}, {\it{flags\/}})\index{t\_write0} \\ 
{\bf else }{\rm{t\_update}}\,({\rm{cdr}}\,({\it{clock\/}}), {\it{i-reg\/}}, {\it{flags\/}})\index{t\_update}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{t\_readb0}}\,({\rm{cdr}}\,({\it{clock\/}}), {\it{i-reg\/}}, {\it{flags\/}})\index{t\_readb0}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{t\_regb} \\  
\=\+{\rm{t\_regb}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_regb} \\ 
$=$$\;\;\;\;$({\tt{2}} $+$ \=\+{\bf if }{\rm{b-and}}\,(\=\+{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{post-inc-p})\-\index{or*}, \\ 
{\rm{unary-op-code-p}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{unary-op-code-p})\-\index{b-and} \\ 
{\bf then }{\rm{t\_sefb1}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_sefb1} \\ 
{\bf else }{\rm{t\_fetch0}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_fetch0}$\;${\bf  endif}\-)\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{t\_rega} \\  
\=\+{\rm{t\_rega}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_rega} \\ 
$=$$\;\;\;\;$({\tt{1}} $+$ \=\+{\bf if }{\rm{reg-direct-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{reg-direct-p} \\ 
{\bf then }\=\+{\bf if }{\rm{unary-op-code-p}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{unary-op-code-p} \\ 
{\bf then }{\rm{t\_update}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_update} \\ 
{\bf else }{\rm{t\_regb}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_regb}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{store-resultp}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, {\it{flags\/}})\index{store-resultp} \\ 
{\bf then }{\rm{t\_write0}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_write0} \\ 
{\bf else }{\rm{t\_update}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_update}$\;${\bf  endif}\-)\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{t\_fetch1} \\  
\=\+{\rm{t\_fetch1}}\,({\it{clock\/}}, {\it{i-reg\/}}, {\it{flags\/}})\index{t\_fetch1} \\ 
$=$$\;\;\;\;$(\=\+($1\;+$ ($1\;+$ ({\rm{car}}\,({\it{clock\/}}) $+$ {\tt{2}}))) \\ 
$+$$\;\;\;\;$\=\+{\bf if }{\rm{b-or}}\,(\=\+{\rm{store-resultp}}\,({\rm{store-cc}}\,({\it{i-reg\/}})\index{store-cc}, {\it{flags\/}})\index{store-resultp}, \\ 
{\rm{set-some-flags}}\,({\rm{set-flags}}\,({\it{i-reg\/}})\index{set-flags})\index{set-some-flags})\-\index{b-or} \\ 
{\bf then }\=\+{\bf if }{\rm{or*}}\,({\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p}, {\rm{reg-direct-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{reg-direct-p})\index{or*} \\ 
{\bf then }\=\+{\bf if }{\rm{b-or}}\,(\=\+{\rm{reg-direct-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{reg-direct-p}, \\ 
{\rm{unary-op-code-p}}\,({\rm{op-code}}\,({\it{i-reg\/}})\index{op-code})\index{unary-op-code-p})\-\index{b-or} \\ 
{\bf then }{\rm{t\_rega}}\,({\rm{cdr}}\,({\it{clock\/}}), {\it{i-reg\/}}, {\it{flags\/}})\index{t\_rega} \\ 
{\bf else }{\rm{t\_readb0}}\,({\rm{cdr}}\,({\it{clock\/}}), {\it{i-reg\/}}, {\it{flags\/}})\index{t\_readb0}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{t\_reada0}}\,({\rm{cdr}}\,({\it{clock\/}}), {\it{i-reg\/}}, {\it{flags\/}})\index{t\_reada0}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{and*}}\,(\=\+{\rm{not*}}\,({\rm{a-immediate-p}}\,({\it{i-reg\/}})\index{a-immediate-p})\index{not*}, \\ 
{\rm{or*}}\,(\=\+{\rm{pre-dec-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{pre-dec-p}, \\ 
{\rm{post-inc-p}}\,({\rm{mode-a}}\,({\it{i-reg\/}})\index{mode-a})\index{post-inc-p})\-\index{or*})\-\index{and*} \\ 
{\bf then }{\rm{t\_sefa0}}\,({\rm{cdr}}\,({\it{clock\/}}), {\it{i-reg\/}}, {\it{flags\/}})\index{t\_sefa0} \\ 
{\bf elseif }{\rm{or*}}\,({\rm{pre-dec-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{pre-dec-p}, {\rm{post-inc-p}}\,({\rm{mode-b}}\,({\it{i-reg\/}})\index{mode-b})\index{post-inc-p})\index{or*} \\ 
{\bf then }{\rm{t\_sefb0}}\,({\rm{cdr}}\,({\it{clock\/}}), {\it{i-reg\/}}, {\it{flags\/}})\index{t\_sefb0} \\ 
{\bf else }{\rm{t\_fetch0}}\,({\rm{cdr}}\,({\it{clock\/}}), {\it{i-reg\/}}, {\it{flags\/}})\index{t\_fetch0}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{operating-inputs-p} \\  
\=\+{\rm{operating-inputs-p}}\,({\it{inputs\/}}, {\it{n\/}})\index{operating-inputs-p} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }\=\+({\rm{reset--input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{reset--input} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{hold--input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{hold--input} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{pc-reg-input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{pc-reg-input})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{pc-reg-input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{pc-reg-input})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{operating-inputs-p}}\,({\rm{cdr}}\,({\it{inputs\/}}), {\it{n\/}} $-\;1$)\index{operating-inputs-p}\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable operating-inputs-p; name this event `operating-inputs-p-off'.\index{operating-inputs-p-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-operating-inputs-p \\ \index{open-operating-inputs-p}
\=\+(({\it{n\/}} $\simeq {\tt{0}}$) $\rightarrow$ ({\rm{operating-inputs-p}}\,({\it{inputs\/}}, {\it{n\/}})\index{operating-inputs-p} $=$ {\bf{t}})) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{operating-inputs-p}}\,({\it{inputs\/}}, {\it{n\/}})\index{operating-inputs-p} \\ 
$=$$\;\;\;\;$(\=\+({\rm{reset--input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{reset--input} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{hold--input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{hold--input} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{pc-reg-input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{pc-reg-input})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{pc-reg-input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{pc-reg-input})\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{operating-inputs-p}}\,({\rm{cdr}}\,({\it{inputs\/}}), {\it{n\/}} $-\;1$)\index{operating-inputs-p})\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  operating-inputs-p-implies-run-inputs-p \\ \index{operating-inputs-p-implies-run-i!nputs-p}
{\rm{operating-inputs-p}}\,({\it{inputs\/}}, {\it{n\/}})\index{operating-inputs-p} $\rightarrow$ {\rm{run-inputs-p}}\,({\it{inputs\/}}, {\it{n\/}})\index{run-inputs-p}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  operating-inputs-p-plus \\ \index{operating-inputs-p-plus}
\=\+{\rm{operating-inputs-p}}\,({\it{inputs\/}}, {\it{n\/}} $+$ {\it{m\/}})\index{operating-inputs-p} \\ 
$=$$\;\;\;\;$(\=\+{\rm{operating-inputs-p}}\,({\it{inputs\/}}, {\it{n\/}})\index{operating-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{operating-inputs-p}}\,({\rm{nthcdr}}\,({\it{n\/}}, {\it{inputs\/}})\index{nthcdr}, {\it{m\/}})\index{operating-inputs-p})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  operating-inputs-p-1 \\ \index{operating-inputs-p-1}
\=\+({\rm{operating-inputs-p}}\,({\it{inputs\/}}, {\it{n\/}})\index{operating-inputs-p} $\wedge$ ({\it{n\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;${\rm{operating-inputs-p}}\,({\it{inputs\/}}, {\tt{1}})\index{operating-inputs-p}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  operating-inputs-p-implies-hold--input \\ \index{operating-inputs-p-implies-hold!--input}
\=\+({\rm{operating-inputs-p}}\,({\it{inputs\/}}, {\it{n\/}})\index{operating-inputs-p} $\wedge$ ({\it{n\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$({\rm{hold--input}}\,({\rm{car}}\,({\it{inputs\/}}))\index{hold--input} $=$ {\bf{t}})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{microcycles} \\  
\=\+{\rm{microcycles}}\,({\it{state\/}})\index{microcycles} \\ 
$=$$\;\;\;\;${\rm{t\_fetch1}}\,(\=\+{\rm{caddadr}}\,({\it{state\/}}), \\ 
{\rm{read-mem}}\,(\=\+{\rm{read-mem}}\,({\rm{caddddddddddar}}\,({\it{state\/}}), {\rm{caaar}}\,({\it{state\/}}))\index{read-mem}, \\ 
{\rm{caadr}}\,({\it{state\/}}))\-\index{read-mem}, \\ 
{\rm{cadar}}\,({\it{state\/}}))\-\index{t\_fetch1}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{total-microcycles} \\  
\=\+{\rm{total-microcycles}}\,({\it{state\/}}, {\it{inputs\/}}, {\it{n\/}})\index{total-microcycles} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{0}} \\ 
{\bf else }\=\+{\rm{microcycles}}\,({\it{state\/}})\index{microcycles} \\ 
$+$$\;\;\;\;${\rm{total-microcycles}}\,(\=\+{\rm{run-fm9001}}\,(\=\+{\it{state\/}}, \\ 
{\it{inputs\/}}, \\ 
{\rm{microcycles}}\,({\it{state\/}})\index{microcycles})\-\index{run-fm9001}, \\ 
{\rm{nthcdr}}\,({\rm{microcycles}}\,({\it{state\/}})\index{microcycles}, {\it{inputs\/}})\index{nthcdr}, \\ 
{\it{n\/}} $-\;1$)\-\index{total-microcycles}\-$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable total-microcycles; name this event `total-microcycles-off'.\index{total-microcycles-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-total-microcycles \\ \index{open-total-microcycles}
\=\+(({\it{n\/}} $\simeq {\tt{0}}$) $\rightarrow$ ({\rm{total-microcycles}}\,({\it{state\/}}, {\it{inputs\/}}, {\it{n\/}})\index{total-microcycles} $=$ {\tt{0}})) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{total-microcycles}}\,({\it{state\/}}, {\it{inputs\/}}, {\it{n\/}})\index{total-microcycles} \\ 
$=$$\;\;\;\;$(\=\+{\rm{microcycles}}\,({\it{state\/}})\index{microcycles} \\ 
$+$$\;\;\;\;${\rm{total-microcycles}}\,(\=\+{\rm{run-fm9001}}\,(\=\+{\it{state\/}}, \\ 
{\it{inputs\/}}, \\ 
{\rm{microcycles}}\,({\it{state\/}})\index{microcycles})\-\index{run-fm9001}, \\ 
{\rm{nthcdr}}\,(\=\+{\rm{microcycles}}\,({\it{state\/}})\index{microcycles}, \\ 
{\it{inputs\/}})\-\index{nthcdr}, \\ 
{\it{n\/}} $-\;1$)\-\index{total-microcycles})\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{macrocycle-invariant} \\  
\=\+{\rm{macrocycle-invariant}}\,({\it{state\/}}, {\it{pc\/}})\index{macrocycle-invariant} \\ 
$=$$\;\;\;\;$(\=\+{\rm{all-ramp-mem}}\,({\tt{4}}, {\rm{caaar}}\,({\it{state\/}}))\index{all-ramp-mem} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{4}}, {\tt{32}}, {\rm{caaar}}\,({\it{state\/}}))\index{memory-okp} \\ 
$\wedge$$\;\;\;\;$({\rm{cadaar}}\,({\it{state\/}}) $=$ {\bf{f}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{caddaar}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{caddaar}}\,({\it{state\/}}))\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cadddaar}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cadddaar}}\,({\it{state\/}}))\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cadar}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cadar}}\,({\it{state\/}}))\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{caddar}}\,({\it{state\/}}) \\ 
$=$$\;\;\;\;${\rm{read-regs}}\,({\rm{caddddddddddar}}\,({\it{state\/}}), {\rm{caar}}\,({\it{state\/}}))\index{read-regs})\- \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cadddar}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cadddar}}\,({\it{state\/}}))\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{caddddar}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{caddddar}}\,({\it{state\/}}))\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cadddddar}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cadddddar}}\,({\it{state\/}}))\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{caddddddar}}\,({\it{state\/}}) \\ 
$=$$\;\;\;\;${\rm{read-regs}}\,({\rm{caddddddddddar}}\,({\it{state\/}}), {\rm{caar}}\,({\it{state\/}}))\index{read-regs})\- \\ 
$\wedge$$\;\;\;\;$({\rm{cadddddddar}}\,({\it{state\/}}) $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{caddddddddar}}\,({\it{state\/}}))\index{boolp} \\ 
$\wedge$$\;\;\;\;$({\rm{cadddddddddar}}\,({\it{state\/}}) $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{caddddddddddar}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{caddddddddddar}}\,({\it{state\/}}))\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;$({\rm{caddddddddddar}}\,({\it{state\/}}) $=$ {\it{pc\/}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{cadddddddddddar}}\,({\it{state\/}}) \\ 
$=$$\;\;\;\;${\rm{cv\_fetch1}}\,(\=\+{\rm{cadddddadr}}\,({\it{state\/}}), \\ 
{\rm{caddddddddddar}}\,({\it{state\/}}), \\ 
{\rm{caddddar}}\,({\it{state\/}}), \\ 
{\rm{cadar}}\,({\it{state\/}}), \\ 
{\rm{caddddddddddar}}\,({\it{state\/}}))\-\index{cv\_fetch1})\- \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\rm{caadr}}\,({\it{state\/}}))\index{memory-okp} \\ 
$\wedge$$\;\;\;\;$({\rm{cadadr}}\,({\it{state\/}}) $=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadddadr}}\,({\it{state\/}}) $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{cadddddadr}}\,({\it{state\/}}))\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{caddddddadr}}\,({\it{state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{caddddddadr}}\,({\it{state\/}}))\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{cadddddddadr}}\,({\it{state\/}}))\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cadddddddadr}}\,({\it{state\/}}))\index{length} $=$ {\tt{32}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  macrocycle-invariant==$>$chip-system-invariant\$help \\ \index{macrocycle-invariant==$>$chip-s!ystem-invariant\$help}
\=\+{\rm{macrocycle-invariant}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,({\it{regs-regs\/}}, {\it{regs-we\/}}, {\it{regs-data\/}}, {\it{regs-address\/}}), \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\it{cntl\/}}, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}}, \\ 
{\it{dtack\/}}, \\ 
{\it{last-rw-\/}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{pc\/}})\-\index{macrocycle-invariant} \\ 
$\rightarrow$$\;\;\;\;${\rm{chip-system-invariant}}\,({\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-address\/}})\-, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\it{cntl\/}}, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}}, \\ 
{\it{dtack\/}}, \\ 
{\it{last-rw-\/}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-)\index{chip-system-invariant}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  macrocycle-invariant==$>$chip-system-invariant \\ \index{macrocycle-invariant==$>$chip-s!ystem-invariant}
\=\+({\rm{fm9001-state-structure}}\,({\it{state\/}})\index{fm9001-state-structure} $\wedge$ {\rm{macrocycle-invariant}}\,({\it{state\/}}, {\it{pc\/}})\index{macrocycle-invariant}) \\ 
$\rightarrow$$\;\;\;\;${\rm{chip-system-invariant}}\,({\it{state\/}})\index{chip-system-invariant}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{macrocycle-invariant*} \\  
{\rm{macrocycle-invariant*}}\,({\it{state\/}}, {\it{pc\/}})\index{macrocycle-invariant*} $=$ {\rm{macrocycle-invariant}}\,({\it{state\/}}, {\it{pc\/}})\index{macrocycle-invariant}
\end{tabbing}


\noindent{\sc Event}:   Enable macrocycle-invariant*; name this event `macrocycle-invariant*-off'.\index{macrocycle-invariant*-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  macrocycle-invariant*=macrocycle-invariant \\ \index{macrocycle-invariant*=macrocycle!-invariant}
{\rm{macrocycle-invariant*}}\,({\rm{cons}}\,({\it{x\/}}, {\it{y\/}}), {\it{pc\/}})\index{macrocycle-invariant*} $=$ {\rm{macrocycle-invariant}}\,({\rm{cons}}\,({\it{x\/}}, {\it{y\/}}), {\it{pc\/}})\index{macrocycle-invariant}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  macrocycle-invariant-is-invariant\$help \\ \index{macrocycle-invariant-is-invaria!nt\$help}
\=\+(\=\+{\rm{macrocycle-invariant}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-address\/}})\-, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\it{cntl\/}}, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}}, \\ 
{\it{dtack\/}}, \\ 
{\it{last-rw-\/}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{pc\/}})\-\index{macrocycle-invariant} \\ 
$\wedge$$\;\;\;\;${\rm{operating-inputs-p}}\,(\=\+{\it{inputs\/}}, \\ 
{\rm{microcycles}}\,({\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-address\/}})\-, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\it{cntl\/}}, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}}, \\ 
{\it{dtack\/}}, \\ 
{\it{last-rw-\/}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-)\index{microcycles})\-\index{operating-inputs-p})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{macrocycle-invariant*}}\,(\=\+{\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-address\/}})\-, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\it{cntl\/}}, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}}, \\ 
{\it{dtack\/}}, \\ 
{\it{last-rw-\/}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\rm{microcycles}}\,({\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-address\/}})\-, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\it{cntl\/}}, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}}, \\ 
{\it{dtack\/}}, \\ 
{\it{last-rw-\/}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-)\index{microcycles})\-\index{run-fm9001}, \\ 
{\it{pc\/}})\-\index{macrocycle-invariant*}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  macrocycle-invariant-is-invariant \\ \index{macrocycle-invariant-is-invaria!nt}
\=\+(\=\+{\rm{fm9001-state-structure}}\,({\it{state\/}})\index{fm9001-state-structure} \\ 
$\wedge$$\;\;\;\;${\rm{macrocycle-invariant}}\,({\it{state\/}}, {\it{pc\/}})\index{macrocycle-invariant} \\ 
$\wedge$$\;\;\;\;${\rm{operating-inputs-p}}\,({\it{inputs\/}}, {\rm{microcycles}}\,({\it{state\/}})\index{microcycles})\index{operating-inputs-p})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{macrocycle-invariant}}\,({\rm{run-fm9001}}\,({\it{state\/}}, {\it{inputs\/}}, {\rm{microcycles}}\,({\it{state\/}})\index{microcycles})\index{run-fm9001}, {\it{pc\/}})\index{macrocycle-invariant}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{p-map-up} \\  
{\rm{p-map-up}}\,({\it{p-state\/}})\index{p-map-up} $=$ {\rm{list}}\,({\rm{car}}\,({\rm{regs}}\,({\it{p-state\/}})\index{regs}), {\rm{flags}}\,({\it{p-state\/}})\index{flags})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{mem-map-up}$\;\;$
{\rm{mem-map-up}}\,({\it{mem-state\/}})\index{mem-map-up} $=$ {\rm{car}}\,({\it{mem-state\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{map-up} \\  
{\rm{map-up}}\,({\it{state\/}})\index{map-up} $=$ {\rm{list}}\,({\rm{p-map-up}}\,({\rm{car}}\,({\it{state\/}}))\index{p-map-up}, {\rm{mem-map-up}}\,({\rm{cadr}}\,({\it{state\/}}))\index{mem-map-up})
\end{tabbing}


\noindent{\sc Event}:   Enable map-up; name this event `map-up-off'.\index{map-up-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-map-up \\ \index{open-map-up}
\=\+{\rm{map-up}}\,({\rm{cons}}\,({\it{x\/}}, {\it{y\/}}))\index{map-up} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,({\rm{car}}\,({\rm{regs}}\,({\rm{car}}\,({\rm{cons}}\,({\it{x\/}}, {\it{y\/}})))\index{regs}), {\rm{flags}}\,({\rm{car}}\,({\rm{cons}}\,({\it{x\/}}, {\it{y\/}})))\index{flags}), \\ 
{\rm{caadr}}\,({\rm{cons}}\,({\it{x\/}}, {\it{y\/}})))\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fm9001-step*} \\  
{\rm{fm9001-step*}}\,({\it{state\/}}, {\it{pc-reg\/}})\index{fm9001-step*} $=$ {\rm{fm9001-step}}\,({\it{state\/}}, {\it{pc-reg\/}})\index{fm9001-step}
\end{tabbing}


\noindent{\sc Event}:   Enable fm9001-step*; name this event `fm9001-step*-off'.\index{fm9001-step*-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  fm9001-step*-lemma \\ \index{fm9001-step*-lemma}
\=\+({\rm{cons}}\,({\it{x\/}}, {\it{y\/}}) $=$ {\rm{fm9001-step*}}\,({\it{state\/}}, {\it{pc-reg\/}})\index{fm9001-step*}) \\ 
$=$$\;\;\;\;$({\rm{cons}}\,({\it{x\/}}, {\it{y\/}}) $=$ {\rm{fm9001-step}}\,({\it{state\/}}, {\it{pc-reg\/}})\index{fm9001-step})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  middle=high\$help \\ \index{middle=high\$help}
\=\+(\=\+{\rm{macrocycle-invariant}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-address\/}})\-, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\it{cntl\/}}, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}}, \\ 
{\it{dtack\/}}, \\ 
{\it{last-rw-\/}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{pc-reg\/}})\-\index{macrocycle-invariant} \\ 
$\wedge$$\;\;\;\;${\rm{operating-inputs-p}}\,(\=\+{\it{inputs\/}}, \\ 
{\rm{microcycles}}\,({\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-address\/}})\-, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\it{cntl\/}}, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}}, \\ 
{\it{dtack\/}}, \\ 
{\it{last-rw-\/}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-)\index{microcycles})\-\index{operating-inputs-p})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{map-up}}\,({\rm{run-fm9001}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-address\/}})\-, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\it{cntl\/}}, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}}, \\ 
{\it{dtack\/}}, \\ 
{\it{last-rw-\/}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-, \\ 
{\it{inputs\/}}, \\ 
{\rm{microcycles}}\,({\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\it{regs-regs\/}}, \\ 
{\it{regs-we\/}}, \\ 
{\it{regs-data\/}}, \\ 
{\it{regs-address\/}})\-, \\ 
{\it{flags\/}}, \\ 
{\it{a-reg\/}}, \\ 
{\it{b-reg\/}}, \\ 
{\it{i-reg\/}}, \\ 
{\it{data-out\/}}, \\ 
{\it{addr-out\/}}, \\ 
{\it{last-reset-\/}}, \\ 
{\it{last-dtack-\/}}, \\ 
{\it{last-hold-\/}}, \\ 
{\it{pc-reg\/}}, \\ 
{\it{cntl-state\/}})\-, \\ 
{\rm{list}}\,(\=\+{\it{mem\/}}, \\ 
{\it{cntl\/}}, \\ 
{\it{clock\/}}, \\ 
{\it{count\/}}, \\ 
{\it{dtack\/}}, \\ 
{\it{last-rw-\/}}, \\ 
{\it{last-address\/}}, \\ 
{\it{last-data\/}})\-)\-)\index{microcycles})\-\index{run-fm9001})\index{map-up} \\ 
$=$$\;\;\;\;${\rm{fm9001-step*}}\,({\rm{list}}\,({\rm{list}}\,({\it{regs-regs\/}}, {\it{flags\/}}), {\it{mem\/}}), {\it{pc-reg\/}})\index{fm9001-step*})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  macrocycle-invariant==$>$pc-reg \\ \index{macrocycle-invariant==$>$pc-reg}
{\rm{macrocycle-invariant}}\,({\it{state\/}}, {\it{pc-reg\/}})\index{macrocycle-invariant} $\rightarrow$ ({\rm{pc-reg}}\,({\rm{car}}\,({\it{state\/}}))\index{pc-reg} $=$ {\it{pc-reg\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  middle=high \\ \index{middle=high}
\=\+(\=\+{\rm{fm9001-state-structure}}\,({\it{state\/}})\index{fm9001-state-structure} \\ 
$\wedge$$\;\;\;\;${\rm{macrocycle-invariant}}\,({\it{state\/}}, {\it{pc\/}})\index{macrocycle-invariant} \\ 
$\wedge$$\;\;\;\;${\rm{operating-inputs-p}}\,({\it{inputs\/}}, {\rm{microcycles}}\,({\it{state\/}})\index{microcycles})\index{operating-inputs-p})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{map-up}}\,({\rm{run-fm9001}}\,({\it{state\/}}, {\it{inputs\/}}, {\rm{microcycles}}\,({\it{state\/}})\index{microcycles})\index{run-fm9001})\index{map-up} \\ 
$=$$\;\;\;\;${\rm{fm9001-step}}\,({\rm{map-up}}\,({\it{state\/}})\index{map-up}, {\it{pc\/}})\index{fm9001-step})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fm9001-interpreter-correct \\ \index{fm9001-interpreter-correct}
\=\+(\=\+{\rm{fm9001-state-structure}}\,({\it{state\/}})\index{fm9001-state-structure} \\ 
$\wedge$$\;\;\;\;${\rm{macrocycle-invariant}}\,({\it{state\/}}, {\it{pc\/}})\index{macrocycle-invariant} \\ 
$\wedge$$\;\;\;\;${\rm{operating-inputs-p}}\,(\=\+{\it{inputs\/}}, \\ 
{\rm{total-microcycles}}\,({\it{state\/}}, {\it{inputs\/}}, {\it{instructions\/}})\index{total-microcycles})\-\index{operating-inputs-p})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{map-up}}\,({\rm{run-fm9001}}\,(\=\+{\it{state\/}}, \\ 
{\it{inputs\/}}, \\ 
{\rm{total-microcycles}}\,({\it{state\/}}, {\it{inputs\/}}, {\it{instructions\/}})\index{total-microcycles})\-\index{run-fm9001})\index{map-up} \\ 
$=$$\;\;\;\;${\rm{fm9001-interpreter}}\,({\rm{map-up}}\,({\it{state\/}})\index{map-up}, {\it{pc\/}}, {\it{instructions\/}})\index{fm9001-interpreter})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  chip-system=fm9001-interpreter \\ \index{chip-system=fm9001-interpreter}
\=\+(\=\+{\rm{chip-system\&}}\,({\it{netlist\/}})\index{chip-system\&} \\ 
$\wedge$$\;\;\;\;${\rm{fm9001-state-structure}}\,({\it{state\/}})\index{fm9001-state-structure} \\ 
$\wedge$$\;\;\;\;${\rm{macrocycle-invariant}}\,({\it{state\/}}, {\it{pc\/}})\index{macrocycle-invariant} \\ 
$\wedge$$\;\;\;\;${\rm{chip-system-operating-inputs-p}}\,(\=\+{\it{inputs\/}}, \\ 
{\rm{total-microcycles}}\,(\=\+{\it{state\/}}, \\ 
{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\it{instructions\/}})\-\index{total-microcycles})\-\index{chip-system-operating-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{operating-inputs-p}}\,(\=\+{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\rm{total-microcycles}}\,(\=\+{\it{state\/}}, \\ 
{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\it{instructions\/}})\-\index{total-microcycles})\-\index{operating-inputs-p})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{map-up}}\,({\rm{simulate-dual-eval-2}}\,(\=\+{\tt{'}}{\tt{chip-system}}, \\ 
{\it{inputs\/}}, \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}}, \\ 
{\rm{total-microcycles}}\,(\=\+{\it{state\/}}, \\ 
{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\it{instructions\/}})\-\index{total-microcycles})\-\index{simulate-dual-eval-2})\index{map-up} \\ 
$=$$\;\;\;\;${\rm{fm9001-interpreter}}\,({\rm{map-up}}\,({\it{state\/}})\index{map-up}, {\it{pc\/}}, {\it{instructions\/}})\index{fm9001-interpreter})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fm9001=fm9001-interpreter \\ \index{fm9001=fm9001-interpreter}
{\rm{fm9001}}\,({\it{state\/}}, {\it{n\/}})\index{fm9001} $=$ {\rm{fm9001-interpreter}}\,({\it{state\/}}, {\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list}, {\it{n\/}})\index{fm9001-interpreter}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{map-down-relation} \\  
\=\+{\rm{map-down-relation}}\,({\it{high-level-state\/}}, {\it{low-level-state\/}})\index{map-down-relation} \\ 
$=$$\;\;\;\;$(\=\+({\rm{regs}}\,({\rm{car}}\,({\it{high-level-state\/}}))\index{regs} $=$ {\rm{car}}\,({\rm{regs}}\,({\rm{car}}\,({\it{low-level-state\/}}))\index{regs})) \\ 
$\wedge$$\;\;\;\;$({\rm{flags}}\,({\rm{car}}\,({\it{high-level-state\/}}))\index{flags} $=$ {\rm{flags}}\,({\rm{car}}\,({\it{low-level-state\/}}))\index{flags}) \\ 
$\wedge$$\;\;\;\;$({\rm{cadr}}\,({\it{high-level-state\/}}) $=$ {\rm{caadr}}\,({\it{low-level-state\/}})))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable map-down-relation; name this event `map-down-relation-off'.\index{map-down-relation-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{high-level-state-structure} \\  
\=\+{\rm{high-level-state-structure}}\,({\it{state\/}})\index{high-level-state-structure} \\ 
$=$$\;\;\;\;$(\=\+{\rm{properp}}\,({\it{state\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{car}}\,({\it{state\/}}))\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{car}}\,({\it{state\/}}))\index{length} $=$ {\tt{2}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{state\/}})\index{length} $=$ {\tt{2}}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable high-level-state-structure; name this event `high-level-state-structure-off'.\index{high-level-state-structure-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  map-down-relation-lemma \\ \index{map-down-relation-lemma}
\=\+(\=\+{\rm{high-level-state-structure}}\,({\it{high-level-state\/}})\index{high-level-state-structure} \\ 
$\wedge$$\;\;\;\;${\rm{map-down-relation}}\,({\it{high-level-state\/}}, {\it{low-level-state\/}})\index{map-down-relation})\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{map-up}}\,({\it{low-level-state\/}})\index{map-up} $=$ {\it{high-level-state\/}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fm9001-interpreter-correct\$map-down \\ \index{fm9001-interpreter-correct\$map!-down}
\=\+(\=\+{\rm{high-level-state-structure}}\,({\it{high-level-state\/}})\index{high-level-state-structure} \\ 
$\wedge$$\;\;\;\;${\rm{map-down-relation}}\,({\it{high-level-state\/}}, {\it{low-level-state\/}})\index{map-down-relation} \\ 
$\wedge$$\;\;\;\;${\rm{fm9001-state-structure}}\,({\it{low-level-state\/}})\index{fm9001-state-structure} \\ 
$\wedge$$\;\;\;\;${\rm{macrocycle-invariant}}\,({\it{low-level-state\/}}, {\it{pc\/}})\index{macrocycle-invariant} \\ 
$\wedge$$\;\;\;\;${\rm{operating-inputs-p}}\,(\=\+{\it{inputs\/}}, \\ 
{\rm{total-microcycles}}\,({\it{low-level-state\/}}, {\it{inputs\/}}, {\it{n\/}})\index{total-microcycles})\-\index{operating-inputs-p})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{map-up}}\,({\rm{run-fm9001}}\,(\=\+{\it{low-level-state\/}}, \\ 
{\it{inputs\/}}, \\ 
{\rm{total-microcycles}}\,({\it{low-level-state\/}}, {\it{inputs\/}}, {\it{n\/}})\index{total-microcycles})\-\index{run-fm9001})\index{map-up} \\ 
$=$$\;\;\;\;${\rm{fm9001-interpreter}}\,({\it{high-level-state\/}}, {\it{pc\/}}, {\it{n\/}})\index{fm9001-interpreter})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fm9001-machine-statep} \\  
\=\+{\rm{fm9001-machine-statep}}\,({\it{p-state\/}})\index{fm9001-machine-statep} \\ 
$=$$\;\;\;\;$(\=\+{\rm{properp}}\,({\it{p-state\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{p-state\/}})\index{length} $=$ {\tt{2}}) \\ 
$\wedge$$\;\;\;\;${\rm{all-ramp-mem}}\,({\tt{4}}, {\rm{car}}\,({\it{p-state\/}}))\index{all-ramp-mem} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{4}}, {\tt{32}}, {\rm{car}}\,({\it{p-state\/}}))\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{bvp}}\,({\rm{cadr}}\,({\it{p-state\/}}))\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cadr}}\,({\it{p-state\/}}))\index{length} $=$ {\tt{4}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fm9001-statep} \\  
\=\+{\rm{fm9001-statep}}\,({\it{state\/}})\index{fm9001-statep} \\ 
$=$$\;\;\;\;$(\=\+{\rm{properp}}\,({\it{state\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{state\/}})\index{length} $=$ {\tt{2}}) \\ 
$\wedge$$\;\;\;\;${\rm{fm9001-machine-statep}}\,({\rm{car}}\,({\it{state\/}}))\index{fm9001-machine-statep} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\rm{cadr}}\,({\it{state\/}}))\index{memory-okp})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{p-map-down} \\  
\=\+{\rm{p-map-down}}\,({\it{p-state\/}})\index{p-map-down} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{list}}\,({\rm{car}}\,({\it{p-state\/}}), {\bf{f}}, {\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, {\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list}), \\ 
{\rm{cadr}}\,({\it{p-state\/}}), \\ 
{\rm{read-mem}}\,({\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list}, {\rm{car}}\,({\it{p-state\/}}))\index{read-mem}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, \\ 
{\rm{read-mem}}\,({\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list}, {\rm{car}}\,({\it{p-state\/}}))\index{read-mem}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list}, \\ 
{\rm{cv\_fetch1}}\,(\=\+{\bf{t}}, \\ 
{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}), \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, \\ 
{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}), \\ 
{\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list})\-\index{cv\_fetch1})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{mem-map-down} \\  
\=\+{\rm{mem-map-down}}\,({\it{memory\/}})\index{mem-map-down} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\it{memory\/}}, {\tt{0}}, {\tt{0}}, {\tt{0}}, {\bf{t}}, {\bf{t}}, {\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, {\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{map-down} \\  
{\rm{map-down}}\,({\it{state\/}})\index{map-down} $=$ {\rm{list}}\,({\rm{p-map-down}}\,({\rm{car}}\,({\it{state\/}}))\index{p-map-down}, {\rm{mem-map-down}}\,({\rm{cadr}}\,({\it{state\/}}))\index{mem-map-down})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  map-up-inverts-map-down \\ \index{map-up-inverts-map-down}
{\rm{fm9001-statep}}\,({\it{state\/}})\index{fm9001-statep} $\rightarrow$ ({\rm{map-up}}\,({\rm{map-down}}\,({\it{state\/}})\index{map-down})\index{map-up} $=$ {\it{state\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fm9001-statep-implies-fm9001-state-structure \\ \index{fm9001-statep-implies-fm9001-st!ate-structure}
{\rm{fm9001-statep}}\,({\it{state\/}})\index{fm9001-statep} $\rightarrow$ {\rm{fm9001-state-structure}}\,({\rm{map-down}}\,({\it{state\/}})\index{map-down})\index{fm9001-state-structure}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fm9001-statep-implies-macrocycle-invariant-lemma1 \\ \index{fm9001-statep-implies-macrocycle!-invariant-lemma1}
\=\+(\=\+{\rm{cv\_fetch1}}\,({\bf{t}}, {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}), {\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}), {\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list})\index{cv\_fetch1} \\ 
$=$$\;\;\;\;${\rm{cv\_fetch1}}\,({\bf{t}}, {\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list}, {\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, {\it{z\/}}, {\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list})\index{cv\_fetch1})\- \\ 
$=$$\;\;\;\;${\bf{t}}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fm9001-statep-implies-macrocycle-invariant \\ \index{fm9001-statep-implies-macrocycle!-invariant}
\=\+{\rm{fm9001-statep}}\,({\it{state\/}})\index{fm9001-statep} \\ 
$\rightarrow$$\;\;\;\;${\rm{macrocycle-invariant}}\,({\rm{map-down}}\,({\it{state\/}})\index{map-down}, {\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list})\index{macrocycle-invariant}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fm9001=chip-system-lemma1 \\ \index{fm9001=chip-system-lemma1}
{\rm{nth}}\,({\tt{10}}, {\rm{car}}\,({\rm{map-down}}\,({\it{state\/}})\index{map-down}))\index{nth} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fm9001=chip-system \\ \index{fm9001=chip-system}
\=\+(\=\+{\rm{chip-system\&}}\,({\it{netlist\/}})\index{chip-system\&} \\ 
$\wedge$$\;\;\;\;${\rm{fm9001-statep}}\,({\it{state\/}})\index{fm9001-statep} \\ 
$\wedge$$\;\;\;\;${\rm{chip-system-operating-inputs-p}}\,(\=\+{\it{inputs\/}}, \\ 
{\rm{total-microcycles}}\,(\=\+{\rm{map-down}}\,({\it{state\/}})\index{map-down}, \\ 
{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\it{n\/}})\-\index{total-microcycles})\-\index{chip-system-operating-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{operating-inputs-p}}\,(\=\+{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\rm{total-microcycles}}\,(\=\+{\rm{map-down}}\,({\it{state\/}})\index{map-down}, \\ 
{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\it{n\/}})\-\index{total-microcycles})\-\index{operating-inputs-p})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{fm9001}}\,({\it{state\/}}, {\it{n\/}})\index{fm9001} \\ 
$=$$\;\;\;\;${\rm{map-up}}\,({\rm{simulate-dual-eval-2}}\,(\=\+{\tt{'}}{\tt{chip-system}}, \\ 
{\it{inputs\/}}, \\ 
{\rm{map-down}}\,({\it{state\/}})\index{map-down}, \\ 
{\it{netlist\/}}, \\ 
{\rm{total-microcycles}}\,(\=\+{\rm{map-down}}\,({\it{state\/}})\index{map-down}, \\ 
{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\it{n\/}})\-\index{total-microcycles})\-\index{simulate-dual-eval-2})\index{map-up})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{no-holds-reset-or-test} \\  
\=\+{\rm{no-holds-reset-or-test}}\,({\it{i\/}}, {\it{c\/}})\index{no-holds-reset-or-test} \\ 
$=$$\;\;\;\;$(\=\+{\rm{chip-system-operating-inputs-p}}\,({\it{i\/}}, {\it{c\/}})\index{chip-system-operating-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{operating-inputs-p}}\,({\rm{map-up-inputs}}\,({\it{i\/}})\index{map-up-inputs}, {\it{c\/}})\index{operating-inputs-p})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fm9001=chip-system-summary \\ \index{fm9001=chip-system-summary}
\=\+(\=\+{\rm{fm9001-statep}}\,({\it{s\/}})\index{fm9001-statep} \\ 
$\wedge$$\;\;\;\;${\rm{no-holds-reset-or-test}}\,(\=\+{\it{i\/}}, \\ 
{\rm{total-microcycles}}\,(\=\+{\rm{map-down}}\,({\it{s\/}})\index{map-down}, \\ 
{\rm{map-up-inputs}}\,({\it{i\/}})\index{map-up-inputs}, \\ 
{\it{n\/}})\-\index{total-microcycles})\-\index{no-holds-reset-or-test})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{fm9001}}\,({\it{s\/}}, {\it{n\/}})\index{fm9001} \\ 
$=$$\;\;\;\;${\rm{map-up}}\,({\rm{simulate-dual-eval-2}}\,(\=\+{\tt{'}}{\tt{chip-system}}, \\ 
{\it{i\/}}, \\ 
{\rm{map-down}}\,({\it{s\/}})\index{map-down}, \\ 
{\sc{chip-system\$netlist}}\index{chip-system\$netlist}, \\ 
{\rm{total-microcycles}}\,(\=\+{\rm{map-down}}\,({\it{s\/}})\index{map-down}, \\ 
{\rm{map-up-inputs}}\,({\it{i\/}})\index{map-up-inputs}, \\ 
{\it{n\/}})\-\index{total-microcycles})\-\index{simulate-dual-eval-2})\index{map-up})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{b-knownp} \\  
{\rm{b-knownp}}\,({\it{x\/}})\index{b-knownp} $=$ (({\it{x\/}} $=$ {\bf{t}}) $\vee$ ({\it{x\/}} $=$ {\bf{f}}) $\vee$ ({\it{x\/}} $=$ {\sc{z}}\index{z}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-knownp-compound-recognizer \\ \index{b-knownp-compound-recognizer}
{\rm{b-knownp}}\,({\it{x\/}})\index{b-knownp} $=$ ({\rm{truep}}\,({\it{x\/}}) $\vee$ {\rm{falsep}}\,({\it{x\/}}) $\vee$ {\rm{zp}}\,({\it{x\/}})\index{zp})
\end{tabbing}


\noindent{\sc Event}:   Enable b-knownp; name this event `b-knownp-off'.\index{b-knownp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*b-knownp; name this event `g*1*b-knownp-off'.\index{g*1*b-knownp-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-approx} \\  
\=\+{\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{b-knownp}}\,({\it{a1\/}})\index{b-knownp}$\;\;${\bf then }{\it{a1\/}} $=$ {\it{a2\/}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-approx} \\  
\=\+{\rm{v-approx}}\,({\it{v1\/}}, {\it{v2\/}})\index{v-approx} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{v1\/}}) \\ 
{\bf then }\=\+{\rm{listp}}\,({\it{v2\/}}) \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\rm{car}}\,({\it{v1\/}}), {\rm{car}}\,({\it{v2\/}}))\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{v-approx}}\,({\rm{cdr}}\,({\it{v1\/}}), {\rm{cdr}}\,({\it{v2\/}}))\index{v-approx}\- \\ 
{\bf else }{\it{v1\/}} $=$ {\it{v2\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-knownp} \\  
\=\+{\rm{v-knownp}}\,({\it{x\/}})\index{v-knownp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}})$\;\;${\bf then }{\rm{b-knownp}}\,({\rm{car}}\,({\it{x\/}}))\index{b-knownp} $\wedge$ {\rm{v-knownp}}\,({\rm{cdr}}\,({\it{x\/}}))\index{v-knownp} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-knownp-implies-v-approx-is-equal \\ \index{v-knownp-implies-v-approx-is-eq!ual}
(({\it{x\/}} $\not=$ {\it{y\/}}) $\wedge$ {\rm{v-knownp}}\,({\it{x\/}})\index{v-knownp}) $\rightarrow$ ($\neg$ {\rm{v-approx}}\,({\it{x\/}}, {\it{y\/}})\index{v-approx})
\end{tabbing}


\noindent{\sc Event}:   Enable plus-add1; name this event `plus-add1-off'.\index{plus-add1-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{mem-width}$\;\;$
{\sc{mem-width}}\index{mem-width} $=$ {\tt{32}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{s-approx} \\  
\=\+{\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{s1\/}}) $\vee$ {\rm{listp}}\,({\it{s2\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\it{s1\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\it{s2\/}}) \\ 
{\bf then }\=\+{\rm{s-approx}}\,({\rm{car}}\,({\it{s1\/}}), {\rm{car}}\,({\it{s2\/}}))\index{s-approx} \\ 
$\wedge$$\;\;\;\;${\rm{s-approx}}\,({\rm{cdr}}\,({\it{s1\/}}), {\rm{cdr}}\,({\it{s2\/}}))\index{s-approx}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }({\it{s1\/}} $=$ {\bf{nil}}) $\vee$ ({\it{s2\/}} $=$ {\bf{nil}})$\;\;${\bf then }{\it{s1\/}} $=$ {\it{s2\/}} \\ 
{\bf elseif }{\rm{ramp}}\,({\it{s1\/}})\index{ramp} $\vee$ {\rm{ramp}}\,({\it{s2\/}})\index{ramp} \\ 
{\bf then }\=\+{\bf if }{\rm{ramp}}\,({\it{s1\/}})\index{ramp} \\ 
{\bf then }\=\+{\bf if }{\rm{ramp}}\,({\it{s2\/}})\index{ramp}$\;\;${\bf then }{\rm{v-approx}}\,({\rm{ram-guts}}\,({\it{s1\/}})\index{ram-guts}, {\rm{ram-guts}}\,({\it{s2\/}})\index{ram-guts})\index{v-approx} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{romp}}\,({\it{s1\/}})\index{romp} $\vee$ {\rm{romp}}\,({\it{s2\/}})\index{romp} \\ 
{\bf then }\=\+{\bf if }{\rm{romp}}\,({\it{s1\/}})\index{romp} \\ 
{\bf then }\=\+{\bf if }{\rm{romp}}\,({\it{s2\/}})\index{romp}$\;\;${\bf then }{\rm{v-approx}}\,({\rm{rom-guts}}\,({\it{s1\/}})\index{rom-guts}, {\rm{rom-guts}}\,({\it{s2\/}})\index{rom-guts})\index{v-approx} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{stubp}}\,({\it{s1\/}})\index{stubp} $\vee$ {\rm{stubp}}\,({\it{s2\/}})\index{stubp} \\ 
{\bf then }\=\+{\bf if }{\rm{stubp}}\,({\it{s1\/}})\index{stubp} \\ 
{\bf then }\=\+{\bf if }{\rm{stubp}}\,({\it{s2\/}})\index{stubp}$\;\;${\bf then }{\rm{v-approx}}\,({\rm{stub-guts}}\,({\it{s1\/}})\index{stub-guts}, {\rm{stub-guts}}\,({\it{s2\/}})\index{stub-guts})\index{v-approx} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{b-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{b-approx}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  s-approx-x-x \\ \index{s-approx-x-x}
{\rm{s-approx}}\,({\it{x\/}}, {\it{x\/}})\index{s-approx}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{good-s} \\  
\=\+{\rm{good-s}}\,({\it{s\/}})\index{good-s} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{s\/}})$\;\;${\bf then }{\rm{good-s}}\,({\rm{car}}\,({\it{s\/}}))\index{good-s} $\wedge$ {\rm{good-s}}\,({\rm{cdr}}\,({\it{s\/}}))\index{good-s} \\ 
{\bf elseif }{\rm{ramp}}\,({\it{s\/}})\index{ramp} \\ 
{\bf then }({\rm{length}}\,({\rm{ram-guts}}\,({\it{s\/}})\index{ram-guts})\index{length} $=$ {\sc{mem-width}}\index{mem-width}) $\wedge$ {\rm{properp}}\,({\rm{ram-guts}}\,({\it{s\/}})\index{ram-guts})\index{properp} \\ 
{\bf elseif }{\rm{romp}}\,({\it{s\/}})\index{romp} \\ 
{\bf then }({\rm{length}}\,({\rm{rom-guts}}\,({\it{s\/}})\index{rom-guts})\index{length} $=$ {\sc{mem-width}}\index{mem-width}) $\wedge$ {\rm{properp}}\,({\rm{rom-guts}}\,({\it{s\/}})\index{rom-guts})\index{properp} \\ 
{\bf elseif }{\rm{stubp}}\,({\it{s\/}})\index{stubp} \\ 
{\bf then }({\rm{length}}\,({\rm{stub-guts}}\,({\it{s\/}})\index{stub-guts})\index{length} $=$ {\sc{mem-width}}\index{mem-width}) $\wedge$ {\rm{properp}}\,({\rm{stub-guts}}\,({\it{s\/}})\index{stub-guts})\index{properp} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{s-knownp} \\  
\=\+{\rm{s-knownp}}\,({\it{s\/}})\index{s-knownp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{s\/}})$\;\;${\bf then }{\rm{s-knownp}}\,({\rm{car}}\,({\it{s\/}}))\index{s-knownp} $\wedge$ {\rm{s-knownp}}\,({\rm{cdr}}\,({\it{s\/}}))\index{s-knownp} \\ 
{\bf elseif }{\it{s\/}} $=$ {\bf{nil}}$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\rm{ramp}}\,({\it{s\/}})\index{ramp}$\;\;${\bf then }{\rm{v-knownp}}\,({\rm{ram-guts}}\,({\it{s\/}})\index{ram-guts})\index{v-knownp} \\ 
{\bf elseif }{\rm{romp}}\,({\it{s\/}})\index{romp}$\;\;${\bf then }{\rm{v-knownp}}\,({\rm{rom-guts}}\,({\it{s\/}})\index{rom-guts})\index{v-knownp} \\ 
{\bf elseif }{\rm{stubp}}\,({\it{s\/}})\index{stubp}$\;\;${\bf then }{\rm{v-knownp}}\,({\rm{stub-guts}}\,({\it{s\/}})\index{stub-guts})\index{v-knownp} \\ 
{\bf else }{\rm{b-knownp}}\,({\it{s\/}})\index{b-knownp}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  s-knownp-implies-s-approx-is-equal \\ \index{s-knownp-implies-s-approx-is-eq!ual}
({\rm{s-knownp}}\,({\it{x\/}})\index{s-knownp} $\wedge$ ({\it{x\/}} $\not=$ {\it{y\/}})) $\rightarrow$ ($\neg$ {\rm{s-approx}}\,({\it{x\/}}, {\it{y\/}})\index{s-approx})
\end{tabbing}


\noindent{\sc Event}:   Disable plus-add1; name this event `plus-add1-on'.\index{plus-add1-on}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-approx-alist} \\  
\=\+{\rm{v-approx-alist}}\,({\it{alist1\/}}, {\it{alist2\/}})\index{v-approx-alist} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{alist1\/}}) \\ 
{\bf then }\=\+{\rm{listp}}\,({\it{alist2\/}}) \\ 
$\wedge$$\;\;\;\;$({\rm{caar}}\,({\it{alist1\/}}) $=$ {\rm{caar}}\,({\it{alist2\/}})) \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\rm{cdar}}\,({\it{alist1\/}}), {\rm{cdar}}\,({\it{alist2\/}}))\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{v-approx-alist}}\,({\rm{cdr}}\,({\it{alist1\/}}), {\rm{cdr}}\,({\it{alist2\/}}))\index{v-approx-alist}\- \\ 
{\bf else }{\it{alist2\/}} $\simeq\;${{\bf{nil}}}${}$$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{s-approx-alist} \\  
\=\+{\rm{s-approx-alist}}\,({\it{alist1\/}}, {\it{alist2\/}})\index{s-approx-alist} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{alist1\/}}) \\ 
{\bf then }\=\+{\rm{listp}}\,({\it{alist2\/}}) \\ 
$\wedge$$\;\;\;\;$({\rm{caar}}\,({\it{alist1\/}}) $=$ {\rm{caar}}\,({\it{alist2\/}})) \\ 
$\wedge$$\;\;\;\;${\rm{s-approx}}\,({\rm{cdar}}\,({\it{alist1\/}}), {\rm{cdar}}\,({\it{alist2\/}}))\index{s-approx} \\ 
$\wedge$$\;\;\;\;${\rm{s-approx-alist}}\,({\rm{cdr}}\,({\it{alist1\/}}), {\rm{cdr}}\,({\it{alist2\/}}))\index{s-approx-alist}\- \\ 
{\bf else }{\it{alist2\/}} $\simeq\;${{\bf{nil}}}${}$$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{monotonicity-property} \\  
\=\+{\rm{monotonicity-property}}\,({\it{flag\/}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{flag\/}}: \\ 
{\bf case = }{\tt{0}} \\ 
{\bf then }\=\+({\rm{v-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{v-approx} $\wedge$ {\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{v-approx}}\,(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\it{fn\/}}, {\it{a1\/}}, {\it{s1\/}}, {\it{netlist\/}})\index{dual-eval}, \\ 
{\rm{dual-eval}}\,({\tt{0}}, {\it{fn\/}}, {\it{a2\/}}, {\it{s2\/}}, {\it{netlist\/}})\index{dual-eval})\-\index{v-approx}\- \\ 
{\bf case = }{\tt{1}} \\ 
{\bf $\;\;$then }\=\+(\=\+{\rm{v-approx-alist}}\,({\it{a1\/}}, {\it{a2\/}})\index{v-approx-alist} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{a1\/}})\index{alistp} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{a2\/}})\index{alistp} \\ 
$\wedge$$\;\;\;\;${\rm{s-approx-alist}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx-alist} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{s1\/}})\index{alistp} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{s2\/}})\index{alistp})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{v-approx-alist}}\,(\=\+{\rm{dual-eval}}\,({\tt{1}}, {\it{fn\/}}, {\it{a1\/}}, {\it{s1\/}}, {\it{netlist\/}})\index{dual-eval}, \\ 
{\rm{dual-eval}}\,({\tt{1}}, {\it{fn\/}}, {\it{a2\/}}, {\it{s2\/}}, {\it{netlist\/}})\index{dual-eval})\-\index{v-approx-alist}\- \\ 
{\bf case = }{\tt{2}} \\ 
{\bf $\;\;$then }\=\+({\rm{v-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{v-approx} $\wedge$ {\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx}}\,(\=\+{\rm{dual-eval}}\,({\tt{2}}, {\it{fn\/}}, {\it{a1\/}}, {\it{s1\/}}, {\it{netlist\/}})\index{dual-eval}, \\ 
{\rm{dual-eval}}\,({\tt{2}}, {\it{fn\/}}, {\it{a2\/}}, {\it{s2\/}}, {\it{netlist\/}})\index{dual-eval})\-\index{s-approx}\- \\ 
{\bf case = }{\tt{3}} \\ 
{\bf $\;\;$then }\=\+(\=\+{\rm{v-approx-alist}}\,({\it{a1\/}}, {\it{a2\/}})\index{v-approx-alist} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{a1\/}})\index{alistp} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{a2\/}})\index{alistp} \\ 
$\wedge$$\;\;\;\;${\rm{s-approx-alist}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx-alist} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{s1\/}})\index{alistp} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{s2\/}})\index{alistp})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx-alist}}\,(\=\+{\rm{dual-eval}}\,({\tt{3}}, {\it{fn\/}}, {\it{a1\/}}, {\it{s1\/}}, {\it{netlist\/}})\index{dual-eval}, \\ 
{\rm{dual-eval}}\,({\tt{3}}, {\it{fn\/}}, {\it{a2\/}}, {\it{s2\/}}, {\it{netlist\/}})\index{dual-eval})\-\index{s-approx-alist}\- \\ 
{\bf otherwise }{\bf{t}}$\;${\bf  endcase}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable monotonicity-property; name this event `monotonicity-property-off'.\index{monotonicity-property-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  monotonicity-property-consequence-0 \\ \index{monotonicity-property-consequen!ce-0}
\=\+(\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{v-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{v-approx} \\ 
$\wedge$$\;\;\;\;${\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{v-approx}}\,({\rm{dual-eval}}\,({\tt{0}}, {\it{fn\/}}, {\it{a1\/}}, {\it{s1\/}}, {\it{netlist\/}})\index{dual-eval}, {\rm{dual-eval}}\,({\tt{0}}, {\it{fn\/}}, {\it{a2\/}}, {\it{s2\/}}, {\it{netlist\/}})\index{dual-eval})\index{v-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  monotonicity-property-consequence-1 \\ \index{monotonicity-property-consequen!ce-1}
\=\+(\=\+{\rm{monotonicity-property}}\,({\tt{1}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{v-approx-alist}}\,({\it{a1\/}}, {\it{a2\/}})\index{v-approx-alist} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{a1\/}})\index{alistp} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{a2\/}})\index{alistp} \\ 
$\wedge$$\;\;\;\;${\rm{s-approx-alist}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx-alist} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{s1\/}})\index{alistp} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{s2\/}})\index{alistp})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{v-approx-alist}}\,(\=\+{\rm{dual-eval}}\,({\tt{1}}, {\it{fn\/}}, {\it{a1\/}}, {\it{s1\/}}, {\it{netlist\/}})\index{dual-eval}, \\ 
{\rm{dual-eval}}\,({\tt{1}}, {\it{fn\/}}, {\it{a2\/}}, {\it{s2\/}}, {\it{netlist\/}})\index{dual-eval})\-\index{v-approx-alist}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  monotonicity-property-consequence-2 \\ \index{monotonicity-property-consequen!ce-2}
\=\+(\=\+{\rm{monotonicity-property}}\,({\tt{2}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{v-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{v-approx} \\ 
$\wedge$$\;\;\;\;${\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx}}\,({\rm{dual-eval}}\,({\tt{2}}, {\it{fn\/}}, {\it{a1\/}}, {\it{s1\/}}, {\it{netlist\/}})\index{dual-eval}, {\rm{dual-eval}}\,({\tt{2}}, {\it{fn\/}}, {\it{a2\/}}, {\it{s2\/}}, {\it{netlist\/}})\index{dual-eval})\index{s-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  monotonicity-property-consequence-3 \\ \index{monotonicity-property-consequen!ce-3}
\=\+(\=\+{\rm{monotonicity-property}}\,({\tt{3}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{v-approx-alist}}\,({\it{a1\/}}, {\it{a2\/}})\index{v-approx-alist} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{a1\/}})\index{alistp} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{a2\/}})\index{alistp} \\ 
$\wedge$$\;\;\;\;${\rm{s-approx-alist}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx-alist} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{s1\/}})\index{alistp} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{s2\/}})\index{alistp})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx-alist}}\,(\=\+{\rm{dual-eval}}\,({\tt{3}}, {\it{fn\/}}, {\it{a1\/}}, {\it{s1\/}}, {\it{netlist\/}})\index{dual-eval}, \\ 
{\rm{dual-eval}}\,({\tt{3}}, {\it{fn\/}}, {\it{a2\/}}, {\it{s2\/}}, {\it{netlist\/}})\index{dual-eval})\-\index{s-approx-alist}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  monotonicity-property-opener-0 \\ \index{monotonicity-property-opener-0}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\leftrightarrow$$\;\;\;\;$(\=\+({\rm{v-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{v-approx} $\wedge$ {\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{v-approx}}\,(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\it{fn\/}}, {\it{a1\/}}, {\it{s1\/}}, {\it{netlist\/}})\index{dual-eval}, \\ 
{\rm{dual-eval}}\,({\tt{0}}, {\it{fn\/}}, {\it{a2\/}}, {\it{s2\/}}, {\it{netlist\/}})\index{dual-eval})\-\index{v-approx})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  monotonicity-property-opener-1 \\ \index{monotonicity-property-opener-1}
\=\+{\rm{monotonicity-property}}\,({\tt{1}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\leftrightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{v-approx-alist}}\,({\it{a1\/}}, {\it{a2\/}})\index{v-approx-alist} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{a1\/}})\index{alistp} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{a2\/}})\index{alistp} \\ 
$\wedge$$\;\;\;\;${\rm{s-approx-alist}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx-alist} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{s1\/}})\index{alistp} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{s2\/}})\index{alistp})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{v-approx-alist}}\,(\=\+{\rm{dual-eval}}\,({\tt{1}}, {\it{fn\/}}, {\it{a1\/}}, {\it{s1\/}}, {\it{netlist\/}})\index{dual-eval}, \\ 
{\rm{dual-eval}}\,({\tt{1}}, {\it{fn\/}}, {\it{a2\/}}, {\it{s2\/}}, {\it{netlist\/}})\index{dual-eval})\-\index{v-approx-alist})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  monotonicity-property-opener-2 \\ \index{monotonicity-property-opener-2}
\=\+{\rm{monotonicity-property}}\,({\tt{2}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\leftrightarrow$$\;\;\;\;$(\=\+({\rm{v-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{v-approx} $\wedge$ {\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx}}\,(\=\+{\rm{dual-eval}}\,({\tt{2}}, {\it{fn\/}}, {\it{a1\/}}, {\it{s1\/}}, {\it{netlist\/}})\index{dual-eval}, \\ 
{\rm{dual-eval}}\,({\tt{2}}, {\it{fn\/}}, {\it{a2\/}}, {\it{s2\/}}, {\it{netlist\/}})\index{dual-eval})\-\index{s-approx})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  monotonicity-property-opener-3 \\ \index{monotonicity-property-opener-3}
\=\+{\rm{monotonicity-property}}\,({\tt{3}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\leftrightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{v-approx-alist}}\,({\it{a1\/}}, {\it{a2\/}})\index{v-approx-alist} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{a1\/}})\index{alistp} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{a2\/}})\index{alistp} \\ 
$\wedge$$\;\;\;\;${\rm{s-approx-alist}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx-alist} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{s1\/}})\index{alistp} \\ 
$\wedge$$\;\;\;\;${\rm{alistp}}\,({\it{s2\/}})\index{alistp})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx-alist}}\,(\=\+{\rm{dual-eval}}\,({\tt{3}}, {\it{fn\/}}, {\it{a1\/}}, {\it{s1\/}}, {\it{netlist\/}})\index{dual-eval}, \\ 
{\rm{dual-eval}}\,({\tt{3}}, {\it{fn\/}}, {\it{a2\/}}, {\it{s2\/}}, {\it{netlist\/}})\index{dual-eval})\-\index{s-approx-alist})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable monotonicity-property-opener-0; name this event `monotonicity-property-opener-0-off'.\index{monotonicity-property-opener-0-!off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable monotonicity-property-opener-1; name this event `monotonicity-property-opener-1-off'.\index{monotonicity-property-opener-1-!off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable monotonicity-property-opener-2; name this event `monotonicity-property-opener-2-off'.\index{monotonicity-property-opener-2-!off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable monotonicity-property-opener-3; name this event `monotonicity-property-opener-3-off'.\index{monotonicity-property-opener-3-!off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  f-buf-monotone \\ \index{f-buf-monotone}
{\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} $\rightarrow$ {\rm{b-approx}}\,({\rm{f-buf}}\,({\it{a1\/}})\index{f-buf}, {\rm{f-buf}}\,({\it{a2\/}})\index{f-buf})\index{b-approx}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-and-monotone \\ \index{f-and-monotone}
\=\+({\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{f-and}}\,({\it{a1\/}}, {\it{b1\/}})\index{f-and}, {\rm{f-and}}\,({\it{a2\/}}, {\it{b2\/}})\index{f-and})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-and3-monotone \\ \index{f-and3-monotone}
\=\+({\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{c1\/}}, {\it{c2\/}})\index{b-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{f-and3}}\,({\it{a1\/}}, {\it{b1\/}}, {\it{c1\/}})\index{f-and3}, {\rm{f-and3}}\,({\it{a2\/}}, {\it{b2\/}}, {\it{c2\/}})\index{f-and3})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-and4-monotone \\ \index{f-and4-monotone}
\=\+({\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{c1\/}}, {\it{c2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{d1\/}}, {\it{d2\/}})\index{b-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{f-and4}}\,({\it{a1\/}}, {\it{b1\/}}, {\it{c1\/}}, {\it{d1\/}})\index{f-and4}, {\rm{f-and4}}\,({\it{a2\/}}, {\it{b2\/}}, {\it{c2\/}}, {\it{d2\/}})\index{f-and4})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-not-monotone \\ \index{f-not-monotone}
{\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} $\rightarrow$ {\rm{b-approx}}\,({\rm{f-not}}\,({\it{a1\/}})\index{f-not}, {\rm{f-not}}\,({\it{a2\/}})\index{f-not})\index{b-approx}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-nand-monotone \\ \index{f-nand-monotone}
\=\+({\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{f-nand}}\,({\it{a1\/}}, {\it{b1\/}})\index{f-nand}, {\rm{f-nand}}\,({\it{a2\/}}, {\it{b2\/}})\index{f-nand})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-nand3-monotone \\ \index{f-nand3-monotone}
\=\+({\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{c1\/}}, {\it{c2\/}})\index{b-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{f-nand3}}\,({\it{a1\/}}, {\it{b1\/}}, {\it{c1\/}})\index{f-nand3}, {\rm{f-nand3}}\,({\it{a2\/}}, {\it{b2\/}}, {\it{c2\/}})\index{f-nand3})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-nand4-monotone \\ \index{f-nand4-monotone}
\=\+({\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{c1\/}}, {\it{c2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{d1\/}}, {\it{d2\/}})\index{b-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{f-nand4}}\,({\it{a1\/}}, {\it{b1\/}}, {\it{c1\/}}, {\it{d1\/}})\index{f-nand4}, {\rm{f-nand4}}\,({\it{a2\/}}, {\it{b2\/}}, {\it{c2\/}}, {\it{d2\/}})\index{f-nand4})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-nand5-monotone \\ \index{f-nand5-monotone}
\=\+(\=\+{\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{c1\/}}, {\it{c2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{d1\/}}, {\it{d2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{e1\/}}, {\it{e2\/}})\index{b-approx})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{f-nand5}}\,({\it{a1\/}}, {\it{b1\/}}, {\it{c1\/}}, {\it{d1\/}}, {\it{e1\/}})\index{f-nand5}, {\rm{f-nand5}}\,({\it{a2\/}}, {\it{b2\/}}, {\it{c2\/}}, {\it{d2\/}}, {\it{e2\/}})\index{f-nand5})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-nand6-monotone \\ \index{f-nand6-monotone}
\=\+(\=\+{\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{c1\/}}, {\it{c2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{d1\/}}, {\it{d2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{e1\/}}, {\it{e2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{g1\/}}, {\it{g2\/}})\index{b-approx})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{f-nand6}}\,({\it{a1\/}}, {\it{b1\/}}, {\it{c1\/}}, {\it{d1\/}}, {\it{e1\/}}, {\it{g1\/}})\index{f-nand6}, {\rm{f-nand6}}\,({\it{a2\/}}, {\it{b2\/}}, {\it{c2\/}}, {\it{d2\/}}, {\it{e2\/}}, {\it{g2\/}})\index{f-nand6})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-nand8-monotone \\ \index{f-nand8-monotone}
\=\+(\=\+{\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{c1\/}}, {\it{c2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{d1\/}}, {\it{d2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{e1\/}}, {\it{e2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{g1\/}}, {\it{g2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{h1\/}}, {\it{h2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{i1\/}}, {\it{i2\/}})\index{b-approx})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,(\=\+{\rm{f-nand8}}\,({\it{a1\/}}, {\it{b1\/}}, {\it{c1\/}}, {\it{d1\/}}, {\it{e1\/}}, {\it{g1\/}}, {\it{h1\/}}, {\it{i1\/}})\index{f-nand8}, \\ 
{\rm{f-nand8}}\,({\it{a2\/}}, {\it{b2\/}}, {\it{c2\/}}, {\it{d2\/}}, {\it{e2\/}}, {\it{g2\/}}, {\it{h2\/}}, {\it{i2\/}})\index{f-nand8})\-\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-or-monotone \\ \index{f-or-monotone}
({\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx}) $\rightarrow$ {\rm{b-approx}}\,({\rm{f-or}}\,({\it{a1\/}}, {\it{b1\/}})\index{f-or}, {\rm{f-or}}\,({\it{a2\/}}, {\it{b2\/}})\index{f-or})\index{b-approx}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-or3-monotone \\ \index{f-or3-monotone}
\=\+({\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{c1\/}}, {\it{c2\/}})\index{b-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{f-or3}}\,({\it{a1\/}}, {\it{b1\/}}, {\it{c1\/}})\index{f-or3}, {\rm{f-or3}}\,({\it{a2\/}}, {\it{b2\/}}, {\it{c2\/}})\index{f-or3})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-or4-monotone \\ \index{f-or4-monotone}
\=\+({\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{c1\/}}, {\it{c2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{d1\/}}, {\it{d2\/}})\index{b-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{f-or4}}\,({\it{a1\/}}, {\it{b1\/}}, {\it{c1\/}}, {\it{d1\/}})\index{f-or4}, {\rm{f-or4}}\,({\it{a2\/}}, {\it{b2\/}}, {\it{c2\/}}, {\it{d2\/}})\index{f-or4})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-nor-monotone \\ \index{f-nor-monotone}
\=\+({\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{f-nor}}\,({\it{a1\/}}, {\it{b1\/}})\index{f-nor}, {\rm{f-nor}}\,({\it{a2\/}}, {\it{b2\/}})\index{f-nor})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-nor3-monotone \\ \index{f-nor3-monotone}
\=\+({\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{c1\/}}, {\it{c2\/}})\index{b-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{f-nor3}}\,({\it{a1\/}}, {\it{b1\/}}, {\it{c1\/}})\index{f-nor3}, {\rm{f-nor3}}\,({\it{a2\/}}, {\it{b2\/}}, {\it{c2\/}})\index{f-nor3})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-nor4-monotone \\ \index{f-nor4-monotone}
\=\+({\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{c1\/}}, {\it{c2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{d1\/}}, {\it{d2\/}})\index{b-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{f-nor4}}\,({\it{a1\/}}, {\it{b1\/}}, {\it{c1\/}}, {\it{d1\/}})\index{f-nor4}, {\rm{f-nor4}}\,({\it{a2\/}}, {\it{b2\/}}, {\it{c2\/}}, {\it{d2\/}})\index{f-nor4})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-nor5-monotone \\ \index{f-nor5-monotone}
\=\+(\=\+{\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{c1\/}}, {\it{c2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{d1\/}}, {\it{d2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{e1\/}}, {\it{e2\/}})\index{b-approx})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{f-nor5}}\,({\it{a1\/}}, {\it{b1\/}}, {\it{c1\/}}, {\it{d1\/}}, {\it{e1\/}})\index{f-nor5}, {\rm{f-nor5}}\,({\it{a2\/}}, {\it{b2\/}}, {\it{c2\/}}, {\it{d2\/}}, {\it{e2\/}})\index{f-nor5})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-nor6-monotone \\ \index{f-nor6-monotone}
\=\+(\=\+{\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{c1\/}}, {\it{c2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{d1\/}}, {\it{d2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{e1\/}}, {\it{e2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{g1\/}}, {\it{g2\/}})\index{b-approx})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{f-nor6}}\,({\it{a1\/}}, {\it{b1\/}}, {\it{c1\/}}, {\it{d1\/}}, {\it{e1\/}}, {\it{g1\/}})\index{f-nor6}, {\rm{f-nor6}}\,({\it{a2\/}}, {\it{b2\/}}, {\it{c2\/}}, {\it{d2\/}}, {\it{e2\/}}, {\it{g2\/}})\index{f-nor6})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-nor8-monotone \\ \index{f-nor8-monotone}
\=\+(\=\+{\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{c1\/}}, {\it{c2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{d1\/}}, {\it{d2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{e1\/}}, {\it{e2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{g1\/}}, {\it{g2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{h1\/}}, {\it{h2\/}})\index{b-approx} \\ 
$\wedge$$\;\;\;\;${\rm{b-approx}}\,({\it{i1\/}}, {\it{i2\/}})\index{b-approx})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,(\=\+{\rm{f-nor8}}\,({\it{a1\/}}, {\it{b1\/}}, {\it{c1\/}}, {\it{d1\/}}, {\it{e1\/}}, {\it{g1\/}}, {\it{h1\/}}, {\it{i1\/}})\index{f-nor8}, \\ 
{\rm{f-nor8}}\,({\it{a2\/}}, {\it{b2\/}}, {\it{c2\/}}, {\it{d2\/}}, {\it{e2\/}}, {\it{g2\/}}, {\it{h2\/}}, {\it{i2\/}})\index{f-nor8})\-\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-xor-monotone \\ \index{f-xor-monotone}
\=\+({\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{f-xor}}\,({\it{a1\/}}, {\it{b1\/}})\index{f-xor}, {\rm{f-xor}}\,({\it{a2\/}}, {\it{b2\/}})\index{f-xor})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-equv-monotone \\ \index{f-equv-monotone}
\=\+({\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{f-equv}}\,({\it{a1\/}}, {\it{b1\/}})\index{f-equv}, {\rm{f-equv}}\,({\it{a2\/}}, {\it{b2\/}})\index{f-equv})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-xor3-monotone \\ \index{f-xor3-monotone}
\=\+({\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{c1\/}}, {\it{c2\/}})\index{b-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{f-xor3}}\,({\it{a1\/}}, {\it{b1\/}}, {\it{c1\/}})\index{f-xor3}, {\rm{f-xor3}}\,({\it{a2\/}}, {\it{b2\/}}, {\it{c2\/}})\index{f-xor3})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-equv3-monotone \\ \index{f-equv3-monotone}
\=\+({\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{c1\/}}, {\it{c2\/}})\index{b-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{f-equv3}}\,({\it{a1\/}}, {\it{b1\/}}, {\it{c1\/}})\index{f-equv3}, {\rm{f-equv3}}\,({\it{a2\/}}, {\it{b2\/}}, {\it{c2\/}})\index{f-equv3})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-if-monotone \\ \index{f-if-monotone}
\=\+({\rm{b-approx}}\,({\it{c1\/}}, {\it{c2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{f-if}}\,({\it{c1\/}}, {\it{a1\/}}, {\it{b1\/}})\index{f-if}, {\rm{f-if}}\,({\it{c2\/}}, {\it{a2\/}}, {\it{b2\/}})\index{f-if})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ft-buf-monotone \\ \index{ft-buf-monotone}
\=\+({\rm{b-approx}}\,({\it{c1\/}}, {\it{c2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{ft-buf}}\,({\it{c1\/}}, {\it{a1\/}})\index{ft-buf}, {\rm{ft-buf}}\,({\it{c2\/}}, {\it{a2\/}})\index{ft-buf})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ft-wire-monotone \\ \index{ft-wire-monotone}
\=\+({\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} $\wedge$ {\rm{b-approx}}\,({\it{b1\/}}, {\it{b2\/}})\index{b-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{ft-wire}}\,({\it{a1\/}}, {\it{b1\/}})\index{ft-wire}, {\rm{ft-wire}}\,({\it{a2\/}}, {\it{b2\/}})\index{ft-wire})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-pullup-monotone \\ \index{f-pullup-monotone}
{\rm{b-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{b-approx} $\rightarrow$ {\rm{b-approx}}\,({\rm{f-pullup}}\,({\it{a1\/}})\index{f-pullup}, {\rm{f-pullup}}\,({\it{a2\/}})\index{f-pullup})\index{b-approx}
\end{tabbing}


\noindent{\sc Event}:   Enable f-buf; name this event `f-buf-off'.\index{f-buf-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-and; name this event `f-and-off'.\index{f-and-off}

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\noindent{\sc Event}:   Enable f-and3; name this event `f-and3-off'.\index{f-and3-off}

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\noindent{\sc Event}:   Enable f-and4; name this event `f-and4-off'.\index{f-and4-off}

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\noindent{\sc Event}:   Enable f-not; name this event `f-not-off'.\index{f-not-off}

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\noindent{\sc Event}:   Enable f-nand; name this event `f-nand-off'.\index{f-nand-off}

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\noindent{\sc Event}:   Enable f-nand3; name this event `f-nand3-off'.\index{f-nand3-off}

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\noindent{\sc Event}:   Enable f-nand4; name this event `f-nand4-off'.\index{f-nand4-off}

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\noindent{\sc Event}:   Enable f-nand5; name this event `f-nand5-off'.\index{f-nand5-off}

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\noindent{\sc Event}:   Enable f-nand6; name this event `f-nand6-off'.\index{f-nand6-off}

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\noindent{\sc Event}:   Enable f-nand8; name this event `f-nand8-off'.\index{f-nand8-off}

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\noindent{\sc Event}:   Enable f-or; name this event `f-or-off'.\index{f-or-off}

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\noindent{\sc Event}:   Enable f-or3; name this event `f-or3-off'.\index{f-or3-off}

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\noindent{\sc Event}:   Enable f-or4; name this event `f-or4-off'.\index{f-or4-off}

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\noindent{\sc Event}:   Enable f-nor; name this event `f-nor-off'.\index{f-nor-off}

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\noindent{\sc Event}:   Enable f-nor3; name this event `f-nor3-off'.\index{f-nor3-off}

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\noindent{\sc Event}:   Enable f-nor4; name this event `f-nor4-off'.\index{f-nor4-off}

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\noindent{\sc Event}:   Enable f-nor5; name this event `f-nor5-off'.\index{f-nor5-off}

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\noindent{\sc Event}:   Enable f-nor6; name this event `f-nor6-off'.\index{f-nor6-off}

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\noindent{\sc Event}:   Enable f-nor8; name this event `f-nor8-off'.\index{f-nor8-off}

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\noindent{\sc Event}:   Enable f-xor; name this event `f-xor-off'.\index{f-xor-off}

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\noindent{\sc Event}:   Enable f-xor3; name this event `f-xor3-off'.\index{f-xor3-off}

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\noindent{\sc Event}:   Enable f-equv; name this event `f-equv-off'.\index{f-equv-off}

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\noindent{\sc Event}:   Enable f-equv3; name this event `f-equv3-off'.\index{f-equv3-off}

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\noindent{\sc Event}:   Enable f-if; name this event `f-if-off'.\index{f-if-off}

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\noindent{\sc Event}:   Enable ft-buf; name this event `ft-buf-off'.\index{ft-buf-off}

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\noindent{\sc Event}:   Enable ft-wire; name this event `ft-wire-off'.\index{ft-wire-off}

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\noindent{\sc Event}:   Enable f-pullup; name this event `f-pullup-off'.\index{f-pullup-off}

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\noindent{\sc Event}:   Let us define the theory {\it{monotonicity-lemmas}} to consist of the following events: f-buf-monotone,
f-and-monotone,
f-and3-monotone,
f-and4-monotone,
f-not-monotone,
f-nand-monotone,
f-nand3-monotone,
f-nand4-monotone,
f-nand5-monotone,
f-nand6-monotone,
f-nand8-monotone,
f-or-monotone,
f-or3-monotone,
f-or4-monotone,
f-nor-monotone,
f-nor3-monotone,
f-nor4-monotone,
f-nor5-monotone,
f-nor6-monotone,
f-nor8-monotone,
f-xor-monotone,
f-xor3-monotone,
f-equv-monotone,
f-equv3-monotone,
f-if-monotone,
ft-buf-monotone,
ft-wire-monotone,
f-pullup-monotone.\index{monotonicity-lemmas}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-approx; name this event `b-approx-off'.\index{b-approx-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  dual-eval-0-primp \\ \index{dual-eval-0-primp}
\=\+{\rm{primp}}\,({\it{name\/}})\index{primp} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{0}}, {\it{name\/}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{dual-apply-value}}\,({\it{name\/}}, {\it{args\/}}, {\it{state\/}})\index{dual-apply-value})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-2-primp \\ \index{dual-eval-2-primp}
\=\+{\rm{primp}}\,({\it{name\/}})\index{primp} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{dual-eval}}\,({\tt{2}}, {\it{name\/}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{dual-apply-state}}\,({\it{name\/}}, {\it{args\/}}, {\it{state\/}})\index{dual-apply-state})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  s-approx-implies-b-approx \\ \index{s-approx-implies-b-approx}
{\rm{s-approx}}\,({\it{x\/}}, {\it{y\/}})\index{s-approx} $\rightarrow$ {\rm{b-approx}}\,({\it{x\/}}, {\it{y\/}})\index{b-approx}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-buf-type-set \\ \index{f-buf-type-set}
{\rm{truep}}\,({\rm{f-buf}}\,({\it{x\/}})\index{f-buf}) $\vee$ {\rm{falsep}}\,({\rm{f-buf}}\,({\it{x\/}})\index{f-buf}) $\vee$ {\rm{xp}}\,({\rm{f-buf}}\,({\it{x\/}})\index{f-buf})\index{xp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fourp-f-buf \\ \index{fourp-f-buf}
{\rm{fourp}}\,({\rm{f-buf}}\,({\it{x\/}})\index{f-buf})\index{fourp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fourp-f-if \\ \index{fourp-f-if}
{\rm{fourp}}\,({\rm{f-if}}\,({\it{x\/}}, {\it{y\/}}, {\it{z\/}})\index{f-if})\index{fourp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fourp-implies-s-approx-is-b-approx \\ \index{fourp-implies-s-approx-is-b-app!rox}
({\rm{fourp}}\,({\it{x\/}})\index{fourp} $\wedge$ {\rm{fourp}}\,({\it{y\/}})\index{fourp} $\wedge$ {\rm{b-approx}}\,({\it{x\/}}, {\it{y\/}})\index{b-approx}) $\rightarrow$ ({\rm{s-approx}}\,({\it{x\/}}, {\it{y\/}})\index{s-approx} $=$ {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ao2-value \\ \index{dual-eval-ao2-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ao2}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nor}}\,(\=\+{\rm{f-and}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}))\index{f-and}, \\ 
{\rm{f-and}}\,({\rm{caddr}}\,({\it{args\/}}), {\rm{cadddr}}\,({\it{args\/}}))\index{f-and})\-\index{f-nor})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ao2-state \\ \index{dual-eval-ao2-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{ao2}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ao2-monotone \\ \index{ao2-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{ao2}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{ao2}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ao4-value \\ \index{dual-eval-ao4-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ao4}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nand}}\,({\rm{f-or}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}))\index{f-or}, {\rm{f-or}}\,({\rm{caddr}}\,({\it{args\/}}), {\rm{cadddr}}\,({\it{args\/}}))\index{f-or})\index{f-nand})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ao4-state \\ \index{dual-eval-ao4-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{ao4}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ao4-monotone \\ \index{ao4-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{ao4}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{ao4}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ao6-value \\ \index{dual-eval-ao6-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ao6}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nor}}\,({\rm{f-and}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}))\index{f-and}, {\rm{caddr}}\,({\it{args\/}}))\index{f-nor})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ao6-state \\ \index{dual-eval-ao6-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{ao6}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ao6-monotone \\ \index{ao6-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{ao6}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{ao6}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ao7-value \\ \index{dual-eval-ao7-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ao7}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nand}}\,({\rm{f-or}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}))\index{f-or}, {\rm{caddr}}\,({\it{args\/}}))\index{f-nand})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ao7-state \\ \index{dual-eval-ao7-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{ao7}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ao7-monotone \\ \index{ao7-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{ao7}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{ao7}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-and-value \\ \index{dual-eval-b-and-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-and}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-and}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}))\index{f-and})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-and-state \\ \index{dual-eval-b-and-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-and}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-and-monotone \\ \index{b-and-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-and}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-and}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-and3-value \\ \index{dual-eval-b-and3-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-and3}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-and3}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}), {\rm{caddr}}\,({\it{args\/}}))\index{f-and3})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-and3-state \\ \index{dual-eval-b-and3-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-and3}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-and3-monotone \\ \index{b-and3-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-and3}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-and3}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-and4-value \\ \index{dual-eval-b-and4-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-and4}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-and4}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}), {\rm{caddr}}\,({\it{args\/}}), {\rm{cadddr}}\,({\it{args\/}}))\index{f-and4})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-and4-state \\ \index{dual-eval-b-and4-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-and4}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-and4-monotone \\ \index{b-and4-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-and4}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-and4}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-equv-value \\ \index{dual-eval-b-equv-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-equv}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-equv}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}))\index{f-equv})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-equv-state \\ \index{dual-eval-b-equv-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-equv}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-equv-monotone \\ \index{b-equv-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-equv}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-equv}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-equv3-value \\ \index{dual-eval-b-equv3-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-equv3}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-equv3}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}), {\rm{caddr}}\,({\it{args\/}}))\index{f-equv3})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-equv3-state \\ \index{dual-eval-b-equv3-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-equv3}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-equv3-monotone \\ \index{b-equv3-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-equv3}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-equv3}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-if-value \\ \index{dual-eval-b-if-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-if}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-if}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}), {\rm{caddr}}\,({\it{args\/}}))\index{f-if})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-if-state \\ \index{dual-eval-b-if-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-if}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-if-monotone \\ \index{b-if-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-if}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-if}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nand-value \\ \index{dual-eval-b-nand-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nand}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nand}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}))\index{f-nand})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nand-state \\ \index{dual-eval-b-nand-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-nand}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nand-monotone \\ \index{b-nand-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-nand}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-nand}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nand3-value \\ \index{dual-eval-b-nand3-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nand3}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nand3}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}), {\rm{caddr}}\,({\it{args\/}}))\index{f-nand3})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nand3-state \\ \index{dual-eval-b-nand3-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-nand3}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nand3-monotone \\ \index{b-nand3-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-nand3}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-nand3}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nand4-value \\ \index{dual-eval-b-nand4-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nand4}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nand4}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}), {\rm{caddr}}\,({\it{args\/}}), {\rm{cadddr}}\,({\it{args\/}}))\index{f-nand4})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nand4-state \\ \index{dual-eval-b-nand4-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-nand4}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nand4-monotone \\ \index{b-nand4-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-nand4}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-nand4}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nand5-value \\ \index{dual-eval-b-nand5-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nand5}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nand5}}\,(\=\+{\rm{car}}\,({\it{args\/}}), \\ 
{\rm{cadr}}\,({\it{args\/}}), \\ 
{\rm{caddr}}\,({\it{args\/}}), \\ 
{\rm{cadddr}}\,({\it{args\/}}), \\ 
{\rm{caddddr}}\,({\it{args\/}}))\-\index{f-nand5})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nand5-state \\ \index{dual-eval-b-nand5-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-nand5}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nand5-monotone \\ \index{b-nand5-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-nand5}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-nand5}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nand6-value \\ \index{dual-eval-b-nand6-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nand6}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nand6}}\,(\=\+{\rm{car}}\,({\it{args\/}}), \\ 
{\rm{cadr}}\,({\it{args\/}}), \\ 
{\rm{caddr}}\,({\it{args\/}}), \\ 
{\rm{cadddr}}\,({\it{args\/}}), \\ 
{\rm{caddddr}}\,({\it{args\/}}), \\ 
{\rm{cadddddr}}\,({\it{args\/}}))\-\index{f-nand6})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nand6-state \\ \index{dual-eval-b-nand6-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-nand6}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nand6-monotone \\ \index{b-nand6-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-nand6}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-nand6}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nand8-value \\ \index{dual-eval-b-nand8-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nand8}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nand8}}\,(\=\+{\rm{car}}\,({\it{args\/}}), \\ 
{\rm{cadr}}\,({\it{args\/}}), \\ 
{\rm{caddr}}\,({\it{args\/}}), \\ 
{\rm{cadddr}}\,({\it{args\/}}), \\ 
{\rm{caddddr}}\,({\it{args\/}}), \\ 
{\rm{cadddddr}}\,({\it{args\/}}), \\ 
{\rm{caddddddr}}\,({\it{args\/}}), \\ 
{\rm{cadddddddr}}\,({\it{args\/}}))\-\index{f-nand8})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nand8-state \\ \index{dual-eval-b-nand8-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-nand8}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nand8-monotone \\ \index{b-nand8-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-nand8}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-nand8}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nbuf-value \\ \index{dual-eval-b-nbuf-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nbuf}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{args\/}}))\index{f-not}, {\rm{f-buf}}\,({\rm{car}}\,({\it{args\/}}))\index{f-buf})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nbuf-state \\ \index{dual-eval-b-nbuf-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-nbuf}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nbuf-monotone \\ \index{b-nbuf-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-nbuf}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-nbuf}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nor-value \\ \index{dual-eval-b-nor-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nor}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nor}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}))\index{f-nor})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nor-state \\ \index{dual-eval-b-nor-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-nor}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nor-monotone \\ \index{b-nor-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-nor}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-nor}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nor3-value \\ \index{dual-eval-b-nor3-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nor3}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nor3}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}), {\rm{caddr}}\,({\it{args\/}}))\index{f-nor3})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nor3-state \\ \index{dual-eval-b-nor3-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-nor3}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nor3-monotone \\ \index{b-nor3-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-nor3}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-nor3}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nor4-value \\ \index{dual-eval-b-nor4-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nor4}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nor4}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}), {\rm{caddr}}\,({\it{args\/}}), {\rm{cadddr}}\,({\it{args\/}}))\index{f-nor4})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nor4-state \\ \index{dual-eval-b-nor4-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-nor4}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nor4-monotone \\ \index{b-nor4-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-nor4}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-nor4}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nor5-value \\ \index{dual-eval-b-nor5-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nor5}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nor5}}\,(\=\+{\rm{car}}\,({\it{args\/}}), \\ 
{\rm{cadr}}\,({\it{args\/}}), \\ 
{\rm{caddr}}\,({\it{args\/}}), \\ 
{\rm{cadddr}}\,({\it{args\/}}), \\ 
{\rm{caddddr}}\,({\it{args\/}}))\-\index{f-nor5})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nor5-state \\ \index{dual-eval-b-nor5-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-nor5}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nor5-monotone \\ \index{b-nor5-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-nor5}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-nor5}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nor6-value \\ \index{dual-eval-b-nor6-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nor6}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nor6}}\,(\=\+{\rm{car}}\,({\it{args\/}}), \\ 
{\rm{cadr}}\,({\it{args\/}}), \\ 
{\rm{caddr}}\,({\it{args\/}}), \\ 
{\rm{cadddr}}\,({\it{args\/}}), \\ 
{\rm{caddddr}}\,({\it{args\/}}), \\ 
{\rm{cadddddr}}\,({\it{args\/}}))\-\index{f-nor6})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nor6-state \\ \index{dual-eval-b-nor6-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-nor6}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nor6-monotone \\ \index{b-nor6-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-nor6}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-nor6}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nor8-value \\ \index{dual-eval-b-nor8-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-nor8}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nor8}}\,(\=\+{\rm{car}}\,({\it{args\/}}), \\ 
{\rm{cadr}}\,({\it{args\/}}), \\ 
{\rm{caddr}}\,({\it{args\/}}), \\ 
{\rm{cadddr}}\,({\it{args\/}}), \\ 
{\rm{caddddr}}\,({\it{args\/}}), \\ 
{\rm{cadddddr}}\,({\it{args\/}}), \\ 
{\rm{caddddddr}}\,({\it{args\/}}), \\ 
{\rm{cadddddddr}}\,({\it{args\/}}))\-\index{f-nor8})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-nor8-state \\ \index{dual-eval-b-nor8-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-nor8}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nor8-monotone \\ \index{b-nor8-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-nor8}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-nor8}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-not-value \\ \index{dual-eval-b-not-value}
{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-not}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{args\/}}))\index{f-not})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-not-state \\ \index{dual-eval-b-not-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-not}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-not-monotone \\ \index{b-not-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-not}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-not}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-not-b4ip-value \\ \index{dual-eval-b-not-b4ip-value}
{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-not-b4ip}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{args\/}}))\index{f-not})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-not-b4ip-state \\ \index{dual-eval-b-not-b4ip-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-not-b4ip}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-not-b4ip-monotone \\ \index{b-not-b4ip-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-not-b4ip}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-not-b4ip}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-not-ivap-value \\ \index{dual-eval-b-not-ivap-value}
{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-not-ivap}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{f-not}}\,({\rm{car}}\,({\it{args\/}}))\index{f-not})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-not-ivap-state \\ \index{dual-eval-b-not-ivap-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-not-ivap}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-not-ivap-monotone \\ \index{b-not-ivap-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-not-ivap}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-not-ivap}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-or-value \\ \index{dual-eval-b-or-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-or}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-or}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}))\index{f-or})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-or-state \\ \index{dual-eval-b-or-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-or}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-or-monotone \\ \index{b-or-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-or}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-or}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-or3-value \\ \index{dual-eval-b-or3-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-or3}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-or3}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}), {\rm{caddr}}\,({\it{args\/}}))\index{f-or3})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-or3-state \\ \index{dual-eval-b-or3-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-or3}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-or3-monotone \\ \index{b-or3-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-or3}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-or3}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-or4-value \\ \index{dual-eval-b-or4-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-or4}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-or4}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}), {\rm{caddr}}\,({\it{args\/}}), {\rm{cadddr}}\,({\it{args\/}}))\index{f-or4})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-or4-state \\ \index{dual-eval-b-or4-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-or4}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-or4-monotone \\ \index{b-or4-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-or4}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-or4}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-xor-value \\ \index{dual-eval-b-xor-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-xor}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-xor}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}))\index{f-xor})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-xor-state \\ \index{dual-eval-b-xor-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-xor}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-xor-monotone \\ \index{b-xor-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-xor}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-xor}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-xor3-value \\ \index{dual-eval-b-xor3-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{b-xor3}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-xor3}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}), {\rm{caddr}}\,({\it{args\/}}))\index{f-xor3})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-b-xor3-state \\ \index{dual-eval-b-xor3-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{b-xor3}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-xor3-monotone \\ \index{b-xor3-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{b-xor3}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{b-xor3}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-del2-value \\ \index{dual-eval-del2-value}
{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{del2}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{f-buf}}\,({\rm{car}}\,({\it{args\/}}))\index{f-buf})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-del2-state \\ \index{dual-eval-del2-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{del2}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  del2-monotone \\ \index{del2-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{del2}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{del2}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-del4-value \\ \index{dual-eval-del4-value}
{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{del4}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{f-buf}}\,({\rm{car}}\,({\it{args\/}}))\index{f-buf})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-del4-state \\ \index{dual-eval-del4-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{del4}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  del4-monotone \\ \index{del4-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{del4}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{del4}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-del10-value \\ \index{dual-eval-del10-value}
{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{del10}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{f-buf}}\,({\rm{car}}\,({\it{args\/}}))\index{f-buf})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-del10-state \\ \index{dual-eval-del10-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{del10}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  del10-monotone \\ \index{del10-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{del10}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{del10}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-procmon-value \\ \index{dual-eval-procmon-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{procmon}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-if}}\,(\=\+{\rm{caddr}}\,({\it{args\/}}), \\ 
{\rm{f-if}}\,({\rm{cadr}}\,({\it{args\/}}), {\rm{f-if}}\,({\rm{car}}\,({\it{args\/}}), {\bf{f}}, {\bf{f}})\index{f-if}, {\rm{car}}\,({\it{args\/}}))\index{f-if}, \\ 
{\rm{cadddr}}\,({\it{args\/}}))\-\index{f-if})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-procmon-state \\ \index{dual-eval-procmon-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{procmon}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  procmon-monotone \\ \index{procmon-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{procmon}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{procmon}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-fd1-value \\ \index{dual-eval-fd1-value}
{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{fd1}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{f-buf}}\,({\it{state\/}})\index{f-buf}, {\rm{f-not}}\,({\it{state\/}})\index{f-not})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-fd1-state \\ \index{dual-eval-fd1-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{fd1}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{f-buf}}\,({\rm{car}}\,({\it{args\/}}))\index{f-buf}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fd1-monotone \\ \index{fd1-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{fd1}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{fd1}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-fd1s-value \\ \index{dual-eval-fd1s-value}
{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{fd1s}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{f-buf}}\,({\it{state\/}})\index{f-buf}, {\rm{f-not}}\,({\it{state\/}})\index{f-not})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-fd1s-state \\ \index{dual-eval-fd1s-state}
\=\+{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{fd1s}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f-if}}\,({\rm{cadddr}}\,({\it{args\/}}), {\rm{caddr}}\,({\it{args\/}}), {\rm{car}}\,({\it{args\/}}))\index{f-if}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fd1s-monotone \\ \index{fd1s-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{fd1s}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{fd1s}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-fd1sp-value \\ \index{dual-eval-fd1sp-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{fd1sp}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-buf}}\,({\it{state\/}})\index{f-buf}, {\rm{f-not}}\,({\it{state\/}})\index{f-not})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-fd1sp-state \\ \index{dual-eval-fd1sp-state}
\=\+{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{fd1sp}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f-if}}\,({\rm{cadddr}}\,({\it{args\/}}), {\rm{caddr}}\,({\it{args\/}}), {\rm{car}}\,({\it{args\/}}))\index{f-if}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fd1sp-monotone \\ \index{fd1sp-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{fd1sp}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{fd1sp}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-fd1slp-value \\ \index{dual-eval-fd1slp-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{fd1slp}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-buf}}\,({\it{state\/}})\index{f-buf}, {\rm{f-not}}\,({\it{state\/}})\index{f-not})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-fd1slp-state \\ \index{dual-eval-fd1slp-state}
\=\+{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{fd1slp}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{f-if}}\,({\rm{caddddr}}\,({\it{args\/}}), {\rm{cadddr}}\,({\it{args\/}}), {\rm{f-if}}\,({\rm{caddr}}\,({\it{args\/}}), {\rm{car}}\,({\it{args\/}}), {\it{state\/}})\index{f-if})\index{f-if}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fd1slp-monotone \\ \index{fd1slp-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{fd1slp}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{fd1slp}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-id-value \\ \index{dual-eval-id-value}
{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{id}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{car}}\,({\it{args\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-id-state \\ \index{dual-eval-id-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{id}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  id-monotone \\ \index{id-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{id}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{id}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ram-enable-circuit-value \\ \index{dual-eval-ram-enable-circuit-va!lue}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ram-enable-circuit}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-nand}}\,({\rm{caddr}}\,({\it{args\/}}), {\rm{cadddr}}\,({\it{args\/}}))\index{f-nand})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ram-enable-circuit-state \\ \index{dual-eval-ram-enable-circuit-st!ate}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{ram-enable-circuit}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ram-enable-circuit-monotone \\ \index{ram-enable-circuit-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{ram-enable-circuit}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{ram-enable-circuit}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-t-buf-value \\ \index{dual-eval-t-buf-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{t-buf}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{ft-buf}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}))\index{ft-buf})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-t-buf-state \\ \index{dual-eval-t-buf-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{t-buf}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  t-buf-monotone \\ \index{t-buf-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{t-buf}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{t-buf}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-t-wire-value \\ \index{dual-eval-t-wire-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{t-wire}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{ft-wire}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}))\index{ft-wire})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-t-wire-state \\ \index{dual-eval-t-wire-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{t-wire}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  t-wire-monotone \\ \index{t-wire-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{t-wire}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{t-wire}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-pullup-value \\ \index{dual-eval-pullup-value}
{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{pullup}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{f-pullup}}\,({\rm{car}}\,({\it{args\/}}))\index{f-pullup})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-pullup-state \\ \index{dual-eval-pullup-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{pullup}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  pullup-monotone \\ \index{pullup-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{pullup}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{pullup}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ttl-bidirect-value \\ \index{dual-eval-ttl-bidirect-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-bidirect}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{ft-buf}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{args\/}}))\index{f-not}, {\rm{cadr}}\,({\it{args\/}}))\index{ft-buf}, \\ 
{\rm{f-buf}}\,({\rm{ft-wire}}\,({\rm{car}}\,({\it{args\/}}), {\rm{ft-buf}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{args\/}}))\index{f-not}, {\rm{cadr}}\,({\it{args\/}}))\index{ft-buf})\index{ft-wire})\index{f-buf}, \\ 
{\rm{f-nand}}\,(\=\+{\rm{ft-wire}}\,({\rm{car}}\,({\it{args\/}}), {\rm{ft-buf}}\,({\rm{f-not}}\,({\rm{caddr}}\,({\it{args\/}}))\index{f-not}, {\rm{cadr}}\,({\it{args\/}}))\index{ft-buf})\index{ft-wire}, \\ 
{\rm{cadddr}}\,({\it{args\/}}))\-\index{f-nand})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ttl-bidirect-state \\ \index{dual-eval-ttl-bidirect-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{ttl-bidirect}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-bidirect-monotone \\ \index{ttl-bidirect-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-bidirect}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{ttl-bidirect}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ttl-clk-input-value \\ \index{dual-eval-ttl-clk-input-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-clk-input}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-buf}}\,({\rm{car}}\,({\it{args\/}}))\index{f-buf}, {\rm{f-nand}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}))\index{f-nand})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ttl-clk-input-state \\ \index{dual-eval-ttl-clk-input-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{ttl-clk-input}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-clk-input-monotone \\ \index{ttl-clk-input-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-clk-input}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{ttl-clk-input}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ttl-input-value \\ \index{dual-eval-ttl-input-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-input}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-buf}}\,({\rm{car}}\,({\it{args\/}}))\index{f-buf}, {\rm{f-nand}}\,({\rm{car}}\,({\it{args\/}}), {\rm{cadr}}\,({\it{args\/}}))\index{f-nand})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ttl-input-state \\ \index{dual-eval-ttl-input-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{ttl-input}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-input-monotone \\ \index{ttl-input-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-input}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{ttl-input}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ttl-output-value \\ \index{dual-eval-ttl-output-value}
{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-output}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\rm{f-buf}}\,({\rm{car}}\,({\it{args\/}}))\index{f-buf})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ttl-output-state \\ \index{dual-eval-ttl-output-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{ttl-output}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-output-monotone \\ \index{ttl-output-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-output}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{ttl-output}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ttl-output-parametric-value \\ \index{dual-eval-ttl-output-parametric!-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-output-parametric}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-buf}}\,({\rm{car}}\,({\it{args\/}}))\index{f-buf})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ttl-output-parametric-state \\ \index{dual-eval-ttl-output-parametric!-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{ttl-output-parametric}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-output-parametric-monotone \\ \index{ttl-output-parametric-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-output-parametric}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,(\=\+{\tt{2}}, \\ 
{\tt{'}}{\tt{ttl-output-parametric}}, \\ 
{\it{netlist\/}}, \\ 
{\it{a1\/}}, \\ 
{\it{a2\/}}, \\ 
{\it{s1\/}}, \\ 
{\it{s2\/}})\-\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ttl-output-fast-value \\ \index{dual-eval-ttl-output-fast-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-output-fast}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{f-buf}}\,({\rm{car}}\,({\it{args\/}}))\index{f-buf})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ttl-output-fast-state \\ \index{dual-eval-ttl-output-fast-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{ttl-output-fast}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-output-fast-monotone \\ \index{ttl-output-fast-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-output-fast}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{ttl-output-fast}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ttl-tri-output-value \\ \index{dual-eval-ttl-tri-output-value}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-tri-output}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{ft-buf}}\,({\rm{f-not}}\,({\rm{cadr}}\,({\it{args\/}}))\index{f-not}, {\rm{car}}\,({\it{args\/}}))\index{ft-buf})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ttl-tri-output-state \\ \index{dual-eval-ttl-tri-output-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{ttl-tri-output}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-tri-output-monotone \\ \index{ttl-tri-output-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-tri-output}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{ttl-tri-output}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ttl-tri-output-fast-value \\ \index{dual-eval-ttl-tri-output-fast-v!alue}
\=\+{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-tri-output-fast}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} \\ 
$=$$\;\;\;\;${\rm{list}}\,({\rm{ft-buf}}\,({\rm{f-not}}\,({\rm{cadr}}\,({\it{args\/}}))\index{f-not}, {\rm{car}}\,({\it{args\/}}))\index{ft-buf})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-ttl-tri-output-fast-state \\ \index{dual-eval-ttl-tri-output-fast-st!ate}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{ttl-tri-output-fast}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-tri-output-fast-monotone \\ \index{ttl-tri-output-fast-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{ttl-tri-output-fast}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,(\=\+{\tt{2}}, \\ 
{\tt{'}}{\tt{ttl-tri-output-fast}}, \\ 
{\it{netlist\/}}, \\ 
{\it{a1\/}}, \\ 
{\it{a2\/}}, \\ 
{\it{s1\/}}, \\ 
{\it{s2\/}})\-\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-vdd-value \\ \index{dual-eval-vdd-value}
{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{vdd}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-vdd-state \\ \index{dual-eval-vdd-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{vdd}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  vdd-monotone \\ \index{vdd-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{vdd}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{vdd}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-vdd-parametric-value \\ \index{dual-eval-vdd-parametric-value}
{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{vdd-parametric}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-vdd-parametric-state \\ \index{dual-eval-vdd-parametric-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{vdd-parametric}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  vdd-parametric-monotone \\ \index{vdd-parametric-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{vdd-parametric}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{vdd-parametric}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-vss-value \\ \index{dual-eval-vss-value}
{\rm{dual-eval}}\,({\tt{0}}, {\tt{'}}{\tt{vss}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\rm{list}}\,({\bf{f}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-vss-state \\ \index{dual-eval-vss-state}
{\rm{dual-eval}}\,({\tt{2}}, {\tt{'}}{\tt{vss}}, {\it{args\/}}, {\it{state\/}}, {\it{netlist\/}})\index{dual-eval} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  vss-monotone \\ \index{vss-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{vss}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{vss}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}


\noindent{\sc Event}:   Let us define the theory {\it{primitives-monotone}} to consist of the following events: ao2-monotone,
ao4-monotone,
ao6-monotone,
ao7-monotone,
b-and-monotone,
b-and3-monotone,
b-and4-monotone,
b-equv-monotone,
b-equv3-monotone,
b-if-monotone,
b-nand-monotone,
b-nand3-monotone,
b-nand4-monotone,
b-nand5-monotone,
b-nand6-monotone,
b-nand8-monotone,
b-nbuf-monotone,
b-nor-monotone,
b-nor3-monotone,
b-nor4-monotone,
b-nor5-monotone,
b-nor6-monotone,
b-nor8-monotone,
b-not-monotone,
b-not-b4ip-monotone,
b-not-ivap-monotone,
b-or-monotone,
b-or3-monotone,
b-or4-monotone,
b-xor-monotone,
b-xor3-monotone,
del2-monotone,
del4-monotone,
del10-monotone,
procmon-monotone,
fd1-monotone,
fd1s-monotone,
fd1sp-monotone,
fd1slp-monotone,
id-monotone,
ram-enable-circuit-monotone,
t-buf-monotone,
t-wire-monotone,
pullup-monotone,
ttl-bidirect-monotone,
ttl-clk-input-monotone,
ttl-input-monotone,
ttl-output-monotone,
ttl-output-parametric-monotone,
ttl-output-fast-monotone,
ttl-tri-output-monotone,
ttl-tri-output-fast-monotone,
vdd-monotone,
vdd-parametric-monotone,
vss-monotone.\index{primitives-monotone}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  bvp-rev1 \\ \index{bvp-rev1}
({\rm{bvp}}\,({\it{x\/}})\index{bvp} $\wedge$ {\rm{bvp}}\,({\it{acc\/}})\index{bvp}) $\rightarrow$ {\rm{bvp}}\,({\rm{rev1}}\,({\it{x\/}}, {\it{acc\/}})\index{rev1})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-reverse \\ \index{bvp-reverse}
{\rm{bvp}}\,({\it{x\/}})\index{bvp} $\rightarrow$ {\rm{bvp}}\,({\rm{reverse}}\,({\it{x\/}})\index{reverse})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-approx-bvp \\ \index{v-approx-bvp}
{\rm{bvp}}\,({\it{x\/}})\index{bvp} $\rightarrow$ ({\rm{v-approx}}\,({\it{x\/}}, {\it{y\/}})\index{v-approx} $=$ ({\it{x\/}} $=$ {\it{y\/}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{read-mem1-monotone-induction} \\  
\=\+{\rm{read-mem1-monotone-induction}}\,({\it{v-addr\/}}, {\it{mem1\/}}, {\it{mem2\/}})\index{read-mem1-monotone-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\rm{stubp}}\,({\it{mem1\/}})\index{stubp} \\ 
$\vee$$\;\;\;\;${\rm{stubp}}\,({\it{mem2\/}})\index{stubp} \\ 
$\vee$$\;\;\;\;$({\it{v-addr\/}} $\simeq\;${{\bf{nil}}}${}$) \\ 
$\vee$$\;\;\;\;$({\it{mem1\/}} $\simeq\;${{\bf{nil}}}${}$) \\ 
$\vee$$\;\;\;\;$({\it{mem2\/}} $\simeq\;${{\bf{nil}}}${}$)\-$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\rm{car}}\,({\it{v-addr\/}}) \\ 
{\bf then }{\rm{read-mem1-monotone-induction}}\,({\rm{cdr}}\,({\it{v-addr\/}}), {\rm{cdr}}\,({\it{mem1\/}}), {\rm{cdr}}\,({\it{mem2\/}}))\index{read-mem1-monotone-induction} \\ 
{\bf else }{\rm{read-mem1-monotone-induction}}\,(\=\+{\rm{cdr}}\,({\it{v-addr\/}}), \\ 
{\rm{car}}\,({\it{mem1\/}}), \\ 
{\rm{car}}\,({\it{mem2\/}}))\-\index{read-mem1-monotone-induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  read-mem1-monotone \\ \index{read-mem1-monotone}
\=\+({\rm{bvp}}\,({\it{v-addr\/}})\index{bvp} $\wedge$ {\rm{s-approx}}\,({\it{mem1\/}}, {\it{mem2\/}})\index{s-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{v-approx}}\,({\rm{read-mem1}}\,({\it{v-addr\/}}, {\it{mem1\/}})\index{read-mem1}, {\rm{read-mem1}}\,({\it{v-addr\/}}, {\it{mem2\/}})\index{read-mem1})\index{v-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-implies-v-knownp \\ \index{bvp-implies-v-knownp}
{\rm{bvp}}\,({\it{x\/}})\index{bvp} $\rightarrow$ {\rm{v-knownp}}\,({\it{x\/}})\index{v-knownp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-approx-x-x \\ \index{v-approx-x-x}
{\rm{v-approx}}\,({\it{x\/}}, {\it{x\/}})\index{v-approx}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-approx-implies-b-approx-nth \\ \index{v-approx-implies-b-approx-nth}
\=\+(({\rm{nth}}\,({\it{n\/}}, {\it{x\/}})\index{nth} $=$ {\it{c\/}}) $\wedge$ ({\rm{nth}}\,({\it{n\/}}, {\it{y\/}})\index{nth} $\not=$ {\it{c\/}}) $\wedge$ {\rm{b-knownp}}\,({\it{c\/}})\index{b-knownp}) \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{v-approx}}\,({\it{x\/}}, {\it{y\/}})\index{v-approx})\-
\end{tabbing}


\noindent{\sc Event}:   Disable *1*b-knownp; name this event `g*1*b-knownp-on'.\index{g*1*b-knownp-on}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-approx-implies-subranges-equal \\ \index{v-approx-implies-subranges-equa!l}
\=\+({\rm{v-approx}}\,({\it{x\/}}, {\it{y\/}})\index{v-approx} $\wedge$ {\rm{bvp}}\,({\rm{subrange}}\,({\it{x\/}}, {\it{i\/}}, {\it{j\/}})\index{subrange})\index{bvp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{subrange}}\,({\it{x\/}}, {\it{i\/}}, {\it{j\/}})\index{subrange} $=$ {\rm{subrange}}\,({\it{y\/}}, {\it{i\/}}, {\it{j\/}})\index{subrange})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-approx-bvp-subrange \\ \index{v-approx-bvp-subrange}
({\rm{v-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{v-approx} $\wedge$ {\rm{bvp}}\,({\rm{subrange}}\,({\it{a1\/}}, {\it{i\/}}, {\it{j\/}})\index{subrange})\index{bvp}) $\rightarrow$ {\rm{bvp}}\,({\rm{subrange}}\,({\it{a2\/}}, {\it{i\/}}, {\it{j\/}})\index{subrange})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-approx-make-list-x \\ \index{v-approx-make-list-x}
(({\rm{length}}\,({\it{y\/}})\index{length} $=$ {\it{bits\/}}) $\wedge$ {\rm{properp}}\,({\it{y\/}})\index{properp}) $\rightarrow$ {\rm{v-approx}}\,({\rm{make-list}}\,({\it{bits\/}}, {\sc{x}}\index{x})\index{make-list}, {\it{y\/}})\index{v-approx}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  read-mem-monotone \\ \index{read-mem-monotone}
\=\+({\rm{bvp}}\,({\it{v-addr\/}})\index{bvp} $\wedge$ {\rm{s-approx}}\,({\it{mem1\/}}, {\it{mem2\/}})\index{s-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{v-approx}}\,({\rm{read-mem}}\,({\it{v-addr\/}}, {\it{mem1\/}})\index{read-mem}, {\rm{read-mem}}\,({\it{v-addr\/}}, {\it{mem2\/}})\index{read-mem})\index{v-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-length-read-mem1 \\ \index{equal-length-read-mem1}
\=\+{\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx} \\ 
$\rightarrow$$\;\;\;\;$(({\rm{length}}\,({\rm{read-mem1}}\,({\it{a\/}}, {\it{s2\/}})\index{read-mem1})\index{length} $=$ {\rm{length}}\,({\rm{read-mem1}}\,({\it{a\/}}, {\it{s1\/}})\index{read-mem1})\index{length}) $=$ {\bf{t}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-length-read-mem \\ \index{equal-length-read-mem}
\=\+{\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx} \\ 
$\rightarrow$$\;\;\;\;$(({\rm{length}}\,({\rm{read-mem}}\,({\it{a\/}}, {\it{s2\/}})\index{read-mem})\index{length} $=$ {\rm{length}}\,({\rm{read-mem}}\,({\it{a\/}}, {\it{s1\/}})\index{read-mem})\index{length}) $=$ {\bf{t}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  s-approx-implies-properp-read-mem1 \\ \index{s-approx-implies-properp-read-me!m1}
({\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx} $\wedge$ {\rm{properp}}\,({\rm{read-mem1}}\,({\it{a\/}}, {\it{s1\/}})\index{read-mem1})\index{properp}) $\rightarrow$ {\rm{properp}}\,({\rm{read-mem1}}\,({\it{a\/}}, {\it{s2\/}})\index{read-mem1})\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  s-approx-implies-properp-read-mem \\ \index{s-approx-implies-properp-read-me!m}
({\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx} $\wedge$ {\rm{properp}}\,({\rm{read-mem}}\,({\it{a\/}}, {\it{s1\/}})\index{read-mem})\index{properp}) $\rightarrow$ {\rm{properp}}\,({\rm{read-mem}}\,({\it{a\/}}, {\it{s2\/}})\index{read-mem})\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-port-ram-value-monotone \\ \index{dual-port-ram-value-monotone}
\=\+(({\it{address-lines\/}} $\in\;${\bf{N}}${}$) $\wedge$ {\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx} $\wedge$ {\rm{v-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{v-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{v-approx}}\,(\=\+{\rm{dual-port-ram-value}}\,({\it{bits\/}}, {\it{address-lines\/}}, {\it{a1\/}}, {\it{s1\/}})\index{dual-port-ram-value}, \\ 
{\rm{dual-port-ram-value}}\,({\it{bits\/}}, {\it{address-lines\/}}, {\it{a2\/}}, {\it{s2\/}})\index{dual-port-ram-value})\-\index{v-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-append \\ \index{eval\$-append}
\=\+({\rm{litatom}}\,({\it{x\/}}) $\wedge$ ({\it{x\/}} $\in$ {\it{lst\/}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\rm{append}}\,({\rm{pairlist}}\,({\it{lst\/}}, {\it{y\/}}), {\it{z\/}})) $=$ {\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\rm{pairlist}}\,({\it{lst\/}}, {\it{y\/}})))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-pairlist-cons \\ \index{eval\$-pairlist-cons}
\=\+{\rm{litatom}}\,({\it{x\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\rm{pairlist}}\,({\rm{cons}}\,({\it{c\/}}, {\it{lst\/}}), {\it{y\/}})) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $=$ {\it{c\/}}$\;\;${\bf then }{\rm{car}}\,({\it{y\/}}) \\ 
{\bf else }{\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\rm{pairlist}}\,({\it{lst\/}}, {\rm{cdr}}\,({\it{y\/}})))$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  eval\$-append-2 \\ \index{eval\$-append-2}
\=\+({\rm{litatom}}\,({\it{x\/}}) $\wedge$ ({\it{x\/}} $\not\in$ {\it{lst\/}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\rm{append}}\,({\rm{pairlist}}\,({\it{lst\/}}, {\it{y\/}}), {\it{z\/}})) $=$ {\rm{eval\$}}\,({\bf{t}}, {\it{x\/}}, {\it{z\/}}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-apply-value-dp-ram-16x32-lemma-1 \\ \index{dual-apply-value-dp-ram-16x32-le!mma-1}
\=\+{\rm{dual-apply-value}}\,({\tt{'}}{\tt{dp-ram-16x32}}, {\it{a\/}}, {\it{s\/}})\index{dual-apply-value} \\ 
$=$$\;\;\;\;${\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\rm{cdr}}\,({\rm{lookup-module}}\,({\tt{'}}{\tt{results}}, {\rm{cdr}}\,({\rm{primp}}\,({\tt{'}}{\tt{dp-ram-16x32}})\index{primp}))\index{lookup-module}), \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\rm{cdr}}\,({\rm{lookup-module}}\,(\=\+{\tt{'}}{\tt{inputs}}, \\ 
{\rm{cdr}}\,({\rm{primp}}\,({\tt{'}}{\tt{dp-ram-16x32}})\index{primp}))\-\index{lookup-module}), \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,(\=\+{\rm{cdr}}\,({\rm{lookup-module}}\,(\=\+{\tt{'}}{\tt{states}}, \\ 
{\rm{cdr}}\,({\rm{primp}}\,({\tt{'}}{\tt{dp-ram-16x32}})\index{primp}))\-\index{lookup-module}), \\ 
{\it{s\/}})\-\index{pairstates})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-apply-value-dp-ram-16x32-lemma-2 \\ \index{dual-apply-value-dp-ram-16x32-le!mma-2}
\=\+{\rm{dual-apply-value}}\,({\tt{'}}{\tt{dp-ram-16x32}}, {\it{a\/}}, {\it{s\/}})\index{dual-apply-value} \\ 
$=$$\;\;\;\;${\rm{dual-port-ram-value}}\,(\=\+{\tt{32}}, \\ 
{\tt{4}}, \\ 
{\rm{list}}\,(\=\+{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{read-a0}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{read-a1}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{read-a2}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{read-a3}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{write-b0}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{write-b1}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{write-b2}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{write-b3}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{wen}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d0}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d1}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d2}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d3}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d4}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d5}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d6}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d7}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d8}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d9}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d10}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d11}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d12}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d13}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d14}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d15}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d16}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d17}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d18}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d19}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d20}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d21}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d22}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d23}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d24}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d25}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d26}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d27}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d28}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d29}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d30}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d31}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{state}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}}{\tt{ }}{\tt{d4}} \\ 
{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}}{\tt{ }}{\tt{d9}}{\tt{ }}{\tt{d10}} \\ 
{\tt{d11}}{\tt{ }}{\tt{d12}}{\tt{ }}{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}} \\ 
{\tt{d16}}{\tt{ }}{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}}{\tt{ }}{\tt{d25}} \\ 
{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}}{\tt{ }}{\tt{d29}}{\tt{ }}{\tt{d30}} \\ 
{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-)\-\index{dual-port-ram-value}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-apply-value-dp-ram-16x32-lemma-3 \\ \index{dual-apply-value-dp-ram-16x32-le!mma-3}
\=\+{\rm{dual-apply-value}}\,({\tt{'}}{\tt{dp-ram-16x32}}, {\it{a\/}}, {\it{s\/}})\index{dual-apply-value} \\ 
$=$$\;\;\;\;${\rm{dual-port-ram-value}}\,(\=\+{\tt{32}}, \\ 
{\tt{4}}, \\ 
{\rm{list}}\,(\=\+{\rm{car}}\,({\it{a\/}}), \\ 
{\rm{cadr}}\,({\it{a\/}}), \\ 
{\rm{caddr}}\,({\it{a\/}}), \\ 
{\rm{cadddr}}\,({\it{a\/}}), \\ 
{\rm{caddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddddddddddddddddddddddr}}\,({\it{a\/}}))\-, \\ 
{\it{s\/}})\-\index{dual-port-ram-value}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{dual-port-ram-value-body} \\  
\=\+{\rm{dual-port-ram-value-body}}\,({\it{bits\/}}, {\it{a-address\/}}, {\it{b-address\/}}, {\it{wen\/}}, {\it{state\/}})\index{dual-port-ram-value-body} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+($\neg$ {\rm{bvp}}\,({\it{a-address\/}})\index{bvp}) \\ 
$\vee$$\;\;\;\;$(\=\+({\it{wen\/}} $\not=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{bvp}}\,({\it{b-address\/}})\index{bvp}) $\vee$ ({\it{a-address\/}} $=$ {\it{b-address\/}})))\-\- \\ 
{\bf then }{\rm{make-list}}\,({\it{bits\/}}, {\sc{x}}\index{x})\index{make-list} \\ 
{\bf elseif }\=\+{\rm{properp}}\,({\rm{read-mem}}\,({\it{a-address\/}}, {\it{state\/}})\index{read-mem})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{read-mem}}\,({\it{a-address\/}}, {\it{state\/}})\index{read-mem})\index{length} $=$ {\it{bits\/}})\- \\ 
{\bf then }{\rm{read-mem}}\,({\it{a-address\/}}, {\it{state\/}})\index{read-mem} \\ 
{\bf else }{\rm{make-list}}\,({\it{bits\/}}, {\sc{x}}\index{x})\index{make-list}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-port-ram-value-is-dual-port-ram-value-body \\ \index{dual-port-ram-value-is-dual-port!-ram-value-body}
\=\+{\rm{dual-port-ram-value}}\,({\it{bits\/}}, {\it{address-lines\/}}, {\it{args\/}}, {\it{state\/}})\index{dual-port-ram-value} \\ 
$=$$\;\;\;\;${\rm{dual-port-ram-value-body}}\,(\=\+{\it{bits\/}}, \\ 
{\rm{subrange}}\,({\it{args\/}}, {\tt{0}}, {\it{address-lines\/}} $-\;1$)\index{subrange}, \\ 
{\rm{subrange}}\,(\=\+{\it{args\/}}, \\ 
{\it{address-lines\/}}, \\ 
({\tt{2}} $*$ {\it{address-lines\/}}) $-\;1$)\-\index{subrange}, \\ 
{\rm{nth}}\,({\tt{2}} $*$ {\it{address-lines\/}}, {\it{args\/}})\index{nth}, \\ 
{\it{state\/}})\-\index{dual-port-ram-value-body}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-apply-value-dp-ram-16x32 \\ \index{dual-apply-value-dp-ram-16x32}
{\rm{dual-apply-value}}\,({\tt{'}}{\tt{dp-ram-16x32}}, {\it{a\/}}, {\it{s\/}})\index{dual-apply-value} $=$ {\rm{dual-port-ram-value}}\,({\tt{32}}, {\tt{4}}, {\it{a\/}}, {\it{s\/}})\index{dual-port-ram-value}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dp-ram-16x32-monotone-value \\ \index{dp-ram-16x32-monotone-value}
{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{dp-ram-16x32}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}
\end{tabbing}


\noindent{\sc Event}:   Enable v-knownp; name this event `v-knownp-off'.\index{v-knownp-off}

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\noindent{\sc Event}:   Enable s-knownp-implies-s-approx-is-equal; name this event `s-knownp-implies-s-approx-is-equal-off'.\index{s-knownp-implies-s-approx-is-eq!ual-off}

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\noindent{\sc Event}:   Enable bvp; name this event `bvp-off1'.\index{bvp-off1}

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\noindent{\sc Event}:   Enable fourp-implies-s-approx-is-b-approx; name this event `fourp-implies-s-approx-is-b-approx-off'.\index{fourp-implies-s-approx-is-b-app!rox-off}

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\noindent{\sc Event}:   Enable v-approx; name this event `v-approx-off'.\index{v-approx-off}

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\noindent{\sc Event}:   Enable s-knownp; name this event `s-knownp-off'.\index{s-knownp-off}

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\begin{tabbing}{\sc Theorem}:  s-approx-opener \\ \index{s-approx-opener}
\=\+(\=\+({\rm{listp}}\,({\it{s1\/}}) $\vee$ {\rm{listp}}\,({\it{s2\/}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{s1\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\it{s2\/}}) \\ 
{\bf then }\=\+{\rm{s-approx}}\,({\rm{car}}\,({\it{s1\/}}), {\rm{car}}\,({\it{s2\/}}))\index{s-approx} \\ 
$\wedge$$\;\;\;\;${\rm{s-approx}}\,({\rm{cdr}}\,({\it{s1\/}}), {\rm{cdr}}\,({\it{s2\/}}))\index{s-approx}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+(({\it{s1\/}} $=$ {\bf{nil}}) $\vee$ ({\it{s2\/}} $=$ {\bf{nil}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx} $=$ ({\it{s1\/}} $=$ {\it{s2\/}})))\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{ramp}}\,({\it{s1\/}})\index{ramp} $\vee$ {\rm{ramp}}\,({\it{s2\/}})\index{ramp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{ramp}}\,({\it{s1\/}})\index{ramp} \\ 
{\bf then }\=\+{\bf if }{\rm{ramp}}\,({\it{s2\/}})\index{ramp} \\ 
{\bf then }{\rm{v-approx}}\,({\rm{ram-guts}}\,({\it{s1\/}})\index{ram-guts}, {\rm{ram-guts}}\,({\it{s2\/}})\index{ram-guts})\index{v-approx} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{romp}}\,({\it{s1\/}})\index{romp} $\vee$ {\rm{romp}}\,({\it{s2\/}})\index{romp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{romp}}\,({\it{s1\/}})\index{romp} \\ 
{\bf then }\=\+{\bf if }{\rm{romp}}\,({\it{s2\/}})\index{romp} \\ 
{\bf then }{\rm{v-approx}}\,({\rm{rom-guts}}\,({\it{s1\/}})\index{rom-guts}, {\rm{rom-guts}}\,({\it{s2\/}})\index{rom-guts})\index{v-approx} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{stubp}}\,({\it{s1\/}})\index{stubp} $\vee$ {\rm{stubp}}\,({\it{s2\/}})\index{stubp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{stubp}}\,({\it{s1\/}})\index{stubp} \\ 
{\bf then }\=\+{\bf if }{\rm{stubp}}\,({\it{s2\/}})\index{stubp} \\ 
{\bf then }{\rm{v-approx}}\,({\rm{stub-guts}}\,({\it{s1\/}})\index{stub-guts}, {\rm{stub-guts}}\,({\it{s2\/}})\index{stub-guts})\index{v-approx} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ (\=\+{\rm{listp}}\,({\it{s1\/}}) \\ 
$\vee$$\;\;\;\;${\rm{listp}}\,({\it{s2\/}}) \\ 
$\vee$$\;\;\;\;$({\it{s1\/}} $=$ {\bf{nil}}) \\ 
$\vee$$\;\;\;\;$({\it{s2\/}} $=$ {\bf{nil}}) \\ 
$\vee$$\;\;\;\;${\rm{ramp}}\,({\it{s1\/}})\index{ramp} \\ 
$\vee$$\;\;\;\;${\rm{ramp}}\,({\it{s2\/}})\index{ramp} \\ 
$\vee$$\;\;\;\;${\rm{romp}}\,({\it{s1\/}})\index{romp} \\ 
$\vee$$\;\;\;\;${\rm{romp}}\,({\it{s2\/}})\index{romp} \\ 
$\vee$$\;\;\;\;${\rm{stubp}}\,({\it{s1\/}})\index{stubp} \\ 
$\vee$$\;\;\;\;${\rm{stubp}}\,({\it{s2\/}})\index{stubp})\-) \\ 
$\rightarrow$$\;\;\;\;$({\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx} $=$ {\rm{b-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{b-approx}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable s-approx; name this event `s-approx-off'.\index{s-approx-off}

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\noindent{\sc Event}:   Enable *1*mem-width; name this event `g*1*mem-width-off'.\index{g*1*mem-width-off}

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\noindent{\sc Event}:   Enable mem-width; name this event `mem-width-off'.\index{mem-width-off}

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\begin{tabbing}{\sc Theorem}:  v-approx-implies-nth-does-not-go-from-f-to-t \\ \index{v-approx-implies-nth-does-not-g!o-from-f-to-t}
(($\neg$ {\rm{nth}}\,({\it{n\/}}, {\it{a1\/}})\index{nth}) $\wedge$ {\rm{nth}}\,({\it{n\/}}, {\it{a2\/}})\index{nth}) $\rightarrow$ ($\neg$ {\rm{v-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{v-approx})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  write-mem1-opener \\ \index{write-mem1-opener}
\=\+({\rm{stubp}}\,({\it{mem\/}})\index{stubp} $\rightarrow$ ({\rm{write-mem1}}\,({\it{v-addr\/}}, {\it{mem\/}}, {\it{value\/}})\index{write-mem1} $=$ {\it{mem\/}})) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{v-addr\/}} $\simeq\;${{\bf{nil}}}${}$) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{write-mem1}}\,({\it{v-addr\/}}, {\it{mem\/}}, {\it{value\/}})\index{write-mem1} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{ramp}}\,({\it{mem\/}})\index{ramp}$\;\;${\bf then }{\rm{ram}}\,({\it{value\/}})\index{ram} \\ 
{\bf else }{\it{mem\/}}$\;${\bf  endif}\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{listp}}\,({\it{v-addr\/}}) $\wedge$ ({\it{mem\/}} $\simeq\;${{\bf{nil}}}${}$)) \\ 
$\rightarrow$$\;\;\;\;$({\rm{write-mem1}}\,({\it{v-addr\/}}, {\it{mem\/}}, {\it{value\/}})\index{write-mem1} $=$ {\it{mem\/}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{listp}}\,({\it{mem\/}}) $\wedge$ {\rm{listp}}\,({\it{v-addr\/}}) $\wedge$ {\rm{car}}\,({\it{v-addr\/}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{write-mem1}}\,({\it{v-addr\/}}, {\it{mem\/}}, {\it{value\/}})\index{write-mem1} \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\rm{car}}\,({\it{mem\/}}), {\rm{write-mem1}}\,({\rm{cdr}}\,({\it{v-addr\/}}), {\rm{cdr}}\,({\it{mem\/}}), {\it{value\/}})\index{write-mem1}))\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{listp}}\,({\it{mem\/}}) $\wedge$ {\rm{listp}}\,({\it{v-addr\/}}) $\wedge$ ($\neg$ {\rm{car}}\,({\it{v-addr\/}}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{write-mem1}}\,({\it{v-addr\/}}, {\it{mem\/}}, {\it{value\/}})\index{write-mem1} \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\rm{write-mem1}}\,({\rm{cdr}}\,({\it{v-addr\/}}), {\rm{car}}\,({\it{mem\/}}), {\it{value\/}})\index{write-mem1}, {\rm{cdr}}\,({\it{mem\/}})))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{write-mem1-monotone-induction} \\  
\=\+{\rm{write-mem1-monotone-induction}}\,({\it{v-addr\/}}, {\it{mem1\/}}, {\it{mem2\/}})\index{write-mem1-monotone-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{stubp}}\,({\it{mem1\/}})\index{stubp} $\vee$ {\rm{stubp}}\,({\it{mem2\/}})\index{stubp}$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\it{v-addr\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }({\it{mem1\/}} $\simeq\;${{\bf{nil}}}${}$) $\vee$ ({\it{mem2\/}} $\simeq\;${{\bf{nil}}}${}$)$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\rm{car}}\,({\it{v-addr\/}}) \\ 
{\bf then }{\rm{write-mem1-monotone-induction}}\,({\rm{cdr}}\,({\it{v-addr\/}}), {\rm{cdr}}\,({\it{mem1\/}}), {\rm{cdr}}\,({\it{mem2\/}}))\index{write-mem1-monotone-induction} \\ 
{\bf else }{\rm{write-mem1-monotone-induction}}\,(\=\+{\rm{cdr}}\,({\it{v-addr\/}}), \\ 
{\rm{car}}\,({\it{mem1\/}}), \\ 
{\rm{car}}\,({\it{mem2\/}}))\-\index{write-mem1-monotone-induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  write-mem1-monotone \\ \index{write-mem1-monotone}
\=\+(\=\+{\rm{s-approx}}\,({\it{mem1\/}}, {\it{mem2\/}})\index{s-approx} \\ 
$\wedge$$\;\;\;\;${\rm{v-approx}}\,({\it{data1\/}}, {\it{data2\/}})\index{v-approx} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{data1\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{data2\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data1\/}})\index{length} $=$ {\sc{mem-width}}\index{mem-width}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data2\/}})\index{length} $=$ {\sc{mem-width}}\index{mem-width}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx}}\,({\rm{write-mem1}}\,({\it{v-addr\/}}, {\it{mem1\/}}, {\it{data1\/}})\index{write-mem1}, {\rm{write-mem1}}\,({\it{v-addr\/}}, {\it{mem2\/}}, {\it{data2\/}})\index{write-mem1})\index{s-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  write-mem-monotone \\ \index{write-mem-monotone}
\=\+(\=\+{\rm{s-approx}}\,({\it{mem1\/}}, {\it{mem2\/}})\index{s-approx} \\ 
$\wedge$$\;\;\;\;${\rm{v-approx}}\,({\it{data1\/}}, {\it{data2\/}})\index{v-approx} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{data1\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{data2\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data1\/}})\index{length} $=$ {\sc{mem-width}}\index{mem-width}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{data2\/}})\index{length} $=$ {\sc{mem-width}}\index{mem-width}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx}}\,({\rm{write-mem}}\,({\it{v-addr\/}}, {\it{mem1\/}}, {\it{data1\/}})\index{write-mem}, {\rm{write-mem}}\,({\it{v-addr\/}}, {\it{mem2\/}}, {\it{data2\/}})\index{write-mem})\index{s-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-approx-length \\ \index{v-approx-length}
{\rm{v-approx}}\,({\it{v1\/}}, {\it{v2\/}})\index{v-approx} $\rightarrow$ ({\rm{length}}\,({\it{v1\/}})\index{length} $\not<$ {\rm{length}}\,({\it{v2\/}})\index{length})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{write-mem1-double-induction} \\  
\=\+{\rm{write-mem1-double-induction}}\,({\it{v-addr\/}}, {\it{mem1\/}}, {\it{mem2\/}})\index{write-mem1-double-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{stubp}}\,({\it{mem1\/}})\index{stubp} $\vee$ {\rm{stubp}}\,({\it{mem2\/}})\index{stubp}$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\it{v-addr\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }({\it{mem1\/}} $\simeq\;${{\bf{nil}}}${}$) $\vee$ ({\it{mem2\/}} $\simeq\;${{\bf{nil}}}${}$)$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\rm{car}}\,({\it{v-addr\/}}) \\ 
{\bf then }{\rm{write-mem1-double-induction}}\,({\rm{cdr}}\,({\it{v-addr\/}}), {\rm{cdr}}\,({\it{mem1\/}}), {\rm{cdr}}\,({\it{mem2\/}}))\index{write-mem1-double-induction} \\ 
{\bf else }{\rm{write-mem1-double-induction}}\,(\=\+{\rm{cdr}}\,({\it{v-addr\/}}), \\ 
{\rm{car}}\,({\it{mem1\/}}), \\ 
{\rm{car}}\,({\it{mem2\/}}))\-\index{write-mem1-double-induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  s-approx-write-mem1-id \\ \index{s-approx-write-mem1-id}
\=\+({\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx} $\wedge$ {\rm{good-s}}\,({\it{s2\/}})\index{good-s}) \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx}}\,({\rm{write-mem1}}\,({\it{v-addr\/}}, {\it{s1\/}}, {\rm{make-list}}\,({\sc{mem-width}}\index{mem-width}, {\sc{x}}\index{x})\index{make-list})\index{write-mem1}, {\it{s2\/}})\index{s-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  s-approx-write-mem-id \\ \index{s-approx-write-mem-id}
\=\+({\rm{good-s}}\,({\it{s2\/}})\index{good-s} $\wedge$ {\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx}}\,({\rm{write-mem}}\,({\it{v-addr\/}}, {\it{s1\/}}, {\rm{make-list}}\,({\sc{mem-width}}\index{mem-width}, {\sc{x}}\index{x})\index{make-list})\index{write-mem}, {\it{s2\/}})\index{s-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  s-approx-constant-ram-x-id \\ \index{s-approx-constant-ram-x-id}
\=\+({\rm{good-s}}\,({\it{s2\/}})\index{good-s} $\wedge$ {\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx}}\,({\rm{constant-ram}}\,({\it{s1\/}}, {\rm{make-list}}\,({\sc{mem-width}}\index{mem-width}, {\sc{x}}\index{x})\index{make-list})\index{constant-ram}, {\it{s2\/}})\index{s-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  s-approx-constant-ram-x-constant-ram-x \\ \index{s-approx-constant-ram-x-constant!-ram-x}
\=\+{\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx} \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx}}\,(\=\+{\rm{constant-ram}}\,({\it{s1\/}}, {\rm{make-list}}\,({\sc{mem-width}}\index{mem-width}, {\sc{x}}\index{x})\index{make-list})\index{constant-ram}, \\ 
{\rm{constant-ram}}\,({\it{s2\/}}, {\rm{make-list}}\,({\sc{mem-width}}\index{mem-width}, {\sc{x}}\index{x})\index{make-list})\index{constant-ram})\-\index{s-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-approx-preserves-length \\ \index{v-approx-preserves-length}
{\rm{v-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{v-approx} $\rightarrow$ ({\rm{length}}\,({\it{a1\/}})\index{length} $=$ {\rm{length}}\,({\it{a2\/}})\index{length})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-approx-subrange \\ \index{v-approx-subrange}
{\rm{v-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{v-approx} $\rightarrow$ {\rm{v-approx}}\,({\rm{subrange}}\,({\it{a1\/}}, {\it{i\/}}, {\it{j\/}})\index{subrange}, {\rm{subrange}}\,({\it{a2\/}}, {\it{i\/}}, {\it{j\/}})\index{subrange})\index{v-approx}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  mem-width-non-zero \\ \index{mem-width-non-zero}
{\sc{mem-width}}\index{mem-width} $\not=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  s-approx-constant-ram-x-write-mem1-case-3 \\ \index{s-approx-constant-ram-x-write-me!m1-case-3}
\=\+(\=\+($\neg$ {\rm{stubp}}\,({\it{s1\/}})\index{stubp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{stubp}}\,({\it{s2\/}})\index{stubp}) \\ 
$\wedge$$\;\;\;\;${\rm{listp}}\,({\it{v-addr\/}}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{listp}}\,({\it{s1\/}})) \\ 
$\wedge$$\;\;\;\;${\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx} \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{v\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{v\/}})\index{length} $=$ {\sc{mem-width}}\index{mem-width}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{ramp}}\,({\it{s1\/}})\index{ramp}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx}}\,({\it{s1\/}}, {\rm{write-mem1}}\,({\it{v-addr\/}}, {\it{s2\/}}, {\it{v\/}})\index{write-mem1})\index{s-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  s-approx-constant-ram-x-write-mem1 \\ \index{s-approx-constant-ram-x-write-me!m1}
\=\+({\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx} $\wedge$ {\rm{properp}}\,({\it{v\/}})\index{properp} $\wedge$ ({\rm{length}}\,({\it{v\/}})\index{length} $=$ {\sc{mem-width}}\index{mem-width}) $\wedge$ {\rm{good-s}}\,({\it{s2\/}})\index{good-s}) \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx}}\,(\=\+{\rm{constant-ram}}\,({\it{s1\/}}, {\rm{make-list}}\,({\sc{mem-width}}\index{mem-width}, {\sc{x}}\index{x})\index{make-list})\index{constant-ram}, \\ 
{\rm{write-mem1}}\,({\it{v-addr\/}}, {\it{s2\/}}, {\it{v\/}})\index{write-mem1})\-\index{s-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  s-approx-constant-ram-x-write-mem \\ \index{s-approx-constant-ram-x-write-me!m}
\=\+({\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx} $\wedge$ {\rm{properp}}\,({\it{v\/}})\index{properp} $\wedge$ ({\rm{length}}\,({\it{v\/}})\index{length} $=$ {\sc{mem-width}}\index{mem-width}) $\wedge$ {\rm{good-s}}\,({\it{s2\/}})\index{good-s}) \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx}}\,(\=\+{\rm{constant-ram}}\,({\it{s1\/}}, {\rm{make-list}}\,({\sc{mem-width}}\index{mem-width}, {\sc{x}}\index{x})\index{make-list})\index{constant-ram}, \\ 
{\rm{write-mem}}\,({\it{v-addr\/}}, {\it{s2\/}}, {\it{v\/}})\index{write-mem})\-\index{s-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-approx-preserves-properp \\ \index{v-approx-preserves-properp}
($\neg$ ({\rm{properp}}\,({\it{v1\/}})\index{properp} $\leftrightarrow$ {\rm{properp}}\,({\it{v2\/}})\index{properp})) $\rightarrow$ ($\neg$ {\rm{v-approx}}\,({\it{v1\/}}, {\it{v2\/}})\index{v-approx})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  mem-width-linear-facts \\ \index{mem-width-linear-facts}
({\tt{31}} $<$ {\sc{mem-width}}\index{mem-width}) $\wedge$ ({\sc{mem-width}}\index{mem-width} $<$ {\tt{33}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-port-ram-state-monotone \\ \index{dual-port-ram-state-monotone}
\=\+({\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx} $\wedge$ {\rm{good-s}}\,({\it{s2\/}})\index{good-s} $\wedge$ {\rm{v-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{v-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx}}\,(\=\+{\rm{dual-port-ram-state}}\,({\sc{mem-width}}\index{mem-width}, {\tt{4}}, {\it{a1\/}}, {\it{s1\/}})\index{dual-port-ram-state}, \\ 
{\rm{dual-port-ram-state}}\,({\sc{mem-width}}\index{mem-width}, {\tt{4}}, {\it{a2\/}}, {\it{s2\/}})\index{dual-port-ram-state})\-\index{s-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-port-ram-state-monotone-rewrite \\ \index{dual-port-ram-state-monotone-re!write}
\=\+({\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx} $\wedge$ {\rm{good-s}}\,({\it{s2\/}})\index{good-s} $\wedge$ {\rm{v-approx}}\,({\it{a1\/}}, {\it{a2\/}})\index{v-approx}) \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx}}\,(\=\+{\rm{dual-port-ram-state}}\,({\tt{32}}, {\tt{4}}, {\it{a1\/}}, {\it{s1\/}})\index{dual-port-ram-state}, \\ 
{\rm{dual-port-ram-state}}\,({\tt{32}}, {\tt{4}}, {\it{a2\/}}, {\it{s2\/}})\index{dual-port-ram-state})\-\index{s-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-apply-state-dp-ram-16x32-lemma-1 \\ \index{dual-apply-state-dp-ram-16x32-le!mma-1}
\=\+{\rm{dual-apply-state}}\,({\tt{'}}{\tt{dp-ram-16x32}}, {\it{a\/}}, {\it{s\/}})\index{dual-apply-state} \\ 
$=$$\;\;\;\;${\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\rm{cdr}}\,({\rm{lookup-module}}\,({\tt{'}}{\tt{new-states}}, {\rm{cdr}}\,({\rm{primp}}\,({\tt{'}}{\tt{dp-ram-16x32}})\index{primp}))\index{lookup-module}), \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\rm{cdr}}\,({\rm{lookup-module}}\,(\=\+{\tt{'}}{\tt{inputs}}, \\ 
{\rm{cdr}}\,({\rm{primp}}\,({\tt{'}}{\tt{dp-ram-16x32}})\index{primp}))\-\index{lookup-module}), \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,(\=\+{\rm{cdr}}\,({\rm{lookup-module}}\,(\=\+{\tt{'}}{\tt{states}}, \\ 
{\rm{cdr}}\,({\rm{primp}}\,({\tt{'}}{\tt{dp-ram-16x32}})\index{primp}))\-\index{lookup-module}), \\ 
{\it{s\/}})\-\index{pairstates})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-apply-state-dp-ram-16x32-lemma-2 \\ \index{dual-apply-state-dp-ram-16x32-le!mma-2}
\=\+{\rm{dual-apply-state}}\,({\tt{'}}{\tt{dp-ram-16x32}}, {\it{a\/}}, {\it{s\/}})\index{dual-apply-state} \\ 
$=$$\;\;\;\;${\rm{dual-port-ram-state}}\,(\=\+{\tt{32}}, \\ 
{\tt{4}}, \\ 
{\rm{list}}\,(\=\+{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{read-a0}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{read-a1}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{read-a2}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{read-a3}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{write-b0}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{write-b1}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{write-b2}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{write-b3}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{wen}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d0}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d1}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d2}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d3}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d4}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d5}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d6}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d7}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d8}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d9}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d10}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d11}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d12}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d13}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d14}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d15}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d16}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d17}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d18}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d19}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d20}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d21}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d22}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d23}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d24}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d25}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d26}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d27}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d28}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d29}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d30}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{d31}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}} \\ 
{\tt{d4}}{\tt{ }}{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}} \\ 
{\tt{d9}}{\tt{ }}{\tt{d10}}{\tt{ }}{\tt{d11}}{\tt{ }}{\tt{d12}} \\ 
{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}}{\tt{ }}{\tt{d16}} \\ 
{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}} \\ 
{\tt{d25}}{\tt{ }}{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}} \\ 
{\tt{d29}}{\tt{ }}{\tt{d30}}{\tt{ }}{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-)\-, \\ 
{\rm{eval\$}}\,(\=\+{\bf{t}}, \\ 
{\tt{'}}{\tt{state}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\tt{'}}{\tt{(}}\=\+{\tt{read-a0}}{\tt{ }}{\tt{read-a1}} \\ 
{\tt{read-a2}}{\tt{ }}{\tt{read-a3}} \\ 
{\tt{write-b0}}{\tt{ }}{\tt{write-b1}} \\ 
{\tt{write-b2}}{\tt{ }}{\tt{write-b3}} \\ 
{\tt{wen}}{\tt{ }}{\tt{d0}}{\tt{ }}{\tt{d1}}{\tt{ }}{\tt{d2}}{\tt{ }}{\tt{d3}}{\tt{ }}{\tt{d4}} \\ 
{\tt{d5}}{\tt{ }}{\tt{d6}}{\tt{ }}{\tt{d7}}{\tt{ }}{\tt{d8}}{\tt{ }}{\tt{d9}}{\tt{ }}{\tt{d10}} \\ 
{\tt{d11}}{\tt{ }}{\tt{d12}}{\tt{ }}{\tt{d13}}{\tt{ }}{\tt{d14}}{\tt{ }}{\tt{d15}} \\ 
{\tt{d16}}{\tt{ }}{\tt{d17}}{\tt{ }}{\tt{d18}}{\tt{ }}{\tt{d19}}{\tt{ }}{\tt{d20}} \\ 
{\tt{d21}}{\tt{ }}{\tt{d22}}{\tt{ }}{\tt{d23}}{\tt{ }}{\tt{d24}}{\tt{ }}{\tt{d25}} \\ 
{\tt{d26}}{\tt{ }}{\tt{d27}}{\tt{ }}{\tt{d28}}{\tt{ }}{\tt{d29}}{\tt{ }}{\tt{d30}} \\ 
{\tt{d31}}{\tt{)}}\-, \\ 
{\it{a\/}})\-, \\ 
{\rm{pairstates}}\,({\tt{'}}{\tt{state}}, {\it{s\/}})\index{pairstates})\-)\-)\-\index{dual-port-ram-state}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-apply-state-dp-ram-16x32-lemma-3 \\ \index{dual-apply-state-dp-ram-16x32-le!mma-3}
\=\+{\rm{dual-apply-state}}\,({\tt{'}}{\tt{dp-ram-16x32}}, {\it{a\/}}, {\it{s\/}})\index{dual-apply-state} \\ 
$=$$\;\;\;\;${\rm{dual-port-ram-state}}\,(\=\+{\tt{32}}, \\ 
{\tt{4}}, \\ 
{\rm{list}}\,(\=\+{\rm{car}}\,({\it{a\/}}), \\ 
{\rm{cadr}}\,({\it{a\/}}), \\ 
{\rm{caddr}}\,({\it{a\/}}), \\ 
{\rm{cadddr}}\,({\it{a\/}}), \\ 
{\rm{caddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{cadddddddddddddddddddddddddddddddddddddddr}}\,({\it{a\/}}), \\ 
{\rm{caddddddddddddddddddddddddddddddddddddddddr}}\,({\it{a\/}}))\-, \\ 
{\it{s\/}})\-\index{dual-port-ram-state}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{dual-port-ram-state-body} \\  
\=\+{\rm{dual-port-ram-state-body}}\,({\it{bits\/}}, {\it{b-address\/}}, {\it{wen\/}}, {\it{data\/}}, {\it{state\/}})\index{dual-port-ram-state-body} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{wen\/}} $=$ {\bf{t}}$\;\;${\bf then }{\it{state\/}} \\ 
{\bf elseif }$\neg$ {\rm{bvp}}\,({\it{b-address\/}})\index{bvp}$\;\;${\bf then }{\rm{constant-ram}}\,({\it{state\/}}, {\rm{make-list}}\,({\it{bits\/}}, {\sc{x}}\index{x})\index{make-list})\index{constant-ram} \\ 
{\bf elseif }{\it{wen\/}} $=$ {\bf{f}}$\;\;${\bf then }{\rm{write-mem}}\,({\it{b-address\/}}, {\it{state\/}}, {\it{data\/}})\index{write-mem} \\ 
{\bf else }{\rm{write-mem}}\,({\it{b-address\/}}, {\it{state\/}}, {\rm{make-list}}\,({\it{bits\/}}, {\sc{x}}\index{x})\index{make-list})\index{write-mem}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-port-ram-state-is-dual-port-ram-state-body \\ \index{dual-port-ram-state-is-dual-port!-ram-state-body}
\=\+{\rm{dual-port-ram-state}}\,({\it{bits\/}}, {\it{address-lines\/}}, {\it{args\/}}, {\it{state\/}})\index{dual-port-ram-state} \\ 
$=$$\;\;\;\;${\rm{dual-port-ram-state-body}}\,(\=\+{\it{bits\/}}, \\ 
{\rm{subrange}}\,(\=\+{\it{args\/}}, \\ 
{\it{address-lines\/}}, \\ 
({\tt{2}} $*$ {\it{address-lines\/}}) $-\;1$)\-\index{subrange}, \\ 
{\rm{nth}}\,({\tt{2}} $*$ {\it{address-lines\/}}, {\it{args\/}})\index{nth}, \\ 
{\rm{subrange}}\,(\=\+{\it{args\/}}, \\ 
$1\;+$ ({\tt{2}} $*$ {\it{address-lines\/}}), \\ 
({\tt{2}} $*$ {\it{address-lines\/}}) $+$ {\it{bits\/}})\-\index{subrange}, \\ 
{\it{state\/}})\-\index{dual-port-ram-state-body}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-apply-state-dp-ram-16x32 \\ \index{dual-apply-state-dp-ram-16x32}
{\rm{dual-apply-state}}\,({\tt{'}}{\tt{dp-ram-16x32}}, {\it{a\/}}, {\it{s\/}})\index{dual-apply-state} $=$ {\rm{dual-port-ram-state}}\,({\tt{32}}, {\tt{4}}, {\it{a\/}}, {\it{s\/}})\index{dual-port-ram-state}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dp-ram-16x32-monotone-state \\ \index{dp-ram-16x32-monotone-state}
\=\+{\rm{good-s}}\,({\it{s2\/}})\index{good-s} \\ 
$\rightarrow$$\;\;\;\;${\rm{monotonicity-property}}\,({\tt{2}}, {\tt{'}}{\tt{dp-ram-16x32}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dp-ram-16x32-monotone \\ \index{dp-ram-16x32-monotone}
\=\+{\rm{monotonicity-property}}\,({\tt{0}}, {\tt{'}}{\tt{dp-ram-16x32}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{good-s}}\,({\it{s2\/}})\index{good-s} \\ 
$\rightarrow$$\;\;\;\;${\rm{monotonicity-property}}\,(\=\+{\tt{2}}, \\ 
{\tt{'}}{\tt{dp-ram-16x32}}, \\ 
{\it{netlist\/}}, \\ 
{\it{a1\/}}, \\ 
{\it{a2\/}}, \\ 
{\it{s1\/}}, \\ 
{\it{s2\/}})\-\index{monotonicity-property})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable bvp-reverse; name this event `bvp-reverse-off'.\index{bvp-reverse-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-bvp; name this event `v-approx-bvp-off'.\index{v-approx-bvp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable read-mem1-monotone; name this event `read-mem1-monotone-off'.\index{read-mem1-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable bvp-implies-v-knownp; name this event `bvp-implies-v-knownp-off'.\index{bvp-implies-v-knownp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-x-x; name this event `v-approx-x-x-off'.\index{v-approx-x-x-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-implies-b-approx-nth; name this event `v-approx-implies-b-approx-nth-off'.\index{v-approx-implies-b-approx-nth-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*b-knownp; name this event `g*1*b-knownp-off1'.\index{g*1*b-knownp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-implies-subranges-equal; name this event `v-approx-implies-subranges-equal-off'.\index{v-approx-implies-subranges-equa!l-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-bvp-subrange; name this event `v-approx-bvp-subrange-off'.\index{v-approx-bvp-subrange-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-make-list-x; name this event `v-approx-make-list-x-off'.\index{v-approx-make-list-x-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable read-mem-monotone; name this event `read-mem-monotone-off'.\index{read-mem-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-length-read-mem1; name this event `equal-length-read-mem1-off'.\index{equal-length-read-mem1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-length-read-mem; name this event `equal-length-read-mem-off'.\index{equal-length-read-mem-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-implies-properp-read-mem1; name this event `s-approx-implies-properp-read-mem1-off'.\index{s-approx-implies-properp-read-me!m1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-implies-properp-read-mem; name this event `s-approx-implies-properp-read-mem-off'.\index{s-approx-implies-properp-read-me!m-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-port-ram-value-monotone; name this event `dual-port-ram-value-monotone-off'.\index{dual-port-ram-value-monotone-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-append; name this event `eval\$-append-off'.\index{eval\$-append-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-pairlist-cons; name this event `eval\$-pairlist-cons-off'.\index{eval\$-pairlist-cons-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-append-2; name this event `eval\$-append-2-off'.\index{eval\$-append-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-apply-value-dp-ram-16x32-lemma-1; name this event `dual-apply-value-dp-ram-16x32-lemma-1-off'.\index{dual-apply-value-dp-ram-16x32-le!mma-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-apply-value-dp-ram-16x32-lemma-2; name this event `dual-apply-value-dp-ram-16x32-lemma-2-off'.\index{dual-apply-value-dp-ram-16x32-le!mma-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-apply-value-dp-ram-16x32-lemma-3; name this event `dual-apply-value-dp-ram-16x32-lemma-3-off'.\index{dual-apply-value-dp-ram-16x32-le!mma-3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-port-ram-value-is-dual-port-ram-value-body; name this event `dual-port-ram-value-is-dual-port-ram-value-body-off'.\index{dual-port-ram-value-is-dual-port!-ram-value-body-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-apply-value-dp-ram-16x32; name this event `dual-apply-value-dp-ram-16x32-off'.\index{dual-apply-value-dp-ram-16x32-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dp-ram-16x32-monotone-value; name this event `dp-ram-16x32-monotone-value-off'.\index{dp-ram-16x32-monotone-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-knownp; name this event `v-knownp-on'.\index{v-knownp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-knownp-implies-s-approx-is-equal; name this event `s-knownp-implies-s-approx-is-equal-on'.\index{s-knownp-implies-s-approx-is-eq!ual-on}

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\noindent{\sc Event}:   Disable bvp; name this event `bvp-on'.\index{bvp-on}

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\noindent{\sc Event}:   Disable fourp-implies-s-approx-is-b-approx; name this event `fourp-implies-s-approx-is-b-approx-on'.\index{fourp-implies-s-approx-is-b-app!rox-on}

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\noindent{\sc Event}:   Disable v-approx; name this event `v-approx-on'.\index{v-approx-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-knownp; name this event `s-knownp-on'.\index{s-knownp-on}

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\noindent{\sc Event}:   Enable s-approx-opener; name this event `s-approx-opener-off'.\index{s-approx-opener-off}

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\noindent{\sc Event}:   Disable s-approx; name this event `s-approx-on'.\index{s-approx-on}

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\noindent{\sc Event}:   Disable *1*mem-width; name this event `g*1*mem-width-on'.\index{g*1*mem-width-on}

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\noindent{\sc Event}:   Disable mem-width; name this event `mem-width-on'.\index{mem-width-on}

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\noindent{\sc Event}:   Enable v-approx-implies-nth-does-not-go-from-f-to-t; name this event `v-approx-implies-nth-does-not-go-from-f-to-t-off'.\index{v-approx-implies-nth-does-not-g!o-from-f-to-t-off}

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\noindent{\sc Event}:   Enable write-mem1-opener; name this event `write-mem1-opener-off'.\index{write-mem1-opener-off}

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\noindent{\sc Event}:   Enable write-mem1-monotone; name this event `write-mem1-monotone-off'.\index{write-mem1-monotone-off}

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\noindent{\sc Event}:   Enable write-mem-monotone; name this event `write-mem-monotone-off'.\index{write-mem-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-length; name this event `v-approx-length-off'.\index{v-approx-length-off}

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\noindent{\sc Event}:   Enable s-approx-write-mem1-id; name this event `s-approx-write-mem1-id-off'.\index{s-approx-write-mem1-id-off}

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\noindent{\sc Event}:   Enable s-approx-write-mem-id; name this event `s-approx-write-mem-id-off'.\index{s-approx-write-mem-id-off}

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\noindent{\sc Event}:   Enable s-approx-constant-ram-x-id; name this event `s-approx-constant-ram-x-id-off'.\index{s-approx-constant-ram-x-id-off}

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\noindent{\sc Event}:   Enable s-approx-constant-ram-x-constant-ram-x; name this event `s-approx-constant-ram-x-constant-ram-x-off'.\index{s-approx-constant-ram-x-constant!-ram-x-off}

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\noindent{\sc Event}:   Enable v-approx-preserves-length; name this event `v-approx-preserves-length-off'.\index{v-approx-preserves-length-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-subrange; name this event `v-approx-subrange-off'.\index{v-approx-subrange-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable mem-width-non-zero; name this event `mem-width-non-zero-off'.\index{mem-width-non-zero-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-constant-ram-x-write-mem1-case-3; name this event `s-approx-constant-ram-x-write-mem1-case-3-off'.\index{s-approx-constant-ram-x-write-me!m1-case-3-off}

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\noindent{\sc Event}:   Enable s-approx-constant-ram-x-write-mem1; name this event `s-approx-constant-ram-x-write-mem1-off'.\index{s-approx-constant-ram-x-write-me!m1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-constant-ram-x-write-mem; name this event `s-approx-constant-ram-x-write-mem-off'.\index{s-approx-constant-ram-x-write-me!m-off}

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\noindent{\sc Event}:   Enable v-approx-preserves-properp; name this event `v-approx-preserves-properp-off'.\index{v-approx-preserves-properp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable mem-width-linear-facts; name this event `mem-width-linear-facts-off'.\index{mem-width-linear-facts-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-port-ram-state-monotone-rewrite; name this event `dual-port-ram-state-monotone-rewrite-off'.\index{dual-port-ram-state-monotone-re!write-off}

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\noindent{\sc Event}:   Enable dual-apply-state-dp-ram-16x32-lemma-1; name this event `dual-apply-state-dp-ram-16x32-lemma-1-off'.\index{dual-apply-state-dp-ram-16x32-le!mma-1-off}

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\noindent{\sc Event}:   Enable dual-apply-state-dp-ram-16x32-lemma-2; name this event `dual-apply-state-dp-ram-16x32-lemma-2-off'.\index{dual-apply-state-dp-ram-16x32-le!mma-2-off}

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\noindent{\sc Event}:   Enable dual-apply-state-dp-ram-16x32-lemma-3; name this event `dual-apply-state-dp-ram-16x32-lemma-3-off'.\index{dual-apply-state-dp-ram-16x32-le!mma-3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-port-ram-state-is-dual-port-ram-state-body; name this event `dual-port-ram-state-is-dual-port-ram-state-body-off'.\index{dual-port-ram-state-is-dual-port!-ram-state-body-off}

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\noindent{\sc Event}:   Enable dual-apply-state-dp-ram-16x32; name this event `dual-apply-state-dp-ram-16x32-off'.\index{dual-apply-state-dp-ram-16x32-o!ff}

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\noindent{\sc Event}:   Enable dp-ram-16x32-monotone-state; name this event `dp-ram-16x32-monotone-state-off'.\index{dp-ram-16x32-monotone-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dp-ram-16x32-monotone; name this event `dp-ram-16x32-monotone-off'.\index{dp-ram-16x32-monotone-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ok-netlistp} \\  
\=\+{\rm{ok-netlistp}}\,({\it{flag\/}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{exceptions\/}})\index{ok-netlistp} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{flag\/}}: \\ 
{\bf case = }{\tt{0}} \\ 
{\bf then }\=\+{\bf if }{\rm{primp}}\,({\it{fn\/}})\index{primp}$\;\;${\bf then }{\it{fn\/}} $\not\in$ {\it{exceptions\/}} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{lookup-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{lookup-module}) \\ 
{\bf then }{\rm{ok-netlistp}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{lookup-module})\index{module-occurrences}, \\ 
{\rm{delete-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{delete-module}, \\ 
{\it{exceptions\/}})\-\index{ok-netlistp} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{1}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\rm{listp}}\,({\it{fn\/}}) \\ 
{\bf then }\=\+{\rm{ok-netlistp}}\,({\tt{0}}, {\rm{occ-function}}\,({\rm{car}}\,({\it{fn\/}}))\index{occ-function}, {\it{netlist\/}}, {\it{exceptions\/}})\index{ok-netlistp} \\ 
$\wedge$$\;\;\;\;${\rm{ok-netlistp}}\,({\tt{1}}, {\rm{cdr}}\,({\it{fn\/}}), {\it{netlist\/}}, {\it{exceptions\/}})\index{ok-netlistp}\- \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{2}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\rm{primp}}\,({\it{fn\/}})\index{primp}$\;\;${\bf then }{\it{fn\/}} $\not\in$ {\it{exceptions\/}} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{lookup-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{lookup-module}) \\ 
{\bf then }{\rm{ok-netlistp}}\,(\=\+{\tt{3}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{lookup-module})\index{module-occurrences}, \\ 
{\rm{delete-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{delete-module}, \\ 
{\it{exceptions\/}})\-\index{ok-netlistp} \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{3}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\rm{listp}}\,({\it{fn\/}}) \\ 
{\bf then }\=\+{\rm{ok-netlistp}}\,({\tt{2}}, {\rm{occ-function}}\,({\rm{car}}\,({\it{fn\/}}))\index{occ-function}, {\it{netlist\/}}, {\it{exceptions\/}})\index{ok-netlistp} \\ 
$\wedge$$\;\;\;\;${\rm{ok-netlistp}}\,({\tt{3}}, {\rm{cdr}}\,({\it{fn\/}}), {\it{netlist\/}}, {\it{exceptions\/}})\index{ok-netlistp}\- \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf otherwise }{\bf{f}}$\;${\bf  endcase}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  primp-monotone \\ \index{primp-monotone}
\=\+(\=\+{\rm{primp}}\,({\it{fn\/}})\index{primp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{flag\/}} $=$ {\tt{0}}) \\ 
$\vee$$\;\;\;\;$(\=\+({\it{flag\/}} $=$ {\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(({\it{fn\/}} $=$ {\tt{'}}{\tt{dp-ram-16x32}}) $\rightarrow$ {\rm{good-s}}\,({\it{s2\/}})\index{good-s}))\-)\- \\ 
$\wedge$$\;\;\;\;$({\it{fn\/}} $\not=$ {\tt{'}}{\tt{mem-32x32}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{monotonicity-property}}\,({\it{flag\/}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property} \\ 
$\wedge$$\;\;\;\;${\rm{monotonicity-property}}\,({\it{flag\/}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{dual-eval-monotone-induction} \\  
\=\+{\rm{dual-eval-monotone-induction}}\,({\it{flag\/}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{dual-eval-monotone-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf case on }{\it{flag\/}}: \\ 
{\bf case = }{\tt{0}} \\ 
{\bf then }\=\+{\bf if }{\rm{primp}}\,({\it{fn\/}})\index{primp}$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{lookup-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{lookup-module}) \\ 
{\bf then }{\rm{dual-eval-monotone-induction}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\rm{delete-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{delete-module}, \\ 
{\rm{pairlist}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\it{a1\/}})\-, \\ 
{\rm{pairlist}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\it{a2\/}})\-, \\ 
{\rm{pairstates}}\,(\=\+{\rm{module-statenames}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-statenames}, \\ 
{\it{s1\/}})\-\index{pairstates}, \\ 
{\rm{pairstates}}\,(\=\+{\rm{module-statenames}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-statenames}, \\ 
{\it{s2\/}})\-\index{pairstates})\-\index{dual-eval-monotone-induction} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{1}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\rm{listp}}\,({\it{fn\/}}) \\ 
{\bf then }\=\+{\rm{dual-eval-monotone-induction}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{fn\/}}))\index{occ-function}, \\ 
{\it{netlist\/}}, \\ 
{\rm{collect-value}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{fn\/}}))\index{occ-inputs}, \\ 
{\it{a1\/}})\-\index{collect-value}, \\ 
{\rm{collect-value}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{fn\/}}))\index{occ-inputs}, \\ 
{\it{a2\/}})\-\index{collect-value}, \\ 
{\rm{value}}\,({\rm{occ-name}}\,({\rm{car}}\,({\it{fn\/}}))\index{occ-name}, {\it{s1\/}})\index{value}, \\ 
{\rm{value}}\,({\rm{occ-name}}\,({\rm{car}}\,({\it{fn\/}}))\index{occ-name}, {\it{s2\/}})\index{value})\-\index{dual-eval-monotone-induction} \\ 
$\wedge$$\;\;\;\;${\rm{dual-eval-monotone-induction}}\,(\=\+{\tt{1}}, \\ 
{\rm{cdr}}\,({\it{fn\/}}), \\ 
{\it{netlist\/}}, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\rm{occ-outputs}}\,({\rm{car}}\,({\it{fn\/}}))\index{occ-outputs}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{fn\/}}))\index{occ-function}, \\ 
{\rm{collect-value}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{fn\/}}))\index{occ-inputs}, \\ 
{\it{a1\/}})\-\index{collect-value}, \\ 
{\rm{value}}\,(\=\+{\rm{occ-name}}\,({\rm{car}}\,({\it{fn\/}}))\index{occ-name}, \\ 
{\it{s1\/}})\-\index{value}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-, \\ 
{\it{a1\/}})\-, \\ 
{\rm{append}}\,(\=\+{\rm{pairlist}}\,(\=\+{\rm{occ-outputs}}\,({\rm{car}}\,({\it{fn\/}}))\index{occ-outputs}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{0}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{fn\/}}))\index{occ-function}, \\ 
{\rm{collect-value}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{fn\/}}))\index{occ-inputs}, \\ 
{\it{a2\/}})\-\index{collect-value}, \\ 
{\rm{value}}\,(\=\+{\rm{occ-name}}\,({\rm{car}}\,({\it{fn\/}}))\index{occ-name}, \\ 
{\it{s2\/}})\-\index{value}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-, \\ 
{\it{a2\/}})\-, \\ 
{\it{s1\/}}, \\ 
{\it{s2\/}})\-\index{dual-eval-monotone-induction}\- \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{2}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\rm{primp}}\,({\it{fn\/}})\index{primp}$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{lookup-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{lookup-module}) \\ 
{\bf then }\=\+{\rm{dual-eval-monotone-induction}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\rm{delete-module}}\,({\it{fn\/}}, {\it{netlist\/}})\index{delete-module}, \\ 
{\rm{pairlist}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\it{a1\/}})\-, \\ 
{\rm{pairlist}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\it{a2\/}})\-, \\ 
{\rm{pairstates}}\,(\=\+{\rm{module-statenames}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-statenames}, \\ 
{\it{s1\/}})\-\index{pairstates}, \\ 
{\rm{pairstates}}\,(\=\+{\rm{module-statenames}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-statenames}, \\ 
{\it{s2\/}})\-\index{pairstates})\-\index{dual-eval-monotone-induction} \\ 
$\wedge$$\;\;\;\;${\rm{dual-eval-monotone-induction}}\,(\=\+{\tt{3}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\rm{delete-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{delete-module}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\rm{pairlist}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\it{a1\/}})\-, \\ 
{\rm{pairstates}}\,(\=\+{\rm{module-statenames}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-statenames}, \\ 
{\it{s1\/}})\-\index{pairstates}, \\ 
{\rm{delete-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{delete-module})\-\index{dual-eval}, \\ 
{\rm{dual-eval}}\,(\=\+{\tt{1}}, \\ 
{\rm{module-occurrences}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-occurrences}, \\ 
{\rm{pairlist}}\,(\=\+{\rm{module-inputs}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-inputs}, \\ 
{\it{a2\/}})\-, \\ 
{\rm{pairstates}}\,(\=\+{\rm{module-statenames}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-statenames}, \\ 
{\it{s2\/}})\-\index{pairstates}, \\ 
{\rm{delete-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{delete-module})\-\index{dual-eval}, \\ 
{\rm{pairstates}}\,(\=\+{\rm{module-statenames}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-statenames}, \\ 
{\it{s1\/}})\-\index{pairstates}, \\ 
{\rm{pairstates}}\,(\=\+{\rm{module-statenames}}\,({\rm{lookup-module}}\,(\=\+{\it{fn\/}}, \\ 
{\it{netlist\/}})\-\index{lookup-module})\index{module-statenames}, \\ 
{\it{s2\/}})\-\index{pairstates})\-\index{dual-eval-monotone-induction}\- \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf case = }{\tt{3}} \\ 
{\bf $\;\;$then }\=\+{\bf if }{\rm{listp}}\,({\it{fn\/}}) \\ 
{\bf then }\=\+{\rm{dual-eval-monotone-induction}}\,(\=\+{\tt{2}}, \\ 
{\rm{occ-function}}\,({\rm{car}}\,({\it{fn\/}}))\index{occ-function}, \\ 
{\it{netlist\/}}, \\ 
{\rm{collect-value}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{fn\/}}))\index{occ-inputs}, \\ 
{\it{a1\/}})\-\index{collect-value}, \\ 
{\rm{collect-value}}\,(\=\+{\rm{occ-inputs}}\,({\rm{car}}\,({\it{fn\/}}))\index{occ-inputs}, \\ 
{\it{a2\/}})\-\index{collect-value}, \\ 
{\rm{value}}\,({\rm{occ-name}}\,({\rm{car}}\,({\it{fn\/}}))\index{occ-name}, {\it{s1\/}})\index{value}, \\ 
{\rm{value}}\,({\rm{occ-name}}\,({\rm{car}}\,({\it{fn\/}}))\index{occ-name}, {\it{s2\/}})\index{value})\-\index{dual-eval-monotone-induction} \\ 
$\wedge$$\;\;\;\;${\rm{dual-eval-monotone-induction}}\,(\=\+{\tt{3}}, \\ 
{\rm{cdr}}\,({\it{fn\/}}), \\ 
{\it{netlist\/}}, \\ 
{\it{a1\/}}, \\ 
{\it{a2\/}}, \\ 
{\it{s1\/}}, \\ 
{\it{s2\/}})\-\index{dual-eval-monotone-induction}\- \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf otherwise }{\bf{t}}$\;${\bf  endcase}\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable v-approx-x-x; name this event `v-approx-x-x-on'.\index{v-approx-x-x-on}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-approx-alist-implies-b-approx-value \\ \index{v-approx-alist-implies-b-approx!-value}
\=\+({\rm{alistp}}\,({\it{alist1\/}})\index{alistp} $\wedge$ {\rm{alistp}}\,({\it{alist2\/}})\index{alistp} $\wedge$ {\rm{v-approx-alist}}\,({\it{alist1\/}}, {\it{alist2\/}})\index{v-approx-alist}) \\ 
$\rightarrow$$\;\;\;\;${\rm{b-approx}}\,({\rm{value}}\,({\it{x\/}}, {\it{alist1\/}})\index{value}, {\rm{value}}\,({\it{x\/}}, {\it{alist2\/}})\index{value})\index{b-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  alistp-pairlist \\ \index{alistp-pairlist}
{\rm{alistp}}\,({\rm{pairlist}}\,({\it{x\/}}, {\it{y\/}}))\index{alistp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  alistp-append \\ \index{alistp-append}
{\rm{alistp}}\,({\it{x\/}})\index{alistp} $\rightarrow$ ({\rm{alistp}}\,({\rm{append}}\,({\it{x\/}}, {\it{y\/}}))\index{alistp} $=$ {\rm{alistp}}\,({\it{y\/}})\index{alistp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  alistp-dual-eval-1 \\ \index{alistp-dual-eval-1}
\=\+({\rm{alistp}}\,({\it{bindings\/}})\index{alistp} $\wedge$ ({\it{flag\/}} $=$ {\tt{1}})) \\ 
$\rightarrow$$\;\;\;\;${\rm{alistp}}\,({\rm{dual-eval}}\,({\it{flag\/}}, {\it{occurrences\/}}, {\it{bindings\/}}, {\it{state-bindints\/}}, {\it{netlist\/}})\index{dual-eval})\index{alistp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-approx-alist-implies-v-approx-collect-value \\ \index{v-approx-alist-implies-v-approx!-collect-value}
\=\+({\rm{alistp}}\,({\it{alist1\/}})\index{alistp} $\wedge$ {\rm{alistp}}\,({\it{alist2\/}})\index{alistp} $\wedge$ {\rm{v-approx-alist}}\,({\it{alist1\/}}, {\it{alist2\/}})\index{v-approx-alist}) \\ 
$\rightarrow$$\;\;\;\;${\rm{v-approx}}\,({\rm{collect-value}}\,({\it{x\/}}, {\it{alist1\/}})\index{collect-value}, {\rm{collect-value}}\,({\it{x\/}}, {\it{alist2\/}})\index{collect-value})\index{v-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{s-approx-list} \\  
\=\+{\rm{s-approx-list}}\,({\it{x\/}}, {\it{y\/}})\index{s-approx-list} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\rm{listp}}\,({\it{y\/}}) \\ 
$\wedge$$\;\;\;\;${\rm{s-approx}}\,({\rm{car}}\,({\it{x\/}}), {\rm{car}}\,({\it{y\/}}))\index{s-approx} \\ 
$\wedge$$\;\;\;\;${\rm{s-approx-list}}\,({\rm{cdr}}\,({\it{x\/}}), {\rm{cdr}}\,({\it{y\/}}))\index{s-approx-list}\- \\ 
{\bf else }{\it{y\/}} $\simeq\;${{\bf{nil}}}${}$$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  s-approx-list-implies-s-approx-alist \\ \index{s-approx-list-implies-s-approx-!alist}
{\rm{s-approx-list}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx-list} $\rightarrow$ {\rm{s-approx-alist}}\,({\rm{pairlist}}\,({\it{x\/}}, {\it{s1\/}}), {\rm{pairlist}}\,({\it{x\/}}, {\it{s2\/}}))\index{s-approx-alist}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-approx-implies-v-approx-alist \\ \index{v-approx-implies-v-approx-alist}
{\rm{v-approx}}\,({\it{v1\/}}, {\it{v2\/}})\index{v-approx} $\rightarrow$ {\rm{v-approx-alist}}\,({\rm{pairlist}}\,({\it{x\/}}, {\it{v1\/}}), {\rm{pairlist}}\,({\it{x\/}}, {\it{v2\/}}))\index{v-approx-alist}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  alistp-opener \\ \index{alistp-opener}
{\rm{alistp}}\,({\rm{cons}}\,({\it{a\/}}, {\it{z\/}}))\index{alistp} $=$ ({\rm{listp}}\,({\it{a\/}}) $\wedge$ {\rm{alistp}}\,({\it{z\/}})\index{alistp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  s-approx-alist-implies-s-approx-value \\ \index{s-approx-alist-implies-s-approx!-value}
\=\+({\rm{s-approx-alist}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx-alist} $\wedge$ {\rm{alistp}}\,({\it{s1\/}})\index{alistp} $\wedge$ {\rm{alistp}}\,({\it{s2\/}})\index{alistp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx}}\,({\rm{value}}\,({\it{w\/}}, {\it{s1\/}})\index{value}, {\rm{value}}\,({\it{w\/}}, {\it{s2\/}})\index{value})\index{s-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-approx-alist-append \\ \index{v-approx-alist-append}
\=\+({\rm{v-approx-alist}}\,({\it{a\/}}, {\it{c\/}})\index{v-approx-alist} $\wedge$ {\rm{v-approx-alist}}\,({\it{b\/}}, {\it{d\/}})\index{v-approx-alist}) \\ 
$\rightarrow$$\;\;\;\;${\rm{v-approx-alist}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}), {\rm{append}}\,({\it{c\/}}, {\it{d\/}}))\index{v-approx-alist}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{double-cdr-induction} \\  
\=\+{\rm{double-cdr-induction}}\,({\it{x\/}}, {\it{y\/}})\index{double-cdr-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) $\wedge$ {\rm{listp}}\,({\it{y\/}})$\;\;${\bf then }{\rm{double-cdr-induction}}\,({\rm{cdr}}\,({\it{x\/}}), {\rm{cdr}}\,({\it{y\/}}))\index{double-cdr-induction} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  s-approx-alist-implies-s-approx-list-collect-value \\ \index{s-approx-alist-implies-s-approx!-list-collect-value}
\=\+({\rm{s-approx-alist}}\,({\it{x\/}}, {\it{y\/}})\index{s-approx-alist} $\wedge$ {\rm{alistp}}\,({\it{x\/}})\index{alistp} $\wedge$ {\rm{alistp}}\,({\it{y\/}})\index{alistp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx-list}}\,({\rm{collect-value}}\,({\it{a\/}}, {\it{x\/}})\index{collect-value}, {\rm{collect-value}}\,({\it{a\/}}, {\it{y\/}})\index{collect-value})\index{s-approx-list}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  alistp-dual-eval-3 \\ \index{alistp-dual-eval-3}
\=\+({\rm{alistp}}\,({\it{state-bindings\/}})\index{alistp} $\wedge$ ({\it{flag\/}} $=$ {\tt{3}})) \\ 
$\rightarrow$$\;\;\;\;${\rm{alistp}}\,({\rm{dual-eval}}\,({\it{flag\/}}, {\it{occurrences\/}}, {\it{bindings\/}}, {\it{state-bindings\/}}, {\it{netlist\/}})\index{dual-eval})\index{alistp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  s-approx-implies-s-approx-alist \\ \index{s-approx-implies-s-approx-alist}
{\rm{s-approx}}\,({\it{s1\/}}, {\it{s2\/}})\index{s-approx} $\rightarrow$ {\rm{s-approx-alist}}\,({\rm{pairlist}}\,({\it{x\/}}, {\it{s1\/}}), {\rm{pairlist}}\,({\it{x\/}}, {\it{s2\/}}))\index{s-approx-alist}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  s-approx-alist-implies-s-approx-collect-value \\ \index{s-approx-alist-implies-s-approx!-collect-value}
\=\+({\rm{s-approx-alist}}\,({\it{x\/}}, {\it{y\/}})\index{s-approx-alist} $\wedge$ {\rm{alistp}}\,({\it{x\/}})\index{alistp} $\wedge$ {\rm{alistp}}\,({\it{y\/}})\index{alistp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx}}\,({\rm{collect-value}}\,({\it{a\/}}, {\it{x\/}})\index{collect-value}, {\rm{collect-value}}\,({\it{a\/}}, {\it{y\/}})\index{collect-value})\index{s-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ok-netlistp-reduction \\ \index{ok-netlistp-reduction}
\=\+(({\it{flag\/}} $=$ {\tt{2}}) $\vee$ ({\it{flag\/}} $=$ {\tt{3}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{ok-netlistp}}\,({\it{flag\/}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{exceptions\/}})\index{ok-netlistp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{flag\/}} $=$ {\tt{2}}$\;\;${\bf then }{\rm{ok-netlistp}}\,({\tt{0}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{exceptions\/}})\index{ok-netlistp} \\ 
{\bf else }{\rm{ok-netlistp}}\,({\tt{1}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{exceptions\/}})\index{ok-netlistp}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ok-netlistp-reduction-rewrite \\ \index{ok-netlistp-reduction-rewrite}
\=\+(\=\+{\rm{ok-netlistp}}\,({\tt{2}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{exceptions\/}})\index{ok-netlistp} \\ 
$=$$\;\;\;\;${\rm{ok-netlistp}}\,({\tt{0}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{exceptions\/}})\index{ok-netlistp})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{ok-netlistp}}\,({\tt{3}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{exceptions\/}})\index{ok-netlistp} \\ 
$=$$\;\;\;\;${\rm{ok-netlistp}}\,({\tt{1}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{exceptions\/}})\index{ok-netlistp})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-monotone-no-ram \\ \index{dual-eval-monotone-no-ram}
\=\+{\rm{ok-netlistp}}\,({\it{flag\/}}, {\it{fn\/}}, {\it{netlist\/}}, {\tt{'}}{\tt{(}}{\tt{mem-32x32}}{\tt{ }}{\tt{dp-ram-16x32}}{\tt{)}})\index{ok-netlistp} \\ 
$\rightarrow$$\;\;\;\;${\rm{monotonicity-property}}\,({\it{flag\/}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{good-s-alist} \\  
\=\+{\rm{good-s-alist}}\,({\it{x\/}})\index{good-s-alist} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }{\rm{listp}}\,({\rm{car}}\,({\it{x\/}})) $\wedge$ {\rm{good-s}}\,({\rm{cdar}}\,({\it{x\/}}))\index{good-s} $\wedge$ {\rm{good-s-alist}}\,({\rm{cdr}}\,({\it{x\/}}))\index{good-s-alist} \\ 
{\bf else }{\it{x\/}} $=$ {\bf{nil}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-s-alist-pairlist \\ \index{good-s-alist-pairlist}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s-alist}}\,({\rm{pairlist}}\,({\it{x\/}}, {\it{s\/}}))\index{good-s-alist}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-s-value \\ \index{good-s-value}
{\rm{good-s-alist}}\,({\it{x\/}})\index{good-s-alist} $\rightarrow$ {\rm{good-s}}\,({\rm{value}}\,({\it{w\/}}, {\it{x\/}})\index{value})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dual-eval-monotone \\ \index{dual-eval-monotone}
\=\+{\rm{ok-netlistp}}\,({\it{flag\/}}, {\it{fn\/}}, {\it{netlist\/}}, {\tt{'}}{\tt{(}}{\tt{mem-32x32}}{\tt{)}})\index{ok-netlistp} \\ 
$\rightarrow$$\;\;\;\;$(\=\+\=\+{\bf if }({\it{flag\/}} $=$ {\tt{0}}) $\vee$ ({\it{flag\/}} $=$ {\tt{2}})$\;\;${\bf then }{\rm{good-s}}\,({\it{s2\/}})\index{good-s} \\ 
{\bf else }{\rm{good-s-alist}}\,({\it{s2\/}})\index{good-s-alist}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;${\rm{monotonicity-property}}\,({\it{flag\/}}, {\it{fn\/}}, {\it{netlist\/}}, {\it{a1\/}}, {\it{a2\/}}, {\it{s1\/}}, {\it{s2\/}})\index{monotonicity-property})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-s-collect-value \\ \index{good-s-collect-value}
{\rm{good-s-alist}}\,({\it{s\/}})\index{good-s-alist} $\rightarrow$ {\rm{good-s}}\,({\rm{collect-value}}\,({\it{keys\/}}, {\it{s\/}})\index{collect-value})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-buf-preserves-good-s \\ \index{f-buf-preserves-good-s}
{\rm{good-s}}\,({\rm{f-buf}}\,({\it{x\/}})\index{f-buf})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  f-if-preserves-good-s \\ \index{f-if-preserves-good-s}
{\rm{good-s}}\,({\rm{f-if}}\,({\it{x\/}}, {\it{y\/}}, {\it{z\/}})\index{f-if})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-s-0 \\ \index{good-s-0}
{\rm{good-s}}\,({\tt{0}})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ao2-preserves-good-s \\ \index{ao2-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{ao2}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ao4-preserves-good-s \\ \index{ao4-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{ao4}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ao6-preserves-good-s \\ \index{ao6-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{ao6}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ao7-preserves-good-s \\ \index{ao7-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{ao7}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-and-preserves-good-s \\ \index{b-and-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-and}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-and3-preserves-good-s \\ \index{b-and3-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-and3}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-and4-preserves-good-s \\ \index{b-and4-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-and4}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-equv-preserves-good-s \\ \index{b-equv-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-equv}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-equv3-preserves-good-s \\ \index{b-equv3-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-equv3}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-if-preserves-good-s \\ \index{b-if-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-if}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nand-preserves-good-s \\ \index{b-nand-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-nand}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nand3-preserves-good-s \\ \index{b-nand3-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-nand3}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nand4-preserves-good-s \\ \index{b-nand4-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-nand4}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nand5-preserves-good-s \\ \index{b-nand5-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-nand5}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nand6-preserves-good-s \\ \index{b-nand6-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-nand6}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nand8-preserves-good-s \\ \index{b-nand8-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-nand8}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nbuf-preserves-good-s \\ \index{b-nbuf-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-nbuf}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nor-preserves-good-s \\ \index{b-nor-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-nor}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nor3-preserves-good-s \\ \index{b-nor3-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-nor3}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nor4-preserves-good-s \\ \index{b-nor4-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-nor4}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nor5-preserves-good-s \\ \index{b-nor5-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-nor5}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nor6-preserves-good-s \\ \index{b-nor6-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-nor6}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-nor8-preserves-good-s \\ \index{b-nor8-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-nor8}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-not-preserves-good-s \\ \index{b-not-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-not}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-not-b4ip-preserves-good-s \\ \index{b-not-b4ip-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-not-b4ip}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-not-ivap-preserves-good-s \\ \index{b-not-ivap-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-not-ivap}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-or-preserves-good-s \\ \index{b-or-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-or}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-or3-preserves-good-s \\ \index{b-or3-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-or3}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-or4-preserves-good-s \\ \index{b-or4-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-or4}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-xor-preserves-good-s \\ \index{b-xor-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-xor}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-xor3-preserves-good-s \\ \index{b-xor3-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{b-xor3}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  del2-preserves-good-s \\ \index{del2-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{del2}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  del4-preserves-good-s \\ \index{del4-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{del4}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  del10-preserves-good-s \\ \index{del10-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{del10}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  procmon-preserves-good-s \\ \index{procmon-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{procmon}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fd1-preserves-good-s \\ \index{fd1-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{fd1}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fd1s-preserves-good-s \\ \index{fd1s-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{fd1s}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fd1sp-preserves-good-s \\ \index{fd1sp-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{fd1sp}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fd1slp-preserves-good-s \\ \index{fd1slp-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{fd1slp}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  id-preserves-good-s \\ \index{id-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{id}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ram-enable-circuit-preserves-good-s \\ \index{ram-enable-circuit-preserves-go!od-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{ram-enable-circuit}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  t-buf-preserves-good-s \\ \index{t-buf-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{t-buf}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  t-wire-preserves-good-s \\ \index{t-wire-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{t-wire}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  pullup-preserves-good-s \\ \index{pullup-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{pullup}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-bidirect-preserves-good-s \\ \index{ttl-bidirect-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{ttl-bidirect}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-clk-input-preserves-good-s \\ \index{ttl-clk-input-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{ttl-clk-input}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-input-preserves-good-s \\ \index{ttl-input-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{ttl-input}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-output-preserves-good-s \\ \index{ttl-output-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{ttl-output}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-output-parametric-preserves-good-s \\ \index{ttl-output-parametric-preserves!-good-s}
\=\+{\rm{good-s}}\,({\it{s\/}})\index{good-s} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{ttl-output-parametric}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-output-fast-preserves-good-s \\ \index{ttl-output-fast-preserves-good-!s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{ttl-output-fast}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-tri-output-preserves-good-s \\ \index{ttl-tri-output-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{ttl-tri-output}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ttl-tri-output-fast-preserves-good-s \\ \index{ttl-tri-output-fast-preserves-g!ood-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{ttl-tri-output-fast}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  vdd-preserves-good-s \\ \index{vdd-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{vdd}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  vdd-parametric-preserves-good-s \\ \index{vdd-parametric-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{vdd-parametric}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  vss-preserves-good-s \\ \index{vss-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{vss}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-s-constant-ram \\ \index{good-s-constant-ram}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{constant-ram}}\,({\it{s\/}}, {\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{constant-ram})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-s-write-mem-1 \\ \index{good-s-write-mem-1}
\=\+({\rm{good-s}}\,({\it{s\/}})\index{good-s} $\wedge$ {\rm{properp}}\,({\it{value\/}})\index{properp} $\wedge$ ({\rm{length}}\,({\it{value\/}})\index{length} $=$ {\tt{32}})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-s}}\,({\rm{write-mem1}}\,({\it{v-addr\/}}, {\it{s\/}}, {\it{value\/}})\index{write-mem1})\index{good-s}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-s-write-mem \\ \index{good-s-write-mem}
\=\+({\rm{good-s}}\,({\it{s\/}})\index{good-s} $\wedge$ {\rm{properp}}\,({\it{value\/}})\index{properp} $\wedge$ ({\rm{length}}\,({\it{value\/}})\index{length} $=$ {\tt{32}})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-s}}\,({\rm{write-mem}}\,({\it{v-addr\/}}, {\it{s\/}}, {\it{value\/}})\index{write-mem})\index{good-s}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  dp-ram-16x32-preserves-good-s \\ \index{dp-ram-16x32-preserves-good-s}
{\rm{good-s}}\,({\it{s\/}})\index{good-s} $\rightarrow$ {\rm{good-s}}\,({\rm{dual-apply-state}}\,({\tt{'}}{\tt{dp-ram-16x32}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}
\end{tabbing}


\noindent{\sc Event}:   Let us define the theory {\it{good-s-primitives-theory}} to consist of the following events: ao2-preserves-good-s,
ao4-preserves-good-s,
ao6-preserves-good-s,
ao7-preserves-good-s,
b-and-preserves-good-s,
b-and3-preserves-good-s,
b-and4-preserves-good-s,
b-equv-preserves-good-s,
b-equv3-preserves-good-s,
b-if-preserves-good-s,
b-nand-preserves-good-s,
b-nand3-preserves-good-s,
b-nand4-preserves-good-s,
b-nand5-preserves-good-s,
b-nand6-preserves-good-s,
b-nand8-preserves-good-s,
b-nbuf-preserves-good-s,
b-nor-preserves-good-s,
b-nor3-preserves-good-s,
b-nor4-preserves-good-s,
b-nor5-preserves-good-s,
b-nor6-preserves-good-s,
b-nor8-preserves-good-s,
b-not-preserves-good-s,
b-not-b4ip-preserves-good-s,
b-not-ivap-preserves-good-s,
b-or-preserves-good-s,
b-or3-preserves-good-s,
b-or4-preserves-good-s,
b-xor-preserves-good-s,
b-xor3-preserves-good-s,
del2-preserves-good-s,
del4-preserves-good-s,
del10-preserves-good-s,
procmon-preserves-good-s,
fd1-preserves-good-s,
fd1s-preserves-good-s,
fd1sp-preserves-good-s,
fd1slp-preserves-good-s,
id-preserves-good-s,
ram-enable-circuit-preserves-good-s,
t-buf-preserves-good-s,
t-wire-preserves-good-s,
pullup-preserves-good-s,
ttl-bidirect-preserves-good-s,
ttl-clk-input-preserves-good-s,
ttl-input-preserves-good-s,
ttl-output-preserves-good-s,
ttl-output-parametric-preserves-good-s,
ttl-output-fast-preserves-good-s,
ttl-tri-output-preserves-good-s,
ttl-tri-output-fast-preserves-good-s,
vdd-preserves-good-s,
vdd-parametric-preserves-good-s,
vss-preserves-good-s,
dp-ram-16x32-preserves-good-s.\index{good-s-primitives-theory}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  primp-preserves-good-s \\ \index{primp-preserves-good-s}
\=\+({\rm{good-s}}\,({\it{s\/}})\index{good-s} $\wedge$ {\rm{primp}}\,({\it{fn\/}})\index{primp} $\wedge$ ({\it{fn\/}} $\not=$ {\tt{'}}{\tt{mem-32x32}})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-s}}\,({\rm{dual-apply-state}}\,({\it{fn\/}}, {\it{args\/}}, {\it{s\/}})\index{dual-apply-state})\index{good-s}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-s-preserved \\ \index{good-s-preserved}
\=\+{\rm{ok-netlistp}}\,({\it{flag\/}}, {\it{fn\/}}, {\it{netlist\/}}, {\tt{'}}{\tt{(}}{\tt{mem-32x32}}{\tt{)}})\index{ok-netlistp} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+(({\it{flag\/}} $=$ {\tt{2}}) $\wedge$ {\rm{good-s}}\,({\it{s\/}})\index{good-s}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-s}}\,({\rm{dual-eval}}\,({\it{flag\/}}, {\it{fn\/}}, {\it{a\/}}, {\it{s\/}}, {\it{netlist\/}})\index{dual-eval})\index{good-s})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(({\it{flag\/}} $=$ {\tt{3}}) $\wedge$ {\rm{good-s-alist}}\,({\it{s\/}})\index{good-s-alist}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-s-alist}}\,({\rm{dual-eval}}\,({\it{flag\/}}, {\it{fn\/}}, {\it{a\/}}, {\it{s\/}}, {\it{netlist\/}})\index{dual-eval})\index{good-s-alist})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-approx-list} \\  
\=\+{\rm{v-approx-list}}\,({\it{x\/}}, {\it{y\/}})\index{v-approx-list} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\rm{listp}}\,({\it{y\/}}) \\ 
$\wedge$$\;\;\;\;${\rm{v-approx}}\,({\rm{car}}\,({\it{x\/}}), {\rm{car}}\,({\it{y\/}}))\index{v-approx} \\ 
$\wedge$$\;\;\;\;${\rm{v-approx-list}}\,({\rm{cdr}}\,({\it{x\/}}), {\rm{cdr}}\,({\it{y\/}}))\index{v-approx-list}\- \\ 
{\bf else }{\it{y\/}} $\simeq\;${{\bf{nil}}}${}$$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-s-approx-list} \\  
\=\+{\rm{v-s-approx-list}}\,({\it{x\/}}, {\it{y\/}})\index{v-s-approx-list} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+{\rm{listp}}\,({\it{y\/}}) \\ 
$\wedge$$\;\;\;\;${\rm{v-approx}}\,({\rm{caar}}\,({\it{x\/}}), {\rm{caar}}\,({\it{y\/}}))\index{v-approx} \\ 
$\wedge$$\;\;\;\;${\rm{s-approx}}\,({\rm{cadar}}\,({\it{x\/}}), {\rm{cadar}}\,({\it{y\/}}))\index{s-approx} \\ 
$\wedge$$\;\;\;\;${\rm{v-s-approx-list}}\,({\rm{cdr}}\,({\it{x\/}}), {\rm{cdr}}\,({\it{y\/}}))\index{v-s-approx-list}\- \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{nat-lst-lst-induction} \\  
\=\+{\rm{nat-lst-lst-induction}}\,({\it{n\/}}, {\it{x\/}}, {\it{y\/}})\index{nat-lst-lst-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{n\/}} $\simeq {\tt{0}}$) $\vee$ ({\it{x\/}} $\simeq\;${{\bf{nil}}}${}$) $\vee$ ({\it{y\/}} $\simeq\;${{\bf{nil}}}${}$)$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{nat-lst-lst-induction}}\,({\it{n\/}} $-\;1$, {\rm{cdr}}\,({\it{x\/}}), {\rm{cdr}}\,({\it{y\/}}))\index{nat-lst-lst-induction}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable open-nth; name this event `open-nth-on'.\index{open-nth-on}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-approx-car-nth \\ \index{v-approx-car-nth}
\=\+({\rm{v-s-approx-list}}\,({\it{final-1\/}}, {\it{final-2\/}})\index{v-s-approx-list} $\wedge$ ({\it{n\/}} $<$ {\rm{length}}\,({\it{final-1\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;${\rm{v-approx}}\,({\rm{car}}\,({\rm{nth}}\,({\it{n\/}}, {\it{final-1\/}})\index{nth}), {\rm{car}}\,({\rm{nth}}\,({\it{n\/}}, {\it{final-2\/}})\index{nth}))\index{v-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  s-approx-cadr-nth \\ \index{s-approx-cadr-nth}
\=\+({\rm{v-s-approx-list}}\,({\it{final-1\/}}, {\it{final-2\/}})\index{v-s-approx-list} $\wedge$ ({\it{n\/}} $<$ {\rm{length}}\,({\it{final-1\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx}}\,({\rm{cadr}}\,({\rm{nth}}\,({\it{n\/}}, {\it{final-1\/}})\index{nth}), {\rm{cadr}}\,({\rm{nth}}\,({\it{n\/}}, {\it{final-2\/}})\index{nth}))\index{s-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{simulate-monotone-induction} \\  
\=\+{\rm{simulate-monotone-induction}}\,({\it{fn\/}}, {\it{inputs-1\/}}, {\it{state-1\/}}, {\it{netlist\/}}, {\it{inputs-2\/}}, {\it{state-2\/}})\index{simulate-monotone-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{inputs-1\/}}) \\ 
{\bf then }{\rm{simulate-monotone-induction}}\,(\=\+{\it{fn\/}}, \\ 
{\rm{cdr}}\,({\it{inputs-1\/}}), \\ 
{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\it{fn\/}}, \\ 
{\rm{car}}\,({\it{inputs-1\/}}), \\ 
{\it{state-1\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval}, \\ 
{\it{netlist\/}}, \\ 
{\rm{cdr}}\,({\it{inputs-2\/}}), \\ 
{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\it{fn\/}}, \\ 
{\rm{car}}\,({\it{inputs-2\/}}), \\ 
{\it{state-2\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval})\-\index{simulate-monotone-induction} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  simulate-monotone \\ \index{simulate-monotone}
\=\+(\=\+{\rm{v-approx-list}}\,({\it{inputs-1\/}}, {\it{inputs-2\/}})\index{v-approx-list} \\ 
$\wedge$$\;\;\;\;${\rm{s-approx}}\,({\it{state-1\/}}, {\it{state-2\/}})\index{s-approx} \\ 
$\wedge$$\;\;\;\;${\rm{good-s}}\,({\it{state-2\/}})\index{good-s} \\ 
$\wedge$$\;\;\;\;${\rm{ok-netlistp}}\,({\tt{0}}, {\it{fn\/}}, {\it{netlist\/}}, {\tt{'}}{\tt{(}}{\tt{mem-32x32}}{\tt{)}})\index{ok-netlistp} \\ 
$\wedge$$\;\;\;\;${\rm{ok-netlistp}}\,({\tt{2}}, {\it{fn\/}}, {\it{netlist\/}}, {\tt{'}}{\tt{(}}{\tt{mem-32x32}}{\tt{)}})\index{ok-netlistp})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{v-s-approx-list}}\,(\=\+{\rm{simulate}}\,({\it{fn\/}}, {\it{inputs-1\/}}, {\it{state-1\/}}, {\it{netlist\/}})\index{simulate}, \\ 
{\rm{simulate}}\,({\it{fn\/}}, {\it{inputs-2\/}}, {\it{state-2\/}}, {\it{netlist\/}})\index{simulate})\-\index{v-s-approx-list}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-approx-list-x-x \\ \index{v-approx-list-x-x}
{\rm{v-approx-list}}\,({\it{x\/}}, {\it{x\/}})\index{v-approx-list}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{doublet-p}$\;\;$
{\rm{doublet-p}}\,({\it{x\/}})\index{doublet-p} $=$ ({\it{x\/}} $=$ {\rm{list}}\,({\rm{car}}\,({\it{x\/}}), {\rm{cadr}}\,({\it{x\/}})))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{doublet-n-simulate-induction} \\  
\=\+{\rm{doublet-n-simulate-induction}}\,({\it{fn\/}}, {\it{inputs\/}}, {\it{state\/}}, {\it{netlist\/}}, {\it{n\/}})\index{doublet-n-simulate-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{doublet-n-simulate-induction}}\,(\=\+{\it{fn\/}}, \\ 
{\rm{cdr}}\,({\it{inputs\/}}), \\ 
{\rm{dual-eval}}\,(\=\+{\tt{2}}, \\ 
{\it{fn\/}}, \\ 
{\rm{car}}\,({\it{inputs\/}}), \\ 
{\it{state\/}}, \\ 
{\it{netlist\/}})\-\index{dual-eval}, \\ 
{\it{netlist\/}}, \\ 
{\it{n\/}} $-\;1$)\-\index{doublet-n-simulate-induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  doublet-n-simulate \\ \index{doublet-n-simulate}
\=\+({\it{n\/}} $<$ {\rm{length}}\,({\it{inputs\/}})\index{length}) \\ 
$\rightarrow$$\;\;\;\;${\rm{doublet-p}}\,({\rm{nth}}\,({\it{n\/}}, {\rm{simulate}}\,({\it{fn\/}}, {\it{inputs\/}}, {\it{state\/}}, {\it{netlist\/}})\index{simulate})\index{nth})\index{doublet-p}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  doublet-p-equal-approx \\ \index{doublet-p-equal-approx}
\=\+(\=\+{\rm{doublet-p}}\,({\it{x\/}})\index{doublet-p} \\ 
$\wedge$$\;\;\;\;${\rm{doublet-p}}\,({\it{y\/}})\index{doublet-p} \\ 
$\wedge$$\;\;\;\;${\rm{v-knownp}}\,({\rm{car}}\,({\it{x\/}}))\index{v-knownp} \\ 
$\wedge$$\;\;\;\;${\rm{s-knownp}}\,({\rm{cadr}}\,({\it{x\/}}))\index{s-knownp} \\ 
$\wedge$$\;\;\;\;${\rm{v-approx}}\,({\rm{car}}\,({\it{x\/}}), {\rm{car}}\,({\it{y\/}}))\index{v-approx} \\ 
$\wedge$$\;\;\;\;${\rm{s-approx}}\,({\rm{cadr}}\,({\it{x\/}}), {\rm{cadr}}\,({\it{y\/}}))\index{s-approx})\- \\ 
$\rightarrow$$\;\;\;\;$({\it{x\/}} $=$ {\it{y\/}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable doublet-p; name this event `doublet-p-off'.\index{doublet-p-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-simulate \\ \index{length-simulate}
{\rm{length}}\,({\rm{simulate}}\,({\it{fn\/}}, {\it{inputs\/}}, {\it{state\/}}, {\it{netlist\/}})\index{simulate})\index{length} $=$ {\rm{length}}\,({\it{inputs\/}})\index{length}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  xs-suffice-for-reset-lemma-verbose \\ \index{xs-suffice-for-reset-lemma-verb!ose}
\=\+(\=\+({\it{n\/}} $<$ {\rm{length}}\,({\it{inputs\/}})\index{length}) \\ 
$\wedge$$\;\;\;\;${\rm{s-approx}}\,({\it{state-1\/}}, {\it{state-2\/}})\index{s-approx} \\ 
$\wedge$$\;\;\;\;${\rm{v-knownp}}\,({\rm{car}}\,({\rm{nth}}\,({\it{n\/}}, {\rm{simulate}}\,({\it{fn\/}}, {\it{inputs\/}}, {\it{state-1\/}}, {\it{netlist\/}})\index{simulate})\index{nth}))\index{v-knownp} \\ 
$\wedge$$\;\;\;\;${\rm{s-knownp}}\,({\rm{cadr}}\,({\rm{nth}}\,({\it{n\/}}, {\rm{simulate}}\,({\it{fn\/}}, {\it{inputs\/}}, {\it{state-1\/}}, {\it{netlist\/}})\index{simulate})\index{nth}))\index{s-knownp} \\ 
$\wedge$$\;\;\;\;${\rm{good-s}}\,({\it{state-2\/}})\index{good-s} \\ 
$\wedge$$\;\;\;\;${\rm{ok-netlistp}}\,({\tt{0}}, {\it{fn\/}}, {\it{netlist\/}}, {\tt{'}}{\tt{(}}{\tt{mem-32x32}}{\tt{)}})\index{ok-netlistp} \\ 
$\wedge$$\;\;\;\;${\rm{ok-netlistp}}\,({\tt{2}}, {\it{fn\/}}, {\it{netlist\/}}, {\tt{'}}{\tt{(}}{\tt{mem-32x32}}{\tt{)}})\index{ok-netlistp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{nth}}\,({\it{n\/}}, {\rm{simulate}}\,({\it{fn\/}}, {\it{inputs\/}}, {\it{state-1\/}}, {\it{netlist\/}})\index{simulate})\index{nth} \\ 
$=$$\;\;\;\;${\rm{nth}}\,({\it{n\/}}, {\rm{simulate}}\,({\it{fn\/}}, {\it{inputs\/}}, {\it{state-2\/}}, {\it{netlist\/}})\index{simulate})\index{nth})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  xs-suffice-for-reset-lemma \\ \index{xs-suffice-for-reset-lemma}
\=\+(\=\+({\it{n\/}} $<$ {\rm{length}}\,({\it{inputs\/}})\index{length}) \\ 
$\wedge$$\;\;\;\;${\rm{s-approx}}\,({\it{state-1\/}}, {\it{state-2\/}})\index{s-approx} \\ 
$\wedge$$\;\;\;\;${\rm{v-knownp}}\,({\rm{car}}\,({\rm{nth}}\,({\it{n\/}}, {\rm{simulate}}\,({\it{fn\/}}, {\it{inputs\/}}, {\it{state-1\/}}, {\it{netlist\/}})\index{simulate})\index{nth}))\index{v-knownp} \\ 
$\wedge$$\;\;\;\;${\rm{s-knownp}}\,({\rm{cadr}}\,({\rm{nth}}\,({\it{n\/}}, {\rm{simulate}}\,({\it{fn\/}}, {\it{inputs\/}}, {\it{state-1\/}}, {\it{netlist\/}})\index{simulate})\index{nth}))\index{s-knownp} \\ 
$\wedge$$\;\;\;\;${\rm{good-s}}\,({\it{state-2\/}})\index{good-s} \\ 
$\wedge$$\;\;\;\;${\rm{ok-netlistp}}\,({\tt{0}}, {\it{fn\/}}, {\it{netlist\/}}, {\tt{'}}{\tt{(}}{\tt{mem-32x32}}{\tt{)}})\index{ok-netlistp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{nth}}\,({\it{n\/}}, {\rm{simulate}}\,({\it{fn\/}}, {\it{inputs\/}}, {\it{state-1\/}}, {\it{netlist\/}})\index{simulate})\index{nth} \\ 
$=$$\;\;\;\;${\rm{nth}}\,({\it{n\/}}, {\rm{simulate}}\,({\it{fn\/}}, {\it{inputs\/}}, {\it{state-2\/}}, {\it{netlist\/}})\index{simulate})\index{nth})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{compile-uncompiled-defns}$\;\;$
{\sc{compile-uncompiled-defns}}\index{compile-uncompiled-defns} $=$ {\bf{t}}
\end{tabbing}


\noindent{\sc Event}:   Disable compile-uncompiled-defns; name this event `compile-uncompiled-defns-on'.\index{compile-uncompiled-defns-on}

\addvspace{18pt}


\noindent{\sc Event}:   For efficiency, compile those definitions not yet compiled.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{unknown-regfile} \\  
\=\+{\sc{unknown-regfile}}\index{unknown-regfile} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{cons}}\,({\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{ram}, {\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{ram}), \\ 
{\rm{cons}}\,({\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{ram}, {\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{ram}))\-, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,({\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{ram}, {\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{ram}), \\ 
{\rm{cons}}\,({\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{ram}, {\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{ram}))\-)\-, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{cons}}\,({\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{ram}, {\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{ram}), \\ 
{\rm{cons}}\,({\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{ram}, {\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{ram}))\-, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,({\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{ram}, {\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{ram}), \\ 
{\rm{cons}}\,({\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{ram}, {\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\index{ram}))\-)\-)\-, \\ 
{\sc{x}}\index{x}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{4}}, {\sc{x}}\index{x})\index{make-list})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{unknown-machine-state} \\  
\=\+{\sc{unknown-machine-state}}\index{unknown-machine-state} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\sc{unknown-regfile}}\index{unknown-regfile}, \\ 
{\rm{make-list}}\,({\tt{4}}, {\sc{x}}\index{x})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list}, \\ 
{\sc{x}}\index{x}, \\ 
{\sc{x}}\index{x}, \\ 
{\sc{x}}\index{x}, \\ 
{\rm{make-list}}\,({\tt{4}}, {\sc{x}}\index{x})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{40}}, {\sc{x}}\index{x})\index{make-list})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{unknown-memory-state} \\  
\=\+{\sc{unknown-memory-state}}\index{unknown-memory-state} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{stub}}\,({\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list})\index{stub}, \\ 
{\tt{0}}, \\ 
{\tt{0}}, \\ 
{\tt{0}}, \\ 
{\sc{x}}\index{x}, \\ 
{\sc{x}}\index{x}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{unknown-state} \\  
{\sc{unknown-state}}\index{unknown-state} $=$ {\rm{list}}\,({\sc{unknown-machine-state}}\index{unknown-machine-state}, {\sc{unknown-memory-state}}\index{unknown-memory-state})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  chip-system-invariant-unknown-state \\ \index{chip-system-invariant-unknown-st!ate}
{\rm{chip-system-invariant}}\,({\sc{unknown-state}}\index{unknown-state})\index{chip-system-invariant}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fm9001-state-structure-unknown-state \\ \index{fm9001-state-structure-unknown-!state}
{\rm{fm9001-state-structure}}\,({\sc{unknown-state}}\index{unknown-state})\index{fm9001-state-structure}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{reset-vector} \\  
\=\+{\sc{reset-vector}}\index{reset-vector} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{x}}\index{x}, \\ 
{\rm{cons}}\,({\sc{x}}\index{x}, {\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{t}}, {\rm{cons}}\,({\bf{t}}, {\rm{cons}}\,({\bf{t}}, {\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list})))))))\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{run-vector} \\  
\=\+{\sc{run-vector}}\index{run-vector} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{x}}\index{x}, \\ 
{\rm{cons}}\,({\sc{x}}\index{x}, {\rm{cons}}\,({\bf{f}}, {\rm{cons}}\,({\bf{t}}, {\rm{cons}}\,({\bf{t}}, {\rm{cons}}\,({\bf{t}}, {\rm{cons}}\,({\bf{t}}, {\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list})))))))\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{reset-sequence} \\  
{\sc{reset-sequence}}\index{reset-sequence} $=$ {\rm{cons}}\,({\sc{reset-vector}}\index{reset-vector}, {\rm{make-list}}\,({\tt{19}}, {\sc{run-vector}}\index{run-vector})\index{make-list})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  chip-system-operating-inputs-p-reset-sequence \\ \index{chip-system-operating-inputs-p-!reset-sequence}
{\rm{chip-system-operating-inputs-p}}\,({\sc{reset-sequence}}\index{reset-sequence}, {\tt{20}})\index{chip-system-operating-inputs-p}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{initialized-regfile} \\  
\=\+{\sc{initialized-regfile}}\index{initialized-regfile} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{cons}}\,({\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list})\index{ram}, {\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list})\index{ram}), \\ 
{\rm{cons}}\,({\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list})\index{ram}, {\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list})\index{ram}))\-, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,({\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list})\index{ram}, {\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list})\index{ram}), \\ 
{\rm{cons}}\,({\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list})\index{ram}, {\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list})\index{ram}))\-)\-, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{cons}}\,({\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list})\index{ram}, {\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list})\index{ram}), \\ 
{\rm{cons}}\,({\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list})\index{ram}, {\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list})\index{ram}))\-, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,({\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list})\index{ram}, {\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list})\index{ram}), \\ 
{\rm{cons}}\,({\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list})\index{ram}, {\rm{ram}}\,({\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list})\index{ram}))\-)\-)\-, \\ 
{\bf{f}}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{initialized-machine-state} \\  
\=\+{\sc{initialized-machine-state}}\index{initialized-machine-state} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\sc{initialized-regfile}}\index{initialized-regfile}, \\ 
{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}), \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list}, \\ 
{\rm{cv\_fetch1}}\,(\=\+{\bf{t}}, \\ 
{\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}}), \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, \\ 
{\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}}), \\ 
{\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list})\-\index{cv\_fetch1})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{initialized-memory-state} \\  
\=\+{\sc{initialized-memory-state}}\index{initialized-memory-state} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\rm{stub}}\,({\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list})\index{stub}, \\ 
{\tt{0}}, \\ 
{\tt{0}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{final-state} \\  
{\sc{final-state}}\index{final-state} $=$ {\rm{list}}\,({\sc{initialized-machine-state}}\index{initialized-machine-state}, {\sc{initialized-memory-state}}\index{initialized-memory-state})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  reset-works \\ \index{reset-works}
\=\+{\rm{run-fm9001}}\,(\=\+{\sc{unknown-state}}\index{unknown-state}, \\ 
{\rm{map-up-inputs}}\,({\sc{reset-sequence}}\index{reset-sequence})\index{map-up-inputs}, \\ 
{\rm{length}}\,({\sc{reset-sequence}}\index{reset-sequence})\index{length})\-\index{run-fm9001} \\ 
$=$$\;\;\;\;${\sc{final-state}}\index{final-state}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  unknown-state-okp \\ \index{unknown-state-okp}
\=\+{\rm{fm9001-state-structure}}\,({\sc{unknown-state}}\index{unknown-state})\index{fm9001-state-structure} \\ 
$\wedge$$\;\;\;\;${\rm{chip-system-invariant}}\,({\sc{unknown-state}}\index{unknown-state})\index{chip-system-invariant} \\ 
$\wedge$$\;\;\;\;${\rm{chip-system-operating-inputs-p}}\,({\sc{reset-sequence}}\index{reset-sequence}, {\tt{20}})\index{chip-system-operating-inputs-p}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  final-state-okp \\ \index{final-state-okp}
\=\+{\rm{chip-system\&}}\,({\sc{chip-system\$netlist}}\index{chip-system\$netlist})\index{chip-system\&} \\ 
$\wedge$$\;\;\;\;${\rm{fm9001-state-structure}}\,({\sc{final-state}}\index{final-state})\index{fm9001-state-structure} \\ 
$\wedge$$\;\;\;\;${\rm{macrocycle-invariant}}\,({\sc{final-state}}\index{final-state}, {\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list})\index{macrocycle-invariant}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  instance-theorem \\ \index{instance-theorem}
\=\+(\=\+{\rm{chip-system\&}}\,({\sc{chip-system\$netlist}}\index{chip-system\$netlist})\index{chip-system\&} \\ 
$\wedge$$\;\;\;\;${\rm{fm9001-state-structure}}\,({\sc{final-state}}\index{final-state})\index{fm9001-state-structure} \\ 
$\wedge$$\;\;\;\;${\rm{macrocycle-invariant}}\,({\sc{final-state}}\index{final-state}, {\it{pc\/}})\index{macrocycle-invariant} \\ 
$\wedge$$\;\;\;\;${\rm{chip-system-operating-inputs-p}}\,(\=\+{\it{inputs\/}}, \\ 
{\rm{total-microcycles}}\,(\=\+{\sc{final-state}}\index{final-state}, \\ 
{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\it{n\/}})\-\index{total-microcycles})\-\index{chip-system-operating-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{operating-inputs-p}}\,(\=\+{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\rm{total-microcycles}}\,(\=\+{\sc{final-state}}\index{final-state}, \\ 
{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\it{n\/}})\-\index{total-microcycles})\-\index{operating-inputs-p})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{map-up}}\,({\rm{simulate-dual-eval-2}}\,(\=\+{\tt{'}}{\tt{chip-system}}, \\ 
{\it{inputs\/}}, \\ 
{\sc{final-state}}\index{final-state}, \\ 
{\sc{chip-system\$netlist}}\index{chip-system\$netlist}, \\ 
{\rm{total-microcycles}}\,(\=\+{\sc{final-state}}\index{final-state}, \\ 
{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\it{n\/}})\-\index{total-microcycles})\-\index{simulate-dual-eval-2})\index{map-up} \\ 
$=$$\;\;\;\;${\rm{fm9001-interpreter}}\,({\rm{map-up}}\,({\sc{final-state}}\index{final-state})\index{map-up}, {\it{pc\/}}, {\it{n\/}})\index{fm9001-interpreter})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fm9001-statep-map-up-final-state \\ \index{fm9001-statep-map-up-final-state}
{\rm{fm9001-statep}}\,({\rm{map-up}}\,({\sc{final-state}}\index{final-state})\index{map-up})\index{fm9001-statep}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{reset-vector-chip} \\  
\=\+{\sc{reset-vector-chip}}\index{reset-vector-chip} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\sc{x}}\index{x}, \\ 
{\rm{cons}}\,(\=\+{\sc{x}}\index{x}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\sc{x}}\index{x}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\rm{append}}\,(\=\+{\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-)\-)\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{run-vector-chip-1} \\  
\=\+{\sc{run-vector-chip-1}}\index{run-vector-chip-1} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\rm{cons}}\,(\=\+{\sc{x}}\index{x}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\rm{append}}\,(\=\+{\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{t}})\index{make-list})\-)\-)\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{run-vector-chip-2} \\  
\=\+{\sc{run-vector-chip-2}}\index{run-vector-chip-2} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\sc{x}}\index{x}, \\ 
{\rm{cons}}\,(\=\+{\bf{f}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\rm{cons}}\,(\=\+{\bf{t}}, \\ 
{\rm{append}}\,(\=\+{\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{t}})\index{make-list})\-)\-)\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{reset-sequence-chip-1} \\  
\=\+{\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1} \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\sc{reset-vector-chip}}\index{reset-vector-chip}, {\rm{make-list}}\,({\tt{19}}, {\sc{run-vector-chip-1}}\index{run-vector-chip-1})\index{make-list})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{reset-sequence-chip-2} \\  
\=\+{\sc{reset-sequence-chip-2}}\index{reset-sequence-chip-2} \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\sc{reset-vector-chip}}\index{reset-vector-chip}, {\rm{make-list}}\,({\tt{19}}, {\sc{run-vector-chip-2}}\index{run-vector-chip-2})\index{make-list})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  reset-sequence-chip-1-vs-2 \\ \index{reset-sequence-chip-1-vs-2}
\=\+{\rm{simulate}}\,({\tt{'}}{\tt{chip}}, {\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1}, {\sc{unknown-machine-state}}\index{unknown-machine-state}, {\sc{chip\$netlist}}\index{chip\$netlist})\index{simulate} \\ 
$=$$\;\;\;\;${\rm{simulate}}\,(\=\+{\tt{'}}{\tt{chip}}, \\ 
{\sc{reset-sequence-chip-2}}\index{reset-sequence-chip-2}, \\ 
{\sc{unknown-machine-state}}\index{unknown-machine-state}, \\ 
{\sc{chip\$netlist}}\index{chip\$netlist})\-\index{simulate}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  simulate-reset-chip-final-state \\ \index{simulate-reset-chip-final-state}
\=\+{\rm{cadr}}\,({\rm{nth}}\,(\=\+{\rm{length}}\,({\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1})\index{length} $-\;1$, \\ 
{\rm{simulate}}\,(\=\+{\tt{'}}{\tt{chip}}, \\ 
{\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1}, \\ 
{\sc{unknown-machine-state}}\index{unknown-machine-state}, \\ 
{\sc{chip\$netlist}}\index{chip\$netlist})\-\index{simulate})\-\index{nth}) \\ 
$=$$\;\;\;\;${\rm{car}}\,({\sc{final-state}}\index{final-state})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  for-final-1-of-reset-sequence-chip \\ \index{for-final-1-of-reset-sequence-c!hip}
\=\+(\=\+(({\rm{length}}\,({\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1})\index{length} $-\;1$) $<$ {\rm{length}}\,({\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1})\index{length}) \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;${\rm{v-knownp}}\,({\rm{car}}\,({\rm{nth}}\,(\=\+{\rm{length}}\,({\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1})\index{length} $-\;1$, \\ 
{\rm{simulate}}\,(\=\+{\tt{'}}{\tt{chip}}, \\ 
{\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1}, \\ 
{\sc{unknown-machine-state}}\index{unknown-machine-state}, \\ 
{\sc{chip\$netlist}}\index{chip\$netlist})\-\index{simulate})\-\index{nth}))\index{v-knownp} \\ 
$\wedge$$\;\;\;\;${\rm{s-knownp}}\,({\rm{cadr}}\,({\rm{nth}}\,(\=\+{\rm{length}}\,({\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1})\index{length} $-\;1$, \\ 
{\rm{simulate}}\,(\=\+{\tt{'}}{\tt{chip}}, \\ 
{\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1}, \\ 
{\sc{unknown-machine-state}}\index{unknown-machine-state}, \\ 
{\sc{chip\$netlist}}\index{chip\$netlist})\-\index{simulate})\-\index{nth}))\index{s-knownp} \\ 
$\wedge$$\;\;\;\;${\rm{ok-netlistp}}\,({\tt{0}}, {\tt{'}}{\tt{chip}}, {\sc{chip\$netlist}}\index{chip\$netlist}, {\tt{'}}{\tt{(}}{\tt{mem-32x32}}{\tt{)}})\index{ok-netlistp}\-
\end{tabbing}


\noindent{\sc Event}:   Enable for-final-1-of-reset-sequence-chip; name this event `for-final-1-of-reset-sequence-chip-off'.\index{for-final-1-of-reset-sequence-c!hip-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  xs-suffice-for-reset-chip-lemma-instance \\ \index{xs-suffice-for-reset-chip-lemma!-instance}
\=\+({\rm{s-approx}}\,({\sc{unknown-machine-state}}\index{unknown-machine-state}, {\it{state-2\/}})\index{s-approx} $\wedge$ {\rm{good-s}}\,({\it{state-2\/}})\index{good-s}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{nth}}\,(\=\+{\rm{length}}\,({\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1})\index{length} $-\;1$, \\ 
{\rm{simulate}}\,(\=\+{\tt{'}}{\tt{chip}}, \\ 
{\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1}, \\ 
{\sc{unknown-machine-state}}\index{unknown-machine-state}, \\ 
{\sc{chip\$netlist}}\index{chip\$netlist})\-\index{simulate})\-\index{nth} \\ 
$=$$\;\;\;\;${\rm{nth}}\,(\=\+{\rm{length}}\,({\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1})\index{length} $-\;1$, \\ 
{\rm{simulate}}\,(\=\+{\tt{'}}{\tt{chip}}, \\ 
{\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1}, \\ 
{\it{state-2\/}}, \\ 
{\sc{chip\$netlist}}\index{chip\$netlist})\-\index{simulate})\-\index{nth})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fm9001-machine-statep-p-map-up-initialized-machine-state \\ \index{fm9001-machine-statep-p-map-up-i!nitialized-machine-state}
{\rm{fm9001-machine-statep}}\,({\rm{p-map-up}}\,({\sc{initialized-machine-state}}\index{initialized-machine-state})\index{p-map-up})\index{fm9001-machine-statep}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-fourp} \\  
\=\+{\rm{v-fourp}}\,({\it{x\/}})\index{v-fourp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{x\/}} $=$ {\bf{nil}} \\ 
{\bf else }{\rm{fourp}}\,({\rm{car}}\,({\it{x\/}}))\index{fourp} $\wedge$ {\rm{v-fourp}}\,({\rm{cdr}}\,({\it{x\/}}))\index{v-fourp}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{all-xs} \\  
\=\+{\rm{all-xs}}\,({\it{vec\/}})\index{all-xs} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{vec\/}} $\simeq\;${{\bf{nil}}}${}$$\;\;${\bf then }{\it{vec\/}} $=$ {\bf{nil}} \\ 
{\bf else }({\rm{car}}\,({\it{vec\/}}) $=$ {\sc{x}}\index{x}) $\wedge$ {\rm{all-xs}}\,({\rm{cdr}}\,({\it{vec\/}}))\index{all-xs}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable b-knownp; name this event `b-knownp-on'.\index{b-knownp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-approx; name this event `b-approx-on'.\index{b-approx-on}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  all-xs-approximates \\ \index{all-xs-approximates}
\=\+({\rm{all-xs}}\,({\it{vec1\/}})\index{all-xs} $\wedge$ ({\rm{length}}\,({\it{vec1\/}})\index{length} $=$ {\rm{length}}\,({\it{vec2\/}})\index{length}) $\wedge$ {\rm{properp}}\,({\it{vec2\/}})\index{properp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{v-approx}}\,({\it{vec1\/}}, {\it{vec2\/}})\index{v-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  all-xs-make-list \\ \index{all-xs-make-list}
{\rm{all-xs}}\,({\rm{make-list}}\,({\it{n\/}}, {\sc{x}}\index{x})\index{make-list})\index{all-xs}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{memory-v-fourp} \\  
\=\+{\rm{memory-v-fourp}}\,({\it{n\/}}, {\it{width\/}}, {\it{mem\/}})\index{memory-v-fourp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{stubp}}\,({\it{mem\/}})\index{stubp} \\ 
{\bf then }{\rm{v-fourp}}\,({\rm{stub-guts}}\,({\it{mem\/}})\index{stub-guts})\index{v-fourp} $\wedge$ ({\rm{length}}\,({\rm{stub-guts}}\,({\it{mem\/}})\index{stub-guts})\index{length} $=$ {\it{width\/}}) \\ 
{\bf elseif }{\it{n\/}} $\simeq {\tt{0}}$ \\ 
{\bf then }\=\+{\bf if }{\rm{ramp}}\,({\it{mem\/}})\index{ramp} \\ 
{\bf then }\=\+{\rm{v-fourp}}\,({\rm{ram-guts}}\,({\it{mem\/}})\index{ram-guts})\index{v-fourp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{ram-guts}}\,({\it{mem\/}})\index{ram-guts})\index{length} $=$ {\it{width\/}})\- \\ 
{\bf elseif }{\rm{romp}}\,({\it{mem\/}})\index{romp} \\ 
{\bf then }\=\+{\rm{v-fourp}}\,({\rm{rom-guts}}\,({\it{mem\/}})\index{rom-guts})\index{v-fourp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{rom-guts}}\,({\it{mem\/}})\index{rom-guts})\index{length} $=$ {\it{width\/}})\- \\ 
{\bf else }{\bf{f}}$\;${\bf  endif}\- \\ 
{\bf else }\=\+{\rm{listp}}\,({\it{mem\/}}) \\ 
$\wedge$$\;\;\;\;${\rm{memory-v-fourp}}\,({\it{n\/}} $-\;1$, {\it{width\/}}, {\rm{car}}\,({\it{mem\/}}))\index{memory-v-fourp} \\ 
$\wedge$$\;\;\;\;${\rm{memory-v-fourp}}\,({\it{n\/}} $-\;1$, {\it{width\/}}, {\rm{cdr}}\,({\it{mem\/}}))\index{memory-v-fourp}\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{new-machine-state-invariant} \\  
\=\+{\rm{new-machine-state-invariant}}\,({\it{machine-state\/}})\index{new-machine-state-invariant} \\ 
$=$$\;\;\;\;$(\=\+({\rm{length}}\,({\it{machine-state\/}})\index{length} $=$ {\tt{12}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{machine-state\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{car}}\,({\it{machine-state\/}}))\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{car}}\,({\it{machine-state\/}}))\index{properp} \\ 
$\wedge$$\;\;\;\;${\rm{all-ramp-mem}}\,({\tt{4}}, {\rm{caar}}\,({\it{machine-state\/}}))\index{all-ramp-mem} \\ 
$\wedge$$\;\;\;\;${\rm{fourp}}\,({\rm{cadar}}\,({\it{machine-state\/}}))\index{fourp} \\ 
$\wedge$$\;\;\;\;${\rm{memory-v-fourp}}\,({\tt{4}}, {\tt{32}}, {\rm{caar}}\,({\it{machine-state\/}}))\index{memory-v-fourp} \\ 
$\wedge$$\;\;\;\;${\rm{v-fourp}}\,({\rm{caddar}}\,({\it{machine-state\/}}))\index{v-fourp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{caddar}}\,({\it{machine-state\/}}))\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{v-fourp}}\,({\rm{cadddar}}\,({\it{machine-state\/}}))\index{v-fourp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cadddar}}\,({\it{machine-state\/}}))\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{v-fourp}}\,({\rm{cadr}}\,({\it{machine-state\/}}))\index{v-fourp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cadr}}\,({\it{machine-state\/}}))\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{v-fourp}}\,({\rm{caddr}}\,({\it{machine-state\/}}))\index{v-fourp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{caddr}}\,({\it{machine-state\/}}))\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{v-fourp}}\,({\rm{cadddr}}\,({\it{machine-state\/}}))\index{v-fourp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cadddr}}\,({\it{machine-state\/}}))\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{v-fourp}}\,({\rm{caddddr}}\,({\it{machine-state\/}}))\index{v-fourp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{caddddr}}\,({\it{machine-state\/}}))\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{v-fourp}}\,({\rm{cadddddr}}\,({\it{machine-state\/}}))\index{v-fourp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cadddddr}}\,({\it{machine-state\/}}))\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{v-fourp}}\,({\rm{caddddddr}}\,({\it{machine-state\/}}))\index{v-fourp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{caddddddr}}\,({\it{machine-state\/}}))\index{length} $=$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{fourp}}\,({\rm{cadddddddr}}\,({\it{machine-state\/}}))\index{fourp} \\ 
$\wedge$$\;\;\;\;${\rm{fourp}}\,({\rm{caddddddddr}}\,({\it{machine-state\/}}))\index{fourp} \\ 
$\wedge$$\;\;\;\;${\rm{fourp}}\,({\rm{cadddddddddr}}\,({\it{machine-state\/}}))\index{fourp} \\ 
$\wedge$$\;\;\;\;${\rm{v-fourp}}\,({\rm{caddddddddddr}}\,({\it{machine-state\/}}))\index{v-fourp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{caddddddddddr}}\,({\it{machine-state\/}}))\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{v-fourp}}\,({\rm{cadddddddddddr}}\,({\it{machine-state\/}}))\index{v-fourp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{cadddddddddddr}}\,({\it{machine-state\/}}))\index{length} $=$ {\tt{40}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  s-approx-make-list \\ \index{s-approx-make-list}
\=\+(({\rm{length}}\,({\it{vec1\/}})\index{length} $=$ {\rm{length}}\,({\it{vec2\/}})\index{length}) $\wedge$ {\rm{v-fourp}}\,({\it{vec2\/}})\index{v-fourp} $\wedge$ {\rm{all-xs}}\,({\it{vec1\/}})\index{all-xs}) \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx}}\,({\it{vec1\/}}, {\it{vec2\/}})\index{s-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-fourp-implies-properp \\ \index{v-fourp-implies-properp}
{\rm{v-fourp}}\,({\it{x\/}})\index{v-fourp} $\rightarrow$ {\rm{properp}}\,({\it{x\/}})\index{properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  listp-implies-not-fourp \\ \index{listp-implies-not-fourp}
{\rm{listp}}\,({\it{x\/}}) $\rightarrow$ ($\neg$ {\rm{fourp}}\,({\it{x\/}})\index{fourp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ramp-implies-not-fourp \\ \index{ramp-implies-not-fourp}
{\rm{ramp}}\,({\it{x\/}})\index{ramp} $\rightarrow$ ($\neg$ {\rm{fourp}}\,({\it{x\/}})\index{fourp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  romp-implies-not-fourp \\ \index{romp-implies-not-fourp}
{\rm{romp}}\,({\it{x\/}})\index{romp} $\rightarrow$ ($\neg$ {\rm{fourp}}\,({\it{x\/}})\index{fourp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  stubp-implies-not-fourp \\ \index{stubp-implies-not-fourp}
{\rm{stubp}}\,({\it{x\/}})\index{stubp} $\rightarrow$ ($\neg$ {\rm{fourp}}\,({\it{x\/}})\index{fourp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-approx-x \\ \index{b-approx-x}
{\rm{b-approx}}\,({\sc{x}}\index{x}, {\it{y\/}})\index{b-approx}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  machine-state-invariant-implies-s-approx-lemma \\ \index{machine-state-invariant-implies!-s-approx-lemma}
\=\+(\=\+{\rm{new-machine-state-invariant}}\,({\it{state\/}})\index{new-machine-state-invariant} \\ 
$\wedge$$\;\;\;\;$({\it{state\/}} $=$ {\rm{list}}\,(\=\+{\rm{list}}\,({\it{s1-1\/}}, {\it{s1-2\/}}, {\it{s1-3\/}}, {\it{s1-4\/}}), \\ 
{\it{s2\/}}, \\ 
{\it{s3\/}}, \\ 
{\it{s4\/}}, \\ 
{\it{s5\/}}, \\ 
{\it{s6\/}}, \\ 
{\it{s7\/}}, \\ 
{\it{s8\/}}, \\ 
{\it{s9\/}}, \\ 
{\it{s10\/}}, \\ 
{\it{s11\/}}, \\ 
{\it{s12\/}})\-))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx}}\,({\sc{unknown-machine-state}}\index{unknown-machine-state}, {\it{state\/}})\index{s-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  machine-state-invariant-implies-s-approx-lemma-2 \\ \index{machine-state-invariant-implies!-s-approx-lemma-2}
\=\+(\=\+({\rm{length}}\,({\it{state\/}})\index{length} $=$ {\tt{12}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{state\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{car}}\,({\it{state\/}}))\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{car}}\,({\it{state\/}}))\index{properp})\- \\ 
$\rightarrow$$\;\;\;\;$({\it{state\/}} $=$ {\rm{list}}\,(\=\+{\rm{list}}\,(\=\+{\rm{caar}}\,({\it{state\/}}), \\ 
{\rm{cadar}}\,({\it{state\/}}), \\ 
{\rm{caddar}}\,({\it{state\/}}), \\ 
{\rm{cadddar}}\,({\it{state\/}}))\-, \\ 
{\rm{cadr}}\,({\it{state\/}}), \\ 
{\rm{caddr}}\,({\it{state\/}}), \\ 
{\rm{cadddr}}\,({\it{state\/}}), \\ 
{\rm{caddddr}}\,({\it{state\/}}), \\ 
{\rm{cadddddr}}\,({\it{state\/}}), \\ 
{\rm{caddddddr}}\,({\it{state\/}}), \\ 
{\rm{cadddddddr}}\,({\it{state\/}}), \\ 
{\rm{caddddddddr}}\,({\it{state\/}}), \\ 
{\rm{cadddddddddr}}\,({\it{state\/}}), \\ 
{\rm{caddddddddddr}}\,({\it{state\/}}), \\ 
{\rm{cadddddddddddr}}\,({\it{state\/}}))\-)\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  machine-state-invariant-implies-s-approx-lemma-3 \\ \index{machine-state-invariant-implies!-s-approx-lemma-3}
\=\+{\rm{new-machine-state-invariant}}\,({\it{state\/}})\index{new-machine-state-invariant} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{length}}\,({\it{state\/}})\index{length} $=$ {\tt{12}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\it{state\/}})\index{properp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\rm{car}}\,({\it{state\/}}))\index{length} $=$ {\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{car}}\,({\it{state\/}}))\index{properp})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  machine-state-invariant-implies-s-approx \\ \index{machine-state-invariant-implies!-s-approx}
\=\+{\rm{new-machine-state-invariant}}\,({\it{state\/}})\index{new-machine-state-invariant} \\ 
$\rightarrow$$\;\;\;\;${\rm{s-approx}}\,({\sc{unknown-machine-state}}\index{unknown-machine-state}, {\it{state\/}})\index{s-approx}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-s-opener \\ \index{good-s-opener}
\=\+({\rm{listp}}\,({\it{s\/}}) $\rightarrow$ ({\rm{good-s}}\,({\it{s\/}})\index{good-s} $=$ ({\rm{good-s}}\,({\rm{car}}\,({\it{s\/}}))\index{good-s} $\wedge$ {\rm{good-s}}\,({\rm{cdr}}\,({\it{s\/}}))\index{good-s}))) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{ramp}}\,({\it{s\/}})\index{ramp} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{good-s}}\,({\it{s\/}})\index{good-s} \\ 
$=$$\;\;\;\;$(\=\+({\rm{length}}\,({\rm{ram-guts}}\,({\it{s\/}})\index{ram-guts})\index{length} $=$ {\sc{mem-width}}\index{mem-width}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{ram-guts}}\,({\it{s\/}})\index{ram-guts})\index{properp})\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{romp}}\,({\it{s\/}})\index{romp} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{good-s}}\,({\it{s\/}})\index{good-s} \\ 
$=$$\;\;\;\;$(\=\+({\rm{length}}\,({\rm{rom-guts}}\,({\it{s\/}})\index{rom-guts})\index{length} $=$ {\sc{mem-width}}\index{mem-width}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{rom-guts}}\,({\it{s\/}})\index{rom-guts})\index{properp})\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{stubp}}\,({\it{s\/}})\index{stubp} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{good-s}}\,({\it{s\/}})\index{good-s} \\ 
$=$$\;\;\;\;$(\=\+({\rm{length}}\,({\rm{stub-guts}}\,({\it{s\/}})\index{stub-guts})\index{length} $=$ {\sc{mem-width}}\index{mem-width}) \\ 
$\wedge$$\;\;\;\;${\rm{properp}}\,({\rm{stub-guts}}\,({\it{s\/}})\index{stub-guts})\index{properp})\-)\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{fourp}}\,({\it{s\/}})\index{fourp} $\rightarrow$ {\rm{good-s}}\,({\it{s\/}})\index{good-s})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  memory-v-fourp-implies-good-s \\ \index{memory-v-fourp-implies-good-s}
{\rm{memory-v-fourp}}\,({\it{n\/}}, {\tt{32}}, {\it{v\/}})\index{memory-v-fourp} $\rightarrow$ {\rm{good-s}}\,({\it{v\/}})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-fourp-is-good-s \\ \index{v-fourp-is-good-s}
{\rm{v-fourp}}\,({\it{v\/}})\index{v-fourp} $\rightarrow$ {\rm{good-s}}\,({\it{v\/}})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  new-machine-state-invariant-implies-good-s \\ \index{new-machine-state-invariant-imp!lies-good-s}
{\rm{new-machine-state-invariant}}\,({\it{state\/}})\index{new-machine-state-invariant} $\rightarrow$ {\rm{good-s}}\,({\it{state\/}})\index{good-s}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  xs-suffice-for-reset-chip-final-state-for-any-unknown-state \\ \index{xs-suffice-for-reset-chip-final!-state-for-any-unknown-state}
\=\+{\rm{new-machine-state-invariant}}\,({\it{state\/}})\index{new-machine-state-invariant} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{cadr}}\,({\rm{nth}}\,(\=\+{\rm{length}}\,({\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1})\index{length} $-\;1$, \\ 
{\rm{simulate}}\,(\=\+{\tt{'}}{\tt{chip}}, \\ 
{\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1}, \\ 
{\sc{unknown-machine-state}}\index{unknown-machine-state}, \\ 
{\sc{chip\$netlist}}\index{chip\$netlist})\-\index{simulate})\-\index{nth}) \\ 
$=$$\;\;\;\;${\rm{cadr}}\,({\rm{nth}}\,(\=\+{\rm{length}}\,({\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1})\index{length} $-\;1$, \\ 
{\rm{simulate}}\,(\=\+{\tt{'}}{\tt{chip}}, \\ 
{\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1}, \\ 
{\it{state\/}}, \\ 
{\sc{chip\$netlist}}\index{chip\$netlist})\-\index{simulate})\-\index{nth}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  xs-suffice-for-reset-chip-final-state-for-any-unknown-state-better \\ \index{xs-suffice-for-reset-chip-final!-state-for-any-unknown-state-better}
\=\+{\rm{new-machine-state-invariant}}\,({\it{state\/}})\index{new-machine-state-invariant} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{cadr}}\,({\rm{nth}}\,(\=\+{\rm{length}}\,({\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1})\index{length} $-\;1$, \\ 
{\rm{simulate}}\,({\tt{'}}{\tt{chip}}, {\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1}, {\it{state\/}}, {\sc{chip\$netlist}}\index{chip\$netlist})\index{simulate})\-\index{nth}) \\ 
$=$$\;\;\;\;${\sc{initialized-machine-state}}\index{initialized-machine-state})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  new-machine-state-invariant-is-non-trivial \\ \index{new-machine-state-invariant-is-!non-trivial}
{\rm{new-machine-state-invariant}}\,({\sc{unknown-machine-state}}\index{unknown-machine-state})\index{new-machine-state-invariant}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  memory-v-fourp-implies-memory-properp \\ \index{memory-v-fourp-implies-memory-p!roperp}
{\rm{memory-v-fourp}}\,({\it{n\/}}, {\it{width\/}}, {\it{mem\/}})\index{memory-v-fourp} $\rightarrow$ {\rm{memory-properp}}\,({\it{n\/}}, {\it{width\/}}, {\it{mem\/}})\index{memory-properp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  new-machine-state-invariant-implies-machine-state-invariant \\ \index{new-machine-state-invariant-imp!lies-machine-state-invariant}
\=\+{\rm{new-machine-state-invariant}}\,({\it{machine-state\/}})\index{new-machine-state-invariant} \\ 
$\rightarrow$$\;\;\;\;${\rm{machine-state-invariant}}\,({\it{machine-state\/}})\index{machine-state-invariant}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fm9001-statep-implies-memory-ok-p-instance \\ \index{fm9001-statep-implies-memory-ok!-p-instance}
\=\+{\rm{memory-okp}}\,(\=\+{\tt{32}}, \\ 
{\tt{32}}, \\ 
{\rm{cadr}}\,({\rm{map-up}}\,({\rm{list}}\,({\sc{initialized-machine-state}}\index{initialized-machine-state}, {\it{machine-memory\/}}))\index{map-up}))\-\index{memory-okp} \\ 
$\rightarrow$$\;\;\;\;${\rm{fm9001-statep}}\,({\rm{map-up}}\,({\rm{list}}\,({\sc{initialized-machine-state}}\index{initialized-machine-state}, {\it{machine-memory\/}}))\index{map-up})\index{fm9001-statep}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fm9001=chip-system-true-after-reset-lemma \\ \index{fm9001=chip-system-true-after-re!set-lemma}
\=\+(\=\+{\rm{chip-system\&}}\,({\it{netlist\/}})\index{chip-system\&} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,(\=\+{\tt{32}}, \\ 
{\tt{32}}, \\ 
{\rm{cadr}}\,({\rm{map-up}}\,({\rm{list}}\,({\sc{initialized-machine-state}}\index{initialized-machine-state}, {\it{machine-memory\/}}))\index{map-up}))\-\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{chip-system-operating-inputs-p}}\,(\=\+{\it{inputs\/}}, \\ 
{\rm{total-microcycles}}\,(\=\+{\rm{map-down}}\,({\rm{map-up}}\,({\rm{list}}\,(\=\+{\sc{initialized-machine-state}}\index{initialized-machine-state}, \\ 
{\it{machine-memory\/}})\-)\index{map-up})\index{map-down}, \\ 
{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\it{n\/}})\-\index{total-microcycles})\-\index{chip-system-operating-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{operating-inputs-p}}\,(\=\+{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\rm{total-microcycles}}\,(\=\+{\rm{map-down}}\,({\rm{map-up}}\,({\rm{list}}\,(\=\+{\sc{initialized-machine-state}}\index{initialized-machine-state}, \\ 
{\it{machine-memory\/}})\-)\index{map-up})\index{map-down}, \\ 
{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\it{n\/}})\-\index{total-microcycles})\-\index{operating-inputs-p})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{fm9001}}\,({\rm{map-up}}\,({\rm{list}}\,({\sc{initialized-machine-state}}\index{initialized-machine-state}, {\it{machine-memory\/}}))\index{map-up}, {\it{n\/}})\index{fm9001} \\ 
$=$$\;\;\;\;${\rm{map-up}}\,({\rm{simulate-dual-eval-2}}\,(\=\+{\tt{'}}{\tt{chip-system}}, \\ 
{\it{inputs\/}}, \\ 
{\rm{map-down}}\,({\rm{map-up}}\,({\rm{list}}\,(\=\+{\sc{initialized-machine-state}}\index{initialized-machine-state}, \\ 
{\it{machine-memory\/}})\-)\index{map-up})\index{map-down}, \\ 
{\it{netlist\/}}, \\ 
{\rm{total-microcycles}}\,(\=\+{\rm{map-down}}\,({\rm{map-up}}\,({\rm{list}}\,(\=\+{\sc{initialized-machine-state}}\index{initialized-machine-state}, \\ 
{\it{machine-memory\/}})\-)\index{map-up})\index{map-down}, \\ 
{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\it{n\/}})\-\index{total-microcycles})\-\index{simulate-dual-eval-2})\index{map-up})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  map-down-inverts-map-up \\ \index{map-down-inverts-map-up}
\=\+{\rm{memory-okp}}\,(\=\+{\tt{32}}, \\ 
{\tt{32}}, \\ 
{\rm{cadr}}\,({\rm{map-up}}\,({\rm{list}}\,(\=\+{\sc{initialized-machine-state}}\index{initialized-machine-state}, \\ 
{\rm{list}}\,(\=\+{\it{memory\/}}, \\ 
{\tt{0}}, \\ 
{\tt{0}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-)\-)\index{map-up}))\-\index{memory-okp} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{map-down}}\,({\rm{map-up}}\,({\rm{list}}\,(\=\+{\sc{initialized-machine-state}}\index{initialized-machine-state}, \\ 
{\rm{list}}\,(\=\+{\it{memory\/}}, \\ 
{\tt{0}}, \\ 
{\tt{0}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-)\-)\index{map-up})\index{map-down} \\ 
$=$$\;\;\;\;${\rm{list}}\,(\=\+{\sc{initialized-machine-state}}\index{initialized-machine-state}, \\ 
{\rm{list}}\,({\it{memory\/}}, {\tt{0}}, {\tt{0}}, {\tt{0}}, {\bf{t}}, {\bf{t}}, {\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, {\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  cadr-map-up \\ \index{cadr-map-up}
{\rm{cadr}}\,({\rm{map-up}}\,({\rm{list}}\,({\it{s\/}}, {\it{mem\/}}))\index{map-up}) $=$ {\rm{car}}\,({\it{mem\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fm9001=chip-system-true-after-reset \\ \index{fm9001=chip-system-true-after-re!set}
\=\+(\=\+{\rm{chip-system\&}}\,({\it{netlist\/}})\index{chip-system\&} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{memory\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{chip-system-operating-inputs-p}}\,(\=\+{\it{inputs\/}}, \\ 
{\rm{total-microcycles}}\,(\=\+{\rm{list}}\,(\=\+{\sc{initialized-machine-state}}\index{initialized-machine-state}, \\ 
{\rm{list}}\,(\=\+{\it{memory\/}}, \\ 
{\tt{0}}, \\ 
{\tt{0}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\rm{make-list}}\,(\=\+{\tt{32}}, \\ 
{\bf{f}})\-\index{make-list}, \\ 
{\rm{make-list}}\,(\=\+{\tt{32}}, \\ 
{\sc{x}}\index{x})\-\index{make-list})\-)\-, \\ 
{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\it{n\/}})\-\index{total-microcycles})\-\index{chip-system-operating-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{operating-inputs-p}}\,(\=\+{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\rm{total-microcycles}}\,(\=\+{\rm{list}}\,(\=\+{\sc{initialized-machine-state}}\index{initialized-machine-state}, \\ 
{\rm{list}}\,(\=\+{\it{memory\/}}, \\ 
{\tt{0}}, \\ 
{\tt{0}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-)\-, \\ 
{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\it{n\/}})\-\index{total-microcycles})\-\index{operating-inputs-p})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{fm9001}}\,(\=\+{\rm{map-up}}\,({\rm{list}}\,(\=\+{\sc{initialized-machine-state}}\index{initialized-machine-state}, \\ 
{\rm{list}}\,(\=\+{\it{memory\/}}, \\ 
{\tt{0}}, \\ 
{\tt{0}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-)\-)\index{map-up}, \\ 
{\it{n\/}})\-\index{fm9001} \\ 
$=$$\;\;\;\;${\rm{map-up}}\,({\rm{simulate-dual-eval-2}}\,(\=\+{\tt{'}}{\tt{chip-system}}, \\ 
{\it{inputs\/}}, \\ 
{\rm{list}}\,(\=\+{\sc{initialized-machine-state}}\index{initialized-machine-state}, \\ 
{\rm{list}}\,(\=\+{\it{memory\/}}, \\ 
{\tt{0}}, \\ 
{\tt{0}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-)\-, \\ 
{\it{netlist\/}}, \\ 
{\rm{total-microcycles}}\,(\=\+{\rm{list}}\,(\=\+{\sc{initialized-machine-state}}\index{initialized-machine-state}, \\ 
{\rm{list}}\,(\=\+{\it{memory\/}}, \\ 
{\tt{0}}, \\ 
{\tt{0}}, \\ 
{\tt{0}}, \\ 
{\bf{t}}, \\ 
{\bf{t}}, \\ 
{\rm{make-list}}\,(\=\+{\tt{32}}, \\ 
{\bf{f}})\-\index{make-list}, \\ 
{\rm{make-list}}\,(\=\+{\tt{32}}, \\ 
{\sc{x}}\index{x})\-\index{make-list})\-)\-, \\ 
{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\it{n\/}})\-\index{total-microcycles})\-\index{simulate-dual-eval-2})\index{map-up})\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable map-down-inverts-map-up; name this event `map-down-inverts-map-up-off'.\index{map-down-inverts-map-up-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-knownp; name this event `b-knownp-off1'.\index{b-knownp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-approx; name this event `b-approx-off1'.\index{b-approx-off1}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  simulate-contains-simulate-dual-eval-2 \\ \index{simulate-contains-simulate-dual!-eval-2}
\=\+(\=\+({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{inputs\/}})\index{length} $<$ {\it{n\/}}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{cadr}}\,({\rm{nth}}\,({\it{n\/}} $-\;1$, {\rm{simulate}}\,({\it{fn\/}}, {\it{inputs\/}}, {\it{state\/}}, {\it{netlist\/}})\index{simulate})\index{nth}) \\ 
$=$$\;\;\;\;${\rm{simulate-dual-eval-2}}\,({\it{fn\/}}, {\it{inputs\/}}, {\it{state\/}}, {\it{netlist\/}}, {\it{n\/}})\index{simulate-dual-eval-2})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-reset-sequence-chip-1 \\ \index{length-reset-sequence-chip-1}
{\rm{length}}\,({\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1})\index{length} $=$ {\tt{20}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  reset-chip \\ \index{reset-chip}
\=\+{\rm{simulate-dual-eval-2}}\,(\=\+{\tt{'}}{\tt{chip}}, \\ 
{\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1}, \\ 
{\sc{unknown-machine-state}}\index{unknown-machine-state}, \\ 
{\sc{chip\$netlist}}\index{chip\$netlist}, \\ 
{\rm{length}}\,({\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1})\index{length})\-\index{simulate-dual-eval-2} \\ 
$=$$\;\;\;\;${\sc{initialized-machine-state}}\index{initialized-machine-state}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  reset-chip-from-any-state \\ \index{reset-chip-from-any-state}
\=\+({\rm{s-approx}}\,({\sc{unknown-machine-state}}\index{unknown-machine-state}, {\it{any-state\/}})\index{s-approx} $\wedge$ {\rm{good-s}}\,({\it{any-state\/}})\index{good-s}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{simulate-dual-eval-2}}\,(\=\+{\tt{'}}{\tt{chip}}, \\ 
{\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1}, \\ 
{\it{any-state\/}}, \\ 
{\sc{chip\$netlist}}\index{chip\$netlist}, \\ 
{\rm{length}}\,({\sc{reset-sequence-chip-1}}\index{reset-sequence-chip-1})\index{length})\-\index{simulate-dual-eval-2} \\ 
$=$$\;\;\;\;${\sc{initialized-machine-state}}\index{initialized-machine-state})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  chip-system=fm9001-interpreter\$after-reset \\ \index{chip-system=fm9001-interpreter\$!after-reset}
\=\+(\=\+{\rm{chip-system\&}}\,({\it{netlist\/}})\index{chip-system\&} \\ 
$\wedge$$\;\;\;\;${\rm{memory-okp}}\,({\tt{32}}, {\tt{32}}, {\it{memory\/}})\index{memory-okp} \\ 
$\wedge$$\;\;\;\;${\rm{chip-system-operating-inputs-p}}\,(\=\+{\it{inputs\/}}, \\ 
{\rm{total-microcycles}}\,(\=\+{\rm{list}}\,(\=\+{\sc{initialized-machine-state}}\index{initialized-machine-state}, \\ 
{\rm{list}}\,(\=\+{\it{memory\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\sc{x}}\index{x}, \\ 
{\bf{t}}, \\ 
{\rm{make-list}}\,(\=\+{\tt{32}}, \\ 
{\bf{f}})\-\index{make-list}, \\ 
{\rm{make-list}}\,(\=\+{\tt{32}}, \\ 
{\sc{x}}\index{x})\-\index{make-list})\-)\-, \\ 
{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\it{instructions\/}})\-\index{total-microcycles})\-\index{chip-system-operating-inputs-p} \\ 
$\wedge$$\;\;\;\;${\rm{operating-inputs-p}}\,(\=\+{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\rm{total-microcycles}}\,(\=\+{\rm{list}}\,(\=\+{\sc{initialized-machine-state}}\index{initialized-machine-state}, \\ 
{\rm{list}}\,(\=\+{\it{memory\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\sc{x}}\index{x}, \\ 
{\bf{t}}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-)\-, \\ 
{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\it{instructions\/}})\-\index{total-microcycles})\-\index{operating-inputs-p})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{map-up}}\,({\rm{simulate-dual-eval-2}}\,(\=\+{\tt{'}}{\tt{chip-system}}, \\ 
{\it{inputs\/}}, \\ 
{\rm{list}}\,(\=\+{\sc{initialized-machine-state}}\index{initialized-machine-state}, \\ 
{\rm{list}}\,(\=\+{\it{memory\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\sc{x}}\index{x}, \\ 
{\bf{t}}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-)\-, \\ 
{\it{netlist\/}}, \\ 
{\rm{total-microcycles}}\,(\=\+{\rm{list}}\,(\=\+{\sc{initialized-machine-state}}\index{initialized-machine-state}, \\ 
{\rm{list}}\,(\=\+{\it{memory\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\sc{x}}\index{x}, \\ 
{\bf{t}}, \\ 
{\rm{make-list}}\,(\=\+{\tt{32}}, \\ 
{\bf{f}})\-\index{make-list}, \\ 
{\rm{make-list}}\,(\=\+{\tt{32}}, \\ 
{\sc{x}}\index{x})\-\index{make-list})\-)\-, \\ 
{\rm{map-up-inputs}}\,({\it{inputs\/}})\index{map-up-inputs}, \\ 
{\it{instructions\/}})\-\index{total-microcycles})\-\index{simulate-dual-eval-2})\index{map-up} \\ 
$=$$\;\;\;\;${\rm{fm9001-interpreter}}\,(\=\+{\rm{map-up}}\,({\rm{list}}\,(\=\+{\sc{initialized-machine-state}}\index{initialized-machine-state}, \\ 
{\rm{list}}\,(\=\+{\it{memory\/}}, \\ 
{\tt{0}}, \\ 
{\it{clock\/}}, \\ 
{\tt{0}}, \\ 
{\sc{x}}\index{x}, \\ 
{\bf{t}}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\bf{f}})\index{make-list}, \\ 
{\rm{make-list}}\,({\tt{32}}, {\sc{x}}\index{x})\index{make-list})\-)\-)\index{map-up}, \\ 
{\rm{make-list}}\,({\tt{4}}, {\bf{t}})\index{make-list}, \\ 
{\it{instructions\/}})\-\index{fm9001-interpreter})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable compile-uncompiled-defns; name this event `compile-uncompiled-defns-on1'.\index{compile-uncompiled-defns-on1}

\addvspace{18pt}


\noindent{\sc Event}:   For efficiency, compile those definitions not yet compiled.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  chip-well-formed \\ \index{chip-well-formed}
\=\+({\rm{top-level-predicate}}\,({\sc{chip-module\$netlist}}\index{chip-module\$netlist})\index{top-level-predicate} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{top-level-predicate}}\,({\sc{chip\$netlist}}\index{chip\$netlist})\index{top-level-predicate} $=$ {\bf{t}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  chip-well-formed-after-indexed-names-removed \\ \index{chip-well-formed-after-indexed-!names-removed}
\=\+({\rm{top-level-predicate}}\,({\rm{lisp-netlist}}\,({\sc{chip-module\$netlist}}\index{chip-module\$netlist})\index{lisp-netlist})\index{top-level-predicate} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{top-level-predicate}}\,({\rm{lisp-netlist}}\,({\sc{chip\$netlist}}\index{chip\$netlist})\index{lisp-netlist})\index{top-level-predicate} $=$ {\bf{t}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  chip-well-formed-simple \\ \index{chip-well-formed-simple}
\=\+({\rm{top-level-predicate-simple}}\,({\sc{chip-module\$netlist}}\index{chip-module\$netlist})\index{top-level-predicate-simple} $=$ {\bf{t}}) \\ 
$\wedge$$\;\;\;\;$({\rm{top-level-predicate-simple}}\,({\rm{lisp-netlist}}\,({\sc{chip-module\$netlist}}\index{chip-module\$netlist})\index{lisp-netlist})\index{top-level-predicate-simple} $=$ {\bf{t}})\-
\end{tabbing}


\noindent{\sc Event}:   Enable chip-well-formed-simple; name this event `chip-well-formed-simple-off'.\index{chip-well-formed-simple-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable chip-well-formed-after-indexed-names-removed; name this event `chip-well-formed-after-indexed-names-removed-off'.\index{chip-well-formed-after-indexed-!names-removed-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable chip-well-formed; name this event `chip-well-formed-off'.\index{chip-well-formed-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable chip-system=fm9001-interpreter\$after-reset; name this event `chip-system=fm9001-interpreter\$after-reset-off'.\index{chip-system=fm9001-interpreter\$!after-reset-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable reset-chip-from-any-state; name this event `reset-chip-from-any-state-off'.\index{reset-chip-from-any-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable reset-chip; name this event `reset-chip-off'.\index{reset-chip-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable length-reset-sequence-chip-1; name this event `length-reset-sequence-chip-1-off'.\index{length-reset-sequence-chip-1-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable simulate-contains-simulate-dual-eval-2; name this event `simulate-contains-simulate-dual-eval-2-off'.\index{simulate-contains-simulate-dual!-eval-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fm9001=chip-system-true-after-reset; name this event `fm9001=chip-system-true-after-reset-off'.\index{fm9001=chip-system-true-after-re!set-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cadr-map-up; name this event `cadr-map-up-off'.\index{cadr-map-up-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fm9001=chip-system-true-after-reset-lemma; name this event `fm9001=chip-system-true-after-reset-lemma-off'.\index{fm9001=chip-system-true-after-re!set-lemma-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fm9001-statep-implies-memory-ok-p-instance; name this event `fm9001-statep-implies-memory-ok-p-instance-off'.\index{fm9001-statep-implies-memory-ok!-p-instance-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable new-machine-state-invariant-implies-machine-state-invariant; name this event `new-machine-state-invariant-implies-machine-state-invariant-off'.\index{new-machine-state-invariant-imp!lies-machine-state-invariant-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable memory-v-fourp-implies-memory-properp; name this event `memory-v-fourp-implies-memory-properp-off'.\index{memory-v-fourp-implies-memory-p!roperp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable new-machine-state-invariant-is-non-trivial; name this event `new-machine-state-invariant-is-non-trivial-off'.\index{new-machine-state-invariant-is-!non-trivial-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable xs-suffice-for-reset-chip-final-state-for-any-unknown-state-better; name this event `xs-suffice-for-reset-chip-final-state-for-any-unknown-state-better-off'.\index{xs-suffice-for-reset-chip-final!-state-for-any-unknown-state-better-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable xs-suffice-for-reset-chip-final-state-for-any-unknown-state; name this event `xs-suffice-for-reset-chip-final-state-for-any-unknown-state-off'.\index{xs-suffice-for-reset-chip-final!-state-for-any-unknown-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable new-machine-state-invariant-implies-good-s; name this event `new-machine-state-invariant-implies-good-s-off'.\index{new-machine-state-invariant-imp!lies-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-fourp-is-good-s; name this event `v-fourp-is-good-s-off'.\index{v-fourp-is-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable memory-v-fourp-implies-good-s; name this event `memory-v-fourp-implies-good-s-off'.\index{memory-v-fourp-implies-good-s-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable good-s-opener; name this event `good-s-opener-off'.\index{good-s-opener-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable machine-state-invariant-implies-s-approx; name this event `machine-state-invariant-implies-s-approx-off'.\index{machine-state-invariant-implies!-s-approx-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable machine-state-invariant-implies-s-approx-lemma-3; name this event `machine-state-invariant-implies-s-approx-lemma-3-off'.\index{machine-state-invariant-implies!-s-approx-lemma-3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable machine-state-invariant-implies-s-approx-lemma-2; name this event `machine-state-invariant-implies-s-approx-lemma-2-off'.\index{machine-state-invariant-implies!-s-approx-lemma-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable machine-state-invariant-implies-s-approx-lemma; name this event `machine-state-invariant-implies-s-approx-lemma-off'.\index{machine-state-invariant-implies!-s-approx-lemma-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-approx-x; name this event `b-approx-x-off'.\index{b-approx-x-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable stubp-implies-not-fourp; name this event `stubp-implies-not-fourp-off'.\index{stubp-implies-not-fourp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable romp-implies-not-fourp; name this event `romp-implies-not-fourp-off'.\index{romp-implies-not-fourp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ramp-implies-not-fourp; name this event `ramp-implies-not-fourp-off'.\index{ramp-implies-not-fourp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable listp-implies-not-fourp; name this event `listp-implies-not-fourp-off'.\index{listp-implies-not-fourp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-fourp-implies-properp; name this event `v-fourp-implies-properp-off'.\index{v-fourp-implies-properp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-make-list; name this event `s-approx-make-list-off'.\index{s-approx-make-list-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable new-machine-state-invariant; name this event `new-machine-state-invariant-off'.\index{new-machine-state-invariant-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*new-machine-state-invariant; name this event `g*1*new-machine-state-invariant-off'.\index{g*1*new-machine-state-invariant!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable memory-v-fourp; name this event `memory-v-fourp-off'.\index{memory-v-fourp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*memory-v-fourp; name this event `g*1*memory-v-fourp-off'.\index{g*1*memory-v-fourp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable all-xs-make-list; name this event `all-xs-make-list-off'.\index{all-xs-make-list-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable all-xs-approximates; name this event `all-xs-approximates-off'.\index{all-xs-approximates-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable all-xs; name this event `all-xs-off'.\index{all-xs-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*all-xs; name this event `g*1*all-xs-off'.\index{g*1*all-xs-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-fourp; name this event `v-fourp-off'.\index{v-fourp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-fourp; name this event `g*1*v-fourp-off'.\index{g*1*v-fourp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fm9001-machine-statep-p-map-up-initialized-machine-state; name this event `fm9001-machine-statep-p-map-up-initialized-machine-state-off'.\index{fm9001-machine-statep-p-map-up-i!nitialized-machine-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable xs-suffice-for-reset-chip-lemma-instance; name this event `xs-suffice-for-reset-chip-lemma-instance-off'.\index{xs-suffice-for-reset-chip-lemma!-instance-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable simulate-reset-chip-final-state; name this event `simulate-reset-chip-final-state-off'.\index{simulate-reset-chip-final-state!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable reset-sequence-chip-1-vs-2; name this event `reset-sequence-chip-1-vs-2-off'.\index{reset-sequence-chip-1-vs-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable reset-sequence-chip-2; name this event `reset-sequence-chip-2-off'.\index{reset-sequence-chip-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*reset-sequence-chip-2; name this event `g*1*reset-sequence-chip-2-off'.\index{g*1*reset-sequence-chip-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable reset-sequence-chip-1; name this event `reset-sequence-chip-1-off'.\index{reset-sequence-chip-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*reset-sequence-chip-1; name this event `g*1*reset-sequence-chip-1-off'.\index{g*1*reset-sequence-chip-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable run-vector-chip-2; name this event `run-vector-chip-2-off'.\index{run-vector-chip-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*run-vector-chip-2; name this event `g*1*run-vector-chip-2-off'.\index{g*1*run-vector-chip-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable run-vector-chip-1; name this event `run-vector-chip-1-off'.\index{run-vector-chip-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*run-vector-chip-1; name this event `g*1*run-vector-chip-1-off'.\index{g*1*run-vector-chip-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable reset-vector-chip; name this event `reset-vector-chip-off'.\index{reset-vector-chip-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*reset-vector-chip; name this event `g*1*reset-vector-chip-off'.\index{g*1*reset-vector-chip-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fm9001-statep-map-up-final-state; name this event `fm9001-statep-map-up-final-state-off'.\index{fm9001-statep-map-up-final-state!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable instance-theorem; name this event `instance-theorem-off'.\index{instance-theorem-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable final-state-okp; name this event `final-state-okp-off'.\index{final-state-okp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable unknown-state-okp; name this event `unknown-state-okp-off'.\index{unknown-state-okp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable reset-works; name this event `reset-works-off'.\index{reset-works-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable final-state; name this event `final-state-off'.\index{final-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*final-state; name this event `g*1*final-state-off'.\index{g*1*final-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable initialized-memory-state; name this event `initialized-memory-state-off'.\index{initialized-memory-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*initialized-memory-state; name this event `g*1*initialized-memory-state-off'.\index{g*1*initialized-memory-state-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable initialized-machine-state; name this event `initialized-machine-state-off'.\index{initialized-machine-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*initialized-machine-state; name this event `g*1*initialized-machine-state-off'.\index{g*1*initialized-machine-state-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable initialized-regfile; name this event `initialized-regfile-off'.\index{initialized-regfile-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*initialized-regfile; name this event `g*1*initialized-regfile-off'.\index{g*1*initialized-regfile-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable chip-system-operating-inputs-p-reset-sequence; name this event `chip-system-operating-inputs-p-reset-sequence-off'.\index{chip-system-operating-inputs-p-!reset-sequence-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable reset-sequence; name this event `reset-sequence-off'.\index{reset-sequence-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*reset-sequence; name this event `g*1*reset-sequence-off'.\index{g*1*reset-sequence-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable run-vector; name this event `run-vector-off'.\index{run-vector-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*run-vector; name this event `g*1*run-vector-off'.\index{g*1*run-vector-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable reset-vector; name this event `reset-vector-off'.\index{reset-vector-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*reset-vector; name this event `g*1*reset-vector-off'.\index{g*1*reset-vector-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fm9001-state-structure-unknown-state; name this event `fm9001-state-structure-unknown-state-off'.\index{fm9001-state-structure-unknown-!state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable chip-system-invariant-unknown-state; name this event `chip-system-invariant-unknown-state-off'.\index{chip-system-invariant-unknown-st!ate-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable unknown-state; name this event `unknown-state-off'.\index{unknown-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*unknown-state; name this event `g*1*unknown-state-off'.\index{g*1*unknown-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable unknown-memory-state; name this event `unknown-memory-state-off'.\index{unknown-memory-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*unknown-memory-state; name this event `g*1*unknown-memory-state-off'.\index{g*1*unknown-memory-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable unknown-machine-state; name this event `unknown-machine-state-off'.\index{unknown-machine-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*unknown-machine-state; name this event `g*1*unknown-machine-state-off'.\index{g*1*unknown-machine-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable unknown-regfile; name this event `unknown-regfile-off'.\index{unknown-regfile-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*unknown-regfile; name this event `g*1*unknown-regfile-off'.\index{g*1*unknown-regfile-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable compile-uncompiled-defns; name this event `compile-uncompiled-defns-off'.\index{compile-uncompiled-defns-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*compile-uncompiled-defns; name this event `g*1*compile-uncompiled-defns-off'.\index{g*1*compile-uncompiled-defns-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable xs-suffice-for-reset-lemma; name this event `xs-suffice-for-reset-lemma-off'.\index{xs-suffice-for-reset-lemma-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable xs-suffice-for-reset-lemma-verbose; name this event `xs-suffice-for-reset-lemma-verbose-off'.\index{xs-suffice-for-reset-lemma-verb!ose-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable length-simulate; name this event `length-simulate-off'.\index{length-simulate-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable doublet-p-equal-approx; name this event `doublet-p-equal-approx-off'.\index{doublet-p-equal-approx-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable doublet-n-simulate; name this event `doublet-n-simulate-off'.\index{doublet-n-simulate-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable doublet-n-simulate-induction; name this event `doublet-n-simulate-induction-off'.\index{doublet-n-simulate-induction-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*doublet-n-simulate-induction; name this event `g*1*doublet-n-simulate-induction-off'.\index{g*1*doublet-n-simulate-inductio!n-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*doublet-p; name this event `g*1*doublet-p-off'.\index{g*1*doublet-p-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-list-x-x; name this event `v-approx-list-x-x-off'.\index{v-approx-list-x-x-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable simulate-monotone; name this event `simulate-monotone-off'.\index{simulate-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable simulate-monotone-induction; name this event `simulate-monotone-induction-off'.\index{simulate-monotone-induction-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*simulate-monotone-induction; name this event `g*1*simulate-monotone-induction-off'.\index{g*1*simulate-monotone-induction!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-cadr-nth; name this event `s-approx-cadr-nth-off'.\index{s-approx-cadr-nth-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-car-nth; name this event `v-approx-car-nth-off'.\index{v-approx-car-nth-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable nat-lst-lst-induction; name this event `nat-lst-lst-induction-off'.\index{nat-lst-lst-induction-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*nat-lst-lst-induction; name this event `g*1*nat-lst-lst-induction-off'.\index{g*1*nat-lst-lst-induction-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-s-approx-list; name this event `v-s-approx-list-off'.\index{v-s-approx-list-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-s-approx-list; name this event `g*1*v-s-approx-list-off'.\index{g*1*v-s-approx-list-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-list; name this event `v-approx-list-off'.\index{v-approx-list-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-approx-list; name this event `g*1*v-approx-list-off'.\index{g*1*v-approx-list-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable good-s-preserved; name this event `good-s-preserved-off'.\index{good-s-preserved-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable primp-preserves-good-s; name this event `primp-preserves-good-s-off'.\index{primp-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dp-ram-16x32-preserves-good-s; name this event `dp-ram-16x32-preserves-good-s-off'.\index{dp-ram-16x32-preserves-good-s-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable good-s-write-mem; name this event `good-s-write-mem-off'.\index{good-s-write-mem-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable good-s-write-mem-1; name this event `good-s-write-mem-1-off'.\index{good-s-write-mem-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable good-s-constant-ram; name this event `good-s-constant-ram-off'.\index{good-s-constant-ram-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable vss-preserves-good-s; name this event `vss-preserves-good-s-off'.\index{vss-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable vdd-parametric-preserves-good-s; name this event `vdd-parametric-preserves-good-s-off'.\index{vdd-parametric-preserves-good-s!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable vdd-preserves-good-s; name this event `vdd-preserves-good-s-off'.\index{vdd-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ttl-tri-output-fast-preserves-good-s; name this event `ttl-tri-output-fast-preserves-good-s-off'.\index{ttl-tri-output-fast-preserves-g!ood-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ttl-tri-output-preserves-good-s; name this event `ttl-tri-output-preserves-good-s-off'.\index{ttl-tri-output-preserves-good-s!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ttl-output-fast-preserves-good-s; name this event `ttl-output-fast-preserves-good-s-off'.\index{ttl-output-fast-preserves-good-!s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ttl-output-parametric-preserves-good-s; name this event `ttl-output-parametric-preserves-good-s-off'.\index{ttl-output-parametric-preserves!-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ttl-output-preserves-good-s; name this event `ttl-output-preserves-good-s-off'.\index{ttl-output-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ttl-input-preserves-good-s; name this event `ttl-input-preserves-good-s-off'.\index{ttl-input-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ttl-clk-input-preserves-good-s; name this event `ttl-clk-input-preserves-good-s-off'.\index{ttl-clk-input-preserves-good-s-!off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ttl-bidirect-preserves-good-s; name this event `ttl-bidirect-preserves-good-s-off'.\index{ttl-bidirect-preserves-good-s-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable pullup-preserves-good-s; name this event `pullup-preserves-good-s-off'.\index{pullup-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable t-wire-preserves-good-s; name this event `t-wire-preserves-good-s-off'.\index{t-wire-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable t-buf-preserves-good-s; name this event `t-buf-preserves-good-s-off'.\index{t-buf-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ram-enable-circuit-preserves-good-s; name this event `ram-enable-circuit-preserves-good-s-off'.\index{ram-enable-circuit-preserves-go!od-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable id-preserves-good-s; name this event `id-preserves-good-s-off'.\index{id-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fd1slp-preserves-good-s; name this event `fd1slp-preserves-good-s-off'.\index{fd1slp-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fd1sp-preserves-good-s; name this event `fd1sp-preserves-good-s-off'.\index{fd1sp-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fd1s-preserves-good-s; name this event `fd1s-preserves-good-s-off'.\index{fd1s-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fd1-preserves-good-s; name this event `fd1-preserves-good-s-off'.\index{fd1-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable procmon-preserves-good-s; name this event `procmon-preserves-good-s-off'.\index{procmon-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable del10-preserves-good-s; name this event `del10-preserves-good-s-off'.\index{del10-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable del4-preserves-good-s; name this event `del4-preserves-good-s-off'.\index{del4-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable del2-preserves-good-s; name this event `del2-preserves-good-s-off'.\index{del2-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-xor3-preserves-good-s; name this event `b-xor3-preserves-good-s-off'.\index{b-xor3-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-xor-preserves-good-s; name this event `b-xor-preserves-good-s-off'.\index{b-xor-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-or4-preserves-good-s; name this event `b-or4-preserves-good-s-off'.\index{b-or4-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-or3-preserves-good-s; name this event `b-or3-preserves-good-s-off'.\index{b-or3-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-or-preserves-good-s; name this event `b-or-preserves-good-s-off'.\index{b-or-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-not-ivap-preserves-good-s; name this event `b-not-ivap-preserves-good-s-off'.\index{b-not-ivap-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-not-b4ip-preserves-good-s; name this event `b-not-b4ip-preserves-good-s-off'.\index{b-not-b4ip-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-not-preserves-good-s; name this event `b-not-preserves-good-s-off'.\index{b-not-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nor8-preserves-good-s; name this event `b-nor8-preserves-good-s-off'.\index{b-nor8-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nor6-preserves-good-s; name this event `b-nor6-preserves-good-s-off'.\index{b-nor6-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nor5-preserves-good-s; name this event `b-nor5-preserves-good-s-off'.\index{b-nor5-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nor4-preserves-good-s; name this event `b-nor4-preserves-good-s-off'.\index{b-nor4-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nor3-preserves-good-s; name this event `b-nor3-preserves-good-s-off'.\index{b-nor3-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nor-preserves-good-s; name this event `b-nor-preserves-good-s-off'.\index{b-nor-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nbuf-preserves-good-s; name this event `b-nbuf-preserves-good-s-off'.\index{b-nbuf-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nand8-preserves-good-s; name this event `b-nand8-preserves-good-s-off'.\index{b-nand8-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nand6-preserves-good-s; name this event `b-nand6-preserves-good-s-off'.\index{b-nand6-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nand5-preserves-good-s; name this event `b-nand5-preserves-good-s-off'.\index{b-nand5-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nand4-preserves-good-s; name this event `b-nand4-preserves-good-s-off'.\index{b-nand4-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nand3-preserves-good-s; name this event `b-nand3-preserves-good-s-off'.\index{b-nand3-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nand-preserves-good-s; name this event `b-nand-preserves-good-s-off'.\index{b-nand-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-if-preserves-good-s; name this event `b-if-preserves-good-s-off'.\index{b-if-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-equv3-preserves-good-s; name this event `b-equv3-preserves-good-s-off'.\index{b-equv3-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-equv-preserves-good-s; name this event `b-equv-preserves-good-s-off'.\index{b-equv-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-and4-preserves-good-s; name this event `b-and4-preserves-good-s-off'.\index{b-and4-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-and3-preserves-good-s; name this event `b-and3-preserves-good-s-off'.\index{b-and3-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-and-preserves-good-s; name this event `b-and-preserves-good-s-off'.\index{b-and-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ao7-preserves-good-s; name this event `ao7-preserves-good-s-off'.\index{ao7-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ao6-preserves-good-s; name this event `ao6-preserves-good-s-off'.\index{ao6-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ao4-preserves-good-s; name this event `ao4-preserves-good-s-off'.\index{ao4-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ao2-preserves-good-s; name this event `ao2-preserves-good-s-off'.\index{ao2-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable good-s-0; name this event `good-s-0-off'.\index{good-s-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-if-preserves-good-s; name this event `f-if-preserves-good-s-off'.\index{f-if-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-buf-preserves-good-s; name this event `f-buf-preserves-good-s-off'.\index{f-buf-preserves-good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable good-s-collect-value; name this event `good-s-collect-value-off'.\index{good-s-collect-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-monotone; name this event `dual-eval-monotone-off'.\index{dual-eval-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable good-s-value; name this event `good-s-value-off'.\index{good-s-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable good-s-alist-pairlist; name this event `good-s-alist-pairlist-off'.\index{good-s-alist-pairlist-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable good-s-alist; name this event `good-s-alist-off'.\index{good-s-alist-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*good-s-alist; name this event `g*1*good-s-alist-off'.\index{g*1*good-s-alist-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-monotone-no-ram; name this event `dual-eval-monotone-no-ram-off'.\index{dual-eval-monotone-no-ram-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ok-netlistp-reduction-rewrite; name this event `ok-netlistp-reduction-rewrite-off'.\index{ok-netlistp-reduction-rewrite-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ok-netlistp-reduction; name this event `ok-netlistp-reduction-off'.\index{ok-netlistp-reduction-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-alist-implies-s-approx-collect-value; name this event `s-approx-alist-implies-s-approx-collect-value-off'.\index{s-approx-alist-implies-s-approx!-collect-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-implies-s-approx-alist; name this event `s-approx-implies-s-approx-alist-off'.\index{s-approx-implies-s-approx-alist!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable alistp-dual-eval-3; name this event `alistp-dual-eval-3-off'.\index{alistp-dual-eval-3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-alist-implies-s-approx-list-collect-value; name this event `s-approx-alist-implies-s-approx-list-collect-value-off'.\index{s-approx-alist-implies-s-approx!-list-collect-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable double-cdr-induction; name this event `double-cdr-induction-off'.\index{double-cdr-induction-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*double-cdr-induction; name this event `g*1*double-cdr-induction-off'.\index{g*1*double-cdr-induction-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-alist-append; name this event `v-approx-alist-append-off'.\index{v-approx-alist-append-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-alist-implies-s-approx-value; name this event `s-approx-alist-implies-s-approx-value-off'.\index{s-approx-alist-implies-s-approx!-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable alistp-opener; name this event `alistp-opener-off'.\index{alistp-opener-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-implies-v-approx-alist; name this event `v-approx-implies-v-approx-alist-off'.\index{v-approx-implies-v-approx-alist!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-list-implies-s-approx-alist; name this event `s-approx-list-implies-s-approx-alist-off'.\index{s-approx-list-implies-s-approx-!alist-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-list; name this event `s-approx-list-off'.\index{s-approx-list-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*s-approx-list; name this event `g*1*s-approx-list-off'.\index{g*1*s-approx-list-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-alist-implies-v-approx-collect-value; name this event `v-approx-alist-implies-v-approx-collect-value-off'.\index{v-approx-alist-implies-v-approx!-collect-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable alistp-dual-eval-1; name this event `alistp-dual-eval-1-off'.\index{alistp-dual-eval-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable alistp-append; name this event `alistp-append-off'.\index{alistp-append-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable alistp-pairlist; name this event `alistp-pairlist-off'.\index{alistp-pairlist-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-alist-implies-b-approx-value; name this event `v-approx-alist-implies-b-approx-value-off'.\index{v-approx-alist-implies-b-approx!-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-monotone-induction; name this event `dual-eval-monotone-induction-off'.\index{dual-eval-monotone-induction-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*dual-eval-monotone-induction; name this event `g*1*dual-eval-monotone-induction-off'.\index{g*1*dual-eval-monotone-inductio!n-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable primp-monotone; name this event `primp-monotone-off'.\index{primp-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ok-netlistp; name this event `ok-netlistp-off'.\index{ok-netlistp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*ok-netlistp; name this event `g*1*ok-netlistp-off'.\index{g*1*ok-netlistp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-port-ram-state-body; name this event `dual-port-ram-state-body-off'.\index{dual-port-ram-state-body-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*dual-port-ram-state-body; name this event `g*1*dual-port-ram-state-body-off'.\index{g*1*dual-port-ram-state-body-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-port-ram-state-monotone; name this event `dual-port-ram-state-monotone-off'.\index{dual-port-ram-state-monotone-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable write-mem1-double-induction; name this event `write-mem1-double-induction-off'.\index{write-mem1-double-induction-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*write-mem1-double-induction; name this event `g*1*write-mem1-double-induction-off'.\index{g*1*write-mem1-double-induction!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable write-mem1-monotone-induction; name this event `write-mem1-monotone-induction-off'.\index{write-mem1-monotone-induction-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*write-mem1-monotone-induction; name this event `g*1*write-mem1-monotone-induction-off'.\index{g*1*write-mem1-monotone-inducti!on-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-port-ram-value-body; name this event `dual-port-ram-value-body-off'.\index{dual-port-ram-value-body-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*dual-port-ram-value-body; name this event `g*1*dual-port-ram-value-body-off'.\index{g*1*dual-port-ram-value-body-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-x-x; name this event `v-approx-x-x-off1'.\index{v-approx-x-x-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable read-mem1-monotone-induction; name this event `read-mem1-monotone-induction-off'.\index{read-mem1-monotone-induction-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*read-mem1-monotone-induction; name this event `g*1*read-mem1-monotone-induction-off'.\index{g*1*read-mem1-monotone-inductio!n-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable bvp-rev1; name this event `bvp-rev1-off'.\index{bvp-rev1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable vss-monotone; name this event `vss-monotone-off'.\index{vss-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-vss-state; name this event `dual-eval-vss-state-off'.\index{dual-eval-vss-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-vss-value; name this event `dual-eval-vss-value-off'.\index{dual-eval-vss-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable vdd-parametric-monotone; name this event `vdd-parametric-monotone-off'.\index{vdd-parametric-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-vdd-parametric-state; name this event `dual-eval-vdd-parametric-state-off'.\index{dual-eval-vdd-parametric-state-!off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-vdd-parametric-value; name this event `dual-eval-vdd-parametric-value-off'.\index{dual-eval-vdd-parametric-value-!off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable vdd-monotone; name this event `vdd-monotone-off'.\index{vdd-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-vdd-state; name this event `dual-eval-vdd-state-off'.\index{dual-eval-vdd-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-vdd-value; name this event `dual-eval-vdd-value-off'.\index{dual-eval-vdd-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ttl-tri-output-fast-monotone; name this event `ttl-tri-output-fast-monotone-off'.\index{ttl-tri-output-fast-monotone-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ttl-tri-output-fast-state; name this event `dual-eval-ttl-tri-output-fast-state-off'.\index{dual-eval-ttl-tri-output-fast-st!ate-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ttl-tri-output-fast-value; name this event `dual-eval-ttl-tri-output-fast-value-off'.\index{dual-eval-ttl-tri-output-fast-v!alue-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ttl-tri-output-monotone; name this event `ttl-tri-output-monotone-off'.\index{ttl-tri-output-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ttl-tri-output-state; name this event `dual-eval-ttl-tri-output-state-off'.\index{dual-eval-ttl-tri-output-state-!off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ttl-tri-output-value; name this event `dual-eval-ttl-tri-output-value-off'.\index{dual-eval-ttl-tri-output-value-!off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ttl-output-fast-monotone; name this event `ttl-output-fast-monotone-off'.\index{ttl-output-fast-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ttl-output-fast-state; name this event `dual-eval-ttl-output-fast-state-off'.\index{dual-eval-ttl-output-fast-state!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ttl-output-fast-value; name this event `dual-eval-ttl-output-fast-value-off'.\index{dual-eval-ttl-output-fast-value!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ttl-output-parametric-monotone; name this event `ttl-output-parametric-monotone-off'.\index{ttl-output-parametric-monotone-!off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ttl-output-parametric-state; name this event `dual-eval-ttl-output-parametric-state-off'.\index{dual-eval-ttl-output-parametric!-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ttl-output-parametric-value; name this event `dual-eval-ttl-output-parametric-value-off'.\index{dual-eval-ttl-output-parametric!-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ttl-output-monotone; name this event `ttl-output-monotone-off'.\index{ttl-output-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ttl-output-state; name this event `dual-eval-ttl-output-state-off'.\index{dual-eval-ttl-output-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ttl-output-value; name this event `dual-eval-ttl-output-value-off'.\index{dual-eval-ttl-output-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ttl-input-monotone; name this event `ttl-input-monotone-off'.\index{ttl-input-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ttl-input-state; name this event `dual-eval-ttl-input-state-off'.\index{dual-eval-ttl-input-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ttl-input-value; name this event `dual-eval-ttl-input-value-off'.\index{dual-eval-ttl-input-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ttl-clk-input-monotone; name this event `ttl-clk-input-monotone-off'.\index{ttl-clk-input-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ttl-clk-input-state; name this event `dual-eval-ttl-clk-input-state-off'.\index{dual-eval-ttl-clk-input-state-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ttl-clk-input-value; name this event `dual-eval-ttl-clk-input-value-off'.\index{dual-eval-ttl-clk-input-value-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ttl-bidirect-monotone; name this event `ttl-bidirect-monotone-off'.\index{ttl-bidirect-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ttl-bidirect-state; name this event `dual-eval-ttl-bidirect-state-off'.\index{dual-eval-ttl-bidirect-state-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ttl-bidirect-value; name this event `dual-eval-ttl-bidirect-value-off'.\index{dual-eval-ttl-bidirect-value-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable pullup-monotone; name this event `pullup-monotone-off'.\index{pullup-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-pullup-state; name this event `dual-eval-pullup-state-off'.\index{dual-eval-pullup-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-pullup-value; name this event `dual-eval-pullup-value-off'.\index{dual-eval-pullup-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable t-wire-monotone; name this event `t-wire-monotone-off'.\index{t-wire-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-t-wire-state; name this event `dual-eval-t-wire-state-off'.\index{dual-eval-t-wire-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-t-wire-value; name this event `dual-eval-t-wire-value-off'.\index{dual-eval-t-wire-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable t-buf-monotone; name this event `t-buf-monotone-off'.\index{t-buf-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-t-buf-state; name this event `dual-eval-t-buf-state-off'.\index{dual-eval-t-buf-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-t-buf-value; name this event `dual-eval-t-buf-value-off'.\index{dual-eval-t-buf-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ram-enable-circuit-monotone; name this event `ram-enable-circuit-monotone-off'.\index{ram-enable-circuit-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ram-enable-circuit-state; name this event `dual-eval-ram-enable-circuit-state-off'.\index{dual-eval-ram-enable-circuit-st!ate-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ram-enable-circuit-value; name this event `dual-eval-ram-enable-circuit-value-off'.\index{dual-eval-ram-enable-circuit-va!lue-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable id-monotone; name this event `id-monotone-off'.\index{id-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-id-state; name this event `dual-eval-id-state-off'.\index{dual-eval-id-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-id-value; name this event `dual-eval-id-value-off'.\index{dual-eval-id-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fd1slp-monotone; name this event `fd1slp-monotone-off'.\index{fd1slp-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-fd1slp-state; name this event `dual-eval-fd1slp-state-off'.\index{dual-eval-fd1slp-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-fd1slp-value; name this event `dual-eval-fd1slp-value-off'.\index{dual-eval-fd1slp-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fd1sp-monotone; name this event `fd1sp-monotone-off'.\index{fd1sp-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-fd1sp-state; name this event `dual-eval-fd1sp-state-off'.\index{dual-eval-fd1sp-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-fd1sp-value; name this event `dual-eval-fd1sp-value-off'.\index{dual-eval-fd1sp-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fd1s-monotone; name this event `fd1s-monotone-off'.\index{fd1s-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-fd1s-state; name this event `dual-eval-fd1s-state-off'.\index{dual-eval-fd1s-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-fd1s-value; name this event `dual-eval-fd1s-value-off'.\index{dual-eval-fd1s-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fd1-monotone; name this event `fd1-monotone-off'.\index{fd1-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-fd1-state; name this event `dual-eval-fd1-state-off'.\index{dual-eval-fd1-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-fd1-value; name this event `dual-eval-fd1-value-off'.\index{dual-eval-fd1-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable procmon-monotone; name this event `procmon-monotone-off'.\index{procmon-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-procmon-state; name this event `dual-eval-procmon-state-off'.\index{dual-eval-procmon-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-procmon-value; name this event `dual-eval-procmon-value-off'.\index{dual-eval-procmon-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable del10-monotone; name this event `del10-monotone-off'.\index{del10-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-del10-state; name this event `dual-eval-del10-state-off'.\index{dual-eval-del10-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-del10-value; name this event `dual-eval-del10-value-off'.\index{dual-eval-del10-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable del4-monotone; name this event `del4-monotone-off'.\index{del4-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-del4-state; name this event `dual-eval-del4-state-off'.\index{dual-eval-del4-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-del4-value; name this event `dual-eval-del4-value-off'.\index{dual-eval-del4-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable del2-monotone; name this event `del2-monotone-off'.\index{del2-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-del2-state; name this event `dual-eval-del2-state-off'.\index{dual-eval-del2-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-del2-value; name this event `dual-eval-del2-value-off'.\index{dual-eval-del2-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-xor3-monotone; name this event `b-xor3-monotone-off'.\index{b-xor3-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-xor3-state; name this event `dual-eval-b-xor3-state-off'.\index{dual-eval-b-xor3-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-xor3-value; name this event `dual-eval-b-xor3-value-off'.\index{dual-eval-b-xor3-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-xor-monotone; name this event `b-xor-monotone-off'.\index{b-xor-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-xor-state; name this event `dual-eval-b-xor-state-off'.\index{dual-eval-b-xor-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-xor-value; name this event `dual-eval-b-xor-value-off'.\index{dual-eval-b-xor-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-or4-monotone; name this event `b-or4-monotone-off'.\index{b-or4-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-or4-state; name this event `dual-eval-b-or4-state-off'.\index{dual-eval-b-or4-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-or4-value; name this event `dual-eval-b-or4-value-off'.\index{dual-eval-b-or4-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-or3-monotone; name this event `b-or3-monotone-off'.\index{b-or3-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-or3-state; name this event `dual-eval-b-or3-state-off'.\index{dual-eval-b-or3-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-or3-value; name this event `dual-eval-b-or3-value-off'.\index{dual-eval-b-or3-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-or-monotone; name this event `b-or-monotone-off'.\index{b-or-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-or-state; name this event `dual-eval-b-or-state-off'.\index{dual-eval-b-or-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-or-value; name this event `dual-eval-b-or-value-off'.\index{dual-eval-b-or-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-not-ivap-monotone; name this event `b-not-ivap-monotone-off'.\index{b-not-ivap-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-not-ivap-state; name this event `dual-eval-b-not-ivap-state-off'.\index{dual-eval-b-not-ivap-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-not-ivap-value; name this event `dual-eval-b-not-ivap-value-off'.\index{dual-eval-b-not-ivap-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-not-b4ip-monotone; name this event `b-not-b4ip-monotone-off'.\index{b-not-b4ip-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-not-b4ip-state; name this event `dual-eval-b-not-b4ip-state-off'.\index{dual-eval-b-not-b4ip-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-not-b4ip-value; name this event `dual-eval-b-not-b4ip-value-off'.\index{dual-eval-b-not-b4ip-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-not-monotone; name this event `b-not-monotone-off'.\index{b-not-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-not-state; name this event `dual-eval-b-not-state-off'.\index{dual-eval-b-not-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-not-value; name this event `dual-eval-b-not-value-off'.\index{dual-eval-b-not-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nor8-monotone; name this event `b-nor8-monotone-off'.\index{b-nor8-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nor8-state; name this event `dual-eval-b-nor8-state-off'.\index{dual-eval-b-nor8-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nor8-value; name this event `dual-eval-b-nor8-value-off'.\index{dual-eval-b-nor8-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nor6-monotone; name this event `b-nor6-monotone-off'.\index{b-nor6-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nor6-state; name this event `dual-eval-b-nor6-state-off'.\index{dual-eval-b-nor6-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nor6-value; name this event `dual-eval-b-nor6-value-off'.\index{dual-eval-b-nor6-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nor5-monotone; name this event `b-nor5-monotone-off'.\index{b-nor5-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nor5-state; name this event `dual-eval-b-nor5-state-off'.\index{dual-eval-b-nor5-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nor5-value; name this event `dual-eval-b-nor5-value-off'.\index{dual-eval-b-nor5-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nor4-monotone; name this event `b-nor4-monotone-off'.\index{b-nor4-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nor4-state; name this event `dual-eval-b-nor4-state-off'.\index{dual-eval-b-nor4-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nor4-value; name this event `dual-eval-b-nor4-value-off'.\index{dual-eval-b-nor4-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nor3-monotone; name this event `b-nor3-monotone-off'.\index{b-nor3-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nor3-state; name this event `dual-eval-b-nor3-state-off'.\index{dual-eval-b-nor3-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nor3-value; name this event `dual-eval-b-nor3-value-off'.\index{dual-eval-b-nor3-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nor-monotone; name this event `b-nor-monotone-off'.\index{b-nor-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nor-state; name this event `dual-eval-b-nor-state-off'.\index{dual-eval-b-nor-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nor-value; name this event `dual-eval-b-nor-value-off'.\index{dual-eval-b-nor-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nbuf-monotone; name this event `b-nbuf-monotone-off'.\index{b-nbuf-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nbuf-state; name this event `dual-eval-b-nbuf-state-off'.\index{dual-eval-b-nbuf-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nbuf-value; name this event `dual-eval-b-nbuf-value-off'.\index{dual-eval-b-nbuf-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nand8-monotone; name this event `b-nand8-monotone-off'.\index{b-nand8-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nand8-state; name this event `dual-eval-b-nand8-state-off'.\index{dual-eval-b-nand8-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nand8-value; name this event `dual-eval-b-nand8-value-off'.\index{dual-eval-b-nand8-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nand6-monotone; name this event `b-nand6-monotone-off'.\index{b-nand6-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nand6-state; name this event `dual-eval-b-nand6-state-off'.\index{dual-eval-b-nand6-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nand6-value; name this event `dual-eval-b-nand6-value-off'.\index{dual-eval-b-nand6-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nand5-monotone; name this event `b-nand5-monotone-off'.\index{b-nand5-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nand5-state; name this event `dual-eval-b-nand5-state-off'.\index{dual-eval-b-nand5-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nand5-value; name this event `dual-eval-b-nand5-value-off'.\index{dual-eval-b-nand5-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nand4-monotone; name this event `b-nand4-monotone-off'.\index{b-nand4-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nand4-state; name this event `dual-eval-b-nand4-state-off'.\index{dual-eval-b-nand4-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nand4-value; name this event `dual-eval-b-nand4-value-off'.\index{dual-eval-b-nand4-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nand3-monotone; name this event `b-nand3-monotone-off'.\index{b-nand3-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nand3-state; name this event `dual-eval-b-nand3-state-off'.\index{dual-eval-b-nand3-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nand3-value; name this event `dual-eval-b-nand3-value-off'.\index{dual-eval-b-nand3-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-nand-monotone; name this event `b-nand-monotone-off'.\index{b-nand-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nand-state; name this event `dual-eval-b-nand-state-off'.\index{dual-eval-b-nand-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-nand-value; name this event `dual-eval-b-nand-value-off'.\index{dual-eval-b-nand-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-if-monotone; name this event `b-if-monotone-off'.\index{b-if-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-if-state; name this event `dual-eval-b-if-state-off'.\index{dual-eval-b-if-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-if-value; name this event `dual-eval-b-if-value-off'.\index{dual-eval-b-if-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-equv3-monotone; name this event `b-equv3-monotone-off'.\index{b-equv3-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-equv3-state; name this event `dual-eval-b-equv3-state-off'.\index{dual-eval-b-equv3-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-equv3-value; name this event `dual-eval-b-equv3-value-off'.\index{dual-eval-b-equv3-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-equv-monotone; name this event `b-equv-monotone-off'.\index{b-equv-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-equv-state; name this event `dual-eval-b-equv-state-off'.\index{dual-eval-b-equv-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-equv-value; name this event `dual-eval-b-equv-value-off'.\index{dual-eval-b-equv-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-and4-monotone; name this event `b-and4-monotone-off'.\index{b-and4-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-and4-state; name this event `dual-eval-b-and4-state-off'.\index{dual-eval-b-and4-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-and4-value; name this event `dual-eval-b-and4-value-off'.\index{dual-eval-b-and4-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-and3-monotone; name this event `b-and3-monotone-off'.\index{b-and3-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-and3-state; name this event `dual-eval-b-and3-state-off'.\index{dual-eval-b-and3-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-and3-value; name this event `dual-eval-b-and3-value-off'.\index{dual-eval-b-and3-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-and-monotone; name this event `b-and-monotone-off'.\index{b-and-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-and-state; name this event `dual-eval-b-and-state-off'.\index{dual-eval-b-and-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-b-and-value; name this event `dual-eval-b-and-value-off'.\index{dual-eval-b-and-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ao7-monotone; name this event `ao7-monotone-off'.\index{ao7-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ao7-state; name this event `dual-eval-ao7-state-off'.\index{dual-eval-ao7-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ao7-value; name this event `dual-eval-ao7-value-off'.\index{dual-eval-ao7-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ao6-monotone; name this event `ao6-monotone-off'.\index{ao6-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ao6-state; name this event `dual-eval-ao6-state-off'.\index{dual-eval-ao6-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ao6-value; name this event `dual-eval-ao6-value-off'.\index{dual-eval-ao6-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ao4-monotone; name this event `ao4-monotone-off'.\index{ao4-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ao4-state; name this event `dual-eval-ao4-state-off'.\index{dual-eval-ao4-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ao4-value; name this event `dual-eval-ao4-value-off'.\index{dual-eval-ao4-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ao2-monotone; name this event `ao2-monotone-off'.\index{ao2-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ao2-state; name this event `dual-eval-ao2-state-off'.\index{dual-eval-ao2-state-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-ao2-value; name this event `dual-eval-ao2-value-off'.\index{dual-eval-ao2-value-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fourp-implies-s-approx-is-b-approx; name this event `fourp-implies-s-approx-is-b-approx-off1'.\index{fourp-implies-s-approx-is-b-app!rox-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fourp-f-if; name this event `fourp-f-if-off'.\index{fourp-f-if-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fourp-f-buf; name this event `fourp-f-buf-off'.\index{fourp-f-buf-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-buf-type-set; name this event `f-buf-type-set-off'.\index{f-buf-type-set-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-implies-b-approx; name this event `s-approx-implies-b-approx-off'.\index{s-approx-implies-b-approx-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-2-primp; name this event `dual-eval-2-primp-off'.\index{dual-eval-2-primp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-eval-0-primp; name this event `dual-eval-0-primp-off'.\index{dual-eval-0-primp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-pullup-monotone; name this event `f-pullup-monotone-off'.\index{f-pullup-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ft-wire-monotone; name this event `ft-wire-monotone-off'.\index{ft-wire-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ft-buf-monotone; name this event `ft-buf-monotone-off'.\index{ft-buf-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-if-monotone; name this event `f-if-monotone-off'.\index{f-if-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-equv3-monotone; name this event `f-equv3-monotone-off'.\index{f-equv3-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-xor3-monotone; name this event `f-xor3-monotone-off'.\index{f-xor3-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-equv-monotone; name this event `f-equv-monotone-off'.\index{f-equv-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-xor-monotone; name this event `f-xor-monotone-off'.\index{f-xor-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nor8-monotone; name this event `f-nor8-monotone-off'.\index{f-nor8-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nor6-monotone; name this event `f-nor6-monotone-off'.\index{f-nor6-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nor5-monotone; name this event `f-nor5-monotone-off'.\index{f-nor5-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nor4-monotone; name this event `f-nor4-monotone-off'.\index{f-nor4-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nor3-monotone; name this event `f-nor3-monotone-off'.\index{f-nor3-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nor-monotone; name this event `f-nor-monotone-off'.\index{f-nor-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-or4-monotone; name this event `f-or4-monotone-off'.\index{f-or4-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-or3-monotone; name this event `f-or3-monotone-off'.\index{f-or3-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-or-monotone; name this event `f-or-monotone-off'.\index{f-or-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nand8-monotone; name this event `f-nand8-monotone-off'.\index{f-nand8-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nand6-monotone; name this event `f-nand6-monotone-off'.\index{f-nand6-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nand5-monotone; name this event `f-nand5-monotone-off'.\index{f-nand5-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nand4-monotone; name this event `f-nand4-monotone-off'.\index{f-nand4-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nand3-monotone; name this event `f-nand3-monotone-off'.\index{f-nand3-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nand-monotone; name this event `f-nand-monotone-off'.\index{f-nand-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-not-monotone; name this event `f-not-monotone-off'.\index{f-not-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-and4-monotone; name this event `f-and4-monotone-off'.\index{f-and4-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-and3-monotone; name this event `f-and3-monotone-off'.\index{f-and3-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-and-monotone; name this event `f-and-monotone-off'.\index{f-and-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-buf-monotone; name this event `f-buf-monotone-off'.\index{f-buf-monotone-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable monotonicity-property-consequence-3; name this event `monotonicity-property-consequence-3-off'.\index{monotonicity-property-consequen!ce-3-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable monotonicity-property-consequence-2; name this event `monotonicity-property-consequence-2-off'.\index{monotonicity-property-consequen!ce-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable monotonicity-property-consequence-1; name this event `monotonicity-property-consequence-1-off'.\index{monotonicity-property-consequen!ce-1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable monotonicity-property-consequence-0; name this event `monotonicity-property-consequence-0-off'.\index{monotonicity-property-consequen!ce-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*monotonicity-property; name this event `g*1*monotonicity-property-off'.\index{g*1*monotonicity-property-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-alist; name this event `s-approx-alist-off'.\index{s-approx-alist-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*s-approx-alist; name this event `g*1*s-approx-alist-off'.\index{g*1*s-approx-alist-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-alist; name this event `v-approx-alist-off'.\index{v-approx-alist-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-approx-alist; name this event `g*1*v-approx-alist-off'.\index{g*1*v-approx-alist-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-knownp-implies-s-approx-is-equal; name this event `s-knownp-implies-s-approx-is-equal-off1'.\index{s-knownp-implies-s-approx-is-eq!ual-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-knownp; name this event `s-knownp-off1'.\index{s-knownp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*s-knownp; name this event `g*1*s-knownp-off'.\index{g*1*s-knownp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable good-s; name this event `good-s-off'.\index{good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*good-s; name this event `g*1*good-s-off'.\index{g*1*good-s-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-x-x; name this event `s-approx-x-x-off'.\index{s-approx-x-x-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx; name this event `s-approx-off1'.\index{s-approx-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*s-approx; name this event `g*1*s-approx-off'.\index{g*1*s-approx-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable mem-width; name this event `mem-width-off1'.\index{mem-width-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*mem-width; name this event `g*1*mem-width-off1'.\index{g*1*mem-width-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-knownp-implies-v-approx-is-equal; name this event `v-knownp-implies-v-approx-is-equal-off'.\index{v-knownp-implies-v-approx-is-eq!ual-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-knownp; name this event `v-knownp-off1'.\index{v-knownp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-knownp; name this event `g*1*v-knownp-off'.\index{g*1*v-knownp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx; name this event `v-approx-off1'.\index{v-approx-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-approx; name this event `g*1*v-approx-off'.\index{g*1*v-approx-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*b-approx; name this event `g*1*b-approx-off'.\index{g*1*b-approx-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-knownp-compound-recognizer; name this event `b-knownp-compound-recognizer-off'.\index{b-knownp-compound-recognizer-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Disable monotonicity-property; name this event `monotonicity-property-on'.\index{monotonicity-property-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable monotonicity-property-opener-0; name this event `monotonicity-property-opener-0-on'.\index{monotonicity-property-opener-0-!on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable monotonicity-property-opener-1; name this event `monotonicity-property-opener-1-on'.\index{monotonicity-property-opener-1-!on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable monotonicity-property-opener-2; name this event `monotonicity-property-opener-2-on'.\index{monotonicity-property-opener-2-!on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable monotonicity-property-opener-3; name this event `monotonicity-property-opener-3-on'.\index{monotonicity-property-opener-3-!on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-buf; name this event `f-buf-on'.\index{f-buf-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-and; name this event `f-and-on'.\index{f-and-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-and3; name this event `f-and3-on'.\index{f-and3-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-and4; name this event `f-and4-on'.\index{f-and4-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-not; name this event `f-not-on'.\index{f-not-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nand; name this event `f-nand-on'.\index{f-nand-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nand3; name this event `f-nand3-on'.\index{f-nand3-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nand4; name this event `f-nand4-on'.\index{f-nand4-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nand5; name this event `f-nand5-on'.\index{f-nand5-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nand6; name this event `f-nand6-on'.\index{f-nand6-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nand8; name this event `f-nand8-on'.\index{f-nand8-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-or; name this event `f-or-on'.\index{f-or-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-or3; name this event `f-or3-on'.\index{f-or3-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-or4; name this event `f-or4-on'.\index{f-or4-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nor; name this event `f-nor-on'.\index{f-nor-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nor3; name this event `f-nor3-on'.\index{f-nor3-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nor4; name this event `f-nor4-on'.\index{f-nor4-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nor5; name this event `f-nor5-on'.\index{f-nor5-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nor6; name this event `f-nor6-on'.\index{f-nor6-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nor8; name this event `f-nor8-on'.\index{f-nor8-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-xor; name this event `f-xor-on'.\index{f-xor-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-xor3; name this event `f-xor3-on'.\index{f-xor3-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-equv; name this event `f-equv-on'.\index{f-equv-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-equv3; name this event `f-equv3-on'.\index{f-equv3-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-if; name this event `f-if-on'.\index{f-if-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ft-buf; name this event `ft-buf-on'.\index{ft-buf-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ft-wire; name this event `ft-wire-on'.\index{ft-wire-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-pullup; name this event `f-pullup-on'.\index{f-pullup-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable bvp-reverse; name this event `bvp-reverse-on'.\index{bvp-reverse-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-approx-bvp; name this event `v-approx-bvp-on'.\index{v-approx-bvp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable read-mem1-monotone; name this event `read-mem1-monotone-on'.\index{read-mem1-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable bvp-implies-v-knownp; name this event `bvp-implies-v-knownp-on'.\index{bvp-implies-v-knownp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-approx-implies-b-approx-nth; name this event `v-approx-implies-b-approx-nth-on'.\index{v-approx-implies-b-approx-nth-o!n}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*b-knownp; name this event `g*1*b-knownp-on1'.\index{g*1*b-knownp-on1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-approx-implies-subranges-equal; name this event `v-approx-implies-subranges-equal-on'.\index{v-approx-implies-subranges-equa!l-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-approx-bvp-subrange; name this event `v-approx-bvp-subrange-on'.\index{v-approx-bvp-subrange-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-approx-make-list-x; name this event `v-approx-make-list-x-on'.\index{v-approx-make-list-x-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable read-mem-monotone; name this event `read-mem-monotone-on'.\index{read-mem-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-length-read-mem1; name this event `equal-length-read-mem1-on'.\index{equal-length-read-mem1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-length-read-mem; name this event `equal-length-read-mem-on'.\index{equal-length-read-mem-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx-implies-properp-read-mem1; name this event `s-approx-implies-properp-read-mem1-on'.\index{s-approx-implies-properp-read-me!m1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx-implies-properp-read-mem; name this event `s-approx-implies-properp-read-mem-on'.\index{s-approx-implies-properp-read-me!m-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-port-ram-value-monotone; name this event `dual-port-ram-value-monotone-on'.\index{dual-port-ram-value-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable eval\$-append; name this event `eval\$-append-on'.\index{eval\$-append-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable eval\$-pairlist-cons; name this event `eval\$-pairlist-cons-on'.\index{eval\$-pairlist-cons-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable eval\$-append-2; name this event `eval\$-append-2-on'.\index{eval\$-append-2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-apply-value-dp-ram-16x32-lemma-1; name this event `dual-apply-value-dp-ram-16x32-lemma-1-on'.\index{dual-apply-value-dp-ram-16x32-le!mma-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-apply-value-dp-ram-16x32-lemma-2; name this event `dual-apply-value-dp-ram-16x32-lemma-2-on'.\index{dual-apply-value-dp-ram-16x32-le!mma-2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-apply-value-dp-ram-16x32-lemma-3; name this event `dual-apply-value-dp-ram-16x32-lemma-3-on'.\index{dual-apply-value-dp-ram-16x32-le!mma-3-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-port-ram-value-is-dual-port-ram-value-body; name this event `dual-port-ram-value-is-dual-port-ram-value-body-on'.\index{dual-port-ram-value-is-dual-port!-ram-value-body-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-apply-value-dp-ram-16x32; name this event `dual-apply-value-dp-ram-16x32-on'.\index{dual-apply-value-dp-ram-16x32-o!n}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dp-ram-16x32-monotone-value; name this event `dp-ram-16x32-monotone-value-on'.\index{dp-ram-16x32-monotone-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Enable bvp; name this event `bvp-off2'.\index{bvp-off2}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx-opener; name this event `s-approx-opener-on'.\index{s-approx-opener-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-approx-implies-nth-does-not-go-from-f-to-t; name this event `v-approx-implies-nth-does-not-go-from-f-to-t-on'.\index{v-approx-implies-nth-does-not-g!o-from-f-to-t-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable write-mem1-opener; name this event `write-mem1-opener-on'.\index{write-mem1-opener-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable write-mem1-monotone; name this event `write-mem1-monotone-on'.\index{write-mem1-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable write-mem-monotone; name this event `write-mem-monotone-on'.\index{write-mem-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-approx-length; name this event `v-approx-length-on'.\index{v-approx-length-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx-write-mem1-id; name this event `s-approx-write-mem1-id-on'.\index{s-approx-write-mem1-id-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx-write-mem-id; name this event `s-approx-write-mem-id-on'.\index{s-approx-write-mem-id-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx-constant-ram-x-id; name this event `s-approx-constant-ram-x-id-on'.\index{s-approx-constant-ram-x-id-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx-constant-ram-x-constant-ram-x; name this event `s-approx-constant-ram-x-constant-ram-x-on'.\index{s-approx-constant-ram-x-constant!-ram-x-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-approx-preserves-length; name this event `v-approx-preserves-length-on'.\index{v-approx-preserves-length-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-approx-subrange; name this event `v-approx-subrange-on'.\index{v-approx-subrange-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable mem-width-non-zero; name this event `mem-width-non-zero-on'.\index{mem-width-non-zero-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx-constant-ram-x-write-mem1-case-3; name this event `s-approx-constant-ram-x-write-mem1-case-3-on'.\index{s-approx-constant-ram-x-write-me!m1-case-3-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx-constant-ram-x-write-mem1; name this event `s-approx-constant-ram-x-write-mem1-on'.\index{s-approx-constant-ram-x-write-me!m1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx-constant-ram-x-write-mem; name this event `s-approx-constant-ram-x-write-mem-on'.\index{s-approx-constant-ram-x-write-me!m-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-approx-preserves-properp; name this event `v-approx-preserves-properp-on'.\index{v-approx-preserves-properp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable mem-width-linear-facts; name this event `mem-width-linear-facts-on'.\index{mem-width-linear-facts-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-port-ram-state-monotone-rewrite; name this event `dual-port-ram-state-monotone-rewrite-on'.\index{dual-port-ram-state-monotone-re!write-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-apply-state-dp-ram-16x32-lemma-1; name this event `dual-apply-state-dp-ram-16x32-lemma-1-on'.\index{dual-apply-state-dp-ram-16x32-le!mma-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-apply-state-dp-ram-16x32-lemma-2; name this event `dual-apply-state-dp-ram-16x32-lemma-2-on'.\index{dual-apply-state-dp-ram-16x32-le!mma-2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-apply-state-dp-ram-16x32-lemma-3; name this event `dual-apply-state-dp-ram-16x32-lemma-3-on'.\index{dual-apply-state-dp-ram-16x32-le!mma-3-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-port-ram-state-is-dual-port-ram-state-body; name this event `dual-port-ram-state-is-dual-port-ram-state-body-on'.\index{dual-port-ram-state-is-dual-port!-ram-state-body-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-apply-state-dp-ram-16x32; name this event `dual-apply-state-dp-ram-16x32-on'.\index{dual-apply-state-dp-ram-16x32-o!n}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dp-ram-16x32-monotone-state; name this event `dp-ram-16x32-monotone-state-on'.\index{dp-ram-16x32-monotone-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dp-ram-16x32-monotone; name this event `dp-ram-16x32-monotone-on'.\index{dp-ram-16x32-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Enable open-nth; name this event `open-nth-off1'.\index{open-nth-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable doublet-p; name this event `doublet-p-on'.\index{doublet-p-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable for-final-1-of-reset-sequence-chip; name this event `for-final-1-of-reset-sequence-chip-on'.\index{for-final-1-of-reset-sequence-c!hip-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable map-down-inverts-map-up; name this event `map-down-inverts-map-up-on'.\index{map-down-inverts-map-up-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-knownp; name this event `b-knownp-on1'.\index{b-knownp-on1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-approx; name this event `b-approx-on1'.\index{b-approx-on1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-constants-ilessp; name this event `cancel-constants-ilessp-on'.\index{cancel-constants-ilessp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-constants-ilessp-lemma-2; name this event `cancel-constants-ilessp-lemma-2-on'.\index{cancel-constants-ilessp-lemma-2!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-constants-ilessp-lemma-1; name this event `cancel-constants-ilessp-lemma-1-on'.\index{cancel-constants-ilessp-lemma-1!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ilessp-add1-iplus; name this event `ilessp-add1-iplus-on'.\index{ilessp-add1-iplus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ilessp-add1; name this event `ilessp-add1-on'.\index{ilessp-add1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-constants-equal; name this event `cancel-constants-equal-on'.\index{cancel-constants-equal-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-constants-equal-lemma; name this event `cancel-constants-equal-lemma-on'.\index{cancel-constants-equal-lemma-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-constants; name this event `iplus-constants-on'.\index{iplus-constants-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable correctness-of-cancel-ineg-terms-from-inequality; name this event `correctness-of-cancel-ineg-terms-from-inequality-on'.\index{correctness-of-cancel-ineg-term!s-from-inequality-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-ineg-terms-from-inequality-cancel-ineg-terms-from-inequality-expanded; name this event `cancel-ineg-terms-from-inequality-cancel-ineg-terms-from-inequality-expanded-on'.\index{cancel-ineg-terms-from-inequalit!y-cancel-ineg-terms-from-inequality-expanded-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-ineg-terms-from-inequality-expanded; name this event `g*1*cancel-ineg-terms-from-inequality-expanded-on'.\index{g*1*cancel-ineg-terms-from-ineq!uality-expanded-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-ineg-terms-from-inequality; name this event `cancel-ineg-terms-from-inequality-on'.\index{cancel-ineg-terms-from-inequalit!y-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-ineg-terms-from-inequality; name this event `g*1*cancel-ineg-terms-from-inequality-on'.\index{g*1*cancel-ineg-terms-from-ineq!uality-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable make-cancel-ineg-terms-inequality; name this event `make-cancel-ineg-terms-inequality-on'.\index{make-cancel-ineg-terms-inequalit!y-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*make-cancel-ineg-terms-inequality; name this event `g*1*make-cancel-ineg-terms-inequality-on'.\index{g*1*make-cancel-ineg-terms-ineq!uality-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable correctness-of-cancel-ineg-terms-from-equality; name this event `correctness-of-cancel-ineg-terms-from-equality-on'.\index{correctness-of-cancel-ineg-term!s-from-equality-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-list-eval\$-car-split-out-ineg-terms; name this event `iplus-list-eval\$-car-split-out-ineg-terms-on'.\index{iplus-list-eval\$-car-split-out!-ineg-terms-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable eval\$-iplus-list-cdr-remove-inegs; name this event `eval\$-iplus-list-cdr-remove-inegs-on'.\index{eval\$-iplus-list-cdr-remove-ine!gs-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable eval\$-iplus-list-car-remove-inegs; name this event `eval\$-iplus-list-car-remove-inegs-on'.\index{eval\$-iplus-list-car-remove-ine!gs-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-ineg-terms-from-equality-cancel-ineg-terms-from-equality-expanded; name this event `cancel-ineg-terms-from-equality-cancel-ineg-terms-from-equality-expanded-on'.\index{cancel-ineg-terms-from-equality!-cancel-ineg-terms-from-equality-expanded-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-ineg-terms-from-equality-expanded; name this event `g*1*cancel-ineg-terms-from-equality-expanded-on'.\index{g*1*cancel-ineg-terms-from-equa!lity-expanded-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-ineg-terms-from-equality; name this event `cancel-ineg-terms-from-equality-on'.\index{cancel-ineg-terms-from-equality!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-ineg-terms-from-equality; name this event `g*1*cancel-ineg-terms-from-equality-on'.\index{g*1*cancel-ineg-terms-from-equa!lity-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable make-cancel-ineg-terms-equality; name this event `make-cancel-ineg-terms-equality-on'.\index{make-cancel-ineg-terms-equality!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*make-cancel-ineg-terms-equality; name this event `g*1*make-cancel-ineg-terms-equality-on'.\index{g*1*make-cancel-ineg-terms-equa!lity-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*iplus-or-ineg-term; name this event `g*1*iplus-or-ineg-term-on'.\index{g*1*iplus-or-ineg-term-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*remove-inegs; name this event `g*1*remove-inegs-on'.\index{g*1*remove-inegs-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable split-out-ineg-terms; name this event `split-out-ineg-terms-on'.\index{split-out-ineg-terms-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*split-out-ineg-terms; name this event `g*1*split-out-ineg-terms-on'.\index{g*1*split-out-ineg-terms-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable correctness-of-cancel-factors-ilessp-0; name this event `correctness-of-cancel-factors-ilessp-0-on'.\index{correctness-of-cancel-factors-i!lessp-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable conjoin-inequalities-with-0-eliminator; name this event `conjoin-inequalities-with-0-eliminator-on'.\index{conjoin-inequalities-with-0-eli!minator-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-factors-ilessp-0; name this event `cancel-factors-ilessp-0-on'.\index{cancel-factors-ilessp-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-factors-ilessp-0; name this event `g*1*cancel-factors-ilessp-0-on'.\index{g*1*cancel-factors-ilessp-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable conjoin-inequalities-with-0; name this event `conjoin-inequalities-with-0-on'.\index{conjoin-inequalities-with-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*conjoin-inequalities-with-0; name this event `g*1*conjoin-inequalities-with-0-on'.\index{g*1*conjoin-inequalities-with-0!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable correctness-of-cancel-factors-0; name this event `correctness-of-cancel-factors-0-on'.\index{correctness-of-cancel-factors-0!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable some-eval\$s-to-0-eliminator; name this event `some-eval\$s-to-0-eliminator-on'.\index{some-eval\$s-to-0-eliminator-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable some-eval\$s-to-0-append; name this event `some-eval\$s-to-0-append-on'.\index{some-eval\$s-to-0-append-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable eval\$-disjoin-equalities-with-0; name this event `eval\$-disjoin-equalities-with-0-on'.\index{eval\$-disjoin-equalities-with-!0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable some-eval\$s-to-0; name this event `some-eval\$s-to-0-on'.\index{some-eval\$s-to-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*some-eval\$s-to-0; name this event `g*1*some-eval\$s-to-0-on'.\index{g*1*some-eval\$s-to-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-factors-0; name this event `cancel-factors-0-on'.\index{cancel-factors-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-factors-0; name this event `g*1*cancel-factors-0-on'.\index{g*1*cancel-factors-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable disjoin-equalities-with-0; name this event `disjoin-equalities-with-0-on'.\index{disjoin-equalities-with-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*disjoin-equalities-with-0; name this event `g*1*disjoin-equalities-with-0-on'.\index{g*1*disjoin-equalities-with-0-o!n}

\addvspace{18pt}


\noindent{\sc Event}:   Disable correctness-of-cancel-itimes-ilessp-factors; name this event `correctness-of-cancel-itimes-ilessp-factors-on'.\index{correctness-of-cancel-itimes-ile!ssp-factors-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-fix-int-to-ilessp; name this event `equal-fix-int-to-ilessp-on'.\index{equal-fix-int-to-ilessp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable eval\$-list-bagint-0-implies-equal-for-ilessp-lemma; name this event `eval\$-list-bagint-0-implies-equal-for-ilessp-lemma-on'.\index{eval\$-list-bagint-0-implies-eq!ual-for-ilessp-lemma-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable eval\$-list-bagint-0-for-ilessp; name this event `eval\$-list-bagint-0-for-ilessp-on'.\index{eval\$-list-bagint-0-for-ilessp!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable member-0-itimes-factors-yields-0-ilessp-consequence-2; name this event `member-0-itimes-factors-yields-0-ilessp-consequence-2-on'.\index{member-0-itimes-factors-yields-!0-ilessp-consequence-2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable member-0-itimes-factors-yields-0-ilessp-consequence-1; name this event `member-0-itimes-factors-yields-0-ilessp-consequence-1-on'.\index{member-0-itimes-factors-yields-!0-ilessp-consequence-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable member-0-itimes-factors-yields-0; name this event `member-0-itimes-factors-yields-0-on'.\index{member-0-itimes-factors-yields-!0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ilessp-itimes-list-eval\$-list-bagdiff-corollary-2; name this event `ilessp-itimes-list-eval\$-list-bagdiff-corollary-2-on'.\index{ilessp-itimes-list-eval\$-list-!bagdiff-corollary-2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ilessp-zero-implies-not-equal; name this event `ilessp-zero-implies-not-equal-on'.\index{ilessp-zero-implies-not-equal-o!n}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ilessp-itimes-list-eval\$-list-bagdiff-corollary-1; name this event `ilessp-itimes-list-eval\$-list-bagdiff-corollary-1-on'.\index{ilessp-itimes-list-eval\$-list-!bagdiff-corollary-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable zero-ilessp-implies-not-equal; name this event `zero-ilessp-implies-not-equal-on'.\index{zero-ilessp-implies-not-equal-o!n}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ilessp-itimes-list-eval\$-list-bagdiff; name this event `ilessp-itimes-list-eval\$-list-bagdiff-on'.\index{ilessp-itimes-list-eval\$-list-!bagdiff-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable bagint-singleton; name this event `bagint-singleton-on'.\index{bagint-singleton-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-itimes-ilessp-factors; name this event `cancel-itimes-ilessp-factors-on'.\index{cancel-itimes-ilessp-factors-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-itimes-ilessp-factors; name this event `g*1*cancel-itimes-ilessp-factors-on'.\index{g*1*cancel-itimes-ilessp-factor!s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable correctness-of-cancel-itimes-factors; name this event `correctness-of-cancel-itimes-factors-on'.\index{correctness-of-cancel-itimes-fa!ctors-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable member-0-eval\$-list; name this event `member-0-eval\$-list-on'.\index{member-0-eval\$-list-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable membership-of-0-implies-itimes-list-is-0; name this event `membership-of-0-implies-itimes-list-is-0-on'.\index{membership-of-0-implies-itimes-!list-is-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-itimes-factors-expanded-cancel-itimes-factors; name this event `cancel-itimes-factors-expanded-cancel-itimes-factors-on'.\index{cancel-itimes-factors-expanded-!cancel-itimes-factors-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-itimes-factors-expanded; name this event `g*1*cancel-itimes-factors-expanded-on'.\index{g*1*cancel-itimes-factors-expan!ded-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-itimes-factors; name this event `cancel-itimes-factors-on'.\index{cancel-itimes-factors-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-itimes-factors; name this event `g*1*cancel-itimes-factors-on'.\index{g*1*cancel-itimes-factors-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*iplus-or-itimes-term; name this event `g*1*iplus-or-itimes-term-on'.\index{g*1*iplus-or-itimes-term-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable itimes-eval\$-itimes-tree-ineg; name this event `itimes-eval\$-itimes-tree-ineg-on'.\index{itimes-eval\$-itimes-tree-ineg-!on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-eval\$-itimes-tree-ineg; name this event `iplus-eval\$-itimes-tree-ineg-on'.\index{iplus-eval\$-itimes-tree-ineg-o!n}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ineg-eval\$-itimes-tree-ineg; name this event `ineg-eval\$-itimes-tree-ineg-on'.\index{ineg-eval\$-itimes-tree-ineg-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable eval\$-itimes-tree-ineg; name this event `eval\$-itimes-tree-ineg-on'.\index{eval\$-itimes-tree-ineg-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fix-int-eval\$-itimes-tree-rec; name this event `fix-int-eval\$-itimes-tree-rec-on'.\index{fix-int-eval\$-itimes-tree-rec-!on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ilessp-ineg-ineg; name this event `ilessp-ineg-ineg-on'.\index{ilessp-ineg-ineg-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-ineg-ineg; name this event `equal-ineg-ineg-on'.\index{equal-ineg-ineg-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable itimes--1; name this event `itimes--1-on'.\index{itimes--1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable itimes-factors; name this event `itimes-factors-on'.\index{itimes-factors-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*itimes-factors; name this event `g*1*itimes-factors-on'.\index{g*1*itimes-factors-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*itimes-tree-ineg; name this event `g*1*itimes-tree-ineg-on'.\index{g*1*itimes-tree-ineg-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ilessp-strict; name this event `ilessp-strict-on'.\index{ilessp-strict-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ilessp-itimes-right-negative; name this event `ilessp-itimes-right-negative-on'.\index{ilessp-itimes-right-negative-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ilessp-itimes-right-positive; name this event `ilessp-itimes-right-positive-on'.\index{ilessp-itimes-right-positive-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-itimes-ilessp; name this event `cancel-itimes-ilessp-on'.\index{cancel-itimes-ilessp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-itimes-ilessp; name this event `g*1*cancel-itimes-ilessp-on'.\index{g*1*cancel-itimes-ilessp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*make-cancel-itimes-inequality; name this event `g*1*make-cancel-itimes-inequality-on'.\index{g*1*make-cancel-itimes-inequalit!y-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*itimes-tree-no-fix-int; name this event `g*1*itimes-tree-no-fix-int-on'.\index{g*1*itimes-tree-no-fix-int-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable subsetp; name this event `subsetp-on'.\index{subsetp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*subsetp; name this event `g*1*subsetp-on'.\index{g*1*subsetp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-fix-int; name this event `equal-fix-int-on'.\index{equal-fix-int-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable member-append; name this event `member-append-on'.\index{member-append-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable itimes-list-append; name this event `itimes-list-append-on'.\index{itimes-list-append-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-itimes; name this event `cancel-itimes-on'.\index{cancel-itimes-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-itimes; name this event `g*1*cancel-itimes-on'.\index{g*1*cancel-itimes-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*make-cancel-itimes-equality; name this event `g*1*make-cancel-itimes-equality-on'.\index{g*1*make-cancel-itimes-equality!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable integerp-itimes-list; name this event `integerp-itimes-list-on'.\index{integerp-itimes-list-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable itimes-list; name this event `itimes-list-on'.\index{itimes-list-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*itimes-list; name this event `g*1*itimes-list-on'.\index{g*1*itimes-list-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*itimes-tree; name this event `g*1*itimes-tree-on'.\index{g*1*itimes-tree-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable itimes-tree-rec; name this event `itimes-tree-rec-on'.\index{itimes-tree-rec-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*itimes-tree-rec; name this event `g*1*itimes-tree-rec-on'.\index{g*1*itimes-tree-rec-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable itimes-fringe; name this event `itimes-fringe-on'.\index{itimes-fringe-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*itimes-fringe; name this event `g*1*itimes-fringe-on'.\index{g*1*itimes-fringe-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fix-int-irem; name this event `fix-int-irem-on'.\index{fix-int-irem-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fix-int-iquo; name this event `fix-int-iquo-on'.\index{fix-int-iquo-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fix-int-imod; name this event `fix-int-imod-on'.\index{fix-int-imod-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fix-int-idiv; name this event `fix-int-idiv-on'.\index{fix-int-idiv-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fix-int-iremainder; name this event `fix-int-iremainder-on'.\index{fix-int-iremainder-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fix-int-iquotient; name this event `fix-int-iquotient-on'.\index{fix-int-iquotient-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable irem-fix-int2; name this event `irem-fix-int2-on'.\index{irem-fix-int2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable irem-fix-int1; name this event `irem-fix-int1-on'.\index{irem-fix-int1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iquo-fix-int2; name this event `iquo-fix-int2-on'.\index{iquo-fix-int2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iquo-fix-int1; name this event `iquo-fix-int1-on'.\index{iquo-fix-int1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable imod-fix-int2; name this event `imod-fix-int2-on'.\index{imod-fix-int2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable imod-fix-int1; name this event `imod-fix-int1-on'.\index{imod-fix-int1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable idiv-fix-int2; name this event `idiv-fix-int2-on'.\index{idiv-fix-int2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable idiv-fix-int1; name this event `idiv-fix-int1-on'.\index{idiv-fix-int1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iremainder-fix-int2; name this event `iremainder-fix-int2-on'.\index{iremainder-fix-int2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iremainder-fix-int1; name this event `iremainder-fix-int1-on'.\index{iremainder-fix-int1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iquotient-fix-int2; name this event `iquotient-fix-int2-on'.\index{iquotient-fix-int2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iquotient-fix-int1; name this event `iquotient-fix-int1-on'.\index{iquotient-fix-int1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable integerp-irem; name this event `integerp-irem-on'.\index{integerp-irem-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable integerp-iquo; name this event `integerp-iquo-on'.\index{integerp-iquo-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable integerp-imod; name this event `integerp-imod-on'.\index{integerp-imod-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable integerp-idiv; name this event `integerp-idiv-on'.\index{integerp-idiv-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable integerp-iremainder; name this event `integerp-iremainder-on'.\index{integerp-iremainder-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable integerp-iquotient; name this event `integerp-iquotient-on'.\index{integerp-iquotient-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable itimes-cancellation-3; name this event `itimes-cancellation-3-on'.\index{itimes-cancellation-3-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable itimes-cancellation-2; name this event `itimes-cancellation-2-on'.\index{itimes-cancellation-2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable itimes-cancellation-1; name this event `itimes-cancellation-1-on'.\index{itimes-cancellation-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable itimes-ineg-2; name this event `itimes-ineg-2-on'.\index{itimes-ineg-2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable itimes-ineg-1; name this event `itimes-ineg-1-on'.\index{itimes-ineg-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iquo-irem-uniqueness; name this event `iquo-irem-uniqueness-on'.\index{iquo-irem-uniqueness-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable division-theorem-for-truncate-to-zero; name this event `division-theorem-for-truncate-to-zero-on'.\index{division-theorem-for-truncate-t!o-zero-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable division-theorem-for-truncate-to-zero-part3; name this event `division-theorem-for-truncate-to-zero-part3-on'.\index{division-theorem-for-truncate-t!o-zero-part3-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable division-theorem-for-truncate-to-zero-part2; name this event `division-theorem-for-truncate-to-zero-part2-on'.\index{division-theorem-for-truncate-t!o-zero-part2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable division-theorem-for-truncate-to-zero-part1; name this event `division-theorem-for-truncate-to-zero-part1-on'.\index{division-theorem-for-truncate-t!o-zero-part1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable idiv-imod-uniqueness; name this event `idiv-imod-uniqueness-on'.\index{idiv-imod-uniqueness-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable division-theorem-for-truncate-to-neginf; name this event `division-theorem-for-truncate-to-neginf-on'.\index{division-theorem-for-truncate-t!o-neginf-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable division-theorem-for-truncate-to-neginf-part3; name this event `division-theorem-for-truncate-to-neginf-part3-on'.\index{division-theorem-for-truncate-t!o-neginf-part3-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable division-theorem-for-truncate-to-neginf-part2; name this event `division-theorem-for-truncate-to-neginf-part2-on'.\index{division-theorem-for-truncate-t!o-neginf-part2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable division-theorem-for-truncate-to-neginf-part1; name this event `division-theorem-for-truncate-to-neginf-part1-on'.\index{division-theorem-for-truncate-t!o-neginf-part1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iquotient-iremainder-uniqueness; name this event `iquotient-iremainder-uniqueness-on'.\index{iquotient-iremainder-uniqueness!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable division-theorem; name this event `division-theorem-on'.\index{division-theorem-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable division-theorem-part3; name this event `division-theorem-part3-on'.\index{division-theorem-part3-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable division-theorem-part2; name this event `division-theorem-part2-on'.\index{division-theorem-part2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable division-theorem-part1; name this event `division-theorem-part1-on'.\index{division-theorem-part1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-remainder-uniqueness; name this event `quotient-remainder-uniqueness-on'.\index{quotient-remainder-uniqueness-o!n}

\addvspace{18pt}


\noindent{\sc Event}:   Disable itimes-1-arg1; name this event `itimes-1-arg1-on'.\index{itimes-1-arg1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-itimes-minus-1; name this event `equal-itimes-minus-1-on'.\index{equal-itimes-minus-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-itimes-1; name this event `equal-itimes-1-on'.\index{equal-itimes-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-itimes-0; name this event `equal-itimes-0-on'.\index{equal-itimes-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable associativity-of-itimes; name this event `associativity-of-itimes-on'.\index{associativity-of-itimes-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable commutativity2-of-itimes; name this event `commutativity2-of-itimes-on'.\index{commutativity2-of-itimes-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable itimes-distributes-over-iplus; name this event `itimes-distributes-over-iplus-on'.\index{itimes-distributes-over-iplus-o!n}

\addvspace{18pt}


\noindent{\sc Event}:   Disable itimes-distributes-over-iplus-proof; name this event `itimes-distributes-over-iplus-proof-on'.\index{itimes-distributes-over-iplus-p!roof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable commutativity-of-itimes; name this event `commutativity-of-itimes-on'.\index{commutativity-of-itimes-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable itimes-fix-int2; name this event `itimes-fix-int2-on'.\index{itimes-fix-int2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable itimes-fix-int1; name this event `itimes-fix-int1-on'.\index{itimes-fix-int1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable itimes-0-right; name this event `itimes-0-right-on'.\index{itimes-0-right-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable itimes-0-left; name this event `itimes-0-left-on'.\index{itimes-0-left-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable correctness-of-cancel-iplus-ilessp; name this event `correctness-of-cancel-iplus-ilessp-on'.\index{correctness-of-cancel-iplus-ile!ssp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-iplus-ilessp; name this event `cancel-iplus-ilessp-on'.\index{cancel-iplus-ilessp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-iplus-ilessp; name this event `g*1*cancel-iplus-ilessp-on'.\index{g*1*cancel-iplus-ilessp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*iplus-tree-no-fix-int; name this event `g*1*iplus-tree-no-fix-int-on'.\index{g*1*iplus-tree-no-fix-int-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-cancellation-2-for-ilessp; name this event `iplus-cancellation-2-for-ilessp-on'.\index{iplus-cancellation-2-for-ilessp!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-cancellation-1-for-ilessp; name this event `iplus-cancellation-1-for-ilessp-on'.\index{iplus-cancellation-1-for-ilessp!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-iplus-ilessp-1; name this event `cancel-iplus-ilessp-1-on'.\index{cancel-iplus-ilessp-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-iplus-ilessp-1; name this event `g*1*cancel-iplus-ilessp-1-on'.\index{g*1*cancel-iplus-ilessp-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*make-cancel-iplus-inequality-1; name this event `g*1*make-cancel-iplus-inequality-1-on'.\index{g*1*make-cancel-iplus-inequalit!y-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ilessp-fix-int-2; name this event `ilessp-fix-int-2-on'.\index{ilessp-fix-int-2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ilessp-fix-int-1; name this event `ilessp-fix-int-1-on'.\index{ilessp-fix-int-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable correctness-of-cancel-iplus; name this event `correctness-of-cancel-iplus-on'.\index{correctness-of-cancel-iplus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-ineg7; name this event `iplus-ineg7-on'.\index{iplus-ineg7-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-list-append; name this event `iplus-list-append-on'.\index{iplus-list-append-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable eval\$-iplus-list-delete; name this event `eval\$-iplus-list-delete-on'.\index{eval\$-iplus-list-delete-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-iplus; name this event `g*1*cancel-iplus-on'.\index{g*1*cancel-iplus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable eval\$-list-append; name this event `eval\$-list-append-on'.\index{eval\$-list-append-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable integerp-iplus-list; name this event `integerp-iplus-list-on'.\index{integerp-iplus-list-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-list; name this event `iplus-list-on'.\index{iplus-list-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*iplus-list; name this event `g*1*iplus-list-on'.\index{g*1*iplus-list-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*iplus-tree; name this event `g*1*iplus-tree-on'.\index{g*1*iplus-tree-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-tree-rec; name this event `iplus-tree-rec-on'.\index{iplus-tree-rec-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*iplus-tree-rec; name this event `g*1*iplus-tree-rec-on'.\index{g*1*iplus-tree-rec-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-fringe; name this event `iplus-fringe-on'.\index{iplus-fringe-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*iplus-fringe; name this event `g*1*iplus-fringe-on'.\index{g*1*iplus-fringe-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable correctness-of-cancel-ineg; name this event `correctness-of-cancel-ineg-on'.\index{correctness-of-cancel-ineg-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-x-y-ineg-x; name this event `iplus-x-y-ineg-x-on'.\index{iplus-x-y-ineg-x-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-ineg4; name this event `iplus-ineg4-on'.\index{iplus-ineg4-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-ineg3; name this event `iplus-ineg3-on'.\index{iplus-ineg3-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable eval\$-cancel-ineg-aux-is-its-fn; name this event `eval\$-cancel-ineg-aux-is-its-fn-on'.\index{eval\$-cancel-ineg-aux-is-its-f!n-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable eval\$-cancel-ineg-aux-fn; name this event `eval\$-cancel-ineg-aux-fn-on'.\index{eval\$-cancel-ineg-aux-fn-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*eval\$-cancel-ineg-aux-fn; name this event `g*1*eval\$-cancel-ineg-aux-fn-on'.\index{g*1*eval\$-cancel-ineg-aux-fn-o!n}

\addvspace{18pt}


\noindent{\sc Event}:   Disable eval\$-other; name this event `eval\$-other-on'.\index{eval\$-other-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable eval\$-litatom; name this event `eval\$-litatom-on'.\index{eval\$-litatom-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable eval\$-list-nlistp; name this event `eval\$-list-nlistp-on'.\index{eval\$-list-nlistp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable eval\$-list-cons; name this event `eval\$-list-cons-on'.\index{eval\$-list-cons-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-ineg; name this event `cancel-ineg-on'.\index{cancel-ineg-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-ineg; name this event `g*1*cancel-ineg-on'.\index{g*1*cancel-ineg-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-ineg-aux; name this event `cancel-ineg-aux-on'.\index{cancel-ineg-aux-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-ineg-aux; name this event `g*1*cancel-ineg-aux-on'.\index{g*1*cancel-ineg-aux-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable idifference-fix-int2; name this event `idifference-fix-int2-on'.\index{idifference-fix-int2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable idifference-fix-int1; name this event `idifference-fix-int1-on'.\index{idifference-fix-int1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-fix-int2; name this event `iplus-fix-int2-on'.\index{iplus-fix-int2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-fix-int1; name this event `iplus-fix-int1-on'.\index{iplus-fix-int1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-ineg2; name this event `iplus-ineg2-on'.\index{iplus-ineg2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-ineg1; name this event `iplus-ineg1-on'.\index{iplus-ineg1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-cancellation-2; name this event `iplus-cancellation-2-on'.\index{iplus-cancellation-2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-cancellation-1; name this event `iplus-cancellation-1-on'.\index{iplus-cancellation-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable associativity-of-iplus; name this event `associativity-of-iplus-on'.\index{associativity-of-iplus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable commutativity-of-iplus; name this event `commutativity-of-iplus-on'.\index{commutativity-of-iplus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable commutativity2-of-iplus; name this event `commutativity2-of-iplus-on'.\index{commutativity2-of-iplus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-0-right; name this event `iplus-0-right-on'.\index{iplus-0-right-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-0-left; name this event `iplus-0-left-on'.\index{iplus-0-left-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ineg-0; name this event `ineg-0-on'.\index{ineg-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ineg-fix-int; name this event `ineg-fix-int-on'.\index{ineg-fix-int-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ineg-ineg; name this event `ineg-ineg-on'.\index{ineg-ineg-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ineg-iplus; name this event `ineg-iplus-on'.\index{ineg-iplus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fix-int-itimes; name this event `fix-int-itimes-on'.\index{fix-int-itimes-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fix-int-iabs; name this event `fix-int-iabs-on'.\index{fix-int-iabs-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fix-int-ineg; name this event `fix-int-ineg-on'.\index{fix-int-ineg-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fix-int-idifference; name this event `fix-int-idifference-on'.\index{fix-int-idifference-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fix-int-iplus; name this event `fix-int-iplus-on'.\index{fix-int-iplus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fix-int-fix-int; name this event `fix-int-fix-int-on'.\index{fix-int-fix-int-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fix-int-remover; name this event `fix-int-remover-on'.\index{fix-int-remover-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable integerp-itimes; name this event `integerp-itimes-on'.\index{integerp-itimes-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable integerp-iabs; name this event `integerp-iabs-on'.\index{integerp-iabs-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable integerp-ineg; name this event `integerp-ineg-on'.\index{integerp-ineg-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable integerp-idifference; name this event `integerp-idifference-on'.\index{integerp-idifference-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable integerp-iplus; name this event `integerp-iplus-on'.\index{integerp-iplus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable integerp-fix-int; name this event `integerp-fix-int-on'.\index{integerp-fix-int-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*irem; name this event `g*1*irem-on'.\index{g*1*irem-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*iquo; name this event `g*1*iquo-on'.\index{g*1*iquo-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*imod; name this event `g*1*imod-on'.\index{g*1*imod-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*idiv; name this event `g*1*idiv-on'.\index{g*1*idiv-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*iremainder; name this event `g*1*iremainder-on'.\index{g*1*iremainder-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*iquotient; name this event `g*1*iquotient-on'.\index{g*1*iquotient-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*itimes; name this event `g*1*itimes-on'.\index{g*1*itimes-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*iabs; name this event `g*1*iabs-on'.\index{g*1*iabs-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable idifference; name this event `idifference-on'.\index{idifference-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*idifference; name this event `g*1*idifference-on'.\index{g*1*idifference-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*ineg; name this event `g*1*ineg-on'.\index{g*1*ineg-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*iplus; name this event `g*1*iplus-on'.\index{g*1*iplus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ileq; name this event `ileq-on'.\index{ileq-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*ileq; name this event `g*1*ileq-on'.\index{g*1*ileq-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*ilessp; name this event `g*1*ilessp-on'.\index{g*1*ilessp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable izerop; name this event `izerop-on'.\index{izerop-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*izerop; name this event `g*1*izerop-on'.\index{g*1*izerop-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*fix-int; name this event `g*1*fix-int-on'.\index{g*1*fix-int-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*integerp; name this event `g*1*integerp-on'.\index{g*1*integerp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable gcd-idempotence; name this event `gcd-idempotence-on'.\index{gcd-idempotence-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable gcd-x-x; name this event `gcd-x-x-on'.\index{gcd-x-x-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable commutativity2-of-gcd; name this event `commutativity2-of-gcd-on'.\index{commutativity2-of-gcd-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable commutativity2-of-gcd-zero-case; name this event `commutativity2-of-gcd-zero-case-on'.\index{commutativity2-of-gcd-zero-case!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable associativity-of-gcd; name this event `associativity-of-gcd-on'.\index{associativity-of-gcd-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable associativity-of-gcd-zero-case; name this event `associativity-of-gcd-zero-case-on'.\index{associativity-of-gcd-zero-case-!on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable common-divisor-divides-gcd; name this event `common-divisor-divides-gcd-on'.\index{common-divisor-divides-gcd-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable gcd-is-the-greatest; name this event `gcd-is-the-greatest-on'.\index{gcd-is-the-greatest-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable distributivity-of-times-over-gcd; name this event `distributivity-of-times-over-gcd-on'.\index{distributivity-of-times-over-gc!d-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable distributivity-of-times-over-gcd-proof; name this event `distributivity-of-times-over-gcd-proof-on'.\index{distributivity-of-times-over-gc!d-proof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-gcd; name this event `remainder-gcd-on'.\index{remainder-gcd-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable gcd-plus-instance; name this event `gcd-plus-instance-on'.\index{gcd-plus-instance-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable gcd-plus; name this event `gcd-plus-on'.\index{gcd-plus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable gcd-plus-proof; name this event `gcd-plus-proof-on'.\index{gcd-plus-proof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable gcd-plus-instance-temp; name this event `gcd-plus-instance-temp-on'.\index{gcd-plus-instance-temp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable gcd-plus-instance-temp-proof; name this event `gcd-plus-instance-temp-proof-on'.\index{gcd-plus-instance-temp-proof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable lessp-gcd; name this event `lessp-gcd-on'.\index{lessp-gcd-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-gcd-0; name this event `equal-gcd-0-on'.\index{equal-gcd-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable gcd-1; name this event `gcd-1-on'.\index{gcd-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable gcd-0; name this event `gcd-0-on'.\index{gcd-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable single-number-induction; name this event `single-number-induction-on'.\index{single-number-induction-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*single-number-induction; name this event `g*1*single-number-induction-on'.\index{g*1*single-number-induction-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable commutativity-of-gcd; name this event `commutativity-of-gcd-on'.\index{commutativity-of-gcd-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable log-exp; name this event `log-exp-on'.\index{log-exp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable log-times-exp; name this event `log-times-exp-on'.\index{log-times-exp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable log-times-exp-proof; name this event `log-times-exp-proof-on'.\index{log-times-exp-proof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable log-times; name this event `log-times-on'.\index{log-times-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable log-times-proof; name this event `log-times-proof-on'.\index{log-times-proof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable log-quotient-exp; name this event `log-quotient-exp-on'.\index{log-quotient-exp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable log-quotient-times; name this event `log-quotient-times-on'.\index{log-quotient-times-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable log-quotient-times-proof; name this event `log-quotient-times-proof-on'.\index{log-quotient-times-proof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable log-quotient; name this event `log-quotient-on'.\index{log-quotient-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable leq-log-log; name this event `leq-log-log-on'.\index{leq-log-log-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable double-log-induction; name this event `double-log-induction-on'.\index{double-log-induction-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*double-log-induction; name this event `g*1*double-log-induction-on'.\index{g*1*double-log-induction-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable log-1; name this event `log-1-on'.\index{log-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable log-0; name this event `log-0-on'.\index{log-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-log-0; name this event `equal-log-0-on'.\index{equal-log-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable exp-difference; name this event `exp-difference-on'.\index{exp-difference-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-exp-1; name this event `equal-exp-1-on'.\index{equal-exp-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-exp-0; name this event `equal-exp-0-on'.\index{equal-exp-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable exp-exp; name this event `exp-exp-on'.\index{exp-exp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable exp-times; name this event `exp-times-on'.\index{exp-times-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable exp-0-arg2; name this event `exp-0-arg2-on'.\index{exp-0-arg2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable exp-1-arg1; name this event `exp-1-arg1-on'.\index{exp-1-arg1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable exp-0-arg1; name this event `exp-0-arg1-on'.\index{exp-0-arg1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable exp-plus; name this event `exp-plus-on'.\index{exp-plus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable exp-add1; name this event `exp-add1-on'.\index{exp-add1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable exp-zero; name this event `exp-zero-on'.\index{exp-zero-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-exp; name this event `quotient-exp-on'.\index{quotient-exp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-exp-exp; name this event `remainder-exp-exp-on'.\index{remainder-exp-exp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable double-number-induction; name this event `double-number-induction-on'.\index{double-number-induction-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*double-number-induction; name this event `g*1*double-number-induction-on'.\index{g*1*double-number-induction-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-exp; name this event `remainder-exp-on'.\index{remainder-exp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable gcd; name this event `gcd-on'.\index{gcd-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*gcd; name this event `g*1*gcd-on'.\index{g*1*gcd-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable log; name this event `log-on'.\index{log-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*log; name this event `g*1*log-on'.\index{g*1*log-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable exp; name this event `exp-on'.\index{exp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*exp; name this event `g*1*exp-on'.\index{g*1*exp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable correctness-of-cancel-quotient-times; name this event `correctness-of-cancel-quotient-times-on'.\index{correctness-of-cancel-quotient-ti!mes-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-quotient-times; name this event `cancel-quotient-times-on'.\index{cancel-quotient-times-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-quotient-times; name this event `g*1*cancel-quotient-times-on'.\index{g*1*cancel-quotient-times-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable lessp-quotient; name this event `lessp-quotient-on'.\index{lessp-quotient-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-x-x; name this event `quotient-x-x-on'.\index{quotient-x-x-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-1-arg1; name this event `quotient-1-arg1-on'.\index{quotient-1-arg1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-1-arg1-casesplit; name this event `quotient-1-arg1-casesplit-on'.\index{quotient-1-arg1-casesplit-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-1-arg2; name this event `quotient-1-arg2-on'.\index{quotient-1-arg2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable leq-quotient; name this event `leq-quotient-on'.\index{leq-quotient-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-quotient; name this event `quotient-quotient-on'.\index{quotient-quotient-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-plus-times-times-instance; name this event `quotient-plus-times-times-instance-on'.\index{quotient-plus-times-times-insta!nce-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-plus-times-times; name this event `quotient-plus-times-times-on'.\index{quotient-plus-times-times-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-plus-times-times-proof; name this event `quotient-plus-times-times-proof-on'.\index{quotient-plus-times-times-proof!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-plus-fact; name this event `quotient-plus-fact-on'.\index{quotient-plus-fact-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-remainder-instance; name this event `quotient-remainder-instance-on'.\index{quotient-remainder-instance-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-remainder; name this event `quotient-remainder-on'.\index{quotient-remainder-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-remainder-times; name this event `quotient-remainder-times-on'.\index{quotient-remainder-times-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-difference3; name this event `quotient-difference3-on'.\index{quotient-difference3-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-difference2; name this event `quotient-difference2-on'.\index{quotient-difference2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-lessp-arg1; name this event `quotient-lessp-arg1-on'.\index{quotient-lessp-arg1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-difference1; name this event `quotient-difference1-on'.\index{quotient-difference1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-times-times-proof; name this event `quotient-times-times-proof-on'.\index{quotient-times-times-proof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-times-instance; name this event `quotient-times-instance-on'.\index{quotient-times-instance-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-times; name this event `quotient-times-on'.\index{quotient-times-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-times-proof; name this event `quotient-times-proof-on'.\index{quotient-times-proof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-times-instance-temp-proof; name this event `quotient-times-instance-temp-proof-on'.\index{quotient-times-instance-temp-pr!oof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-plus; name this event `quotient-plus-on'.\index{quotient-plus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-plus-proof; name this event `quotient-plus-proof-on'.\index{quotient-plus-proof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-sub1; name this event `quotient-sub1-on'.\index{quotient-sub1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-quotient-0; name this event `equal-quotient-0-on'.\index{equal-quotient-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-add1; name this event `quotient-add1-on'.\index{quotient-add1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-zero; name this event `quotient-zero-on'.\index{quotient-zero-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-of-non-number; name this event `quotient-of-non-number-on'.\index{quotient-of-non-number-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-noop; name this event `quotient-noop-on'.\index{quotient-noop-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable transitivity-of-divides; name this event `transitivity-of-divides-on'.\index{transitivity-of-divides-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-x-x; name this event `remainder-x-x-on'.\index{remainder-x-x-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-1-arg2; name this event `remainder-1-arg2-on'.\index{remainder-1-arg2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-1-arg1; name this event `remainder-1-arg1-on'.\index{remainder-1-arg1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-remainder; name this event `remainder-remainder-on'.\index{remainder-remainder-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-plus-times-times-instance; name this event `remainder-plus-times-times-instance-on'.\index{remainder-plus-times-times-inst!ance-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-plus-times-times; name this event `remainder-plus-times-times-on'.\index{remainder-plus-times-times-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-plus-times-times-proof; name this event `remainder-plus-times-times-proof-on'.\index{remainder-plus-times-times-proo!f-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-plus-fact; name this event `remainder-plus-fact-on'.\index{remainder-plus-fact-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-difference2; name this event `remainder-difference2-on'.\index{remainder-difference2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable double-remainder-induction; name this event `double-remainder-induction-on'.\index{double-remainder-induction-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*double-remainder-induction; name this event `g*1*double-remainder-induction-on'.\index{g*1*double-remainder-induction-!on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-difference1; name this event `remainder-difference1-on'.\index{remainder-difference1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-times2-instance; name this event `remainder-times2-instance-on'.\index{remainder-times2-instance-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-times2; name this event `remainder-times2-on'.\index{remainder-times2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-times2-proof; name this event `remainder-times2-proof-on'.\index{remainder-times2-proof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-times-times-proof; name this event `remainder-times-times-proof-on'.\index{remainder-times-times-proof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-times1-instance; name this event `remainder-times1-instance-on'.\index{remainder-times1-instance-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-times1-instance-proof; name this event `remainder-times1-instance-proof-on'.\index{remainder-times1-instance-proof!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-times1; name this event `remainder-times1-on'.\index{remainder-times1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-times1-proof; name this event `remainder-times1-proof-on'.\index{remainder-times1-proof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-remainder-plus-remainder-proof; name this event `equal-remainder-plus-remainder-proof-on'.\index{equal-remainder-plus-remainder-p!roof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-remainder-plus-0; name this event `equal-remainder-plus-0-on'.\index{equal-remainder-plus-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-remainder-plus-0-proof; name this event `equal-remainder-plus-0-proof-on'.\index{equal-remainder-plus-0-proof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-plus; name this event `remainder-plus-on'.\index{remainder-plus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-plus-proof; name this event `remainder-plus-proof-on'.\index{remainder-plus-proof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-add1; name this event `remainder-add1-on'.\index{remainder-add1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-quotient-elim; name this event `remainder-quotient-elim-on'.\index{remainder-quotient-elim-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-zero; name this event `remainder-zero-on'.\index{remainder-zero-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-of-non-number; name this event `remainder-of-non-number-on'.\index{remainder-of-non-number-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable remainder-noop; name this event `remainder-noop-on'.\index{remainder-noop-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable lessp-remainder; name this event `lessp-remainder-on'.\index{lessp-remainder-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable correctness-of-cancel-equal-times; name this event `correctness-of-cancel-equal-times-on'.\index{correctness-of-cancel-equal-time!s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-equal-times; name this event `cancel-equal-times-on'.\index{cancel-equal-times-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-equal-times; name this event `g*1*cancel-equal-times-on'.\index{g*1*cancel-equal-times-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable correctness-of-cancel-lessp-times; name this event `correctness-of-cancel-lessp-times-on'.\index{correctness-of-cancel-lessp-time!s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-lessp-times; name this event `cancel-lessp-times-on'.\index{cancel-lessp-times-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-lessp-times; name this event `g*1*cancel-lessp-times-on'.\index{g*1*cancel-lessp-times-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable infer-equality-from-not-lessp; name this event `infer-equality-from-not-lessp-on'.\index{infer-equality-from-not-lessp-o!n}

\addvspace{18pt}


\noindent{\sc Event}:   Disable lessp-times-arg1; name this event `lessp-times-arg1-on'.\index{lessp-times-arg1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable eval\$-equal; name this event `eval\$-equal-on1'.\index{eval\$-equal-on1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable and-not-zerop-tree; name this event `and-not-zerop-tree-on'.\index{and-not-zerop-tree-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*and-not-zerop-tree; name this event `g*1*and-not-zerop-tree-on'.\index{g*1*and-not-zerop-tree-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable or-zerop-tree; name this event `or-zerop-tree-on'.\index{or-zerop-tree-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*or-zerop-tree; name this event `g*1*or-zerop-tree-on'.\index{g*1*or-zerop-tree-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable times-fringe; name this event `times-fringe-on'.\index{times-fringe-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*times-fringe; name this event `g*1*times-fringe-on'.\index{g*1*times-fringe-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable times-tree; name this event `times-tree-on'.\index{times-tree-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*times-tree; name this event `g*1*times-tree-on'.\index{g*1*times-tree-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable lessp-1-times; name this event `lessp-1-times-on'.\index{lessp-1-times-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable lessp-plus-times2; name this event `lessp-plus-times2-on'.\index{lessp-plus-times2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable lessp-plus-times1; name this event `lessp-plus-times1-on'.\index{lessp-plus-times1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable lessp-plus-times-proof; name this event `lessp-plus-times-proof-on'.\index{lessp-plus-times-proof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable lessp-times-cancellation-proof; name this event `lessp-times-cancellation-proof-on'.\index{lessp-times-cancellation-proof-!on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable lessp-times3; name this event `lessp-times3-on'.\index{lessp-times3-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable lessp-times3-proof2; name this event `lessp-times3-proof2-on'.\index{lessp-times3-proof2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable lessp-times3-proof1; name this event `lessp-times3-proof1-on'.\index{lessp-times3-proof1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable lessp-times2; name this event `lessp-times2-on'.\index{lessp-times2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable lessp-times2-proof; name this event `lessp-times2-proof-on'.\index{lessp-times2-proof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable lessp-times1; name this event `lessp-times1-on'.\index{lessp-times1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable lessp-times1-proof; name this event `lessp-times1-proof-on'.\index{lessp-times1-proof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable times-1-arg1; name this event `times-1-arg1-on'.\index{times-1-arg1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable times-quotient; name this event `times-quotient-on'.\index{times-quotient-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable times-quotient-proof; name this event `times-quotient-proof-on'.\index{times-quotient-proof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable times-distributes-over-difference; name this event `times-distributes-over-difference-on'.\index{times-distributes-over-differen!ce-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable times-distributes-over-difference-proof; name this event `times-distributes-over-difference-proof-on'.\index{times-distributes-over-differen!ce-proof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable associativity-of-times; name this event `associativity-of-times-on'.\index{associativity-of-times-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable commutativity2-of-times; name this event `commutativity2-of-times-on'.\index{commutativity2-of-times-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable times-distributes-over-plus; name this event `times-distributes-over-plus-on'.\index{times-distributes-over-plus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable times-distributes-over-plus-proof; name this event `times-distributes-over-plus-proof-on'.\index{times-distributes-over-plus-pro!of-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable commutativity-of-times; name this event `commutativity-of-times-on'.\index{commutativity-of-times-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable times-add1; name this event `times-add1-on'.\index{times-add1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable times-zero; name this event `times-zero-on'.\index{times-zero-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-sub1-0; name this event `equal-sub1-0-on'.\index{equal-sub1-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-times-1; name this event `equal-times-1-on'.\index{equal-times-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-times-0; name this event `equal-times-0-on'.\index{equal-times-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable correctness-of-cancel-lessp-plus; name this event `correctness-of-cancel-lessp-plus-on'.\index{correctness-of-cancel-lessp-plu!s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-lessp-plus; name this event `cancel-lessp-plus-on'.\index{cancel-lessp-plus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-lessp-plus; name this event `g*1*cancel-lessp-plus-on'.\index{g*1*cancel-lessp-plus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable difference-x-x; name this event `difference-x-x-on'.\index{difference-x-x-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable difference-difference-arg2; name this event `difference-difference-arg2-on'.\index{difference-difference-arg2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable difference-difference-arg1; name this event `difference-difference-arg1-on'.\index{difference-difference-arg1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable difference-sub1-arg2; name this event `difference-sub1-arg2-on'.\index{difference-sub1-arg2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable difference-add1-arg2; name this event `difference-add1-arg2-on'.\index{difference-add1-arg2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable difference-leq-arg1; name this event `difference-leq-arg1-on'.\index{difference-leq-arg1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable difference-elim; name this event `difference-elim-on'.\index{difference-elim-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable correctness-of-cancel-difference-plus; name this event `correctness-of-cancel-difference-plus-on'.\index{correctness-of-cancel-difference!-plus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-difference-plus; name this event `cancel-difference-plus-on'.\index{cancel-difference-plus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-difference-plus; name this event `g*1*cancel-difference-plus-on'.\index{g*1*cancel-difference-plus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable correctness-of-cancel-equal-plus; name this event `correctness-of-cancel-equal-plus-on'.\index{correctness-of-cancel-equal-plu!s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cancel-equal-plus; name this event `cancel-equal-plus-on'.\index{cancel-equal-plus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*cancel-equal-plus; name this event `g*1*cancel-equal-plus-on'.\index{g*1*cancel-equal-plus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable eval\$-quote; name this event `eval\$-quote-on1'.\index{eval\$-quote-on1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable plus-tree; name this event `plus-tree-on'.\index{plus-tree-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*plus-tree; name this event `g*1*plus-tree-on'.\index{g*1*plus-tree-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable plus-fringe; name this event `plus-fringe-on'.\index{plus-fringe-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*plus-fringe; name this event `g*1*plus-fringe-on'.\index{g*1*plus-fringe-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable diff-diff-arg2; name this event `diff-diff-arg2-on'.\index{diff-diff-arg2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable diff-diff-arg1; name this event `diff-diff-arg1-on'.\index{diff-diff-arg1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable difference-plus-plus-cancellation-proof; name this event `difference-plus-plus-cancellation-proof-on'.\index{difference-plus-plus-cancellati!on-proof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable difference-plus-cancellation-proof; name this event `difference-plus-cancellation-proof-on'.\index{difference-plus-cancellation-pr!oof-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable plus-difference-arg2; name this event `plus-difference-arg2-on'.\index{plus-difference-arg2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable plus-difference-arg1; name this event `plus-difference-arg1-on'.\index{plus-difference-arg1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable associativity-of-plus; name this event `associativity-of-plus-on'.\index{associativity-of-plus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable plus-add1-arg2; name this event `plus-add1-arg2-on'.\index{plus-add1-arg2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable plus-add1-arg1; name this event `plus-add1-arg1-on'.\index{plus-add1-arg1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable plus-zero-arg2; name this event `plus-zero-arg2-on'.\index{plus-zero-arg2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable commutativity2-of-plus; name this event `commutativity2-of-plus-on'.\index{commutativity2-of-plus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable commutativity-of-plus; name this event `commutativity-of-plus-on'.\index{commutativity-of-plus-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-difference-0; name this event `equal-difference-0-on'.\index{equal-difference-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-plus-0; name this event `equal-plus-0-on'.\index{equal-plus-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable member-bagint; name this event `member-bagint-on'.\index{member-bagint-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable occurrences-bagdiff; name this event `occurrences-bagdiff-on'.\index{occurrences-bagdiff-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable occurrences-bagint; name this event `occurrences-bagint-on'.\index{occurrences-bagint-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable subbagp-bagint2; name this event `subbagp-bagint2-on'.\index{subbagp-bagint2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable subbagp-bagint1; name this event `subbagp-bagint1-on'.\index{subbagp-bagint1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable subbagp-cdr2; name this event `subbagp-cdr2-on'.\index{subbagp-cdr2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable subbagp-cdr1; name this event `subbagp-cdr1-on'.\index{subbagp-cdr1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable subbagp-delete; name this event `subbagp-delete-on'.\index{subbagp-delete-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable bagdiff-delete; name this event `bagdiff-delete-on'.\index{bagdiff-delete-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable member-bagdiff; name this event `member-bagdiff-on'.\index{member-bagdiff-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable occurrences-delete; name this event `occurrences-delete-on'.\index{occurrences-delete-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable member-delete-implies-membership; name this event `member-delete-implies-membership-on'.\index{member-delete-implies-membership!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable member-delete; name this event `member-delete-on'.\index{member-delete-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable member-non-list; name this event `member-non-list-on'.\index{member-non-list-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-occurrences-zero; name this event `equal-occurrences-zero-on'.\index{equal-occurrences-zero-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable delete-delete; name this event `delete-delete-on'.\index{delete-delete-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable delete-non-member; name this event `delete-non-member-on'.\index{delete-non-member-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable subbagp; name this event `subbagp-on'.\index{subbagp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*subbagp; name this event `g*1*subbagp-on'.\index{g*1*subbagp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable occurrences; name this event `occurrences-on'.\index{occurrences-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*occurrences; name this event `g*1*occurrences-on'.\index{g*1*occurrences-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable bagint; name this event `bagint-on'.\index{bagint-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*bagint; name this event `g*1*bagint-on'.\index{g*1*bagint-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable bagdiff; name this event `bagdiff-on'.\index{bagdiff-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*bagdiff; name this event `g*1*bagdiff-on'.\index{g*1*bagdiff-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable delete; name this event `delete-on'.\index{delete-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*delete; name this event `g*1*delete-on'.\index{g*1*delete-on}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{b-to-nat} \\  
\=\+{\rm{b-to-nat}}\,({\it{c\/}})\index{b-to-nat} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{c\/}}$\;\;${\bf then }{\tt{1}} \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-adder-output=v-sum; name this event `v-adder-output=v-sum-off'.\index{v-adder-output=v-sum-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-adder-carry-out=v-carry; name this event `v-adder-carry-out=v-carry-off'.\index{v-adder-carry-out=v-carry-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  bvp-cdr \\ \index{bvp-cdr}
({\rm{bvp}}\,({\it{x\/}})\index{bvp} $\wedge$ {\rm{listp}}\,({\it{x\/}})) $\rightarrow$ {\rm{bvp}}\,({\rm{cdr}}\,({\it{x\/}}))\index{bvp}
\end{tabbing}


\noindent{\sc Event}:   Let us define the theory {\it{integer-metas}} to consist of the following events: correctness-of-cancel-ineg,
correctness-of-cancel-iplus,
correctness-of-cancel-iplus-ilessp,
correctness-of-cancel-itimes,
correctness-of-cancel-itimes-ilessp,
correctness-of-cancel-itimes-factors,
correctness-of-cancel-itimes-ilessp-factors,
correctness-of-cancel-factors-0,
correctness-of-cancel-factors-ilessp-0,
correctness-of-cancel-ineg-terms-from-equality,
correctness-of-cancel-ineg-terms-from-inequality.\index{integer-metas}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-ineg; name this event `correctness-of-cancel-ineg-off1'.\index{correctness-of-cancel-ineg-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-iplus; name this event `correctness-of-cancel-iplus-off1'.\index{correctness-of-cancel-iplus-off!1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-iplus-ilessp; name this event `correctness-of-cancel-iplus-ilessp-off1'.\index{correctness-of-cancel-iplus-ile!ssp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-itimes; name this event `correctness-of-cancel-itimes-off1'.\index{correctness-of-cancel-itimes-of!f1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-itimes-ilessp; name this event `correctness-of-cancel-itimes-ilessp-off1'.\index{correctness-of-cancel-itimes-ile!ssp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-itimes-factors; name this event `correctness-of-cancel-itimes-factors-off1'.\index{correctness-of-cancel-itimes-fa!ctors-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-itimes-ilessp-factors; name this event `correctness-of-cancel-itimes-ilessp-factors-off1'.\index{correctness-of-cancel-itimes-ile!ssp-factors-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-factors-0; name this event `correctness-of-cancel-factors-0-off1'.\index{correctness-of-cancel-factors-0!-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-factors-ilessp-0; name this event `correctness-of-cancel-factors-ilessp-0-off1'.\index{correctness-of-cancel-factors-i!lessp-0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-ineg-terms-from-equality; name this event `correctness-of-cancel-ineg-terms-from-equality-off1'.\index{correctness-of-cancel-ineg-term!s-from-equality-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-ineg-terms-from-inequality; name this event `correctness-of-cancel-ineg-terms-from-inequality-off1'.\index{correctness-of-cancel-ineg-term!s-from-inequality-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{naturals-metas}} to consist of the following events: correctness-of-cancel-equal-plus,
correctness-of-cancel-difference-plus,
correctness-of-cancel-lessp-plus,
correctness-of-cancel-lessp-times,
correctness-of-cancel-equal-times,
correctness-of-cancel-quotient-times.\index{naturals-metas}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-equal-plus; name this event `correctness-of-cancel-equal-plus-off1'.\index{correctness-of-cancel-equal-plu!s-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-difference-plus; name this event `correctness-of-cancel-difference-plus-off1'.\index{correctness-of-cancel-difference!-plus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-lessp-plus; name this event `correctness-of-cancel-lessp-plus-off1'.\index{correctness-of-cancel-lessp-plu!s-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-lessp-times; name this event `correctness-of-cancel-lessp-times-off1'.\index{correctness-of-cancel-lessp-time!s-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-equal-times; name this event `correctness-of-cancel-equal-times-off1'.\index{correctness-of-cancel-equal-time!s-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable correctness-of-cancel-quotient-times; name this event `correctness-of-cancel-quotient-times-off1'.\index{correctness-of-cancel-quotient-ti!mes-off1}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{v-alu-nat-int-buf}$\;\;$
{\rm{v-alu-nat-int-buf}}\,({\it{a\/}})\index{v-alu-nat-int-buf} $=$ {\rm{cvzbv}}\,({\bf{f}}, {\bf{f}}, {\it{a\/}})\index{cvzbv}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-nat-int-buf \\ \index{v-alu-correct-nat-int-buf}
{\rm{bvp}}\,({\it{a\/}})\index{bvp} $\rightarrow$ ({\rm{cvzbv}}\,({\bf{f}}, {\bf{f}}, {\rm{v-buf}}\,({\it{a\/}})\index{v-buf})\index{cvzbv} $=$ {\rm{v-alu-nat-int-buf}}\,({\it{a\/}})\index{v-alu-nat-int-buf})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  nth-length-v \\ \index{nth-length-v}
\=\+({\rm{bvp}}\,({\it{bv\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{bv\/}})\index{length} $=$ ($1\;+$ {\it{n\/}}))) \\ 
$\rightarrow$$\;\;\;\;$({\rm{nth}}\,({\it{n\/}}, {\it{bv\/}})\index{nth} $=$ ({\rm{v-to-nat}}\,({\it{bv\/}})\index{v-to-nat} $\not<$ {\rm{exp}}\,({\tt{2}}, {\it{n\/}})\index{exp}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-plus-multiple \\ \index{remainder-plus-multiple}
(({\it{z1\/}} $<$ {\it{y1\/}}) $\wedge$ (({\it{a\/}} ${}${\bf{mod}}${}$ {\it{y1\/}}) $=$ {\tt{0}})) $\rightarrow$ ((({\it{z1\/}} $+$ {\it{a\/}}) ${}${\bf{mod}}${}$ {\it{y1\/}}) $=$ {\rm{fix}}\,({\it{z1\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  divides-plus-plus \\ \index{divides-plus-plus}
(({\it{x\/}} ${}${\bf{mod}}${}$ {\it{y\/}}) $=$ {\tt{0}}) $\rightarrow$ ((({\it{x\/}} $+$ {\it{x\/}}) ${}${\bf{mod}}${}$ ({\it{y\/}} $+$ {\it{y\/}})) $=$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-to-nat-firstn-hack1 \\ \index{v-to-nat-firstn-hack1}
\=\+({\it{z\/}} $<$ {\it{y\/}}) \\ 
$\rightarrow$$\;\;\;\;$((({\it{z\/}} $+$ {\it{z\/}} $+$ ({\it{w\/}} $*$ {\it{y\/}}) $+$ ({\it{w\/}} $*$ {\it{y\/}})) ${}${\bf{mod}}${}$ ({\it{y\/}} $+$ {\it{y\/}})) $=$ ({\it{z\/}} $+$ {\it{z\/}}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-add1-plus-multiple \\ \index{remainder-add1-plus-multiple}
\=\+((($1\;+$ {\it{z1\/}}) $<$ {\it{y1\/}}) $\wedge$ (({\it{a\/}} ${}${\bf{mod}}${}$ {\it{y1\/}}) $=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$((($1\;+$ ({\it{z1\/}} $+$ {\it{a\/}})) ${}${\bf{mod}}${}$ {\it{y1\/}}) $=$ ($1\;+$ {\it{z1\/}}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-to-nat-firstn-hack2 \\ \index{v-to-nat-firstn-hack2}
\=\+({\it{z\/}} $<$ {\it{y\/}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(($1\;+$ ({\it{z\/}} $+$ {\it{z\/}} $+$ ({\it{d\/}} $*$ {\it{y\/}}) $+$ ({\it{d\/}} $*$ {\it{y\/}}))) ${}${\bf{mod}}${}$ ({\it{y\/}} $+$ {\it{y\/}})) \\ 
$=$$\;\;\;\;$($1\;+$ ({\it{z\/}} $+$ {\it{z\/}})))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-to-nat-firstn \\ \index{v-to-nat-firstn}
{\rm{v-to-nat}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{v\/}})\index{firstn})\index{v-to-nat} $=$ ({\rm{v-to-nat}}\,({\it{v\/}})\index{v-to-nat} ${}${\bf{mod}}${}$ {\rm{exp}}\,({\tt{2}}, {\it{n\/}})\index{exp})
\end{tabbing}


\noindent{\sc Event}:   Enable v-to-nat-firstn-hack1; name this event `v-to-nat-firstn-hack1-off'.\index{v-to-nat-firstn-hack1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-to-nat-firstn-hack2; name this event `v-to-nat-firstn-hack2-off'.\index{v-to-nat-firstn-hack2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-to-nat-of-nat-to-v-hack \\ \index{v-to-nat-of-nat-to-v-hack}
\=\+({\it{v\/}} $<$ {\rm{exp}}\,({\tt{2}}, {\it{x\/}})\index{exp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+($1\;+$ ({\it{v\/}} $+$ {\it{v\/}} $+$ ({\it{w\/}} $*$ {\rm{exp}}\,({\tt{2}}, {\it{x\/}})\index{exp}) $+$ ({\it{w\/}} $*$ {\rm{exp}}\,({\tt{2}}, {\it{x\/}})\index{exp}))) \\ 
${}${\bf{mod}}${}$$\;\;\;\;$({\rm{exp}}\,({\tt{2}}, {\it{x\/}})\index{exp} $+$ {\rm{exp}}\,({\tt{2}}, {\it{x\/}})\index{exp}))\- \\ 
$=$$\;\;\;\;$($1\;+$ ({\it{v\/}} $+$ {\it{v\/}})))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-to-nat-of-nat-to-v \\ \index{v-to-nat-of-nat-to-v}
{\rm{v-to-nat}}\,({\rm{nat-to-v}}\,({\it{n\/}}, {\it{len\/}})\index{nat-to-v})\index{v-to-nat} $=$ ({\it{n\/}} ${}${\bf{mod}}${}$ {\rm{exp}}\,({\tt{2}}, {\it{len\/}})\index{exp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-plus-x-x-2 \\ \index{remainder-plus-x-x-2}
(({\it{x\/}} $+$ {\it{x\/}}) ${}${\bf{mod}}${}$ {\tt{2}}) $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-plus-x-x-2 \\ \index{quotient-plus-x-x-2}
(({\it{x\/}} $+$ {\it{x\/}}) $\div$ {\tt{2}}) $=$ {\rm{fix}}\,({\it{x\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  nat-to-v-plus-x-x \\ \index{nat-to-v-plus-x-x}
{\rm{nat-to-v}}\,({\it{x\/}} $+$ {\it{x\/}}, $1\;+$ {\it{n\/}})\index{nat-to-v} $=$ {\rm{cons}}\,({\bf{f}}, {\rm{nat-to-v}}\,({\it{x\/}}, {\it{n\/}})\index{nat-to-v})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  firstn-add1-cons \\ \index{firstn-add1-cons}
{\rm{firstn}}\,($1\;+$ {\it{n\/}}, {\rm{cons}}\,({\it{a\/}}, {\it{x\/}}))\index{firstn} $=$ {\rm{cons}}\,({\it{a\/}}, {\rm{firstn}}\,({\it{n\/}}, {\it{x\/}})\index{firstn})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  firstn-zerop \\ \index{firstn-zerop}
({\it{n\/}} $\simeq {\tt{0}}$) $\rightarrow$ ({\rm{firstn}}\,({\it{n\/}}, {\it{x\/}})\index{firstn} $=$ {\bf{nil}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  firstn-nlistp \\ \index{firstn-nlistp}
({\it{x\/}} $\simeq\;${{\bf{nil}}}${}$) $\rightarrow$ ({\rm{firstn}}\,({\it{n\/}}, {\it{x\/}})\index{firstn} $=$ {\bf{nil}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  nat-to-v-of-v-to-nat-general \\ \index{nat-to-v-of-v-to-nat-general}
\=\+({\rm{bvp}}\,({\it{v\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{v\/}})\index{length} $\not<$ {\it{n\/}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{nat-to-v}}\,({\rm{v-to-nat}}\,({\it{v\/}})\index{v-to-nat}, {\it{n\/}})\index{nat-to-v} $=$ {\rm{firstn}}\,({\it{n\/}}, {\it{v\/}})\index{firstn})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  firstn-length \\ \index{firstn-length}
{\rm{properp}}\,({\it{x\/}})\index{properp} $\rightarrow$ ({\rm{firstn}}\,({\rm{length}}\,({\it{x\/}})\index{length}, {\it{x\/}})\index{firstn} $=$ {\it{x\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  nat-to-v-of-v-to-nat \\ \index{nat-to-v-of-v-to-nat}
{\rm{bvp}}\,({\it{v\/}})\index{bvp} $\rightarrow$ ({\rm{nat-to-v}}\,({\rm{v-to-nat}}\,({\it{v\/}})\index{v-to-nat}, {\rm{length}}\,({\it{v\/}})\index{length})\index{nat-to-v} $=$ {\it{v\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  nat-to-v-zerop \\ \index{nat-to-v-zerop}
({\it{len\/}} $\simeq {\tt{0}}$) $\rightarrow$ ({\rm{nat-to-v}}\,({\it{n\/}}, {\it{len\/}})\index{nat-to-v} $=$ {\bf{nil}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-nat-to-v-inverter-hack1 \\ \index{equal-nat-to-v-inverter-hack1}
\=\+(({\it{len\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{v\/}} $=$ {\rm{nat-to-v}}\,({\it{n\/}}, {\it{len\/}})\index{nat-to-v})) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{v-to-nat}}\,({\it{v\/}})\index{v-to-nat} $=$ ({\it{n\/}} ${}${\bf{mod}}${}$ {\rm{exp}}\,({\tt{2}}, {\it{len\/}})\index{exp})) $=$ {\bf{t}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-nat-to-v-inverter-hack2-lemma \\ \index{equal-nat-to-v-inverter-hack2-le!mma}
\=\+({\rm{bvp}}\,({\it{v\/}})\index{bvp} $\wedge$ ({\rm{v-to-nat}}\,({\it{v\/}})\index{v-to-nat} $=$ ({\it{n\/}} ${}${\bf{mod}}${}$ {\rm{exp}}\,({\tt{2}}, {\it{len\/}})\index{exp}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{nat-to-v}}\,({\rm{v-to-nat}}\,({\it{v\/}})\index{v-to-nat}, {\it{len\/}})\index{nat-to-v} $=$ {\rm{nat-to-v}}\,({\it{n\/}} ${}${\bf{mod}}${}$ {\rm{exp}}\,({\tt{2}}, {\it{len\/}})\index{exp}, {\it{len\/}})\index{nat-to-v}) \\ 
$=$$\;\;\;\;${\bf{t}})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  nat-to-v-remainder \\ \index{nat-to-v-remainder}
{\rm{nat-to-v}}\,({\it{n\/}} ${}${\bf{mod}}${}$ {\rm{exp}}\,({\tt{2}}, {\it{len\/}})\index{exp}, {\it{len\/}})\index{nat-to-v} $=$ {\rm{nat-to-v}}\,({\it{n\/}}, {\it{len\/}})\index{nat-to-v}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-nat-to-v-inverter-hack2 \\ \index{equal-nat-to-v-inverter-hack2}
\=\+({\rm{bvp}}\,({\it{v\/}})\index{bvp} $\wedge$ ({\rm{v-to-nat}}\,({\it{v\/}})\index{v-to-nat} $=$ ({\it{n\/}} ${}${\bf{mod}}${}$ {\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{v\/}})\index{length})\index{exp}))) \\ 
$\rightarrow$$\;\;\;\;$(({\it{v\/}} $=$ {\rm{nat-to-v}}\,({\it{n\/}}, {\rm{length}}\,({\it{v\/}})\index{length})\index{nat-to-v}) $=$ {\bf{t}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-nat-to-v-inverter \\ \index{equal-nat-to-v-inverter}
\=\+({\it{v\/}} $=$ {\rm{nat-to-v}}\,({\it{n\/}}, {\it{len\/}})\index{nat-to-v}) \\ 
$\leftrightarrow$$\;\;\;\;$(\=\+{\rm{bvp}}\,({\it{v\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{v\/}})\index{length} $=$ {\rm{fix}}\,({\it{len\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{v-to-nat}}\,({\it{v\/}})\index{v-to-nat} $=$ ({\it{n\/}} ${}${\bf{mod}}${}$ {\rm{exp}}\,({\tt{2}}, {\it{len\/}})\index{exp})))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable equal-nat-to-v-inverter-hack1; name this event `equal-nat-to-v-inverter-hack1-off'.\index{equal-nat-to-v-inverter-hack1-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-nat-to-v-inverter-hack2; name this event `equal-nat-to-v-inverter-hack2-off'.\index{equal-nat-to-v-inverter-hack2-o!ff}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-to-nat-v-not-lemma \\ \index{v-to-nat-v-not-lemma}
\=\+{\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\rightarrow$$\;\;\;\;$(({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $+$ {\rm{v-to-nat}}\,({\rm{v-not}}\,({\it{a\/}})\index{v-not})\index{v-to-nat}) $=$ ({\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{exp} $-\;1$))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-to-nat-v-not \\ \index{v-to-nat-v-not}
\=\+{\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\rightarrow$$\;\;\;\;$({\rm{v-to-nat}}\,({\rm{v-not}}\,({\it{a\/}})\index{v-not})\index{v-to-nat} $=$ (({\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{exp} $-$ {\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat}) $-\;1$))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-v-to-nat-exp \\ \index{lessp-v-to-nat-exp}
{\rm{bvp}}\,({\it{a\/}})\index{bvp} $\rightarrow$ ({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $<$ {\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{exp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-iff \\ \index{equal-iff}
({\rm{boolp}}\,({\it{x\/}})\index{boolp} $\wedge$ {\rm{boolp}}\,({\it{y\/}})\index{boolp}) $\rightarrow$ (({\it{x\/}} $=$ {\it{y\/}}) $=$ ({\it{x\/}} $\leftrightarrow$ {\it{y\/}}))
\end{tabbing}


\noindent{\sc Event}:   Enable equal-iff; name this event `equal-iff-off'.\index{equal-iff-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-nat-subtracter-output-lemma \\ \index{v-alu-correct-nat-subtracter-outp!ut-lemma}
\=\+(({\it{a-nat\/}} $<$ {\it{bound\/}}) $\wedge$ ({\it{b-nat\/}} $<$ {\it{bound\/}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\it{b-nat\/}} $+$ (({\it{bound\/}} $-$ {\it{a-nat\/}}) $-\;1$)) \\ 
$=$$\;\;\;\;$((({\it{b-nat\/}} $+$ {\it{bound\/}}) $-$ {\it{a-nat\/}}) $-\;1$))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-v-to-nat-exp-rewrite \\ \index{lessp-v-to-nat-exp-rewrite}
({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\it{len\/}})) $\rightarrow$ (({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $<$ {\rm{exp}}\,({\tt{2}}, {\it{len\/}})\index{exp}) $=$ {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  not-lessp-quotient \\ \index{not-lessp-quotient}
{\it{n\/}} $\not<$ ({\it{n\/}} $\div$ {\it{k\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-to-nat-append \\ \index{v-to-nat-append}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ {\rm{bvp}}\,({\it{b\/}})\index{bvp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-to-nat}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{v-to-nat} \\ 
$=$$\;\;\;\;$({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $+$ ({\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{exp} $*$ {\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat})))\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-nat-adder-output} \\  
\=\+{\rm{v-alu-nat-adder-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-nat-adder-output} \\ 
$=$$\;\;\;\;${\rm{nat-to-v}}\,(\=\+\=\+({\rm{b-to-nat}}\,({\it{c\/}})\index{b-to-nat} $+$ {\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $+$ {\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat}) \\ 
${}${\bf{mod}}${}$$\;\;\;\;${\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{exp}\-, \\ 
{\rm{length}}\,({\it{a\/}})\index{length})\-\index{nat-to-v}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-nat-adder-carry-out} \\  
\=\+{\rm{v-alu-nat-adder-carry-out}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-nat-adder-carry-out} \\ 
$=$$\;\;\;\;$(({\rm{b-to-nat}}\,({\it{c\/}})\index{b-to-nat} $+$ {\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $+$ {\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat}) $\not<$ {\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{exp})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-nat-adder} \\  
\=\+{\rm{v-alu-nat-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-nat-adder} \\ 
$=$$\;\;\;\;${\rm{cvzbv}}\,(\=\+{\rm{v-alu-nat-adder-carry-out}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-nat-adder-carry-out}, \\ 
{\rm{v-adder-overflowp}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder-overflowp}, \\ 
{\rm{v-alu-nat-adder-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-nat-adder-output})\-\index{cvzbv}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-nat-adder-carry-out \\ \index{v-alu-correct-nat-adder-carry-o!ut}
\=\+{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} \\ 
$\rightarrow$$\;\;\;\;$({\rm{v-adder-carry-out}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder-carry-out} $=$ {\rm{v-alu-nat-adder-carry-out}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-nat-adder-carry-out})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-nat-adder-output \\ \index{v-alu-correct-nat-adder-output}
{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\rightarrow$ ({\rm{v-adder-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder-output} $=$ {\rm{v-alu-nat-adder-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-nat-adder-output})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-nat-adder \\ \index{v-alu-correct-nat-adder}
{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\rightarrow$ ({\rm{cvzbv-v-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{cvzbv-v-adder} $=$ {\rm{v-alu-nat-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-nat-adder})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-nat-inc} \\  
{\rm{v-alu-nat-inc}}\,({\it{a\/}})\index{v-alu-nat-inc} $=$ {\rm{v-alu-nat-adder}}\,({\bf{t}}, {\it{a\/}}, {\rm{nat-to-v}}\,({\tt{0}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{nat-to-v})\index{v-alu-nat-adder}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-nat-inc \\ \index{v-alu-correct-nat-inc}
{\rm{bvp}}\,({\it{a\/}})\index{bvp} $\rightarrow$ ({\rm{cvzbv-inc}}\,({\it{a\/}})\index{cvzbv-inc} $=$ {\rm{v-alu-nat-inc}}\,({\it{a\/}})\index{v-alu-nat-inc})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-nat-subtracter-output} \\  
\=\+{\rm{v-alu-nat-subtracter-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-nat-subtracter-output} \\ 
$=$$\;\;\;\;${\rm{nat-to-v}}\,(\=\+\=\+(\=\+({\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat} $+$ {\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{exp}) \\ 
$-$$\;\;\;\;$({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $+$ {\rm{b-to-nat}}\,({\it{c\/}})\index{b-to-nat}))\- \\ 
${}${\bf{mod}}${}$$\;\;\;\;${\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{exp}\-, \\ 
{\rm{length}}\,({\it{a\/}})\index{length})\-\index{nat-to-v}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-nat-subtracter-carry-out} \\  
\=\+{\rm{v-alu-nat-subtracter-carry-out}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-nat-subtracter-carry-out} \\ 
$=$$\;\;\;\;$({\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat} $<$ ({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $+$ {\rm{b-to-nat}}\,({\it{c\/}})\index{b-to-nat}))\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-nat-subtracter} \\  
\=\+{\rm{v-alu-nat-subtracter}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-nat-subtracter} \\ 
$=$$\;\;\;\;${\rm{cvzbv}}\,(\=\+{\rm{v-alu-nat-subtracter-carry-out}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-nat-subtracter-carry-out}, \\ 
{\rm{v-subtracter-overflowp}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-subtracter-overflowp}, \\ 
{\rm{v-alu-nat-subtracter-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-nat-subtracter-output})\-\index{cvzbv}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-nat-subtracter-carry-out \\ \index{v-alu-correct-nat-subtracter-ca!rry-out}
\=\+{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-subtracter-carry-out}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-subtracter-carry-out} \\ 
$=$$\;\;\;\;${\rm{v-alu-nat-subtracter-carry-out}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-nat-subtracter-carry-out})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-nat-subtracter-output \\ \index{v-alu-correct-nat-subtracter-outp!ut}
\=\+{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} \\ 
$\rightarrow$$\;\;\;\;$({\rm{v-subtracter-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-subtracter-output} $=$ {\rm{v-alu-nat-subtracter-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-nat-subtracter-output})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-nat-subtracter \\ \index{v-alu-correct-nat-subtracter}
{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\rightarrow$ ({\rm{cvzbv-v-subtracter}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{cvzbv-v-subtracter} $=$ {\rm{v-alu-nat-subtracter}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-nat-subtracter})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-nat-dec} \\  
{\rm{v-alu-nat-dec}}\,({\it{a\/}})\index{v-alu-nat-dec} $=$ {\rm{v-alu-nat-subtracter}}\,({\bf{t}}, {\rm{nat-to-v}}\,({\tt{0}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{nat-to-v}, {\it{a\/}})\index{v-alu-nat-subtracter}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-nat-dec \\ \index{v-alu-correct-nat-dec}
{\rm{bvp}}\,({\it{a\/}})\index{bvp} $\rightarrow$ ({\rm{cvzbv-dec}}\,({\it{a\/}})\index{cvzbv-dec} $=$ {\rm{v-alu-nat-dec}}\,({\it{a\/}})\index{v-alu-nat-dec})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-nat-lsr-output} \\  
{\rm{v-alu-nat-lsr-output}}\,({\it{a\/}})\index{v-alu-nat-lsr-output} $=$ {\rm{nat-to-v}}\,({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $\div$ {\tt{2}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{nat-to-v}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-nat-lsr-carry-out} \\  
{\rm{v-alu-nat-lsr-carry-out}}\,({\it{a\/}})\index{v-alu-nat-lsr-carry-out} $=$ (({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} ${}${\bf{mod}}${}$ {\tt{2}}) $\not=$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-nat-lsr} \\  
\=\+{\rm{v-alu-nat-lsr}}\,({\it{a\/}})\index{v-alu-nat-lsr} \\ 
$=$$\;\;\;\;${\rm{cvzbv}}\,({\rm{v-alu-nat-lsr-carry-out}}\,({\it{a\/}})\index{v-alu-nat-lsr-carry-out}, {\bf{f}}, {\rm{v-alu-nat-lsr-output}}\,({\it{a\/}})\index{v-alu-nat-lsr-output})\index{cvzbv}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-nat-lsr-carry-out \\ \index{v-alu-correct-nat-lsr-carry-out}
({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ {\rm{listp}}\,({\it{a\/}})) $\rightarrow$ ({\rm{nth}}\,({\tt{0}}, {\it{a\/}})\index{nth} $=$ {\rm{v-alu-nat-lsr-carry-out}}\,({\it{a\/}})\index{v-alu-nat-lsr-carry-out})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-nat-lsr-output \\ \index{v-alu-correct-nat-lsr-output}
{\rm{bvp}}\,({\it{a\/}})\index{bvp} $\rightarrow$ ({\rm{v-lsr}}\,({\it{a\/}})\index{v-lsr} $=$ {\rm{v-alu-nat-lsr-output}}\,({\it{a\/}})\index{v-alu-nat-lsr-output})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-nat-lsr \\ \index{v-alu-correct-nat-lsr}
{\rm{bvp}}\,({\it{a\/}})\index{bvp} $\rightarrow$ ({\rm{cvzbv-v-lsr}}\,({\it{a\/}})\index{cvzbv-v-lsr} $=$ {\rm{v-alu-nat-lsr}}\,({\it{a\/}})\index{v-alu-nat-lsr})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-nat-not-output} \\  
\=\+{\rm{v-alu-nat-not-output}}\,({\it{a\/}})\index{v-alu-nat-not-output} \\ 
$=$$\;\;\;\;${\rm{nat-to-v}}\,(({\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{exp} $-$ {\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat}) $-\;1$, {\rm{length}}\,({\it{a\/}})\index{length})\index{nat-to-v}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-nat-not} \\  
{\rm{v-alu-nat-not}}\,({\it{a\/}})\index{v-alu-nat-not} $=$ {\rm{cvzbv}}\,({\bf{f}}, {\bf{f}}, {\rm{v-alu-nat-not-output}}\,({\it{a\/}})\index{v-alu-nat-not-output})\index{cvzbv}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-nat-not-output \\ \index{v-alu-correct-nat-not-output}
{\rm{bvp}}\,({\it{a\/}})\index{bvp} $\rightarrow$ ({\rm{v-not}}\,({\it{a\/}})\index{v-not} $=$ {\rm{v-alu-nat-not-output}}\,({\it{a\/}})\index{v-alu-nat-not-output})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-nat-not \\ \index{v-alu-correct-nat-not}
{\rm{bvp}}\,({\it{a\/}})\index{bvp} $\rightarrow$ ({\rm{cvzbv-v-not}}\,({\it{a\/}})\index{cvzbv-v-not} $=$ {\rm{v-alu-nat-not}}\,({\it{a\/}})\index{v-alu-nat-not})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-nat} \\  
\=\+{\rm{v-alu-nat}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu-nat} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\rm{v-alu-nat-int-buf}}\,({\it{a\/}})\index{v-alu-nat-int-buf} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\rm{v-alu-nat-inc}}\,({\it{a\/}})\index{v-alu-nat-inc} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\rm{v-alu-nat-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-nat-adder} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\rm{v-alu-nat-adder}}\,({\bf{f}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-nat-adder} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }{\rm{v-alu-nat-dec}}\,({\it{a\/}})\index{v-alu-nat-dec} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }{\rm{v-alu-nat-subtracter}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-nat-subtracter} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }{\rm{v-alu-nat-subtracter}}\,({\bf{f}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-nat-subtracter} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}})$\;\;${\bf then }{\rm{v-alu-nat-lsr}}\,({\it{a\/}})\index{v-alu-nat-lsr} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}})$\;\;${\bf then }{\rm{v-alu-nat-not}}\,({\it{a\/}})\index{v-alu-nat-not} \\ 
{\bf else }{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-nat \\ \index{v-alu-correct-nat}
{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\rightarrow$ ({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu} $=$ {\rm{v-alu-nat}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu-nat})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{int-to-v} \\  
\=\+{\rm{int-to-v}}\,({\it{i\/}}, {\it{l\/}})\index{int-to-v} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{ilessp}}\,({\it{i\/}}, {\tt{0}})\index{ilessp}$\;\;${\bf then }{\rm{nat-to-v}}\,({\rm{iplus}}\,({\it{i\/}}, {\rm{exp}}\,({\tt{2}}, {\it{l\/}})\index{exp})\index{iplus}, {\it{l\/}})\index{nat-to-v} \\ 
{\bf else }{\rm{nat-to-v}}\,({\it{i\/}}, {\it{l\/}})\index{nat-to-v}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-to-int} \\  
\=\+{\rm{v-to-int}}\,({\it{v\/}})\index{v-to-int} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{v-to-nat}}\,({\it{v\/}})\index{v-to-nat} $<$ {\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{v\/}})\index{length} $-\;1$)\index{exp}$\;\;${\bf then }{\rm{v-to-nat}}\,({\it{v\/}})\index{v-to-nat} \\ 
{\bf else }{\rm{idifference}}\,({\rm{v-to-nat}}\,({\it{v\/}})\index{v-to-nat}, {\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{v\/}})\index{length})\index{exp})\index{idifference}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{integer-in-rangep} \\  
\=\+{\rm{integer-in-rangep}}\,({\it{i\/}}, {\it{l\/}})\index{integer-in-rangep} \\ 
$=$$\;\;\;\;$({\rm{ileq}}\,({\rm{ineg}}\,({\rm{exp}}\,({\tt{2}}, {\it{l\/}} $-\;1$)\index{exp})\index{ineg}, {\it{i\/}})\index{ileq} $\wedge$ {\rm{ilessp}}\,({\it{i\/}}, {\rm{exp}}\,({\tt{2}}, {\it{l\/}} $-\;1$)\index{exp})\index{ilessp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-plus \\ \index{iplus-plus}
(({\it{x\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{y\/}} $\in\;${\bf{N}}${}$)) $\rightarrow$ ({\rm{iplus}}\,({\it{x\/}}, {\it{y\/}})\index{iplus} $=$ ({\it{x\/}} $+$ {\it{y\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ilessp-lessp \\ \index{ilessp-lessp}
(({\it{x\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{y\/}} $\in\;${\bf{N}}${}$)) $\rightarrow$ ({\rm{ilessp}}\,({\it{x\/}}, {\it{y\/}})\index{ilessp} $=$ ({\it{x\/}} $<$ {\it{y\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  times-2 \\ \index{times-2}
({\tt{2}} $*$ {\it{x\/}}) $=$ ({\it{x\/}} $+$ {\it{x\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  b-to-nat-leq \\ \index{b-to-nat-leq}
{\tt{1}} $\not<$ {\rm{b-to-nat}}\,({\it{x\/}})\index{b-to-nat}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-v-to-nat-exp-with-exp-opened \\ \index{lessp-v-to-nat-exp-with-exp-ope!ned}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\rm{length}}\,({\it{b\/}})\index{length}) $\wedge$ ({\rm{length}}\,({\it{b\/}})\index{length} $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $<$ ({\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{b\/}})\index{length} $-\;1$)\index{exp} $+$ {\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{b\/}})\index{length} $-\;1$)\index{exp}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fix-int-numberp \\ \index{fix-int-numberp}
({\it{x\/}} $\in\;${\bf{N}}${}$) $\rightarrow$ ({\rm{fix-int}}\,({\it{x\/}})\index{fix-int} $=$ {\it{x\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus3-plus-difference \\ \index{iplus3-plus-difference}
\=\+(\=\+({\it{c0\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$({\it{a0\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$({\it{b0\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$({\it{d\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(({\it{c0\/}} $+$ {\it{a0\/}} $+$ {\it{b0\/}}) $\not<$ {\it{d\/}}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{iplus}}\,({\it{c0\/}}, {\rm{iplus}}\,({\it{a0\/}}, {\rm{iplus}}\,({\it{b0\/}}, {\rm{ineg}}\,({\it{d\/}})\index{ineg})\index{iplus})\index{iplus})\index{iplus} $=$ (({\it{c0\/}} $+$ {\it{a0\/}} $+$ {\it{b0\/}}) $-$ {\it{d\/}}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-to-int-v-not \\ \index{v-to-int-v-not}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{v-to-int}}\,({\rm{v-not}}\,({\it{a\/}})\index{v-not})\index{v-to-int} $=$ {\rm{iplus}}\,({\tt{-1}}, {\rm{ineg}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{ineg})\index{iplus})\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-alu-correct-nat-not-output; name this event `v-alu-correct-nat-not-output-off'.\index{v-alu-correct-nat-not-output-of!f}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-int-subtracter-overflowp-lemma \\ \index{v-alu-correct-int-subtracter-ove!rflowp-lemma}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{iplus}}\,({\rm{b-to-nat}}\,({\rm{b-not}}\,({\it{c\/}})\index{b-not})\index{b-to-nat}, {\rm{iplus}}\,({\rm{v-to-int}}\,({\rm{v-not}}\,({\it{a\/}})\index{v-not})\index{v-to-int}, {\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int})\index{iplus})\index{iplus} \\ 
$=$$\;\;\;\;${\rm{idifference}}\,({\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int}, {\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{b-to-nat}}\,({\it{c\/}})\index{b-to-nat})\index{iplus})\index{idifference})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  idifference-difference \\ \index{idifference-difference}
\=\+(({\it{x\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{y\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{x\/}} $\not<$ {\it{y\/}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{iplus}}\,({\it{x\/}}, {\rm{ineg}}\,({\it{y\/}})\index{ineg})\index{iplus} $=$ ({\it{x\/}} $-$ {\it{y\/}})) \\ 
$\wedge$$\;\;\;\;$({\rm{iplus}}\,({\rm{ineg}}\,({\it{y\/}})\index{ineg}, {\it{x\/}})\index{iplus} $=$ ({\it{x\/}} $-$ {\it{y\/}})))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  idiv-quotient \\ \index{idiv-quotient}
(({\it{x\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{y\/}} $\in\;${\bf{N}}${}$)) $\rightarrow$ ({\rm{idiv}}\,({\it{x\/}}, {\it{y\/}})\index{idiv} $=$ ({\it{x\/}} $\div$ {\it{y\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  idiv-ilessp-0 \\ \index{idiv-ilessp-0}
(({\it{y\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{y\/}} $\not=$ {\tt{0}})) $\rightarrow$ ({\rm{ilessp}}\,({\rm{idiv}}\,({\it{x\/}}, {\it{y\/}})\index{idiv}, {\tt{0}})\index{ilessp} $=$ {\rm{ilessp}}\,({\it{x\/}}, {\tt{0}})\index{ilessp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-plus-x-x-2-with-extra-arg \\ \index{quotient-plus-x-x-2-with-extra-!arg}
(({\it{x\/}} $+$ {\it{x\/}} $+$ {\it{y\/}}) $\div$ {\tt{2}}) $=$ ({\it{x\/}} $+$ ({\it{y\/}} $\div$ {\tt{2}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plus-quotient-2-lemma \\ \index{plus-quotient-2-lemma}
(({\it{v\/}} $+$ ({\tt{2}} $*$ {\it{z\/}})) $\div$ {\tt{2}}) $=$ ({\it{z\/}} $+$ ({\it{v\/}} $\div$ {\tt{2}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plus-quotient-2 \\ \index{plus-quotient-2}
({\it{a0\/}} $\not<$ {\it{exp\/}}) $\rightarrow$ (({\it{exp\/}} $+$ (({\it{a0\/}} $-$ {\it{exp\/}}) $\div$ {\tt{2}})) $=$ (({\it{a0\/}} $+$ {\it{exp\/}}) $\div$ {\tt{2}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  iplus-div-hack1 \\ \index{iplus-div-hack1}
\=\+(({\it{a0\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{exp\/}} $\in\;${\bf{N}}${}$)) \\ 
$\rightarrow$$\;\;\;\;$({\rm{iplus}}\,({\rm{idiv}}\,({\rm{iplus}}\,({\it{a0\/}}, {\rm{ineg}}\,({\it{exp\/}})\index{ineg})\index{iplus}, {\tt{2}})\index{idiv}, {\it{exp\/}})\index{iplus} $=$ (({\it{a0\/}} $+$ {\it{exp\/}}) $\div$ {\tt{2}}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable quotient-plus-x-x-2-with-extra-arg; name this event `quotient-plus-x-x-2-with-extra-arg-off'.\index{quotient-plus-x-x-2-with-extra-!arg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable plus-quotient-2-lemma; name this event `plus-quotient-2-lemma-off'.\index{plus-quotient-2-lemma-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable plus-quotient-2; name this event `plus-quotient-2-off'.\index{plus-quotient-2-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-quotient-2 \\ \index{lessp-quotient-2}
(({\it{x\/}} $\div$ {\tt{2}}) $<$ {\it{y\/}}) $\leftrightarrow$ ({\it{x\/}} $<$ ({\it{y\/}} $+$ {\it{y\/}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-int-adder-output} \\  
\=\+{\rm{v-alu-int-adder-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-int-adder-output} \\ 
$=$$\;\;\;\;${\rm{int-to-v}}\,({\rm{iplus}}\,({\rm{b-to-nat}}\,({\it{c\/}})\index{b-to-nat}, {\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int})\index{iplus})\index{iplus}, {\rm{length}}\,({\it{a\/}})\index{length})\index{int-to-v}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-int-adder-overflowp} \\  
\=\+{\rm{v-alu-int-adder-overflowp}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-int-adder-overflowp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{integer-in-rangep}}\,(\=\+{\rm{iplus}}\,(\=\+{\rm{b-to-nat}}\,({\it{c\/}})\index{b-to-nat}, \\ 
{\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int})\index{iplus})\-\index{iplus}, \\ 
{\rm{length}}\,({\it{a\/}})\index{length})\-\index{integer-in-rangep})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-int-adder} \\  
\=\+{\rm{v-alu-int-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-int-adder} \\ 
$=$$\;\;\;\;${\rm{cvzbv}}\,(\=\+{\rm{v-adder-carry-out}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder-carry-out}, \\ 
{\rm{v-alu-int-adder-overflowp}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-int-adder-overflowp}, \\ 
{\rm{v-alu-int-adder-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-int-adder-output})\-\index{cvzbv}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-int-adder-overflowp \\ \index{v-alu-correct-int-adder-overflo!wp}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{v-adder-overflowp}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder-overflowp} $=$ {\rm{v-alu-int-adder-overflowp}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-int-adder-overflowp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-int-adder-output \\ \index{v-alu-correct-int-adder-output}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{v-adder-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder-output} $=$ {\rm{v-alu-int-adder-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-int-adder-output})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-int-adder \\ \index{v-alu-correct-int-adder}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{cvzbv-v-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{cvzbv-v-adder} $=$ {\rm{v-alu-int-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-int-adder})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-int-inc} \\  
{\rm{v-alu-int-inc}}\,({\it{a\/}})\index{v-alu-int-inc} $=$ {\rm{v-alu-int-adder}}\,({\bf{t}}, {\it{a\/}}, {\rm{int-to-v}}\,({\tt{0}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{int-to-v})\index{v-alu-int-adder}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-int-inc \\ \index{v-alu-correct-int-inc}
({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}})) $\rightarrow$ ({\rm{cvzbv-inc}}\,({\it{a\/}})\index{cvzbv-inc} $=$ {\rm{v-alu-int-inc}}\,({\it{a\/}})\index{v-alu-int-inc})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-int-subtracter-output} \\  
\=\+{\rm{v-alu-int-subtracter-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-int-subtracter-output} \\ 
$=$$\;\;\;\;${\rm{int-to-v}}\,(\=\+{\rm{idifference}}\,({\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int}, {\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{b-to-nat}}\,({\it{c\/}})\index{b-to-nat})\index{iplus})\index{idifference}, \\ 
{\rm{length}}\,({\it{a\/}})\index{length})\-\index{int-to-v}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-int-subtracter-overflowp} \\  
\=\+{\rm{v-alu-int-subtracter-overflowp}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-int-subtracter-overflowp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{integer-in-rangep}}\,(\=\+{\rm{idifference}}\,(\=\+{\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int}, \\ 
{\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{b-to-nat}}\,({\it{c\/}})\index{b-to-nat})\index{iplus})\-\index{idifference}, \\ 
{\rm{length}}\,({\it{a\/}})\index{length})\-\index{integer-in-rangep})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-int-subtracter} \\  
\=\+{\rm{v-alu-int-subtracter}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-int-subtracter} \\ 
$=$$\;\;\;\;${\rm{cvzbv}}\,(\=\+{\rm{v-subtracter-carry-out}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-subtracter-carry-out}, \\ 
{\rm{v-alu-int-subtracter-overflowp}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-int-subtracter-overflowp}, \\ 
{\rm{v-alu-int-subtracter-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-int-subtracter-output})\-\index{cvzbv}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-int-subtracter-overflowp \\ \index{v-alu-correct-int-subtracter-ove!rflowp}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{v-subtracter-overflowp}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-subtracter-overflowp} \\ 
$=$$\;\;\;\;${\rm{v-alu-int-subtracter-overflowp}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-int-subtracter-overflowp})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-int-subtracter-output \\ \index{v-alu-correct-int-subtracter-outp!ut}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{v-subtracter-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-subtracter-output} $=$ {\rm{v-alu-int-subtracter-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-int-subtracter-output})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-int-subtracter \\ \index{v-alu-correct-int-subtracter}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{cvzbv-v-subtracter}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{cvzbv-v-subtracter} $=$ {\rm{v-alu-int-subtracter}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-int-subtracter})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-int-dec} \\  
{\rm{v-alu-int-dec}}\,({\it{a\/}})\index{v-alu-int-dec} $=$ {\rm{v-alu-int-subtracter}}\,({\bf{t}}, {\rm{int-to-v}}\,({\tt{0}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{int-to-v}, {\it{a\/}})\index{v-alu-int-subtracter}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-int-dec \\ \index{v-alu-correct-int-dec}
({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}})) $\rightarrow$ ({\rm{cvzbv-dec}}\,({\it{a\/}})\index{cvzbv-dec} $=$ {\rm{v-alu-int-dec}}\,({\it{a\/}})\index{v-alu-int-dec})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-int-asr-output} \\  
{\rm{v-alu-int-asr-output}}\,({\it{a\/}})\index{v-alu-int-asr-output} $=$ {\rm{int-to-v}}\,({\rm{idiv}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{2}})\index{idiv}, {\rm{length}}\,({\it{a\/}})\index{length})\index{int-to-v}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-int-asr} \\  
\=\+{\rm{v-alu-int-asr}}\,({\it{a\/}})\index{v-alu-int-asr} \\ 
$=$$\;\;\;\;${\rm{cvzbv}}\,({\rm{v-alu-nat-lsr-carry-out}}\,({\it{a\/}})\index{v-alu-nat-lsr-carry-out}, {\bf{f}}, {\rm{v-alu-int-asr-output}}\,({\it{a\/}})\index{v-alu-int-asr-output})\index{cvzbv}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-int-asr-output \\ \index{v-alu-correct-int-asr-output}
({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}})) $\rightarrow$ ({\rm{v-asr}}\,({\it{a\/}})\index{v-asr} $=$ {\rm{v-alu-int-asr-output}}\,({\it{a\/}})\index{v-alu-int-asr-output})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-int-asr \\ \index{v-alu-correct-int-asr}
{\rm{bvp}}\,({\it{a\/}})\index{bvp} $\rightarrow$ ({\rm{cvzbv-v-asr}}\,({\it{a\/}})\index{cvzbv-v-asr} $=$ {\rm{v-alu-int-asr}}\,({\it{a\/}})\index{v-alu-int-asr})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-int-neg} \\  
{\rm{v-alu-int-neg}}\,({\it{a\/}})\index{v-alu-int-neg} $=$ {\rm{v-alu-int-subtracter}}\,({\bf{f}}, {\it{a\/}}, {\rm{int-to-v}}\,({\tt{0}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{int-to-v})\index{v-alu-int-subtracter}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-int-neg \\ \index{v-alu-correct-int-neg}
({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}})) $\rightarrow$ ({\rm{cvzbv-neg}}\,({\it{a\/}})\index{cvzbv-neg} $=$ {\rm{v-alu-int-neg}}\,({\it{a\/}})\index{v-alu-int-neg})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-int-not-output} \\  
\=\+{\rm{v-alu-int-not-output}}\,({\it{a\/}})\index{v-alu-int-not-output} \\ 
$=$$\;\;\;\;${\rm{v-alu-int-subtracter-output}}\,({\bf{t}}, {\it{a\/}}, {\rm{int-to-v}}\,({\tt{0}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{int-to-v})\index{v-alu-int-subtracter-output}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-int-not} \\  
{\rm{v-alu-int-not}}\,({\it{a\/}})\index{v-alu-int-not} $=$ {\rm{cvzbv}}\,({\bf{f}}, {\bf{f}}, {\rm{v-alu-int-not-output}}\,({\it{a\/}})\index{v-alu-int-not-output})\index{cvzbv}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-int-not-output \\ \index{v-alu-correct-int-not-output}
({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}})) $\rightarrow$ ({\rm{v-not}}\,({\it{a\/}})\index{v-not} $=$ {\rm{v-alu-int-not-output}}\,({\it{a\/}})\index{v-alu-int-not-output})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-int-not \\ \index{v-alu-correct-int-not}
({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}})) $\rightarrow$ ({\rm{cvzbv-v-not}}\,({\it{a\/}})\index{cvzbv-v-not} $=$ {\rm{v-alu-int-not}}\,({\it{a\/}})\index{v-alu-int-not})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-alu-int} \\  
\=\+{\rm{v-alu-int}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu-int} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\rm{v-alu-nat-int-buf}}\,({\it{a\/}})\index{v-alu-nat-int-buf} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\rm{v-alu-int-inc}}\,({\it{a\/}})\index{v-alu-int-inc} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\rm{v-alu-int-adder}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-int-adder} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\rm{v-alu-int-adder}}\,({\bf{f}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-int-adder} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }{\rm{v-alu-int-neg}}\,({\it{a\/}})\index{v-alu-int-neg} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }{\rm{v-alu-int-dec}}\,({\it{a\/}})\index{v-alu-int-dec} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }{\rm{v-alu-int-subtracter}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-int-subtracter} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }{\rm{v-alu-int-subtracter}}\,({\bf{f}}, {\it{a\/}}, {\it{b\/}})\index{v-alu-int-subtracter} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}})$\;\;${\bf then }{\rm{v-alu-int-asr}}\,({\it{a\/}})\index{v-alu-int-asr} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}})$\;\;${\bf then }{\rm{v-alu-int-not}}\,({\it{a\/}})\index{v-alu-int-not} \\ 
{\bf else }{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-int \\ \index{v-alu-correct-int}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu} $=$ {\rm{v-alu-int}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu-int})\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-alu-correct-nat-int-buf; name this event `v-alu-correct-nat-int-buf-off'.\index{v-alu-correct-nat-int-buf-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-nat-adder-carry-out; name this event `v-alu-correct-nat-adder-carry-out-off'.\index{v-alu-correct-nat-adder-carry-o!ut-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-nat-adder-output; name this event `v-alu-correct-nat-adder-output-off'.\index{v-alu-correct-nat-adder-output-!off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-nat-adder; name this event `v-alu-correct-nat-adder-off'.\index{v-alu-correct-nat-adder-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-nat-inc; name this event `v-alu-correct-nat-inc-off'.\index{v-alu-correct-nat-inc-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-nat-subtracter-carry-out; name this event `v-alu-correct-nat-subtracter-carry-out-off'.\index{v-alu-correct-nat-subtracter-ca!rry-out-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-nat-subtracter-output; name this event `v-alu-correct-nat-subtracter-output-off'.\index{v-alu-correct-nat-subtracter-outp!ut-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-nat-subtracter; name this event `v-alu-correct-nat-subtracter-off'.\index{v-alu-correct-nat-subtracter-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-nat-dec; name this event `v-alu-correct-nat-dec-off'.\index{v-alu-correct-nat-dec-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-nat-lsr-carry-out; name this event `v-alu-correct-nat-lsr-carry-out-off'.\index{v-alu-correct-nat-lsr-carry-out!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-nat-lsr-output; name this event `v-alu-correct-nat-lsr-output-off'.\index{v-alu-correct-nat-lsr-output-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-nat-lsr; name this event `v-alu-correct-nat-lsr-off'.\index{v-alu-correct-nat-lsr-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-nat-not-output; name this event `v-alu-correct-nat-not-output-off1'.\index{v-alu-correct-nat-not-output-of!f1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-nat-not; name this event `v-alu-correct-nat-not-off'.\index{v-alu-correct-nat-not-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-int-adder-overflowp; name this event `v-alu-correct-int-adder-overflowp-off'.\index{v-alu-correct-int-adder-overflo!wp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-int-adder-output; name this event `v-alu-correct-int-adder-output-off'.\index{v-alu-correct-int-adder-output-!off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-int-adder; name this event `v-alu-correct-int-adder-off'.\index{v-alu-correct-int-adder-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-int-inc; name this event `v-alu-correct-int-inc-off'.\index{v-alu-correct-int-inc-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-int-subtracter-overflowp; name this event `v-alu-correct-int-subtracter-overflowp-off'.\index{v-alu-correct-int-subtracter-ove!rflowp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-int-subtracter-output; name this event `v-alu-correct-int-subtracter-output-off'.\index{v-alu-correct-int-subtracter-outp!ut-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-int-subtracter; name this event `v-alu-correct-int-subtracter-off'.\index{v-alu-correct-int-subtracter-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-int-dec; name this event `v-alu-correct-int-dec-off'.\index{v-alu-correct-int-dec-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-int-asr-output; name this event `v-alu-correct-int-asr-output-off'.\index{v-alu-correct-int-asr-output-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-int-asr; name this event `v-alu-correct-int-asr-off'.\index{v-alu-correct-int-asr-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-int-neg; name this event `v-alu-correct-int-neg-off'.\index{v-alu-correct-int-neg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-int-not; name this event `v-alu-correct-int-not-off'.\index{v-alu-correct-int-not-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-int; name this event `v-alu-correct-int-off'.\index{v-alu-correct-int-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-int; name this event `v-alu-int-off'.\index{v-alu-int-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-int; name this event `g*1*v-alu-int-off'.\index{g*1*v-alu-int-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-int-not-output; name this event `v-alu-correct-int-not-output-off'.\index{v-alu-correct-int-not-output-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-int-not; name this event `v-alu-int-not-off'.\index{v-alu-int-not-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-int-not; name this event `g*1*v-alu-int-not-off'.\index{g*1*v-alu-int-not-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-int-not-output; name this event `v-alu-int-not-output-off'.\index{v-alu-int-not-output-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-int-not-output; name this event `g*1*v-alu-int-not-output-off'.\index{g*1*v-alu-int-not-output-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-int-neg; name this event `v-alu-int-neg-off'.\index{v-alu-int-neg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-int-neg; name this event `g*1*v-alu-int-neg-off'.\index{g*1*v-alu-int-neg-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-int-asr; name this event `v-alu-int-asr-off'.\index{v-alu-int-asr-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-int-asr; name this event `g*1*v-alu-int-asr-off'.\index{g*1*v-alu-int-asr-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-int-asr-output; name this event `v-alu-int-asr-output-off'.\index{v-alu-int-asr-output-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-int-asr-output; name this event `g*1*v-alu-int-asr-output-off'.\index{g*1*v-alu-int-asr-output-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-int-dec; name this event `v-alu-int-dec-off'.\index{v-alu-int-dec-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-int-dec; name this event `g*1*v-alu-int-dec-off'.\index{g*1*v-alu-int-dec-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-int-subtracter; name this event `v-alu-int-subtracter-off'.\index{v-alu-int-subtracter-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-int-subtracter; name this event `g*1*v-alu-int-subtracter-off'.\index{g*1*v-alu-int-subtracter-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-int-subtracter-overflowp; name this event `v-alu-int-subtracter-overflowp-off'.\index{v-alu-int-subtracter-overflowp-!off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-int-subtracter-overflowp; name this event `g*1*v-alu-int-subtracter-overflowp-off'.\index{g*1*v-alu-int-subtracter-overfl!owp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-int-subtracter-output; name this event `v-alu-int-subtracter-output-off'.\index{v-alu-int-subtracter-output-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-int-subtracter-output; name this event `g*1*v-alu-int-subtracter-output-off'.\index{g*1*v-alu-int-subtracter-output!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-int-inc; name this event `v-alu-int-inc-off'.\index{v-alu-int-inc-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-int-inc; name this event `g*1*v-alu-int-inc-off'.\index{g*1*v-alu-int-inc-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-int-adder; name this event `v-alu-int-adder-off'.\index{v-alu-int-adder-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-int-adder; name this event `g*1*v-alu-int-adder-off'.\index{g*1*v-alu-int-adder-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-int-adder-overflowp; name this event `v-alu-int-adder-overflowp-off'.\index{v-alu-int-adder-overflowp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-int-adder-overflowp; name this event `g*1*v-alu-int-adder-overflowp-off'.\index{g*1*v-alu-int-adder-overflowp-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-int-adder-output; name this event `v-alu-int-adder-output-off'.\index{v-alu-int-adder-output-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-int-adder-output; name this event `g*1*v-alu-int-adder-output-off'.\index{g*1*v-alu-int-adder-output-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-quotient-2; name this event `lessp-quotient-2-off'.\index{lessp-quotient-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-div-hack1; name this event `iplus-div-hack1-off'.\index{iplus-div-hack1-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable idiv-ilessp-0; name this event `idiv-ilessp-0-off'.\index{idiv-ilessp-0-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable idiv-quotient; name this event `idiv-quotient-off'.\index{idiv-quotient-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable idifference-difference; name this event `idifference-difference-off'.\index{idifference-difference-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-int-subtracter-overflowp-lemma; name this event `v-alu-correct-int-subtracter-overflowp-lemma-off'.\index{v-alu-correct-int-subtracter-ove!rflowp-lemma-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-to-int-v-not; name this event `v-to-int-v-not-off'.\index{v-to-int-v-not-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus3-plus-difference; name this event `iplus3-plus-difference-off'.\index{iplus3-plus-difference-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-numberp; name this event `fix-int-numberp-off'.\index{fix-int-numberp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-v-to-nat-exp-with-exp-opened; name this event `lessp-v-to-nat-exp-with-exp-opened-off'.\index{lessp-v-to-nat-exp-with-exp-ope!ned-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-to-nat-leq; name this event `b-to-nat-leq-off'.\index{b-to-nat-leq-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-2; name this event `times-2-off'.\index{times-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-lessp; name this event `ilessp-lessp-off'.\index{ilessp-lessp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-plus; name this event `iplus-plus-off'.\index{iplus-plus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integer-in-rangep; name this event `integer-in-rangep-off'.\index{integer-in-rangep-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*integer-in-rangep; name this event `g*1*integer-in-rangep-off'.\index{g*1*integer-in-rangep-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-to-int; name this event `v-to-int-off'.\index{v-to-int-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-to-int; name this event `g*1*v-to-int-off'.\index{g*1*v-to-int-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable int-to-v; name this event `int-to-v-off'.\index{int-to-v-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*int-to-v; name this event `g*1*int-to-v-off'.\index{g*1*int-to-v-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-nat; name this event `v-alu-correct-nat-off'.\index{v-alu-correct-nat-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-nat; name this event `v-alu-nat-off'.\index{v-alu-nat-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-nat; name this event `g*1*v-alu-nat-off'.\index{g*1*v-alu-nat-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-nat-not; name this event `v-alu-nat-not-off'.\index{v-alu-nat-not-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-nat-not; name this event `g*1*v-alu-nat-not-off'.\index{g*1*v-alu-nat-not-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-nat-not-output; name this event `v-alu-nat-not-output-off'.\index{v-alu-nat-not-output-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-nat-not-output; name this event `g*1*v-alu-nat-not-output-off'.\index{g*1*v-alu-nat-not-output-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-nat-lsr; name this event `v-alu-nat-lsr-off'.\index{v-alu-nat-lsr-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-nat-lsr; name this event `g*1*v-alu-nat-lsr-off'.\index{g*1*v-alu-nat-lsr-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-nat-lsr-carry-out; name this event `v-alu-nat-lsr-carry-out-off'.\index{v-alu-nat-lsr-carry-out-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-nat-lsr-carry-out; name this event `g*1*v-alu-nat-lsr-carry-out-off'.\index{g*1*v-alu-nat-lsr-carry-out-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-nat-lsr-output; name this event `v-alu-nat-lsr-output-off'.\index{v-alu-nat-lsr-output-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-nat-lsr-output; name this event `g*1*v-alu-nat-lsr-output-off'.\index{g*1*v-alu-nat-lsr-output-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-nat-dec; name this event `v-alu-nat-dec-off'.\index{v-alu-nat-dec-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-nat-dec; name this event `g*1*v-alu-nat-dec-off'.\index{g*1*v-alu-nat-dec-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-nat-subtracter; name this event `v-alu-nat-subtracter-off'.\index{v-alu-nat-subtracter-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-nat-subtracter; name this event `g*1*v-alu-nat-subtracter-off'.\index{g*1*v-alu-nat-subtracter-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-nat-subtracter-carry-out; name this event `v-alu-nat-subtracter-carry-out-off'.\index{v-alu-nat-subtracter-carry-out-!off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-nat-subtracter-carry-out; name this event `g*1*v-alu-nat-subtracter-carry-out-off'.\index{g*1*v-alu-nat-subtracter-carry-!out-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-nat-subtracter-output; name this event `v-alu-nat-subtracter-output-off'.\index{v-alu-nat-subtracter-output-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-nat-subtracter-output; name this event `g*1*v-alu-nat-subtracter-output-off'.\index{g*1*v-alu-nat-subtracter-output!-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-nat-inc; name this event `v-alu-nat-inc-off'.\index{v-alu-nat-inc-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-nat-inc; name this event `g*1*v-alu-nat-inc-off'.\index{g*1*v-alu-nat-inc-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-nat-adder; name this event `v-alu-nat-adder-off'.\index{v-alu-nat-adder-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-nat-adder; name this event `g*1*v-alu-nat-adder-off'.\index{g*1*v-alu-nat-adder-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-nat-adder-carry-out; name this event `v-alu-nat-adder-carry-out-off'.\index{v-alu-nat-adder-carry-out-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-nat-adder-carry-out; name this event `g*1*v-alu-nat-adder-carry-out-off'.\index{g*1*v-alu-nat-adder-carry-out-o!ff}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-nat-adder-output; name this event `v-alu-nat-adder-output-off'.\index{v-alu-nat-adder-output-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-nat-adder-output; name this event `g*1*v-alu-nat-adder-output-off'.\index{g*1*v-alu-nat-adder-output-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-to-nat-append; name this event `v-to-nat-append-off'.\index{v-to-nat-append-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable not-lessp-quotient; name this event `not-lessp-quotient-off'.\index{not-lessp-quotient-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-v-to-nat-exp-rewrite; name this event `lessp-v-to-nat-exp-rewrite-off'.\index{lessp-v-to-nat-exp-rewrite-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-nat-subtracter-output-lemma; name this event `v-alu-correct-nat-subtracter-output-lemma-off'.\index{v-alu-correct-nat-subtracter-outp!ut-lemma-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-v-to-nat-exp; name this event `lessp-v-to-nat-exp-off'.\index{lessp-v-to-nat-exp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-to-nat-v-not; name this event `v-to-nat-v-not-off'.\index{v-to-nat-v-not-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-to-nat-v-not-lemma; name this event `v-to-nat-v-not-lemma-off'.\index{v-to-nat-v-not-lemma-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-nat-to-v-inverter; name this event `equal-nat-to-v-inverter-off'.\index{equal-nat-to-v-inverter-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable nat-to-v-remainder; name this event `nat-to-v-remainder-off'.\index{nat-to-v-remainder-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-nat-to-v-inverter-hack2-lemma; name this event `equal-nat-to-v-inverter-hack2-lemma-off'.\index{equal-nat-to-v-inverter-hack2-le!mma-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable nat-to-v-zerop; name this event `nat-to-v-zerop-off'.\index{nat-to-v-zerop-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable nat-to-v-of-v-to-nat; name this event `nat-to-v-of-v-to-nat-off'.\index{nat-to-v-of-v-to-nat-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable firstn-length; name this event `firstn-length-off'.\index{firstn-length-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable nat-to-v-of-v-to-nat-general; name this event `nat-to-v-of-v-to-nat-general-off'.\index{nat-to-v-of-v-to-nat-general-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable firstn-nlistp; name this event `firstn-nlistp-off'.\index{firstn-nlistp-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable firstn-zerop; name this event `firstn-zerop-off'.\index{firstn-zerop-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable firstn-add1-cons; name this event `firstn-add1-cons-off'.\index{firstn-add1-cons-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable nat-to-v-plus-x-x; name this event `nat-to-v-plus-x-x-off'.\index{nat-to-v-plus-x-x-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-plus-x-x-2; name this event `quotient-plus-x-x-2-off'.\index{quotient-plus-x-x-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-plus-x-x-2; name this event `remainder-plus-x-x-2-off'.\index{remainder-plus-x-x-2-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-to-nat-of-nat-to-v; name this event `v-to-nat-of-nat-to-v-off'.\index{v-to-nat-of-nat-to-v-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-to-nat-of-nat-to-v-hack; name this event `v-to-nat-of-nat-to-v-hack-off'.\index{v-to-nat-of-nat-to-v-hack-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-to-nat-firstn; name this event `v-to-nat-firstn-off'.\index{v-to-nat-firstn-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-add1-plus-multiple; name this event `remainder-add1-plus-multiple-off'.\index{remainder-add1-plus-multiple-of!f}

\addvspace{18pt}


\noindent{\sc Event}:   Enable divides-plus-plus; name this event `divides-plus-plus-off'.\index{divides-plus-plus-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-plus-multiple; name this event `remainder-plus-multiple-off'.\index{remainder-plus-multiple-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable nth-length-v; name this event `nth-length-v-off'.\index{nth-length-v-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-nat-int-buf; name this event `v-alu-nat-int-buf-off'.\index{v-alu-nat-int-buf-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*v-alu-nat-int-buf; name this event `g*1*v-alu-nat-int-buf-off'.\index{g*1*v-alu-nat-int-buf-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable bvp-cdr; name this event `bvp-cdr-off'.\index{bvp-cdr-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-to-nat; name this event `b-to-nat-off'.\index{b-to-nat-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*b-to-nat; name this event `g*1*b-to-nat-off'.\index{g*1*b-to-nat-off}

\addvspace{18pt}


\noindent{\sc Event}:   Enable map-down-inverts-map-up; name this event `map-down-inverts-map-up-off1'.\index{map-down-inverts-map-up-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable for-final-1-of-reset-sequence-chip; name this event `for-final-1-of-reset-sequence-chip-off1'.\index{for-final-1-of-reset-sequence-c!hip-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable chip-well-formed-simple; name this event `chip-well-formed-simple-on'.\index{chip-well-formed-simple-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable chip-well-formed-after-indexed-names-removed; name this event `chip-well-formed-after-indexed-names-removed-on'.\index{chip-well-formed-after-indexed-!names-removed-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable chip-well-formed; name this event `chip-well-formed-on'.\index{chip-well-formed-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable chip-system=fm9001-interpreter\$after-reset; name this event `chip-system=fm9001-interpreter\$after-reset-on'.\index{chip-system=fm9001-interpreter\$!after-reset-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable reset-chip-from-any-state; name this event `reset-chip-from-any-state-on'.\index{reset-chip-from-any-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable reset-chip; name this event `reset-chip-on'.\index{reset-chip-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable length-reset-sequence-chip-1; name this event `length-reset-sequence-chip-1-on'.\index{length-reset-sequence-chip-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable simulate-contains-simulate-dual-eval-2; name this event `simulate-contains-simulate-dual-eval-2-on'.\index{simulate-contains-simulate-dual!-eval-2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fm9001=chip-system-true-after-reset; name this event `fm9001=chip-system-true-after-reset-on'.\index{fm9001=chip-system-true-after-re!set-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable cadr-map-up; name this event `cadr-map-up-on'.\index{cadr-map-up-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fm9001=chip-system-true-after-reset-lemma; name this event `fm9001=chip-system-true-after-reset-lemma-on'.\index{fm9001=chip-system-true-after-re!set-lemma-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fm9001-statep-implies-memory-ok-p-instance; name this event `fm9001-statep-implies-memory-ok-p-instance-on'.\index{fm9001-statep-implies-memory-ok!-p-instance-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable new-machine-state-invariant-implies-machine-state-invariant; name this event `new-machine-state-invariant-implies-machine-state-invariant-on'.\index{new-machine-state-invariant-imp!lies-machine-state-invariant-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable memory-v-fourp-implies-memory-properp; name this event `memory-v-fourp-implies-memory-properp-on'.\index{memory-v-fourp-implies-memory-p!roperp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable new-machine-state-invariant-is-non-trivial; name this event `new-machine-state-invariant-is-non-trivial-on'.\index{new-machine-state-invariant-is-!non-trivial-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable xs-suffice-for-reset-chip-final-state-for-any-unknown-state-better; name this event `xs-suffice-for-reset-chip-final-state-for-any-unknown-state-better-on'.\index{xs-suffice-for-reset-chip-final!-state-for-any-unknown-state-better-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable xs-suffice-for-reset-chip-final-state-for-any-unknown-state; name this event `xs-suffice-for-reset-chip-final-state-for-any-unknown-state-on'.\index{xs-suffice-for-reset-chip-final!-state-for-any-unknown-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable new-machine-state-invariant-implies-good-s; name this event `new-machine-state-invariant-implies-good-s-on'.\index{new-machine-state-invariant-imp!lies-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-fourp-is-good-s; name this event `v-fourp-is-good-s-on'.\index{v-fourp-is-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable memory-v-fourp-implies-good-s; name this event `memory-v-fourp-implies-good-s-on'.\index{memory-v-fourp-implies-good-s-o!n}

\addvspace{18pt}


\noindent{\sc Event}:   Disable good-s-opener; name this event `good-s-opener-on'.\index{good-s-opener-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable machine-state-invariant-implies-s-approx; name this event `machine-state-invariant-implies-s-approx-on'.\index{machine-state-invariant-implies!-s-approx-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable machine-state-invariant-implies-s-approx-lemma-3; name this event `machine-state-invariant-implies-s-approx-lemma-3-on'.\index{machine-state-invariant-implies!-s-approx-lemma-3-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable machine-state-invariant-implies-s-approx-lemma-2; name this event `machine-state-invariant-implies-s-approx-lemma-2-on'.\index{machine-state-invariant-implies!-s-approx-lemma-2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable machine-state-invariant-implies-s-approx-lemma; name this event `machine-state-invariant-implies-s-approx-lemma-on'.\index{machine-state-invariant-implies!-s-approx-lemma-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-approx-x; name this event `b-approx-x-on'.\index{b-approx-x-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable stubp-implies-not-fourp; name this event `stubp-implies-not-fourp-on'.\index{stubp-implies-not-fourp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable romp-implies-not-fourp; name this event `romp-implies-not-fourp-on'.\index{romp-implies-not-fourp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ramp-implies-not-fourp; name this event `ramp-implies-not-fourp-on'.\index{ramp-implies-not-fourp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable listp-implies-not-fourp; name this event `listp-implies-not-fourp-on'.\index{listp-implies-not-fourp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-fourp-implies-properp; name this event `v-fourp-implies-properp-on'.\index{v-fourp-implies-properp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx-make-list; name this event `s-approx-make-list-on'.\index{s-approx-make-list-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable new-machine-state-invariant; name this event `new-machine-state-invariant-on'.\index{new-machine-state-invariant-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*new-machine-state-invariant; name this event `g*1*new-machine-state-invariant-on'.\index{g*1*new-machine-state-invariant!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable memory-v-fourp; name this event `memory-v-fourp-on'.\index{memory-v-fourp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*memory-v-fourp; name this event `g*1*memory-v-fourp-on'.\index{g*1*memory-v-fourp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable all-xs-make-list; name this event `all-xs-make-list-on'.\index{all-xs-make-list-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable all-xs-approximates; name this event `all-xs-approximates-on'.\index{all-xs-approximates-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable all-xs; name this event `all-xs-on'.\index{all-xs-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*all-xs; name this event `g*1*all-xs-on'.\index{g*1*all-xs-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-fourp; name this event `v-fourp-on'.\index{v-fourp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*v-fourp; name this event `g*1*v-fourp-on'.\index{g*1*v-fourp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fm9001-machine-statep-p-map-up-initialized-machine-state; name this event `fm9001-machine-statep-p-map-up-initialized-machine-state-on'.\index{fm9001-machine-statep-p-map-up-i!nitialized-machine-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable xs-suffice-for-reset-chip-lemma-instance; name this event `xs-suffice-for-reset-chip-lemma-instance-on'.\index{xs-suffice-for-reset-chip-lemma!-instance-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable simulate-reset-chip-final-state; name this event `simulate-reset-chip-final-state-on'.\index{simulate-reset-chip-final-state!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable reset-sequence-chip-1-vs-2; name this event `reset-sequence-chip-1-vs-2-on'.\index{reset-sequence-chip-1-vs-2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable reset-sequence-chip-2; name this event `reset-sequence-chip-2-on'.\index{reset-sequence-chip-2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*reset-sequence-chip-2; name this event `g*1*reset-sequence-chip-2-on'.\index{g*1*reset-sequence-chip-2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable reset-sequence-chip-1; name this event `reset-sequence-chip-1-on'.\index{reset-sequence-chip-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*reset-sequence-chip-1; name this event `g*1*reset-sequence-chip-1-on'.\index{g*1*reset-sequence-chip-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable run-vector-chip-2; name this event `run-vector-chip-2-on'.\index{run-vector-chip-2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*run-vector-chip-2; name this event `g*1*run-vector-chip-2-on'.\index{g*1*run-vector-chip-2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable run-vector-chip-1; name this event `run-vector-chip-1-on'.\index{run-vector-chip-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*run-vector-chip-1; name this event `g*1*run-vector-chip-1-on'.\index{g*1*run-vector-chip-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable reset-vector-chip; name this event `reset-vector-chip-on'.\index{reset-vector-chip-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*reset-vector-chip; name this event `g*1*reset-vector-chip-on'.\index{g*1*reset-vector-chip-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fm9001-statep-map-up-final-state; name this event `fm9001-statep-map-up-final-state-on'.\index{fm9001-statep-map-up-final-state!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable instance-theorem; name this event `instance-theorem-on'.\index{instance-theorem-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable final-state-okp; name this event `final-state-okp-on'.\index{final-state-okp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable unknown-state-okp; name this event `unknown-state-okp-on'.\index{unknown-state-okp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable reset-works; name this event `reset-works-on'.\index{reset-works-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable final-state; name this event `final-state-on'.\index{final-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*final-state; name this event `g*1*final-state-on'.\index{g*1*final-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable initialized-memory-state; name this event `initialized-memory-state-on'.\index{initialized-memory-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*initialized-memory-state; name this event `g*1*initialized-memory-state-on'.\index{g*1*initialized-memory-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable initialized-machine-state; name this event `initialized-machine-state-on'.\index{initialized-machine-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*initialized-machine-state; name this event `g*1*initialized-machine-state-on'.\index{g*1*initialized-machine-state-o!n}

\addvspace{18pt}


\noindent{\sc Event}:   Disable initialized-regfile; name this event `initialized-regfile-on'.\index{initialized-regfile-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*initialized-regfile; name this event `g*1*initialized-regfile-on'.\index{g*1*initialized-regfile-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable chip-system-operating-inputs-p-reset-sequence; name this event `chip-system-operating-inputs-p-reset-sequence-on'.\index{chip-system-operating-inputs-p-!reset-sequence-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable reset-sequence; name this event `reset-sequence-on'.\index{reset-sequence-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*reset-sequence; name this event `g*1*reset-sequence-on'.\index{g*1*reset-sequence-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable run-vector; name this event `run-vector-on'.\index{run-vector-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*run-vector; name this event `g*1*run-vector-on'.\index{g*1*run-vector-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable reset-vector; name this event `reset-vector-on'.\index{reset-vector-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*reset-vector; name this event `g*1*reset-vector-on'.\index{g*1*reset-vector-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fm9001-state-structure-unknown-state; name this event `fm9001-state-structure-unknown-state-on'.\index{fm9001-state-structure-unknown-!state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable chip-system-invariant-unknown-state; name this event `chip-system-invariant-unknown-state-on'.\index{chip-system-invariant-unknown-st!ate-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable unknown-state; name this event `unknown-state-on'.\index{unknown-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*unknown-state; name this event `g*1*unknown-state-on'.\index{g*1*unknown-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable unknown-memory-state; name this event `unknown-memory-state-on'.\index{unknown-memory-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*unknown-memory-state; name this event `g*1*unknown-memory-state-on'.\index{g*1*unknown-memory-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable unknown-machine-state; name this event `unknown-machine-state-on'.\index{unknown-machine-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*unknown-machine-state; name this event `g*1*unknown-machine-state-on'.\index{g*1*unknown-machine-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable unknown-regfile; name this event `unknown-regfile-on'.\index{unknown-regfile-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*unknown-regfile; name this event `g*1*unknown-regfile-on'.\index{g*1*unknown-regfile-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable compile-uncompiled-defns; name this event `compile-uncompiled-defns-on2'.\index{compile-uncompiled-defns-on2}

\addvspace{18pt}


\noindent{\sc Event}:   For efficiency, compile those definitions not yet compiled.

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*compile-uncompiled-defns; name this event `g*1*compile-uncompiled-defns-on'.\index{g*1*compile-uncompiled-defns-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable xs-suffice-for-reset-lemma; name this event `xs-suffice-for-reset-lemma-on'.\index{xs-suffice-for-reset-lemma-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable xs-suffice-for-reset-lemma-verbose; name this event `xs-suffice-for-reset-lemma-verbose-on'.\index{xs-suffice-for-reset-lemma-verb!ose-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable length-simulate; name this event `length-simulate-on'.\index{length-simulate-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable doublet-p-equal-approx; name this event `doublet-p-equal-approx-on'.\index{doublet-p-equal-approx-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable doublet-n-simulate; name this event `doublet-n-simulate-on'.\index{doublet-n-simulate-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable doublet-n-simulate-induction; name this event `doublet-n-simulate-induction-on'.\index{doublet-n-simulate-induction-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*doublet-n-simulate-induction; name this event `g*1*doublet-n-simulate-induction-on'.\index{g*1*doublet-n-simulate-inductio!n-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*doublet-p; name this event `g*1*doublet-p-on'.\index{g*1*doublet-p-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-approx-list-x-x; name this event `v-approx-list-x-x-on'.\index{v-approx-list-x-x-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable simulate-monotone; name this event `simulate-monotone-on'.\index{simulate-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable simulate-monotone-induction; name this event `simulate-monotone-induction-on'.\index{simulate-monotone-induction-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*simulate-monotone-induction; name this event `g*1*simulate-monotone-induction-on'.\index{g*1*simulate-monotone-induction!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx-cadr-nth; name this event `s-approx-cadr-nth-on'.\index{s-approx-cadr-nth-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-approx-car-nth; name this event `v-approx-car-nth-on'.\index{v-approx-car-nth-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable nat-lst-lst-induction; name this event `nat-lst-lst-induction-on'.\index{nat-lst-lst-induction-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*nat-lst-lst-induction; name this event `g*1*nat-lst-lst-induction-on'.\index{g*1*nat-lst-lst-induction-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-s-approx-list; name this event `v-s-approx-list-on'.\index{v-s-approx-list-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*v-s-approx-list; name this event `g*1*v-s-approx-list-on'.\index{g*1*v-s-approx-list-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-approx-list; name this event `v-approx-list-on'.\index{v-approx-list-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*v-approx-list; name this event `g*1*v-approx-list-on'.\index{g*1*v-approx-list-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable good-s-preserved; name this event `good-s-preserved-on'.\index{good-s-preserved-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable primp-preserves-good-s; name this event `primp-preserves-good-s-on'.\index{primp-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dp-ram-16x32-preserves-good-s; name this event `dp-ram-16x32-preserves-good-s-on'.\index{dp-ram-16x32-preserves-good-s-o!n}

\addvspace{18pt}


\noindent{\sc Event}:   Disable good-s-write-mem; name this event `good-s-write-mem-on'.\index{good-s-write-mem-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable good-s-write-mem-1; name this event `good-s-write-mem-1-on'.\index{good-s-write-mem-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable good-s-constant-ram; name this event `good-s-constant-ram-on'.\index{good-s-constant-ram-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable vss-preserves-good-s; name this event `vss-preserves-good-s-on'.\index{vss-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable vdd-parametric-preserves-good-s; name this event `vdd-parametric-preserves-good-s-on'.\index{vdd-parametric-preserves-good-s!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable vdd-preserves-good-s; name this event `vdd-preserves-good-s-on'.\index{vdd-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ttl-tri-output-fast-preserves-good-s; name this event `ttl-tri-output-fast-preserves-good-s-on'.\index{ttl-tri-output-fast-preserves-g!ood-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ttl-tri-output-preserves-good-s; name this event `ttl-tri-output-preserves-good-s-on'.\index{ttl-tri-output-preserves-good-s!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ttl-output-fast-preserves-good-s; name this event `ttl-output-fast-preserves-good-s-on'.\index{ttl-output-fast-preserves-good-!s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ttl-output-parametric-preserves-good-s; name this event `ttl-output-parametric-preserves-good-s-on'.\index{ttl-output-parametric-preserves!-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ttl-output-preserves-good-s; name this event `ttl-output-preserves-good-s-on'.\index{ttl-output-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ttl-input-preserves-good-s; name this event `ttl-input-preserves-good-s-on'.\index{ttl-input-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ttl-clk-input-preserves-good-s; name this event `ttl-clk-input-preserves-good-s-on'.\index{ttl-clk-input-preserves-good-s-!on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ttl-bidirect-preserves-good-s; name this event `ttl-bidirect-preserves-good-s-on'.\index{ttl-bidirect-preserves-good-s-o!n}

\addvspace{18pt}


\noindent{\sc Event}:   Disable pullup-preserves-good-s; name this event `pullup-preserves-good-s-on'.\index{pullup-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable t-wire-preserves-good-s; name this event `t-wire-preserves-good-s-on'.\index{t-wire-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable t-buf-preserves-good-s; name this event `t-buf-preserves-good-s-on'.\index{t-buf-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ram-enable-circuit-preserves-good-s; name this event `ram-enable-circuit-preserves-good-s-on'.\index{ram-enable-circuit-preserves-go!od-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable id-preserves-good-s; name this event `id-preserves-good-s-on'.\index{id-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fd1slp-preserves-good-s; name this event `fd1slp-preserves-good-s-on'.\index{fd1slp-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fd1sp-preserves-good-s; name this event `fd1sp-preserves-good-s-on'.\index{fd1sp-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fd1s-preserves-good-s; name this event `fd1s-preserves-good-s-on'.\index{fd1s-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fd1-preserves-good-s; name this event `fd1-preserves-good-s-on'.\index{fd1-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable procmon-preserves-good-s; name this event `procmon-preserves-good-s-on'.\index{procmon-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable del10-preserves-good-s; name this event `del10-preserves-good-s-on'.\index{del10-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable del4-preserves-good-s; name this event `del4-preserves-good-s-on'.\index{del4-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable del2-preserves-good-s; name this event `del2-preserves-good-s-on'.\index{del2-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-xor3-preserves-good-s; name this event `b-xor3-preserves-good-s-on'.\index{b-xor3-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-xor-preserves-good-s; name this event `b-xor-preserves-good-s-on'.\index{b-xor-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-or4-preserves-good-s; name this event `b-or4-preserves-good-s-on'.\index{b-or4-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-or3-preserves-good-s; name this event `b-or3-preserves-good-s-on'.\index{b-or3-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-or-preserves-good-s; name this event `b-or-preserves-good-s-on'.\index{b-or-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-not-ivap-preserves-good-s; name this event `b-not-ivap-preserves-good-s-on'.\index{b-not-ivap-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-not-b4ip-preserves-good-s; name this event `b-not-b4ip-preserves-good-s-on'.\index{b-not-b4ip-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-not-preserves-good-s; name this event `b-not-preserves-good-s-on'.\index{b-not-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nor8-preserves-good-s; name this event `b-nor8-preserves-good-s-on'.\index{b-nor8-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nor6-preserves-good-s; name this event `b-nor6-preserves-good-s-on'.\index{b-nor6-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nor5-preserves-good-s; name this event `b-nor5-preserves-good-s-on'.\index{b-nor5-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nor4-preserves-good-s; name this event `b-nor4-preserves-good-s-on'.\index{b-nor4-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nor3-preserves-good-s; name this event `b-nor3-preserves-good-s-on'.\index{b-nor3-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nor-preserves-good-s; name this event `b-nor-preserves-good-s-on'.\index{b-nor-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nbuf-preserves-good-s; name this event `b-nbuf-preserves-good-s-on'.\index{b-nbuf-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nand8-preserves-good-s; name this event `b-nand8-preserves-good-s-on'.\index{b-nand8-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nand6-preserves-good-s; name this event `b-nand6-preserves-good-s-on'.\index{b-nand6-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nand5-preserves-good-s; name this event `b-nand5-preserves-good-s-on'.\index{b-nand5-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nand4-preserves-good-s; name this event `b-nand4-preserves-good-s-on'.\index{b-nand4-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nand3-preserves-good-s; name this event `b-nand3-preserves-good-s-on'.\index{b-nand3-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nand-preserves-good-s; name this event `b-nand-preserves-good-s-on'.\index{b-nand-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-if-preserves-good-s; name this event `b-if-preserves-good-s-on'.\index{b-if-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-equv3-preserves-good-s; name this event `b-equv3-preserves-good-s-on'.\index{b-equv3-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-equv-preserves-good-s; name this event `b-equv-preserves-good-s-on'.\index{b-equv-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-and4-preserves-good-s; name this event `b-and4-preserves-good-s-on'.\index{b-and4-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-and3-preserves-good-s; name this event `b-and3-preserves-good-s-on'.\index{b-and3-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-and-preserves-good-s; name this event `b-and-preserves-good-s-on'.\index{b-and-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ao7-preserves-good-s; name this event `ao7-preserves-good-s-on'.\index{ao7-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ao6-preserves-good-s; name this event `ao6-preserves-good-s-on'.\index{ao6-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ao4-preserves-good-s; name this event `ao4-preserves-good-s-on'.\index{ao4-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ao2-preserves-good-s; name this event `ao2-preserves-good-s-on'.\index{ao2-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable good-s-0; name this event `good-s-0-on'.\index{good-s-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-if-preserves-good-s; name this event `f-if-preserves-good-s-on'.\index{f-if-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-buf-preserves-good-s; name this event `f-buf-preserves-good-s-on'.\index{f-buf-preserves-good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable good-s-collect-value; name this event `good-s-collect-value-on'.\index{good-s-collect-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-monotone; name this event `dual-eval-monotone-on'.\index{dual-eval-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable good-s-value; name this event `good-s-value-on'.\index{good-s-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable good-s-alist-pairlist; name this event `good-s-alist-pairlist-on'.\index{good-s-alist-pairlist-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable good-s-alist; name this event `good-s-alist-on'.\index{good-s-alist-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*good-s-alist; name this event `g*1*good-s-alist-on'.\index{g*1*good-s-alist-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-monotone-no-ram; name this event `dual-eval-monotone-no-ram-on'.\index{dual-eval-monotone-no-ram-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ok-netlistp-reduction-rewrite; name this event `ok-netlistp-reduction-rewrite-on'.\index{ok-netlistp-reduction-rewrite-o!n}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ok-netlistp-reduction; name this event `ok-netlistp-reduction-on'.\index{ok-netlistp-reduction-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx-alist-implies-s-approx-collect-value; name this event `s-approx-alist-implies-s-approx-collect-value-on'.\index{s-approx-alist-implies-s-approx!-collect-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx-implies-s-approx-alist; name this event `s-approx-implies-s-approx-alist-on'.\index{s-approx-implies-s-approx-alist!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable alistp-dual-eval-3; name this event `alistp-dual-eval-3-on'.\index{alistp-dual-eval-3-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx-alist-implies-s-approx-list-collect-value; name this event `s-approx-alist-implies-s-approx-list-collect-value-on'.\index{s-approx-alist-implies-s-approx!-list-collect-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable double-cdr-induction; name this event `double-cdr-induction-on'.\index{double-cdr-induction-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*double-cdr-induction; name this event `g*1*double-cdr-induction-on'.\index{g*1*double-cdr-induction-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-approx-alist-append; name this event `v-approx-alist-append-on'.\index{v-approx-alist-append-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx-alist-implies-s-approx-value; name this event `s-approx-alist-implies-s-approx-value-on'.\index{s-approx-alist-implies-s-approx!-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable alistp-opener; name this event `alistp-opener-on'.\index{alistp-opener-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-approx-implies-v-approx-alist; name this event `v-approx-implies-v-approx-alist-on'.\index{v-approx-implies-v-approx-alist!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx-list-implies-s-approx-alist; name this event `s-approx-list-implies-s-approx-alist-on'.\index{s-approx-list-implies-s-approx-!alist-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx-list; name this event `s-approx-list-on'.\index{s-approx-list-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*s-approx-list; name this event `g*1*s-approx-list-on'.\index{g*1*s-approx-list-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-approx-alist-implies-v-approx-collect-value; name this event `v-approx-alist-implies-v-approx-collect-value-on'.\index{v-approx-alist-implies-v-approx!-collect-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable alistp-dual-eval-1; name this event `alistp-dual-eval-1-on'.\index{alistp-dual-eval-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable alistp-append; name this event `alistp-append-on'.\index{alistp-append-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable alistp-pairlist; name this event `alistp-pairlist-on'.\index{alistp-pairlist-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-approx-alist-implies-b-approx-value; name this event `v-approx-alist-implies-b-approx-value-on'.\index{v-approx-alist-implies-b-approx!-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-monotone-induction; name this event `dual-eval-monotone-induction-on'.\index{dual-eval-monotone-induction-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*dual-eval-monotone-induction; name this event `g*1*dual-eval-monotone-induction-on'.\index{g*1*dual-eval-monotone-inductio!n-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable primp-monotone; name this event `primp-monotone-on'.\index{primp-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ok-netlistp; name this event `ok-netlistp-on'.\index{ok-netlistp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*ok-netlistp; name this event `g*1*ok-netlistp-on'.\index{g*1*ok-netlistp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-port-ram-state-body; name this event `dual-port-ram-state-body-on'.\index{dual-port-ram-state-body-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*dual-port-ram-state-body; name this event `g*1*dual-port-ram-state-body-on'.\index{g*1*dual-port-ram-state-body-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-port-ram-state-monotone; name this event `dual-port-ram-state-monotone-on'.\index{dual-port-ram-state-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable write-mem1-double-induction; name this event `write-mem1-double-induction-on'.\index{write-mem1-double-induction-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*write-mem1-double-induction; name this event `g*1*write-mem1-double-induction-on'.\index{g*1*write-mem1-double-induction!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable write-mem1-monotone-induction; name this event `write-mem1-monotone-induction-on'.\index{write-mem1-monotone-induction-o!n}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*write-mem1-monotone-induction; name this event `g*1*write-mem1-monotone-induction-on'.\index{g*1*write-mem1-monotone-inducti!on-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-port-ram-value-body; name this event `dual-port-ram-value-body-on'.\index{dual-port-ram-value-body-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*dual-port-ram-value-body; name this event `g*1*dual-port-ram-value-body-on'.\index{g*1*dual-port-ram-value-body-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-approx-x-x; name this event `v-approx-x-x-on1'.\index{v-approx-x-x-on1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable read-mem1-monotone-induction; name this event `read-mem1-monotone-induction-on'.\index{read-mem1-monotone-induction-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*read-mem1-monotone-induction; name this event `g*1*read-mem1-monotone-induction-on'.\index{g*1*read-mem1-monotone-inductio!n-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable bvp-rev1; name this event `bvp-rev1-on'.\index{bvp-rev1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable vss-monotone; name this event `vss-monotone-on'.\index{vss-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-vss-state; name this event `dual-eval-vss-state-on'.\index{dual-eval-vss-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-vss-value; name this event `dual-eval-vss-value-on'.\index{dual-eval-vss-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable vdd-parametric-monotone; name this event `vdd-parametric-monotone-on'.\index{vdd-parametric-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-vdd-parametric-state; name this event `dual-eval-vdd-parametric-state-on'.\index{dual-eval-vdd-parametric-state-!on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-vdd-parametric-value; name this event `dual-eval-vdd-parametric-value-on'.\index{dual-eval-vdd-parametric-value-!on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable vdd-monotone; name this event `vdd-monotone-on'.\index{vdd-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-vdd-state; name this event `dual-eval-vdd-state-on'.\index{dual-eval-vdd-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-vdd-value; name this event `dual-eval-vdd-value-on'.\index{dual-eval-vdd-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ttl-tri-output-fast-monotone; name this event `ttl-tri-output-fast-monotone-on'.\index{ttl-tri-output-fast-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ttl-tri-output-fast-state; name this event `dual-eval-ttl-tri-output-fast-state-on'.\index{dual-eval-ttl-tri-output-fast-st!ate-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ttl-tri-output-fast-value; name this event `dual-eval-ttl-tri-output-fast-value-on'.\index{dual-eval-ttl-tri-output-fast-v!alue-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ttl-tri-output-monotone; name this event `ttl-tri-output-monotone-on'.\index{ttl-tri-output-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ttl-tri-output-state; name this event `dual-eval-ttl-tri-output-state-on'.\index{dual-eval-ttl-tri-output-state-!on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ttl-tri-output-value; name this event `dual-eval-ttl-tri-output-value-on'.\index{dual-eval-ttl-tri-output-value-!on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ttl-output-fast-monotone; name this event `ttl-output-fast-monotone-on'.\index{ttl-output-fast-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ttl-output-fast-state; name this event `dual-eval-ttl-output-fast-state-on'.\index{dual-eval-ttl-output-fast-state!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ttl-output-fast-value; name this event `dual-eval-ttl-output-fast-value-on'.\index{dual-eval-ttl-output-fast-value!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ttl-output-parametric-monotone; name this event `ttl-output-parametric-monotone-on'.\index{ttl-output-parametric-monotone-!on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ttl-output-parametric-state; name this event `dual-eval-ttl-output-parametric-state-on'.\index{dual-eval-ttl-output-parametric!-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ttl-output-parametric-value; name this event `dual-eval-ttl-output-parametric-value-on'.\index{dual-eval-ttl-output-parametric!-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ttl-output-monotone; name this event `ttl-output-monotone-on'.\index{ttl-output-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ttl-output-state; name this event `dual-eval-ttl-output-state-on'.\index{dual-eval-ttl-output-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ttl-output-value; name this event `dual-eval-ttl-output-value-on'.\index{dual-eval-ttl-output-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ttl-input-monotone; name this event `ttl-input-monotone-on'.\index{ttl-input-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ttl-input-state; name this event `dual-eval-ttl-input-state-on'.\index{dual-eval-ttl-input-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ttl-input-value; name this event `dual-eval-ttl-input-value-on'.\index{dual-eval-ttl-input-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ttl-clk-input-monotone; name this event `ttl-clk-input-monotone-on'.\index{ttl-clk-input-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ttl-clk-input-state; name this event `dual-eval-ttl-clk-input-state-on'.\index{dual-eval-ttl-clk-input-state-o!n}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ttl-clk-input-value; name this event `dual-eval-ttl-clk-input-value-on'.\index{dual-eval-ttl-clk-input-value-o!n}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ttl-bidirect-monotone; name this event `ttl-bidirect-monotone-on'.\index{ttl-bidirect-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ttl-bidirect-state; name this event `dual-eval-ttl-bidirect-state-on'.\index{dual-eval-ttl-bidirect-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ttl-bidirect-value; name this event `dual-eval-ttl-bidirect-value-on'.\index{dual-eval-ttl-bidirect-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable pullup-monotone; name this event `pullup-monotone-on'.\index{pullup-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-pullup-state; name this event `dual-eval-pullup-state-on'.\index{dual-eval-pullup-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-pullup-value; name this event `dual-eval-pullup-value-on'.\index{dual-eval-pullup-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable t-wire-monotone; name this event `t-wire-monotone-on'.\index{t-wire-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-t-wire-state; name this event `dual-eval-t-wire-state-on'.\index{dual-eval-t-wire-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-t-wire-value; name this event `dual-eval-t-wire-value-on'.\index{dual-eval-t-wire-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable t-buf-monotone; name this event `t-buf-monotone-on'.\index{t-buf-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-t-buf-state; name this event `dual-eval-t-buf-state-on'.\index{dual-eval-t-buf-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-t-buf-value; name this event `dual-eval-t-buf-value-on'.\index{dual-eval-t-buf-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ram-enable-circuit-monotone; name this event `ram-enable-circuit-monotone-on'.\index{ram-enable-circuit-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ram-enable-circuit-state; name this event `dual-eval-ram-enable-circuit-state-on'.\index{dual-eval-ram-enable-circuit-st!ate-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ram-enable-circuit-value; name this event `dual-eval-ram-enable-circuit-value-on'.\index{dual-eval-ram-enable-circuit-va!lue-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable id-monotone; name this event `id-monotone-on'.\index{id-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-id-state; name this event `dual-eval-id-state-on'.\index{dual-eval-id-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-id-value; name this event `dual-eval-id-value-on'.\index{dual-eval-id-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fd1slp-monotone; name this event `fd1slp-monotone-on'.\index{fd1slp-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-fd1slp-state; name this event `dual-eval-fd1slp-state-on'.\index{dual-eval-fd1slp-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-fd1slp-value; name this event `dual-eval-fd1slp-value-on'.\index{dual-eval-fd1slp-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fd1sp-monotone; name this event `fd1sp-monotone-on'.\index{fd1sp-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-fd1sp-state; name this event `dual-eval-fd1sp-state-on'.\index{dual-eval-fd1sp-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-fd1sp-value; name this event `dual-eval-fd1sp-value-on'.\index{dual-eval-fd1sp-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fd1s-monotone; name this event `fd1s-monotone-on'.\index{fd1s-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-fd1s-state; name this event `dual-eval-fd1s-state-on'.\index{dual-eval-fd1s-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-fd1s-value; name this event `dual-eval-fd1s-value-on'.\index{dual-eval-fd1s-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fd1-monotone; name this event `fd1-monotone-on'.\index{fd1-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-fd1-state; name this event `dual-eval-fd1-state-on'.\index{dual-eval-fd1-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-fd1-value; name this event `dual-eval-fd1-value-on'.\index{dual-eval-fd1-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable procmon-monotone; name this event `procmon-monotone-on'.\index{procmon-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-procmon-state; name this event `dual-eval-procmon-state-on'.\index{dual-eval-procmon-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-procmon-value; name this event `dual-eval-procmon-value-on'.\index{dual-eval-procmon-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable del10-monotone; name this event `del10-monotone-on'.\index{del10-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-del10-state; name this event `dual-eval-del10-state-on'.\index{dual-eval-del10-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-del10-value; name this event `dual-eval-del10-value-on'.\index{dual-eval-del10-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable del4-monotone; name this event `del4-monotone-on'.\index{del4-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-del4-state; name this event `dual-eval-del4-state-on'.\index{dual-eval-del4-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-del4-value; name this event `dual-eval-del4-value-on'.\index{dual-eval-del4-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable del2-monotone; name this event `del2-monotone-on'.\index{del2-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-del2-state; name this event `dual-eval-del2-state-on'.\index{dual-eval-del2-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-del2-value; name this event `dual-eval-del2-value-on'.\index{dual-eval-del2-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-xor3-monotone; name this event `b-xor3-monotone-on'.\index{b-xor3-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-xor3-state; name this event `dual-eval-b-xor3-state-on'.\index{dual-eval-b-xor3-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-xor3-value; name this event `dual-eval-b-xor3-value-on'.\index{dual-eval-b-xor3-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-xor-monotone; name this event `b-xor-monotone-on'.\index{b-xor-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-xor-state; name this event `dual-eval-b-xor-state-on'.\index{dual-eval-b-xor-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-xor-value; name this event `dual-eval-b-xor-value-on'.\index{dual-eval-b-xor-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-or4-monotone; name this event `b-or4-monotone-on'.\index{b-or4-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-or4-state; name this event `dual-eval-b-or4-state-on'.\index{dual-eval-b-or4-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-or4-value; name this event `dual-eval-b-or4-value-on'.\index{dual-eval-b-or4-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-or3-monotone; name this event `b-or3-monotone-on'.\index{b-or3-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-or3-state; name this event `dual-eval-b-or3-state-on'.\index{dual-eval-b-or3-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-or3-value; name this event `dual-eval-b-or3-value-on'.\index{dual-eval-b-or3-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-or-monotone; name this event `b-or-monotone-on'.\index{b-or-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-or-state; name this event `dual-eval-b-or-state-on'.\index{dual-eval-b-or-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-or-value; name this event `dual-eval-b-or-value-on'.\index{dual-eval-b-or-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-not-ivap-monotone; name this event `b-not-ivap-monotone-on'.\index{b-not-ivap-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-not-ivap-state; name this event `dual-eval-b-not-ivap-state-on'.\index{dual-eval-b-not-ivap-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-not-ivap-value; name this event `dual-eval-b-not-ivap-value-on'.\index{dual-eval-b-not-ivap-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-not-b4ip-monotone; name this event `b-not-b4ip-monotone-on'.\index{b-not-b4ip-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-not-b4ip-state; name this event `dual-eval-b-not-b4ip-state-on'.\index{dual-eval-b-not-b4ip-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-not-b4ip-value; name this event `dual-eval-b-not-b4ip-value-on'.\index{dual-eval-b-not-b4ip-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-not-monotone; name this event `b-not-monotone-on'.\index{b-not-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-not-state; name this event `dual-eval-b-not-state-on'.\index{dual-eval-b-not-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-not-value; name this event `dual-eval-b-not-value-on'.\index{dual-eval-b-not-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nor8-monotone; name this event `b-nor8-monotone-on'.\index{b-nor8-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nor8-state; name this event `dual-eval-b-nor8-state-on'.\index{dual-eval-b-nor8-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nor8-value; name this event `dual-eval-b-nor8-value-on'.\index{dual-eval-b-nor8-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nor6-monotone; name this event `b-nor6-monotone-on'.\index{b-nor6-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nor6-state; name this event `dual-eval-b-nor6-state-on'.\index{dual-eval-b-nor6-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nor6-value; name this event `dual-eval-b-nor6-value-on'.\index{dual-eval-b-nor6-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nor5-monotone; name this event `b-nor5-monotone-on'.\index{b-nor5-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nor5-state; name this event `dual-eval-b-nor5-state-on'.\index{dual-eval-b-nor5-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nor5-value; name this event `dual-eval-b-nor5-value-on'.\index{dual-eval-b-nor5-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nor4-monotone; name this event `b-nor4-monotone-on'.\index{b-nor4-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nor4-state; name this event `dual-eval-b-nor4-state-on'.\index{dual-eval-b-nor4-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nor4-value; name this event `dual-eval-b-nor4-value-on'.\index{dual-eval-b-nor4-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nor3-monotone; name this event `b-nor3-monotone-on'.\index{b-nor3-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nor3-state; name this event `dual-eval-b-nor3-state-on'.\index{dual-eval-b-nor3-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nor3-value; name this event `dual-eval-b-nor3-value-on'.\index{dual-eval-b-nor3-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nor-monotone; name this event `b-nor-monotone-on'.\index{b-nor-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nor-state; name this event `dual-eval-b-nor-state-on'.\index{dual-eval-b-nor-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nor-value; name this event `dual-eval-b-nor-value-on'.\index{dual-eval-b-nor-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nbuf-monotone; name this event `b-nbuf-monotone-on'.\index{b-nbuf-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nbuf-state; name this event `dual-eval-b-nbuf-state-on'.\index{dual-eval-b-nbuf-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nbuf-value; name this event `dual-eval-b-nbuf-value-on'.\index{dual-eval-b-nbuf-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nand8-monotone; name this event `b-nand8-monotone-on'.\index{b-nand8-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nand8-state; name this event `dual-eval-b-nand8-state-on'.\index{dual-eval-b-nand8-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nand8-value; name this event `dual-eval-b-nand8-value-on'.\index{dual-eval-b-nand8-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nand6-monotone; name this event `b-nand6-monotone-on'.\index{b-nand6-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nand6-state; name this event `dual-eval-b-nand6-state-on'.\index{dual-eval-b-nand6-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nand6-value; name this event `dual-eval-b-nand6-value-on'.\index{dual-eval-b-nand6-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nand5-monotone; name this event `b-nand5-monotone-on'.\index{b-nand5-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nand5-state; name this event `dual-eval-b-nand5-state-on'.\index{dual-eval-b-nand5-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nand5-value; name this event `dual-eval-b-nand5-value-on'.\index{dual-eval-b-nand5-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nand4-monotone; name this event `b-nand4-monotone-on'.\index{b-nand4-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nand4-state; name this event `dual-eval-b-nand4-state-on'.\index{dual-eval-b-nand4-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nand4-value; name this event `dual-eval-b-nand4-value-on'.\index{dual-eval-b-nand4-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nand3-monotone; name this event `b-nand3-monotone-on'.\index{b-nand3-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nand3-state; name this event `dual-eval-b-nand3-state-on'.\index{dual-eval-b-nand3-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nand3-value; name this event `dual-eval-b-nand3-value-on'.\index{dual-eval-b-nand3-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-nand-monotone; name this event `b-nand-monotone-on'.\index{b-nand-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nand-state; name this event `dual-eval-b-nand-state-on'.\index{dual-eval-b-nand-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-nand-value; name this event `dual-eval-b-nand-value-on'.\index{dual-eval-b-nand-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-if-monotone; name this event `b-if-monotone-on'.\index{b-if-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-if-state; name this event `dual-eval-b-if-state-on'.\index{dual-eval-b-if-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-if-value; name this event `dual-eval-b-if-value-on'.\index{dual-eval-b-if-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-equv3-monotone; name this event `b-equv3-monotone-on'.\index{b-equv3-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-equv3-state; name this event `dual-eval-b-equv3-state-on'.\index{dual-eval-b-equv3-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-equv3-value; name this event `dual-eval-b-equv3-value-on'.\index{dual-eval-b-equv3-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-equv-monotone; name this event `b-equv-monotone-on'.\index{b-equv-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-equv-state; name this event `dual-eval-b-equv-state-on'.\index{dual-eval-b-equv-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-equv-value; name this event `dual-eval-b-equv-value-on'.\index{dual-eval-b-equv-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-and4-monotone; name this event `b-and4-monotone-on'.\index{b-and4-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-and4-state; name this event `dual-eval-b-and4-state-on'.\index{dual-eval-b-and4-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-and4-value; name this event `dual-eval-b-and4-value-on'.\index{dual-eval-b-and4-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-and3-monotone; name this event `b-and3-monotone-on'.\index{b-and3-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-and3-state; name this event `dual-eval-b-and3-state-on'.\index{dual-eval-b-and3-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-and3-value; name this event `dual-eval-b-and3-value-on'.\index{dual-eval-b-and3-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-and-monotone; name this event `b-and-monotone-on'.\index{b-and-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-and-state; name this event `dual-eval-b-and-state-on'.\index{dual-eval-b-and-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-b-and-value; name this event `dual-eval-b-and-value-on'.\index{dual-eval-b-and-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ao7-monotone; name this event `ao7-monotone-on'.\index{ao7-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ao7-state; name this event `dual-eval-ao7-state-on'.\index{dual-eval-ao7-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ao7-value; name this event `dual-eval-ao7-value-on'.\index{dual-eval-ao7-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ao6-monotone; name this event `ao6-monotone-on'.\index{ao6-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ao6-state; name this event `dual-eval-ao6-state-on'.\index{dual-eval-ao6-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ao6-value; name this event `dual-eval-ao6-value-on'.\index{dual-eval-ao6-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ao4-monotone; name this event `ao4-monotone-on'.\index{ao4-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ao4-state; name this event `dual-eval-ao4-state-on'.\index{dual-eval-ao4-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ao4-value; name this event `dual-eval-ao4-value-on'.\index{dual-eval-ao4-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ao2-monotone; name this event `ao2-monotone-on'.\index{ao2-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ao2-state; name this event `dual-eval-ao2-state-on'.\index{dual-eval-ao2-state-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-ao2-value; name this event `dual-eval-ao2-value-on'.\index{dual-eval-ao2-value-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fourp-implies-s-approx-is-b-approx; name this event `fourp-implies-s-approx-is-b-approx-on1'.\index{fourp-implies-s-approx-is-b-app!rox-on1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fourp-f-if; name this event `fourp-f-if-on'.\index{fourp-f-if-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable fourp-f-buf; name this event `fourp-f-buf-on'.\index{fourp-f-buf-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-buf-type-set; name this event `f-buf-type-set-on'.\index{f-buf-type-set-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx-implies-b-approx; name this event `s-approx-implies-b-approx-on'.\index{s-approx-implies-b-approx-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-2-primp; name this event `dual-eval-2-primp-on'.\index{dual-eval-2-primp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable dual-eval-0-primp; name this event `dual-eval-0-primp-on'.\index{dual-eval-0-primp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-pullup-monotone; name this event `f-pullup-monotone-on'.\index{f-pullup-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ft-wire-monotone; name this event `ft-wire-monotone-on'.\index{ft-wire-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable ft-buf-monotone; name this event `ft-buf-monotone-on'.\index{ft-buf-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-if-monotone; name this event `f-if-monotone-on'.\index{f-if-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-equv3-monotone; name this event `f-equv3-monotone-on'.\index{f-equv3-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-xor3-monotone; name this event `f-xor3-monotone-on'.\index{f-xor3-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-equv-monotone; name this event `f-equv-monotone-on'.\index{f-equv-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-xor-monotone; name this event `f-xor-monotone-on'.\index{f-xor-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nor8-monotone; name this event `f-nor8-monotone-on'.\index{f-nor8-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nor6-monotone; name this event `f-nor6-monotone-on'.\index{f-nor6-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nor5-monotone; name this event `f-nor5-monotone-on'.\index{f-nor5-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nor4-monotone; name this event `f-nor4-monotone-on'.\index{f-nor4-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nor3-monotone; name this event `f-nor3-monotone-on'.\index{f-nor3-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nor-monotone; name this event `f-nor-monotone-on'.\index{f-nor-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-or4-monotone; name this event `f-or4-monotone-on'.\index{f-or4-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-or3-monotone; name this event `f-or3-monotone-on'.\index{f-or3-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-or-monotone; name this event `f-or-monotone-on'.\index{f-or-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nand8-monotone; name this event `f-nand8-monotone-on'.\index{f-nand8-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nand6-monotone; name this event `f-nand6-monotone-on'.\index{f-nand6-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nand5-monotone; name this event `f-nand5-monotone-on'.\index{f-nand5-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nand4-monotone; name this event `f-nand4-monotone-on'.\index{f-nand4-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nand3-monotone; name this event `f-nand3-monotone-on'.\index{f-nand3-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-nand-monotone; name this event `f-nand-monotone-on'.\index{f-nand-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-not-monotone; name this event `f-not-monotone-on'.\index{f-not-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-and4-monotone; name this event `f-and4-monotone-on'.\index{f-and4-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-and3-monotone; name this event `f-and3-monotone-on'.\index{f-and3-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-and-monotone; name this event `f-and-monotone-on'.\index{f-and-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable f-buf-monotone; name this event `f-buf-monotone-on'.\index{f-buf-monotone-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable monotonicity-property-consequence-3; name this event `monotonicity-property-consequence-3-on'.\index{monotonicity-property-consequen!ce-3-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable monotonicity-property-consequence-2; name this event `monotonicity-property-consequence-2-on'.\index{monotonicity-property-consequen!ce-2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable monotonicity-property-consequence-1; name this event `monotonicity-property-consequence-1-on'.\index{monotonicity-property-consequen!ce-1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable monotonicity-property-consequence-0; name this event `monotonicity-property-consequence-0-on'.\index{monotonicity-property-consequen!ce-0-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*monotonicity-property; name this event `g*1*monotonicity-property-on'.\index{g*1*monotonicity-property-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx-alist; name this event `s-approx-alist-on'.\index{s-approx-alist-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*s-approx-alist; name this event `g*1*s-approx-alist-on'.\index{g*1*s-approx-alist-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-approx-alist; name this event `v-approx-alist-on'.\index{v-approx-alist-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*v-approx-alist; name this event `g*1*v-approx-alist-on'.\index{g*1*v-approx-alist-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-knownp-implies-s-approx-is-equal; name this event `s-knownp-implies-s-approx-is-equal-on1'.\index{s-knownp-implies-s-approx-is-eq!ual-on1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-knownp; name this event `s-knownp-on1'.\index{s-knownp-on1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*s-knownp; name this event `g*1*s-knownp-on'.\index{g*1*s-knownp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable good-s; name this event `good-s-on'.\index{good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*good-s; name this event `g*1*good-s-on'.\index{g*1*good-s-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx-x-x; name this event `s-approx-x-x-on'.\index{s-approx-x-x-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable s-approx; name this event `s-approx-on1'.\index{s-approx-on1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*s-approx; name this event `g*1*s-approx-on'.\index{g*1*s-approx-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable mem-width; name this event `mem-width-on1'.\index{mem-width-on1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*mem-width; name this event `g*1*mem-width-on1'.\index{g*1*mem-width-on1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-knownp-implies-v-approx-is-equal; name this event `v-knownp-implies-v-approx-is-equal-on'.\index{v-knownp-implies-v-approx-is-eq!ual-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-knownp; name this event `v-knownp-on1'.\index{v-knownp-on1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*v-knownp; name this event `g*1*v-knownp-on'.\index{g*1*v-knownp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-approx; name this event `v-approx-on1'.\index{v-approx-on1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*v-approx; name this event `g*1*v-approx-on'.\index{g*1*v-approx-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable *1*b-approx; name this event `g*1*b-approx-on'.\index{g*1*b-approx-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable b-knownp-compound-recognizer; name this event `b-knownp-compound-recognizer-on'.\index{b-knownp-compound-recognizer-on}

\addvspace{18pt}


\noindent{\sc Event}:   Enable monotonicity-property; name this event `monotonicity-property-off1'.\index{monotonicity-property-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable monotonicity-property-opener-0; name this event `monotonicity-property-opener-0-off1'.\index{monotonicity-property-opener-0-!off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable monotonicity-property-opener-1; name this event `monotonicity-property-opener-1-off1'.\index{monotonicity-property-opener-1-!off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable monotonicity-property-opener-2; name this event `monotonicity-property-opener-2-off1'.\index{monotonicity-property-opener-2-!off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable monotonicity-property-opener-3; name this event `monotonicity-property-opener-3-off1'.\index{monotonicity-property-opener-3-!off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-buf; name this event `f-buf-off1'.\index{f-buf-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-and; name this event `f-and-off1'.\index{f-and-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-and3; name this event `f-and3-off1'.\index{f-and3-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-and4; name this event `f-and4-off1'.\index{f-and4-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-not; name this event `f-not-off1'.\index{f-not-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nand; name this event `f-nand-off1'.\index{f-nand-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nand3; name this event `f-nand3-off1'.\index{f-nand3-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nand4; name this event `f-nand4-off1'.\index{f-nand4-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nand5; name this event `f-nand5-off1'.\index{f-nand5-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nand6; name this event `f-nand6-off1'.\index{f-nand6-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nand8; name this event `f-nand8-off1'.\index{f-nand8-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-or; name this event `f-or-off1'.\index{f-or-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-or3; name this event `f-or3-off1'.\index{f-or3-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-or4; name this event `f-or4-off1'.\index{f-or4-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nor; name this event `f-nor-off1'.\index{f-nor-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nor3; name this event `f-nor3-off1'.\index{f-nor3-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nor4; name this event `f-nor4-off1'.\index{f-nor4-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nor5; name this event `f-nor5-off1'.\index{f-nor5-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nor6; name this event `f-nor6-off1'.\index{f-nor6-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-nor8; name this event `f-nor8-off1'.\index{f-nor8-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-xor; name this event `f-xor-off1'.\index{f-xor-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-xor3; name this event `f-xor3-off1'.\index{f-xor3-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-equv; name this event `f-equv-off1'.\index{f-equv-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-equv3; name this event `f-equv3-off1'.\index{f-equv3-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-if; name this event `f-if-off1'.\index{f-if-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ft-buf; name this event `ft-buf-off1'.\index{ft-buf-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ft-wire; name this event `ft-wire-off1'.\index{ft-wire-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable f-pullup; name this event `f-pullup-off1'.\index{f-pullup-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable bvp-reverse; name this event `bvp-reverse-off1'.\index{bvp-reverse-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-bvp; name this event `v-approx-bvp-off1'.\index{v-approx-bvp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable read-mem1-monotone; name this event `read-mem1-monotone-off1'.\index{read-mem1-monotone-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable bvp-implies-v-knownp; name this event `bvp-implies-v-knownp-off1'.\index{bvp-implies-v-knownp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-implies-b-approx-nth; name this event `v-approx-implies-b-approx-nth-off1'.\index{v-approx-implies-b-approx-nth-o!ff1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*b-knownp; name this event `g*1*b-knownp-off2'.\index{g*1*b-knownp-off2}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-implies-subranges-equal; name this event `v-approx-implies-subranges-equal-off1'.\index{v-approx-implies-subranges-equa!l-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-bvp-subrange; name this event `v-approx-bvp-subrange-off1'.\index{v-approx-bvp-subrange-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-make-list-x; name this event `v-approx-make-list-x-off1'.\index{v-approx-make-list-x-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable read-mem-monotone; name this event `read-mem-monotone-off1'.\index{read-mem-monotone-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-length-read-mem1; name this event `equal-length-read-mem1-off1'.\index{equal-length-read-mem1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-length-read-mem; name this event `equal-length-read-mem-off1'.\index{equal-length-read-mem-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-implies-properp-read-mem1; name this event `s-approx-implies-properp-read-mem1-off1'.\index{s-approx-implies-properp-read-me!m1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-implies-properp-read-mem; name this event `s-approx-implies-properp-read-mem-off1'.\index{s-approx-implies-properp-read-me!m-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-port-ram-value-monotone; name this event `dual-port-ram-value-monotone-off1'.\index{dual-port-ram-value-monotone-of!f1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-append; name this event `eval\$-append-off1'.\index{eval\$-append-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-pairlist-cons; name this event `eval\$-pairlist-cons-off1'.\index{eval\$-pairlist-cons-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-append-2; name this event `eval\$-append-2-off1'.\index{eval\$-append-2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-apply-value-dp-ram-16x32-lemma-1; name this event `dual-apply-value-dp-ram-16x32-lemma-1-off1'.\index{dual-apply-value-dp-ram-16x32-le!mma-1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-apply-value-dp-ram-16x32-lemma-2; name this event `dual-apply-value-dp-ram-16x32-lemma-2-off1'.\index{dual-apply-value-dp-ram-16x32-le!mma-2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-apply-value-dp-ram-16x32-lemma-3; name this event `dual-apply-value-dp-ram-16x32-lemma-3-off1'.\index{dual-apply-value-dp-ram-16x32-le!mma-3-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-port-ram-value-is-dual-port-ram-value-body; name this event `dual-port-ram-value-is-dual-port-ram-value-body-off1'.\index{dual-port-ram-value-is-dual-port!-ram-value-body-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-apply-value-dp-ram-16x32; name this event `dual-apply-value-dp-ram-16x32-off1'.\index{dual-apply-value-dp-ram-16x32-o!ff1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dp-ram-16x32-monotone-value; name this event `dp-ram-16x32-monotone-value-off1'.\index{dp-ram-16x32-monotone-value-off!1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable bvp; name this event `bvp-on1'.\index{bvp-on1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-opener; name this event `s-approx-opener-off1'.\index{s-approx-opener-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-implies-nth-does-not-go-from-f-to-t; name this event `v-approx-implies-nth-does-not-go-from-f-to-t-off1'.\index{v-approx-implies-nth-does-not-g!o-from-f-to-t-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable write-mem1-opener; name this event `write-mem1-opener-off1'.\index{write-mem1-opener-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable write-mem1-monotone; name this event `write-mem1-monotone-off1'.\index{write-mem1-monotone-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable write-mem-monotone; name this event `write-mem-monotone-off1'.\index{write-mem-monotone-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-length; name this event `v-approx-length-off1'.\index{v-approx-length-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-write-mem1-id; name this event `s-approx-write-mem1-id-off1'.\index{s-approx-write-mem1-id-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-write-mem-id; name this event `s-approx-write-mem-id-off1'.\index{s-approx-write-mem-id-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-constant-ram-x-id; name this event `s-approx-constant-ram-x-id-off1'.\index{s-approx-constant-ram-x-id-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-constant-ram-x-constant-ram-x; name this event `s-approx-constant-ram-x-constant-ram-x-off1'.\index{s-approx-constant-ram-x-constant!-ram-x-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-preserves-length; name this event `v-approx-preserves-length-off1'.\index{v-approx-preserves-length-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-subrange; name this event `v-approx-subrange-off1'.\index{v-approx-subrange-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable mem-width-non-zero; name this event `mem-width-non-zero-off1'.\index{mem-width-non-zero-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-constant-ram-x-write-mem1-case-3; name this event `s-approx-constant-ram-x-write-mem1-case-3-off1'.\index{s-approx-constant-ram-x-write-me!m1-case-3-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-constant-ram-x-write-mem1; name this event `s-approx-constant-ram-x-write-mem1-off1'.\index{s-approx-constant-ram-x-write-me!m1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable s-approx-constant-ram-x-write-mem; name this event `s-approx-constant-ram-x-write-mem-off1'.\index{s-approx-constant-ram-x-write-me!m-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-approx-preserves-properp; name this event `v-approx-preserves-properp-off1'.\index{v-approx-preserves-properp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable mem-width-linear-facts; name this event `mem-width-linear-facts-off1'.\index{mem-width-linear-facts-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-port-ram-state-monotone-rewrite; name this event `dual-port-ram-state-monotone-rewrite-off1'.\index{dual-port-ram-state-monotone-re!write-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-apply-state-dp-ram-16x32-lemma-1; name this event `dual-apply-state-dp-ram-16x32-lemma-1-off1'.\index{dual-apply-state-dp-ram-16x32-le!mma-1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-apply-state-dp-ram-16x32-lemma-2; name this event `dual-apply-state-dp-ram-16x32-lemma-2-off1'.\index{dual-apply-state-dp-ram-16x32-le!mma-2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-apply-state-dp-ram-16x32-lemma-3; name this event `dual-apply-state-dp-ram-16x32-lemma-3-off1'.\index{dual-apply-state-dp-ram-16x32-le!mma-3-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-port-ram-state-is-dual-port-ram-state-body; name this event `dual-port-ram-state-is-dual-port-ram-state-body-off1'.\index{dual-port-ram-state-is-dual-port!-ram-state-body-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dual-apply-state-dp-ram-16x32; name this event `dual-apply-state-dp-ram-16x32-off1'.\index{dual-apply-state-dp-ram-16x32-o!ff1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dp-ram-16x32-monotone-state; name this event `dp-ram-16x32-monotone-state-off1'.\index{dp-ram-16x32-monotone-state-off!1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable dp-ram-16x32-monotone; name this event `dp-ram-16x32-monotone-off1'.\index{dp-ram-16x32-monotone-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable open-nth; name this event `open-nth-on1'.\index{open-nth-on1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable doublet-p; name this event `doublet-p-off1'.\index{doublet-p-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-knownp; name this event `b-knownp-off2'.\index{b-knownp-off2}

\addvspace{18pt}


\noindent{\sc Event}:   Enable b-approx; name this event `b-approx-off2'.\index{b-approx-off2}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-constants-ilessp; name this event `cancel-constants-ilessp-off1'.\index{cancel-constants-ilessp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-constants-ilessp-lemma-2; name this event `cancel-constants-ilessp-lemma-2-off1'.\index{cancel-constants-ilessp-lemma-2!-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-constants-ilessp-lemma-1; name this event `cancel-constants-ilessp-lemma-1-off1'.\index{cancel-constants-ilessp-lemma-1!-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-add1-iplus; name this event `ilessp-add1-iplus-off1'.\index{ilessp-add1-iplus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-add1; name this event `ilessp-add1-off1'.\index{ilessp-add1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-constants-equal; name this event `cancel-constants-equal-off1'.\index{cancel-constants-equal-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-constants-equal-lemma; name this event `cancel-constants-equal-lemma-off1'.\index{cancel-constants-equal-lemma-of!f1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-constants; name this event `iplus-constants-off1'.\index{iplus-constants-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-ineg-terms-from-inequality-cancel-ineg-terms-from-inequality-expanded; name this event `cancel-ineg-terms-from-inequality-cancel-ineg-terms-from-inequality-expanded-off1'.\index{cancel-ineg-terms-from-inequalit!y-cancel-ineg-terms-from-inequality-expanded-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-ineg-terms-from-inequality-expanded; name this event `g*1*cancel-ineg-terms-from-inequality-expanded-off1'.\index{g*1*cancel-ineg-terms-from-ineq!uality-expanded-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-ineg-terms-from-inequality; name this event `cancel-ineg-terms-from-inequality-off1'.\index{cancel-ineg-terms-from-inequalit!y-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-ineg-terms-from-inequality; name this event `g*1*cancel-ineg-terms-from-inequality-off1'.\index{g*1*cancel-ineg-terms-from-ineq!uality-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable make-cancel-ineg-terms-inequality; name this event `make-cancel-ineg-terms-inequality-off1'.\index{make-cancel-ineg-terms-inequalit!y-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*make-cancel-ineg-terms-inequality; name this event `g*1*make-cancel-ineg-terms-inequality-off1'.\index{g*1*make-cancel-ineg-terms-ineq!uality-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-list-eval\$-car-split-out-ineg-terms; name this event `iplus-list-eval\$-car-split-out-ineg-terms-off1'.\index{iplus-list-eval\$-car-split-out!-ineg-terms-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-iplus-list-cdr-remove-inegs; name this event `eval\$-iplus-list-cdr-remove-inegs-off1'.\index{eval\$-iplus-list-cdr-remove-ine!gs-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-iplus-list-car-remove-inegs; name this event `eval\$-iplus-list-car-remove-inegs-off1'.\index{eval\$-iplus-list-car-remove-ine!gs-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-ineg-terms-from-equality-cancel-ineg-terms-from-equality-expanded; name this event `cancel-ineg-terms-from-equality-cancel-ineg-terms-from-equality-expanded-off1'.\index{cancel-ineg-terms-from-equality!-cancel-ineg-terms-from-equality-expanded-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-ineg-terms-from-equality-expanded; name this event `g*1*cancel-ineg-terms-from-equality-expanded-off1'.\index{g*1*cancel-ineg-terms-from-equa!lity-expanded-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-ineg-terms-from-equality; name this event `cancel-ineg-terms-from-equality-off1'.\index{cancel-ineg-terms-from-equality!-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-ineg-terms-from-equality; name this event `g*1*cancel-ineg-terms-from-equality-off1'.\index{g*1*cancel-ineg-terms-from-equa!lity-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable make-cancel-ineg-terms-equality; name this event `make-cancel-ineg-terms-equality-off1'.\index{make-cancel-ineg-terms-equality!-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*make-cancel-ineg-terms-equality; name this event `g*1*make-cancel-ineg-terms-equality-off1'.\index{g*1*make-cancel-ineg-terms-equa!lity-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iplus-or-ineg-term; name this event `g*1*iplus-or-ineg-term-off1'.\index{g*1*iplus-or-ineg-term-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*remove-inegs; name this event `g*1*remove-inegs-off1'.\index{g*1*remove-inegs-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable split-out-ineg-terms; name this event `split-out-ineg-terms-off1'.\index{split-out-ineg-terms-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*split-out-ineg-terms; name this event `g*1*split-out-ineg-terms-off1'.\index{g*1*split-out-ineg-terms-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable conjoin-inequalities-with-0-eliminator; name this event `conjoin-inequalities-with-0-eliminator-off1'.\index{conjoin-inequalities-with-0-eli!minator-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-factors-ilessp-0; name this event `cancel-factors-ilessp-0-off1'.\index{cancel-factors-ilessp-0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-factors-ilessp-0; name this event `g*1*cancel-factors-ilessp-0-off1'.\index{g*1*cancel-factors-ilessp-0-off!1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable conjoin-inequalities-with-0; name this event `conjoin-inequalities-with-0-off1'.\index{conjoin-inequalities-with-0-off!1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*conjoin-inequalities-with-0; name this event `g*1*conjoin-inequalities-with-0-off1'.\index{g*1*conjoin-inequalities-with-0!-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable some-eval\$s-to-0-eliminator; name this event `some-eval\$s-to-0-eliminator-off1'.\index{some-eval\$s-to-0-eliminator-of!f1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable some-eval\$s-to-0-append; name this event `some-eval\$s-to-0-append-off1'.\index{some-eval\$s-to-0-append-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-disjoin-equalities-with-0; name this event `eval\$-disjoin-equalities-with-0-off1'.\index{eval\$-disjoin-equalities-with-!0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable some-eval\$s-to-0; name this event `some-eval\$s-to-0-off1'.\index{some-eval\$s-to-0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*some-eval\$s-to-0; name this event `g*1*some-eval\$s-to-0-off1'.\index{g*1*some-eval\$s-to-0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-factors-0; name this event `cancel-factors-0-off1'.\index{cancel-factors-0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-factors-0; name this event `g*1*cancel-factors-0-off1'.\index{g*1*cancel-factors-0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable disjoin-equalities-with-0; name this event `disjoin-equalities-with-0-off1'.\index{disjoin-equalities-with-0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*disjoin-equalities-with-0; name this event `g*1*disjoin-equalities-with-0-off1'.\index{g*1*disjoin-equalities-with-0-o!ff1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-fix-int-to-ilessp; name this event `equal-fix-int-to-ilessp-off1'.\index{equal-fix-int-to-ilessp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-list-bagint-0-implies-equal-for-ilessp-lemma; name this event `eval\$-list-bagint-0-implies-equal-for-ilessp-lemma-off1'.\index{eval\$-list-bagint-0-implies-eq!ual-for-ilessp-lemma-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-list-bagint-0-for-ilessp; name this event `eval\$-list-bagint-0-for-ilessp-off1'.\index{eval\$-list-bagint-0-for-ilessp!-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable member-0-itimes-factors-yields-0-ilessp-consequence-2; name this event `member-0-itimes-factors-yields-0-ilessp-consequence-2-off1'.\index{member-0-itimes-factors-yields-!0-ilessp-consequence-2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable member-0-itimes-factors-yields-0-ilessp-consequence-1; name this event `member-0-itimes-factors-yields-0-ilessp-consequence-1-off1'.\index{member-0-itimes-factors-yields-!0-ilessp-consequence-1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable member-0-itimes-factors-yields-0; name this event `member-0-itimes-factors-yields-0-off1'.\index{member-0-itimes-factors-yields-!0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-itimes-list-eval\$-list-bagdiff-corollary-2; name this event `ilessp-itimes-list-eval\$-list-bagdiff-corollary-2-off1'.\index{ilessp-itimes-list-eval\$-list-!bagdiff-corollary-2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-zero-implies-not-equal; name this event `ilessp-zero-implies-not-equal-off1'.\index{ilessp-zero-implies-not-equal-o!ff1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-itimes-list-eval\$-list-bagdiff-corollary-1; name this event `ilessp-itimes-list-eval\$-list-bagdiff-corollary-1-off1'.\index{ilessp-itimes-list-eval\$-list-!bagdiff-corollary-1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable zero-ilessp-implies-not-equal; name this event `zero-ilessp-implies-not-equal-off1'.\index{zero-ilessp-implies-not-equal-o!ff1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-itimes-list-eval\$-list-bagdiff; name this event `ilessp-itimes-list-eval\$-list-bagdiff-off1'.\index{ilessp-itimes-list-eval\$-list-!bagdiff-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable bagint-singleton; name this event `bagint-singleton-off1'.\index{bagint-singleton-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-itimes-ilessp-factors; name this event `cancel-itimes-ilessp-factors-off1'.\index{cancel-itimes-ilessp-factors-of!f1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-itimes-ilessp-factors; name this event `g*1*cancel-itimes-ilessp-factors-off1'.\index{g*1*cancel-itimes-ilessp-factor!s-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable member-0-eval\$-list; name this event `member-0-eval\$-list-off1'.\index{member-0-eval\$-list-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable membership-of-0-implies-itimes-list-is-0; name this event `membership-of-0-implies-itimes-list-is-0-off1'.\index{membership-of-0-implies-itimes-!list-is-0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-itimes-factors-expanded-cancel-itimes-factors; name this event `cancel-itimes-factors-expanded-cancel-itimes-factors-off1'.\index{cancel-itimes-factors-expanded-!cancel-itimes-factors-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-itimes-factors-expanded; name this event `g*1*cancel-itimes-factors-expanded-off1'.\index{g*1*cancel-itimes-factors-expan!ded-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-itimes-factors; name this event `cancel-itimes-factors-off1'.\index{cancel-itimes-factors-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-itimes-factors; name this event `g*1*cancel-itimes-factors-off1'.\index{g*1*cancel-itimes-factors-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iplus-or-itimes-term; name this event `g*1*iplus-or-itimes-term-off1'.\index{g*1*iplus-or-itimes-term-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-eval\$-itimes-tree-ineg; name this event `itimes-eval\$-itimes-tree-ineg-off1'.\index{itimes-eval\$-itimes-tree-ineg-!off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-eval\$-itimes-tree-ineg; name this event `iplus-eval\$-itimes-tree-ineg-off1'.\index{iplus-eval\$-itimes-tree-ineg-o!ff1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ineg-eval\$-itimes-tree-ineg; name this event `ineg-eval\$-itimes-tree-ineg-off1'.\index{ineg-eval\$-itimes-tree-ineg-of!f1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-itimes-tree-ineg; name this event `eval\$-itimes-tree-ineg-off1'.\index{eval\$-itimes-tree-ineg-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-eval\$-itimes-tree-rec; name this event `fix-int-eval\$-itimes-tree-rec-off1'.\index{fix-int-eval\$-itimes-tree-rec-!off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-ineg-ineg; name this event `ilessp-ineg-ineg-off1'.\index{ilessp-ineg-ineg-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-ineg-ineg; name this event `equal-ineg-ineg-off1'.\index{equal-ineg-ineg-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes--1; name this event `itimes--1-off1'.\index{itimes--1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-factors; name this event `itimes-factors-off1'.\index{itimes-factors-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*itimes-factors; name this event `g*1*itimes-factors-off1'.\index{g*1*itimes-factors-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*itimes-tree-ineg; name this event `g*1*itimes-tree-ineg-off1'.\index{g*1*itimes-tree-ineg-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-strict; name this event `ilessp-strict-off1'.\index{ilessp-strict-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-itimes-right-negative; name this event `ilessp-itimes-right-negative-off1'.\index{ilessp-itimes-right-negative-of!f1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-itimes-right-positive; name this event `ilessp-itimes-right-positive-off1'.\index{ilessp-itimes-right-positive-of!f1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-itimes-ilessp; name this event `cancel-itimes-ilessp-off1'.\index{cancel-itimes-ilessp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-itimes-ilessp; name this event `g*1*cancel-itimes-ilessp-off1'.\index{g*1*cancel-itimes-ilessp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*make-cancel-itimes-inequality; name this event `g*1*make-cancel-itimes-inequality-off1'.\index{g*1*make-cancel-itimes-inequalit!y-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*itimes-tree-no-fix-int; name this event `g*1*itimes-tree-no-fix-int-off1'.\index{g*1*itimes-tree-no-fix-int-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable subsetp; name this event `subsetp-off1'.\index{subsetp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*subsetp; name this event `g*1*subsetp-off1'.\index{g*1*subsetp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-fix-int; name this event `equal-fix-int-off1'.\index{equal-fix-int-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable member-append; name this event `member-append-off1'.\index{member-append-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-list-append; name this event `itimes-list-append-off1'.\index{itimes-list-append-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-itimes; name this event `cancel-itimes-off1'.\index{cancel-itimes-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-itimes; name this event `g*1*cancel-itimes-off1'.\index{g*1*cancel-itimes-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*make-cancel-itimes-equality; name this event `g*1*make-cancel-itimes-equality-off1'.\index{g*1*make-cancel-itimes-equality!-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-itimes-list; name this event `integerp-itimes-list-off1'.\index{integerp-itimes-list-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-list; name this event `itimes-list-off1'.\index{itimes-list-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*itimes-list; name this event `g*1*itimes-list-off1'.\index{g*1*itimes-list-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*itimes-tree; name this event `g*1*itimes-tree-off1'.\index{g*1*itimes-tree-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-tree-rec; name this event `itimes-tree-rec-off1'.\index{itimes-tree-rec-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*itimes-tree-rec; name this event `g*1*itimes-tree-rec-off1'.\index{g*1*itimes-tree-rec-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-fringe; name this event `itimes-fringe-off1'.\index{itimes-fringe-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*itimes-fringe; name this event `g*1*itimes-fringe-off1'.\index{g*1*itimes-fringe-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-irem; name this event `fix-int-irem-off1'.\index{fix-int-irem-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-iquo; name this event `fix-int-iquo-off1'.\index{fix-int-iquo-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-imod; name this event `fix-int-imod-off1'.\index{fix-int-imod-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-idiv; name this event `fix-int-idiv-off1'.\index{fix-int-idiv-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-iremainder; name this event `fix-int-iremainder-off1'.\index{fix-int-iremainder-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-iquotient; name this event `fix-int-iquotient-off1'.\index{fix-int-iquotient-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable irem-fix-int2; name this event `irem-fix-int2-off1'.\index{irem-fix-int2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable irem-fix-int1; name this event `irem-fix-int1-off1'.\index{irem-fix-int1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iquo-fix-int2; name this event `iquo-fix-int2-off1'.\index{iquo-fix-int2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iquo-fix-int1; name this event `iquo-fix-int1-off1'.\index{iquo-fix-int1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable imod-fix-int2; name this event `imod-fix-int2-off1'.\index{imod-fix-int2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable imod-fix-int1; name this event `imod-fix-int1-off1'.\index{imod-fix-int1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable idiv-fix-int2; name this event `idiv-fix-int2-off1'.\index{idiv-fix-int2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable idiv-fix-int1; name this event `idiv-fix-int1-off1'.\index{idiv-fix-int1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iremainder-fix-int2; name this event `iremainder-fix-int2-off1'.\index{iremainder-fix-int2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iremainder-fix-int1; name this event `iremainder-fix-int1-off1'.\index{iremainder-fix-int1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iquotient-fix-int2; name this event `iquotient-fix-int2-off1'.\index{iquotient-fix-int2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iquotient-fix-int1; name this event `iquotient-fix-int1-off1'.\index{iquotient-fix-int1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-irem; name this event `integerp-irem-off1'.\index{integerp-irem-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-iquo; name this event `integerp-iquo-off1'.\index{integerp-iquo-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-imod; name this event `integerp-imod-off1'.\index{integerp-imod-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-idiv; name this event `integerp-idiv-off1'.\index{integerp-idiv-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-iremainder; name this event `integerp-iremainder-off1'.\index{integerp-iremainder-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-iquotient; name this event `integerp-iquotient-off1'.\index{integerp-iquotient-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-cancellation-3; name this event `itimes-cancellation-3-off1'.\index{itimes-cancellation-3-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-cancellation-2; name this event `itimes-cancellation-2-off1'.\index{itimes-cancellation-2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-cancellation-1; name this event `itimes-cancellation-1-off1'.\index{itimes-cancellation-1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-ineg-2; name this event `itimes-ineg-2-off1'.\index{itimes-ineg-2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-ineg-1; name this event `itimes-ineg-1-off1'.\index{itimes-ineg-1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iquo-irem-uniqueness; name this event `iquo-irem-uniqueness-off1'.\index{iquo-irem-uniqueness-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-for-truncate-to-zero; name this event `division-theorem-for-truncate-to-zero-off1'.\index{division-theorem-for-truncate-t!o-zero-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-for-truncate-to-zero-part3; name this event `division-theorem-for-truncate-to-zero-part3-off1'.\index{division-theorem-for-truncate-t!o-zero-part3-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-for-truncate-to-zero-part2; name this event `division-theorem-for-truncate-to-zero-part2-off1'.\index{division-theorem-for-truncate-t!o-zero-part2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-for-truncate-to-zero-part1; name this event `division-theorem-for-truncate-to-zero-part1-off1'.\index{division-theorem-for-truncate-t!o-zero-part1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable idiv-imod-uniqueness; name this event `idiv-imod-uniqueness-off1'.\index{idiv-imod-uniqueness-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-for-truncate-to-neginf; name this event `division-theorem-for-truncate-to-neginf-off1'.\index{division-theorem-for-truncate-t!o-neginf-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-for-truncate-to-neginf-part3; name this event `division-theorem-for-truncate-to-neginf-part3-off1'.\index{division-theorem-for-truncate-t!o-neginf-part3-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-for-truncate-to-neginf-part2; name this event `division-theorem-for-truncate-to-neginf-part2-off1'.\index{division-theorem-for-truncate-t!o-neginf-part2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-for-truncate-to-neginf-part1; name this event `division-theorem-for-truncate-to-neginf-part1-off1'.\index{division-theorem-for-truncate-t!o-neginf-part1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iquotient-iremainder-uniqueness; name this event `iquotient-iremainder-uniqueness-off1'.\index{iquotient-iremainder-uniqueness!-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem; name this event `division-theorem-off1'.\index{division-theorem-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-part3; name this event `division-theorem-part3-off1'.\index{division-theorem-part3-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-part2; name this event `division-theorem-part2-off1'.\index{division-theorem-part2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable division-theorem-part1; name this event `division-theorem-part1-off1'.\index{division-theorem-part1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-remainder-uniqueness; name this event `quotient-remainder-uniqueness-off1'.\index{quotient-remainder-uniqueness-o!ff1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-1-arg1; name this event `itimes-1-arg1-off1'.\index{itimes-1-arg1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-itimes-minus-1; name this event `equal-itimes-minus-1-off1'.\index{equal-itimes-minus-1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-itimes-1; name this event `equal-itimes-1-off1'.\index{equal-itimes-1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-itimes-0; name this event `equal-itimes-0-off1'.\index{equal-itimes-0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable associativity-of-itimes; name this event `associativity-of-itimes-off1'.\index{associativity-of-itimes-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity2-of-itimes; name this event `commutativity2-of-itimes-off1'.\index{commutativity2-of-itimes-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-distributes-over-iplus; name this event `itimes-distributes-over-iplus-off1'.\index{itimes-distributes-over-iplus-o!ff1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-distributes-over-iplus-proof; name this event `itimes-distributes-over-iplus-proof-off1'.\index{itimes-distributes-over-iplus-p!roof-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity-of-itimes; name this event `commutativity-of-itimes-off1'.\index{commutativity-of-itimes-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-fix-int2; name this event `itimes-fix-int2-off1'.\index{itimes-fix-int2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-fix-int1; name this event `itimes-fix-int1-off1'.\index{itimes-fix-int1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-0-right; name this event `itimes-0-right-off1'.\index{itimes-0-right-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable itimes-0-left; name this event `itimes-0-left-off1'.\index{itimes-0-left-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-iplus-ilessp; name this event `cancel-iplus-ilessp-off1'.\index{cancel-iplus-ilessp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-iplus-ilessp; name this event `g*1*cancel-iplus-ilessp-off1'.\index{g*1*cancel-iplus-ilessp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iplus-tree-no-fix-int; name this event `g*1*iplus-tree-no-fix-int-off1'.\index{g*1*iplus-tree-no-fix-int-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-cancellation-2-for-ilessp; name this event `iplus-cancellation-2-for-ilessp-off1'.\index{iplus-cancellation-2-for-ilessp!-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-cancellation-1-for-ilessp; name this event `iplus-cancellation-1-for-ilessp-off1'.\index{iplus-cancellation-1-for-ilessp!-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-iplus-ilessp-1; name this event `cancel-iplus-ilessp-1-off1'.\index{cancel-iplus-ilessp-1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-iplus-ilessp-1; name this event `g*1*cancel-iplus-ilessp-1-off1'.\index{g*1*cancel-iplus-ilessp-1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*make-cancel-iplus-inequality-1; name this event `g*1*make-cancel-iplus-inequality-1-off1'.\index{g*1*make-cancel-iplus-inequalit!y-1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-fix-int-2; name this event `ilessp-fix-int-2-off1'.\index{ilessp-fix-int-2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ilessp-fix-int-1; name this event `ilessp-fix-int-1-off1'.\index{ilessp-fix-int-1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-ineg7; name this event `iplus-ineg7-off1'.\index{iplus-ineg7-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-list-append; name this event `iplus-list-append-off1'.\index{iplus-list-append-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-iplus-list-delete; name this event `eval\$-iplus-list-delete-off1'.\index{eval\$-iplus-list-delete-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-iplus; name this event `g*1*cancel-iplus-off1'.\index{g*1*cancel-iplus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-list-append; name this event `eval\$-list-append-off1'.\index{eval\$-list-append-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-iplus-list; name this event `integerp-iplus-list-off1'.\index{integerp-iplus-list-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-list; name this event `iplus-list-off1'.\index{iplus-list-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iplus-list; name this event `g*1*iplus-list-off1'.\index{g*1*iplus-list-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iplus-tree; name this event `g*1*iplus-tree-off1'.\index{g*1*iplus-tree-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-tree-rec; name this event `iplus-tree-rec-off1'.\index{iplus-tree-rec-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iplus-tree-rec; name this event `g*1*iplus-tree-rec-off1'.\index{g*1*iplus-tree-rec-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-fringe; name this event `iplus-fringe-off1'.\index{iplus-fringe-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iplus-fringe; name this event `g*1*iplus-fringe-off1'.\index{g*1*iplus-fringe-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-x-y-ineg-x; name this event `iplus-x-y-ineg-x-off1'.\index{iplus-x-y-ineg-x-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-ineg4; name this event `iplus-ineg4-off1'.\index{iplus-ineg4-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-ineg3; name this event `iplus-ineg3-off1'.\index{iplus-ineg3-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-cancel-ineg-aux-is-its-fn; name this event `eval\$-cancel-ineg-aux-is-its-fn-off1'.\index{eval\$-cancel-ineg-aux-is-its-f!n-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-cancel-ineg-aux-fn; name this event `eval\$-cancel-ineg-aux-fn-off1'.\index{eval\$-cancel-ineg-aux-fn-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*eval\$-cancel-ineg-aux-fn; name this event `g*1*eval\$-cancel-ineg-aux-fn-off1'.\index{g*1*eval\$-cancel-ineg-aux-fn-o!ff1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-other; name this event `eval\$-other-off1'.\index{eval\$-other-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-litatom; name this event `eval\$-litatom-off1'.\index{eval\$-litatom-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-list-nlistp; name this event `eval\$-list-nlistp-off1'.\index{eval\$-list-nlistp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-list-cons; name this event `eval\$-list-cons-off1'.\index{eval\$-list-cons-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-ineg; name this event `cancel-ineg-off1'.\index{cancel-ineg-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-ineg; name this event `g*1*cancel-ineg-off1'.\index{g*1*cancel-ineg-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-ineg-aux; name this event `cancel-ineg-aux-off1'.\index{cancel-ineg-aux-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-ineg-aux; name this event `g*1*cancel-ineg-aux-off1'.\index{g*1*cancel-ineg-aux-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable idifference-fix-int2; name this event `idifference-fix-int2-off1'.\index{idifference-fix-int2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable idifference-fix-int1; name this event `idifference-fix-int1-off1'.\index{idifference-fix-int1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-fix-int2; name this event `iplus-fix-int2-off1'.\index{iplus-fix-int2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-fix-int1; name this event `iplus-fix-int1-off1'.\index{iplus-fix-int1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-ineg2; name this event `iplus-ineg2-off1'.\index{iplus-ineg2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-ineg1; name this event `iplus-ineg1-off1'.\index{iplus-ineg1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-cancellation-2; name this event `iplus-cancellation-2-off1'.\index{iplus-cancellation-2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-cancellation-1; name this event `iplus-cancellation-1-off1'.\index{iplus-cancellation-1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable associativity-of-iplus; name this event `associativity-of-iplus-off1'.\index{associativity-of-iplus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity-of-iplus; name this event `commutativity-of-iplus-off1'.\index{commutativity-of-iplus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity2-of-iplus; name this event `commutativity2-of-iplus-off1'.\index{commutativity2-of-iplus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-0-right; name this event `iplus-0-right-off1'.\index{iplus-0-right-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable iplus-0-left; name this event `iplus-0-left-off1'.\index{iplus-0-left-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ineg-0; name this event `ineg-0-off1'.\index{ineg-0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ineg-fix-int; name this event `ineg-fix-int-off1'.\index{ineg-fix-int-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ineg-ineg; name this event `ineg-ineg-off1'.\index{ineg-ineg-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ineg-iplus; name this event `ineg-iplus-off1'.\index{ineg-iplus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-itimes; name this event `fix-int-itimes-off1'.\index{fix-int-itimes-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-iabs; name this event `fix-int-iabs-off1'.\index{fix-int-iabs-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-ineg; name this event `fix-int-ineg-off1'.\index{fix-int-ineg-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-idifference; name this event `fix-int-idifference-off1'.\index{fix-int-idifference-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-iplus; name this event `fix-int-iplus-off1'.\index{fix-int-iplus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-fix-int; name this event `fix-int-fix-int-off1'.\index{fix-int-fix-int-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable fix-int-remover; name this event `fix-int-remover-off1'.\index{fix-int-remover-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-itimes; name this event `integerp-itimes-off1'.\index{integerp-itimes-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-iabs; name this event `integerp-iabs-off1'.\index{integerp-iabs-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-ineg; name this event `integerp-ineg-off1'.\index{integerp-ineg-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-idifference; name this event `integerp-idifference-off1'.\index{integerp-idifference-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-iplus; name this event `integerp-iplus-off1'.\index{integerp-iplus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable integerp-fix-int; name this event `integerp-fix-int-off1'.\index{integerp-fix-int-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*irem; name this event `g*1*irem-off1'.\index{g*1*irem-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iquo; name this event `g*1*iquo-off1'.\index{g*1*iquo-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*imod; name this event `g*1*imod-off1'.\index{g*1*imod-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*idiv; name this event `g*1*idiv-off1'.\index{g*1*idiv-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iremainder; name this event `g*1*iremainder-off1'.\index{g*1*iremainder-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iquotient; name this event `g*1*iquotient-off1'.\index{g*1*iquotient-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*itimes; name this event `g*1*itimes-off1'.\index{g*1*itimes-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iabs; name this event `g*1*iabs-off1'.\index{g*1*iabs-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable idifference; name this event `idifference-off1'.\index{idifference-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*idifference; name this event `g*1*idifference-off1'.\index{g*1*idifference-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*ineg; name this event `g*1*ineg-off1'.\index{g*1*ineg-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*iplus; name this event `g*1*iplus-off1'.\index{g*1*iplus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable ileq; name this event `ileq-off1'.\index{ileq-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*ileq; name this event `g*1*ileq-off1'.\index{g*1*ileq-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*ilessp; name this event `g*1*ilessp-off1'.\index{g*1*ilessp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable izerop; name this event `izerop-off1'.\index{izerop-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*izerop; name this event `g*1*izerop-off1'.\index{g*1*izerop-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*fix-int; name this event `g*1*fix-int-off1'.\index{g*1*fix-int-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*integerp; name this event `g*1*integerp-off1'.\index{g*1*integerp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd-idempotence; name this event `gcd-idempotence-off1'.\index{gcd-idempotence-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd-x-x; name this event `gcd-x-x-off1'.\index{gcd-x-x-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity2-of-gcd; name this event `commutativity2-of-gcd-off1'.\index{commutativity2-of-gcd-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity2-of-gcd-zero-case; name this event `commutativity2-of-gcd-zero-case-off1'.\index{commutativity2-of-gcd-zero-case!-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable associativity-of-gcd; name this event `associativity-of-gcd-off1'.\index{associativity-of-gcd-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable associativity-of-gcd-zero-case; name this event `associativity-of-gcd-zero-case-off1'.\index{associativity-of-gcd-zero-case-!off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable common-divisor-divides-gcd; name this event `common-divisor-divides-gcd-off1'.\index{common-divisor-divides-gcd-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd-is-the-greatest; name this event `gcd-is-the-greatest-off1'.\index{gcd-is-the-greatest-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable distributivity-of-times-over-gcd; name this event `distributivity-of-times-over-gcd-off1'.\index{distributivity-of-times-over-gc!d-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable distributivity-of-times-over-gcd-proof; name this event `distributivity-of-times-over-gcd-proof-off1'.\index{distributivity-of-times-over-gc!d-proof-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-gcd; name this event `remainder-gcd-off1'.\index{remainder-gcd-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd-plus-instance; name this event `gcd-plus-instance-off1'.\index{gcd-plus-instance-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd-plus; name this event `gcd-plus-off1'.\index{gcd-plus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd-plus-proof; name this event `gcd-plus-proof-off1'.\index{gcd-plus-proof-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd-plus-instance-temp; name this event `gcd-plus-instance-temp-off1'.\index{gcd-plus-instance-temp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd-plus-instance-temp-proof; name this event `gcd-plus-instance-temp-proof-off1'.\index{gcd-plus-instance-temp-proof-of!f1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-gcd; name this event `lessp-gcd-off1'.\index{lessp-gcd-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-gcd-0; name this event `equal-gcd-0-off1'.\index{equal-gcd-0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd-1; name this event `gcd-1-off1'.\index{gcd-1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd-0; name this event `gcd-0-off1'.\index{gcd-0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable single-number-induction; name this event `single-number-induction-off1'.\index{single-number-induction-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*single-number-induction; name this event `g*1*single-number-induction-off1'.\index{g*1*single-number-induction-off!1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity-of-gcd; name this event `commutativity-of-gcd-off1'.\index{commutativity-of-gcd-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-exp; name this event `log-exp-off1'.\index{log-exp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-times-exp; name this event `log-times-exp-off1'.\index{log-times-exp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-times-exp-proof; name this event `log-times-exp-proof-off1'.\index{log-times-exp-proof-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-times; name this event `log-times-off1'.\index{log-times-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-times-proof; name this event `log-times-proof-off1'.\index{log-times-proof-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-quotient-exp; name this event `log-quotient-exp-off1'.\index{log-quotient-exp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-quotient-times; name this event `log-quotient-times-off1'.\index{log-quotient-times-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-quotient-times-proof; name this event `log-quotient-times-proof-off1'.\index{log-quotient-times-proof-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-quotient; name this event `log-quotient-off1'.\index{log-quotient-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable leq-log-log; name this event `leq-log-log-off1'.\index{leq-log-log-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable double-log-induction; name this event `double-log-induction-off1'.\index{double-log-induction-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*double-log-induction; name this event `g*1*double-log-induction-off1'.\index{g*1*double-log-induction-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-1; name this event `log-1-off1'.\index{log-1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log-0; name this event `log-0-off1'.\index{log-0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-log-0; name this event `equal-log-0-off1'.\index{equal-log-0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable exp-difference; name this event `exp-difference-off1'.\index{exp-difference-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-exp-1; name this event `equal-exp-1-off1'.\index{equal-exp-1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-exp-0; name this event `equal-exp-0-off1'.\index{equal-exp-0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable exp-exp; name this event `exp-exp-off1'.\index{exp-exp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable exp-times; name this event `exp-times-off1'.\index{exp-times-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable exp-0-arg2; name this event `exp-0-arg2-off1'.\index{exp-0-arg2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable exp-1-arg1; name this event `exp-1-arg1-off1'.\index{exp-1-arg1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable exp-0-arg1; name this event `exp-0-arg1-off1'.\index{exp-0-arg1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable exp-plus; name this event `exp-plus-off1'.\index{exp-plus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable exp-add1; name this event `exp-add1-off1'.\index{exp-add1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable exp-zero; name this event `exp-zero-off1'.\index{exp-zero-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-exp; name this event `quotient-exp-off1'.\index{quotient-exp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-exp-exp; name this event `remainder-exp-exp-off1'.\index{remainder-exp-exp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable double-number-induction; name this event `double-number-induction-off1'.\index{double-number-induction-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*double-number-induction; name this event `g*1*double-number-induction-off1'.\index{g*1*double-number-induction-off!1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-exp; name this event `remainder-exp-off1'.\index{remainder-exp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable gcd; name this event `gcd-off1'.\index{gcd-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*gcd; name this event `g*1*gcd-off1'.\index{g*1*gcd-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable log; name this event `log-off1'.\index{log-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*log; name this event `g*1*log-off1'.\index{g*1*log-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable exp; name this event `exp-off1'.\index{exp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*exp; name this event `g*1*exp-off1'.\index{g*1*exp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-quotient-times; name this event `cancel-quotient-times-off1'.\index{cancel-quotient-times-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-quotient-times; name this event `g*1*cancel-quotient-times-off1'.\index{g*1*cancel-quotient-times-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-quotient; name this event `lessp-quotient-off1'.\index{lessp-quotient-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-x-x; name this event `quotient-x-x-off1'.\index{quotient-x-x-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-1-arg1; name this event `quotient-1-arg1-off1'.\index{quotient-1-arg1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-1-arg1-casesplit; name this event `quotient-1-arg1-casesplit-off1'.\index{quotient-1-arg1-casesplit-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-1-arg2; name this event `quotient-1-arg2-off1'.\index{quotient-1-arg2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable leq-quotient; name this event `leq-quotient-off1'.\index{leq-quotient-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-quotient; name this event `quotient-quotient-off1'.\index{quotient-quotient-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-plus-times-times-instance; name this event `quotient-plus-times-times-instance-off1'.\index{quotient-plus-times-times-insta!nce-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-plus-times-times; name this event `quotient-plus-times-times-off1'.\index{quotient-plus-times-times-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-plus-times-times-proof; name this event `quotient-plus-times-times-proof-off1'.\index{quotient-plus-times-times-proof!-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-plus-fact; name this event `quotient-plus-fact-off1'.\index{quotient-plus-fact-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-remainder-instance; name this event `quotient-remainder-instance-off1'.\index{quotient-remainder-instance-off!1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-remainder; name this event `quotient-remainder-off1'.\index{quotient-remainder-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-remainder-times; name this event `quotient-remainder-times-off1'.\index{quotient-remainder-times-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-difference3; name this event `quotient-difference3-off1'.\index{quotient-difference3-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-difference2; name this event `quotient-difference2-off1'.\index{quotient-difference2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-lessp-arg1; name this event `quotient-lessp-arg1-off1'.\index{quotient-lessp-arg1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-difference1; name this event `quotient-difference1-off1'.\index{quotient-difference1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-times-times-proof; name this event `quotient-times-times-proof-off1'.\index{quotient-times-times-proof-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-times-instance; name this event `quotient-times-instance-off1'.\index{quotient-times-instance-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-times; name this event `quotient-times-off1'.\index{quotient-times-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-times-proof; name this event `quotient-times-proof-off1'.\index{quotient-times-proof-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-times-instance-temp-proof; name this event `quotient-times-instance-temp-proof-off1'.\index{quotient-times-instance-temp-pr!oof-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-plus; name this event `quotient-plus-off1'.\index{quotient-plus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-plus-proof; name this event `quotient-plus-proof-off1'.\index{quotient-plus-proof-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-sub1; name this event `quotient-sub1-off1'.\index{quotient-sub1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-quotient-0; name this event `equal-quotient-0-off1'.\index{equal-quotient-0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-add1; name this event `quotient-add1-off1'.\index{quotient-add1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-zero; name this event `quotient-zero-off1'.\index{quotient-zero-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-of-non-number; name this event `quotient-of-non-number-off1'.\index{quotient-of-non-number-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable quotient-noop; name this event `quotient-noop-off1'.\index{quotient-noop-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable transitivity-of-divides; name this event `transitivity-of-divides-off1'.\index{transitivity-of-divides-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-x-x; name this event `remainder-x-x-off1'.\index{remainder-x-x-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-1-arg2; name this event `remainder-1-arg2-off1'.\index{remainder-1-arg2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-1-arg1; name this event `remainder-1-arg1-off1'.\index{remainder-1-arg1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-remainder; name this event `remainder-remainder-off1'.\index{remainder-remainder-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-plus-times-times-instance; name this event `remainder-plus-times-times-instance-off1'.\index{remainder-plus-times-times-inst!ance-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-plus-times-times; name this event `remainder-plus-times-times-off1'.\index{remainder-plus-times-times-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-plus-times-times-proof; name this event `remainder-plus-times-times-proof-off1'.\index{remainder-plus-times-times-proo!f-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-plus-fact; name this event `remainder-plus-fact-off1'.\index{remainder-plus-fact-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-difference2; name this event `remainder-difference2-off1'.\index{remainder-difference2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable double-remainder-induction; name this event `double-remainder-induction-off1'.\index{double-remainder-induction-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*double-remainder-induction; name this event `g*1*double-remainder-induction-off1'.\index{g*1*double-remainder-induction-!off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-difference1; name this event `remainder-difference1-off1'.\index{remainder-difference1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-times2-instance; name this event `remainder-times2-instance-off1'.\index{remainder-times2-instance-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-times2; name this event `remainder-times2-off1'.\index{remainder-times2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-times2-proof; name this event `remainder-times2-proof-off1'.\index{remainder-times2-proof-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-times-times-proof; name this event `remainder-times-times-proof-off1'.\index{remainder-times-times-proof-off!1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-times1-instance; name this event `remainder-times1-instance-off1'.\index{remainder-times1-instance-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-times1-instance-proof; name this event `remainder-times1-instance-proof-off1'.\index{remainder-times1-instance-proof!-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-times1; name this event `remainder-times1-off1'.\index{remainder-times1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-times1-proof; name this event `remainder-times1-proof-off1'.\index{remainder-times1-proof-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-remainder-plus-remainder-proof; name this event `equal-remainder-plus-remainder-proof-off1'.\index{equal-remainder-plus-remainder-p!roof-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-remainder-plus-0; name this event `equal-remainder-plus-0-off1'.\index{equal-remainder-plus-0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-remainder-plus-0-proof; name this event `equal-remainder-plus-0-proof-off1'.\index{equal-remainder-plus-0-proof-of!f1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-plus; name this event `remainder-plus-off1'.\index{remainder-plus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-plus-proof; name this event `remainder-plus-proof-off1'.\index{remainder-plus-proof-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-add1; name this event `remainder-add1-off1'.\index{remainder-add1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-quotient-elim; name this event `remainder-quotient-elim-off1'.\index{remainder-quotient-elim-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-zero; name this event `remainder-zero-off1'.\index{remainder-zero-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-of-non-number; name this event `remainder-of-non-number-off1'.\index{remainder-of-non-number-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable remainder-noop; name this event `remainder-noop-off1'.\index{remainder-noop-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-remainder; name this event `lessp-remainder-off1'.\index{lessp-remainder-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-equal-times; name this event `cancel-equal-times-off1'.\index{cancel-equal-times-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-equal-times; name this event `g*1*cancel-equal-times-off1'.\index{g*1*cancel-equal-times-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-lessp-times; name this event `cancel-lessp-times-off1'.\index{cancel-lessp-times-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-lessp-times; name this event `g*1*cancel-lessp-times-off1'.\index{g*1*cancel-lessp-times-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable infer-equality-from-not-lessp; name this event `infer-equality-from-not-lessp-off1'.\index{infer-equality-from-not-lessp-o!ff1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-times-arg1; name this event `lessp-times-arg1-off1'.\index{lessp-times-arg1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-equal; name this event `eval\$-equal-off2'.\index{eval\$-equal-off2}

\addvspace{18pt}


\noindent{\sc Event}:   Enable and-not-zerop-tree; name this event `and-not-zerop-tree-off1'.\index{and-not-zerop-tree-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*and-not-zerop-tree; name this event `g*1*and-not-zerop-tree-off1'.\index{g*1*and-not-zerop-tree-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable or-zerop-tree; name this event `or-zerop-tree-off1'.\index{or-zerop-tree-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*or-zerop-tree; name this event `g*1*or-zerop-tree-off1'.\index{g*1*or-zerop-tree-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-fringe; name this event `times-fringe-off1'.\index{times-fringe-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*times-fringe; name this event `g*1*times-fringe-off1'.\index{g*1*times-fringe-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-tree; name this event `times-tree-off1'.\index{times-tree-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*times-tree; name this event `g*1*times-tree-off1'.\index{g*1*times-tree-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-1-times; name this event `lessp-1-times-off1'.\index{lessp-1-times-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-plus-times2; name this event `lessp-plus-times2-off1'.\index{lessp-plus-times2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-plus-times1; name this event `lessp-plus-times1-off1'.\index{lessp-plus-times1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-plus-times-proof; name this event `lessp-plus-times-proof-off1'.\index{lessp-plus-times-proof-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-times-cancellation-proof; name this event `lessp-times-cancellation-proof-off1'.\index{lessp-times-cancellation-proof-!off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-times3; name this event `lessp-times3-off1'.\index{lessp-times3-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-times3-proof2; name this event `lessp-times3-proof2-off1'.\index{lessp-times3-proof2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-times3-proof1; name this event `lessp-times3-proof1-off1'.\index{lessp-times3-proof1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-times2; name this event `lessp-times2-off1'.\index{lessp-times2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-times2-proof; name this event `lessp-times2-proof-off1'.\index{lessp-times2-proof-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-times1; name this event `lessp-times1-off1'.\index{lessp-times1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable lessp-times1-proof; name this event `lessp-times1-proof-off1'.\index{lessp-times1-proof-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-1-arg1; name this event `times-1-arg1-off1'.\index{times-1-arg1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-quotient; name this event `times-quotient-off1'.\index{times-quotient-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-quotient-proof; name this event `times-quotient-proof-off1'.\index{times-quotient-proof-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-distributes-over-difference; name this event `times-distributes-over-difference-off1'.\index{times-distributes-over-differen!ce-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-distributes-over-difference-proof; name this event `times-distributes-over-difference-proof-off1'.\index{times-distributes-over-differen!ce-proof-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable associativity-of-times; name this event `associativity-of-times-off1'.\index{associativity-of-times-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity2-of-times; name this event `commutativity2-of-times-off1'.\index{commutativity2-of-times-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-distributes-over-plus; name this event `times-distributes-over-plus-off1'.\index{times-distributes-over-plus-off!1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-distributes-over-plus-proof; name this event `times-distributes-over-plus-proof-off1'.\index{times-distributes-over-plus-pro!of-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity-of-times; name this event `commutativity-of-times-off1'.\index{commutativity-of-times-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-add1; name this event `times-add1-off1'.\index{times-add1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable times-zero; name this event `times-zero-off1'.\index{times-zero-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-sub1-0; name this event `equal-sub1-0-off1'.\index{equal-sub1-0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-times-1; name this event `equal-times-1-off1'.\index{equal-times-1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-times-0; name this event `equal-times-0-off1'.\index{equal-times-0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-lessp-plus; name this event `cancel-lessp-plus-off1'.\index{cancel-lessp-plus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-lessp-plus; name this event `g*1*cancel-lessp-plus-off1'.\index{g*1*cancel-lessp-plus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable difference-x-x; name this event `difference-x-x-off1'.\index{difference-x-x-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable difference-difference-arg2; name this event `difference-difference-arg2-off1'.\index{difference-difference-arg2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable difference-difference-arg1; name this event `difference-difference-arg1-off1'.\index{difference-difference-arg1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable difference-sub1-arg2; name this event `difference-sub1-arg2-off1'.\index{difference-sub1-arg2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable difference-add1-arg2; name this event `difference-add1-arg2-off1'.\index{difference-add1-arg2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable difference-leq-arg1; name this event `difference-leq-arg1-off1'.\index{difference-leq-arg1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable difference-elim; name this event `difference-elim-off1'.\index{difference-elim-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-difference-plus; name this event `cancel-difference-plus-off1'.\index{cancel-difference-plus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-difference-plus; name this event `g*1*cancel-difference-plus-off1'.\index{g*1*cancel-difference-plus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable cancel-equal-plus; name this event `cancel-equal-plus-off1'.\index{cancel-equal-plus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*cancel-equal-plus; name this event `g*1*cancel-equal-plus-off1'.\index{g*1*cancel-equal-plus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable eval\$-quote; name this event `eval\$-quote-off2'.\index{eval\$-quote-off2}

\addvspace{18pt}


\noindent{\sc Event}:   Enable plus-tree; name this event `plus-tree-off1'.\index{plus-tree-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*plus-tree; name this event `g*1*plus-tree-off1'.\index{g*1*plus-tree-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable plus-fringe; name this event `plus-fringe-off1'.\index{plus-fringe-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*plus-fringe; name this event `g*1*plus-fringe-off1'.\index{g*1*plus-fringe-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable diff-diff-arg2; name this event `diff-diff-arg2-off1'.\index{diff-diff-arg2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable diff-diff-arg1; name this event `diff-diff-arg1-off1'.\index{diff-diff-arg1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable difference-plus-plus-cancellation-proof; name this event `difference-plus-plus-cancellation-proof-off1'.\index{difference-plus-plus-cancellati!on-proof-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable difference-plus-cancellation-proof; name this event `difference-plus-cancellation-proof-off1'.\index{difference-plus-cancellation-pr!oof-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable plus-difference-arg2; name this event `plus-difference-arg2-off1'.\index{plus-difference-arg2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable plus-difference-arg1; name this event `plus-difference-arg1-off1'.\index{plus-difference-arg1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable associativity-of-plus; name this event `associativity-of-plus-off1'.\index{associativity-of-plus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable plus-add1-arg2; name this event `plus-add1-arg2-off1'.\index{plus-add1-arg2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable plus-add1-arg1; name this event `plus-add1-arg1-off1'.\index{plus-add1-arg1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable plus-zero-arg2; name this event `plus-zero-arg2-off1'.\index{plus-zero-arg2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity2-of-plus; name this event `commutativity2-of-plus-off1'.\index{commutativity2-of-plus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable commutativity-of-plus; name this event `commutativity-of-plus-off1'.\index{commutativity-of-plus-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-difference-0; name this event `equal-difference-0-off1'.\index{equal-difference-0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-plus-0; name this event `equal-plus-0-off1'.\index{equal-plus-0-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable member-bagint; name this event `member-bagint-off1'.\index{member-bagint-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable occurrences-bagdiff; name this event `occurrences-bagdiff-off1'.\index{occurrences-bagdiff-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable occurrences-bagint; name this event `occurrences-bagint-off1'.\index{occurrences-bagint-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable subbagp-bagint2; name this event `subbagp-bagint2-off1'.\index{subbagp-bagint2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable subbagp-bagint1; name this event `subbagp-bagint1-off1'.\index{subbagp-bagint1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable subbagp-cdr2; name this event `subbagp-cdr2-off1'.\index{subbagp-cdr2-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable subbagp-cdr1; name this event `subbagp-cdr1-off1'.\index{subbagp-cdr1-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable subbagp-delete; name this event `subbagp-delete-off1'.\index{subbagp-delete-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable bagdiff-delete; name this event `bagdiff-delete-off1'.\index{bagdiff-delete-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable member-bagdiff; name this event `member-bagdiff-off1'.\index{member-bagdiff-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable occurrences-delete; name this event `occurrences-delete-off1'.\index{occurrences-delete-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable member-delete-implies-membership; name this event `member-delete-implies-membership-off1'.\index{member-delete-implies-membership!-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable member-delete; name this event `member-delete-off1'.\index{member-delete-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable member-non-list; name this event `member-non-list-off1'.\index{member-non-list-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable equal-occurrences-zero; name this event `equal-occurrences-zero-off1'.\index{equal-occurrences-zero-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable delete-delete; name this event `delete-delete-off1'.\index{delete-delete-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable delete-non-member; name this event `delete-non-member-off1'.\index{delete-non-member-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable subbagp; name this event `subbagp-off1'.\index{subbagp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*subbagp; name this event `g*1*subbagp-off1'.\index{g*1*subbagp-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable occurrences; name this event `occurrences-off1'.\index{occurrences-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*occurrences; name this event `g*1*occurrences-off1'.\index{g*1*occurrences-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable bagint; name this event `bagint-off1'.\index{bagint-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*bagint; name this event `g*1*bagint-off1'.\index{g*1*bagint-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable bagdiff; name this event `bagdiff-off1'.\index{bagdiff-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*bagdiff; name this event `g*1*bagdiff-off1'.\index{g*1*bagdiff-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable delete; name this event `delete-off1'.\index{delete-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable *1*delete; name this event `g*1*delete-off1'.\index{g*1*delete-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-adder-output=v-sum; name this event `v-adder-output=v-sum-on'.\index{v-adder-output=v-sum-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-adder-carry-out=v-carry; name this event `v-adder-carry-out=v-carry-on'.\index{v-adder-carry-out=v-carry-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-to-nat-firstn-hack1; name this event `v-to-nat-firstn-hack1-on'.\index{v-to-nat-firstn-hack1-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-to-nat-firstn-hack2; name this event `v-to-nat-firstn-hack2-on'.\index{v-to-nat-firstn-hack2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-nat-to-v-inverter-hack1; name this event `equal-nat-to-v-inverter-hack1-on'.\index{equal-nat-to-v-inverter-hack1-o!n}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-nat-to-v-inverter-hack2; name this event `equal-nat-to-v-inverter-hack2-on'.\index{equal-nat-to-v-inverter-hack2-o!n}

\addvspace{18pt}


\noindent{\sc Event}:   Disable equal-iff; name this event `equal-iff-on'.\index{equal-iff-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable quotient-plus-x-x-2-with-extra-arg; name this event `quotient-plus-x-x-2-with-extra-arg-on'.\index{quotient-plus-x-x-2-with-extra-!arg-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable plus-quotient-2-lemma; name this event `plus-quotient-2-lemma-on'.\index{plus-quotient-2-lemma-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable plus-quotient-2; name this event `plus-quotient-2-on'.\index{plus-quotient-2-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-nat-int-buf; name this event `v-alu-correct-nat-int-buf-on'.\index{v-alu-correct-nat-int-buf-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-nat-adder-carry-out; name this event `v-alu-correct-nat-adder-carry-out-on'.\index{v-alu-correct-nat-adder-carry-o!ut-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-nat-adder-output; name this event `v-alu-correct-nat-adder-output-on'.\index{v-alu-correct-nat-adder-output-!on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-nat-adder; name this event `v-alu-correct-nat-adder-on'.\index{v-alu-correct-nat-adder-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-nat-inc; name this event `v-alu-correct-nat-inc-on'.\index{v-alu-correct-nat-inc-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-nat-subtracter-carry-out; name this event `v-alu-correct-nat-subtracter-carry-out-on'.\index{v-alu-correct-nat-subtracter-ca!rry-out-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-nat-subtracter-output; name this event `v-alu-correct-nat-subtracter-output-on'.\index{v-alu-correct-nat-subtracter-outp!ut-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-nat-subtracter; name this event `v-alu-correct-nat-subtracter-on'.\index{v-alu-correct-nat-subtracter-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-nat-dec; name this event `v-alu-correct-nat-dec-on'.\index{v-alu-correct-nat-dec-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-nat-lsr-carry-out; name this event `v-alu-correct-nat-lsr-carry-out-on'.\index{v-alu-correct-nat-lsr-carry-out!-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-nat-lsr-output; name this event `v-alu-correct-nat-lsr-output-on'.\index{v-alu-correct-nat-lsr-output-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-nat-lsr; name this event `v-alu-correct-nat-lsr-on'.\index{v-alu-correct-nat-lsr-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-nat-not-output; name this event `v-alu-correct-nat-not-output-on'.\index{v-alu-correct-nat-not-output-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-nat-not; name this event `v-alu-correct-nat-not-on'.\index{v-alu-correct-nat-not-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-int-adder-overflowp; name this event `v-alu-correct-int-adder-overflowp-on'.\index{v-alu-correct-int-adder-overflo!wp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-int-adder-output; name this event `v-alu-correct-int-adder-output-on'.\index{v-alu-correct-int-adder-output-!on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-int-adder; name this event `v-alu-correct-int-adder-on'.\index{v-alu-correct-int-adder-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-int-inc; name this event `v-alu-correct-int-inc-on'.\index{v-alu-correct-int-inc-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-int-subtracter-overflowp; name this event `v-alu-correct-int-subtracter-overflowp-on'.\index{v-alu-correct-int-subtracter-ove!rflowp-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-int-subtracter-output; name this event `v-alu-correct-int-subtracter-output-on'.\index{v-alu-correct-int-subtracter-outp!ut-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-int-subtracter; name this event `v-alu-correct-int-subtracter-on'.\index{v-alu-correct-int-subtracter-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-int-dec; name this event `v-alu-correct-int-dec-on'.\index{v-alu-correct-int-dec-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-int-asr-output; name this event `v-alu-correct-int-asr-output-on'.\index{v-alu-correct-int-asr-output-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-int-asr; name this event `v-alu-correct-int-asr-on'.\index{v-alu-correct-int-asr-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-int-neg; name this event `v-alu-correct-int-neg-on'.\index{v-alu-correct-int-neg-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-alu-correct-int-not; name this event `v-alu-correct-int-not-on'.\index{v-alu-correct-int-not-on}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-int-not-output; name this event `v-alu-correct-int-not-output-off1'.\index{v-alu-correct-int-not-output-of!f1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-nat-not-output; name this event `v-alu-correct-nat-not-output-off2'.\index{v-alu-correct-nat-not-output-of!f2}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-nat-lsr-carry-out; name this event `v-alu-correct-nat-lsr-carry-out-off1'.\index{v-alu-correct-nat-lsr-carry-out!-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-adder-output=v-sum; name this event `v-adder-output=v-sum-off1'.\index{v-adder-output=v-sum-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-nat-inc; name this event `v-alu-correct-nat-inc-off1'.\index{v-alu-correct-nat-inc-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-nat-adder; name this event `v-alu-correct-nat-adder-off1'.\index{v-alu-correct-nat-adder-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-int-asr; name this event `v-alu-correct-int-asr-off1'.\index{v-alu-correct-int-asr-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Enable v-alu-correct-nat-lsr; name this event `v-alu-correct-nat-lsr-off1'.\index{v-alu-correct-nat-lsr-off1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable v-to-nat-of-nat-to-v; name this event `v-to-nat-of-nat-to-v-on'.\index{v-to-nat-of-nat-to-v-on}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-0-left; name this event `iplus-0-left-on1'.\index{iplus-0-left-on1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable iplus-0-right; name this event `iplus-0-right-on1'.\index{iplus-0-right-on1}

\addvspace{18pt}


\noindent{\sc Event}:   Disable commutativity-of-iplus; name this event `commutativity-of-iplus-on1'.\index{commutativity-of-iplus-on1}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-negp-$>$v-nzerop \\ \index{v-negp-$>$v-nzerop}
{\rm{v-negp}}\,({\it{v\/}})\index{v-negp} $\rightarrow$ {\rm{v-nzerop}}\,({\it{v\/}})\index{v-nzerop}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-zerop-implies-v-to-nat-0 \\ \index{v-zerop-implies-v-to-nat-0}
{\rm{v-zerop}}\,({\it{a\/}})\index{v-zerop} $\rightarrow$ ({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $=$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  boolp-flag-extracters \\ \index{boolp-flag-extracters}
\=\+{\rm{boolp}}\,({\rm{c-flag}}\,({\rm{update-flags}}\,({\it{flags\/}}, {\it{set-flags\/}}, {\it{cvzbv\/}})\index{update-flags})\index{c-flag})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{v-flag}}\,({\rm{update-flags}}\,({\it{flags\/}}, {\it{set-flags\/}}, {\it{cvzbv\/}})\index{update-flags})\index{v-flag})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{n-flag}}\,({\rm{update-flags}}\,({\it{flags\/}}, {\it{set-flags\/}}, {\it{cvzbv\/}})\index{update-flags})\index{n-flag})\index{boolp} \\ 
$\wedge$$\;\;\;\;${\rm{boolp}}\,({\rm{z-flag}}\,({\rm{update-flags}}\,({\it{flags\/}}, {\it{set-flags\/}}, {\it{cvzbv\/}})\index{update-flags})\index{z-flag})\index{boolp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-to-nat-equal \\ \index{v-to-nat-equal}
{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\rightarrow$ (({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $=$ {\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat}) $=$ ({\it{a\/}} $=$ {\it{b\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-nzerop-nat-to-v-zero \\ \index{v-nzerop-nat-to-v-zero}
({\it{z\/}} $\simeq {\tt{0}}$) $\rightarrow$ ($\neg$ {\rm{v-nzerop}}\,({\rm{nat-to-v}}\,({\it{z\/}}, {\it{l\/}})\index{nat-to-v})\index{v-nzerop})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-not-v-not \\ \index{v-not-v-not}
{\rm{bvp}}\,({\it{a\/}})\index{bvp} $\rightarrow$ ({\rm{v-not}}\,({\rm{v-not}}\,({\it{a\/}})\index{v-not})\index{v-not} $=$ {\it{a\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-equal-v-to-nat-0 \\ \index{rewrite-equal-v-to-nat-0}
({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $=$ {\tt{0}}) $=$ {\rm{v-zerop}}\,({\it{a\/}})\index{v-zerop}
\end{tabbing}


\noindent{\sc Event}:   Enable rewrite-equal-v-to-nat-0; name this event `rewrite-equal-v-to-nat-0-off'.\index{rewrite-equal-v-to-nat-0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{cc-cc}$\;\;$
{\sc{cc-cc}}\index{cc-cc} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cc-cs}$\;\;$
{\sc{cc-cs}}\index{cc-cs} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cc-vc}$\;\;$
{\sc{cc-vc}}\index{cc-vc} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cc-vs}$\;\;$
{\sc{cc-vs}}\index{cc-vs} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cc-pl}$\;\;$
{\sc{cc-pl}}\index{cc-pl} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cc-mi}$\;\;$
{\sc{cc-mi}}\index{cc-mi} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cc-ne}$\;\;$
{\sc{cc-ne}}\index{cc-ne} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cc-eq}$\;\;$
{\sc{cc-eq}}\index{cc-eq} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cc-hi}$\;\;$
{\sc{cc-hi}}\index{cc-hi} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cc-ls}$\;\;$
{\sc{cc-ls}}\index{cc-ls} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cc-ge}$\;\;$
{\sc{cc-ge}}\index{cc-ge} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cc-lt}$\;\;$
{\sc{cc-lt}}\index{cc-lt} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cc-gt}$\;\;$
{\sc{cc-gt}}\index{cc-gt} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cc-le}$\;\;$
{\sc{cc-le}}\index{cc-le} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cc-t}$\;\;$
{\sc{cc-t}}\index{cc-t} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{cc-f}$\;\;$
{\sc{cc-f}}\index{cc-f} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}})
\end{tabbing}


\noindent{\sc Event}:   Let us define the theory {\it{condition-code-theory}} to consist of the following events: cc-cc,
cc-cs,
cc-vc,
cc-vs,
cc-pl,
cc-mi,
cc-ne,
cc-eq,
cc-hi,
cc-ls,
cc-ge,
cc-lt,
cc-gt,
cc-le,
cc-t,
cc-f.\index{condition-code-theory}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{op-move}$\;\;$
{\sc{op-move}}\index{op-move} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{op-inc}$\;\;$
{\sc{op-inc}}\index{op-inc} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{op-addc}$\;\;$
{\sc{op-addc}}\index{op-addc} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{op-add}$\;\;$
{\sc{op-add}}\index{op-add} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{op-neg}$\;\;$
{\sc{op-neg}}\index{op-neg} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{op-dec}$\;\;$
{\sc{op-dec}}\index{op-dec} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{op-subb}$\;\;$
{\sc{op-subb}}\index{op-subb} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{op-sub}$\;\;$
{\sc{op-sub}}\index{op-sub} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{op-ror}$\;\;$
{\sc{op-ror}}\index{op-ror} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{op-asr}$\;\;$
{\sc{op-asr}}\index{op-asr} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{op-lsr}$\;\;$
{\sc{op-lsr}}\index{op-lsr} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{op-xor}$\;\;$
{\sc{op-xor}}\index{op-xor} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{op-or}$\;\;$
{\sc{op-or}}\index{op-or} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{op-and}$\;\;$
{\sc{op-and}}\index{op-and} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{op-not}$\;\;$
{\sc{op-not}}\index{op-not} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{op-m15}$\;\;$
{\sc{op-m15}}\index{op-m15} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{t}})
\end{tabbing}


\noindent{\sc Event}:   Let us define the theory {\it{opcode-theory}} to consist of the following events: op-move,
op-inc,
op-addc,
op-add,
op-neg,
op-dec,
op-subb,
op-sub,
op-ror,
op-asr,
op-lsr,
op-xor,
op-or,
op-and,
op-not,
op-m15.\index{opcode-theory}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  zb-v-alu \\ \index{zb-v-alu}
{\rm{zb}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op-code\/}})\index{v-alu})\index{zb} $=$ {\rm{v-zerop}}\,({\rm{bv}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op-code\/}})\index{v-alu})\index{bv})\index{v-zerop}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  n-v-alu \\ \index{n-v-alu}
{\rm{n}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op-code\/}})\index{v-alu})\index{n} $=$ {\rm{v-negp}}\,({\rm{bv}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op-code\/}})\index{v-alu})\index{bv})\index{v-negp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  universal-flags-interpretations \\ \index{universal-flags-interpretations}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{z-set}}\,({\it{set-flags\/}})\index{z-set} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ne}}\index{cc-ne}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op-code\/}})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{v-nzerop}}\,({\rm{bv}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op-code\/}})\index{v-alu})\index{bv})\index{v-nzerop})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-eq}}\index{cc-eq}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op-code\/}})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{v-nzerop}}\,({\rm{bv}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op-code\/}})\index{v-alu})\index{bv})\index{v-nzerop}))\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{n-set}}\,({\it{set-flags\/}})\index{n-set} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-pl}}\index{cc-pl}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op-code\/}})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{v-negp}}\,({\rm{bv}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op-code\/}})\index{v-alu})\index{bv})\index{v-negp}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-mi}}\index{cc-mi}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\it{c\/}}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\it{op-code\/}})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{v-negp}}\,({\rm{bv}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op-code\/}})\index{v-alu})\index{bv})\index{v-negp})\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-t}}\index{cc-t}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op-code\/}})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\bf{t}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-f}}\index{cc-f}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op-code\/}})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\bf{f}})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-sum-on-not-a-a \\ \index{v-sum-on-not-a-a}
{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\rightarrow$ ({\rm{v-nzerop}}\,({\rm{v-sum}}\,({\bf{t}}, {\it{a\/}}, {\it{b\/}})\index{v-sum})\index{v-nzerop} $=$ ({\rm{v-not}}\,({\it{a\/}})\index{v-not} $\not=$ {\it{b\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  if-v-subtracter-output=0-then-a=b \\ \index{if-v-subtracter-output=0-then-a!=b}
{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\rightarrow$ ({\rm{v-nzerop}}\,({\rm{v-subtracter-output}}\,({\bf{f}}, {\it{a\/}}, {\it{b\/}})\index{v-subtracter-output})\index{v-nzerop} $=$ ({\it{a\/}} $\not=$ {\it{b\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  zero-flag-interpretation-for-sub \\ \index{zero-flag-interpretation-for-su!b}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ {\rm{z-set}}\,({\it{set-flags\/}})\index{z-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{z-flag}}\,({\rm{update-flags}}\,({\it{flags\/}}, {\it{set-flags\/}}, {\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-sub}}\index{op-sub})\index{v-alu})\index{update-flags})\index{z-flag} \\ 
$=$$\;\;\;\;$({\it{a\/}} $=$ {\it{b\/}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-sub \\ \index{flags-interpretation-sub}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ {\rm{z-set}}\,({\it{set-flags\/}})\index{z-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ne}}\index{cc-ne}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-sub}}\index{op-sub})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\it{a\/}} $\not=$ {\it{b\/}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-eq}}\index{cc-eq}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-sub}}\index{op-sub})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\it{a\/}} $=$ {\it{b\/}}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-negp-v-shift-right \\ \index{v-negp-v-shift-right}
(({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}}) $\wedge$ {\rm{boolp}}\,({\it{c\/}})\index{boolp}) $\rightarrow$ ({\rm{v-negp}}\,({\rm{v-shift-right}}\,({\it{a\/}}, {\it{c\/}})\index{v-shift-right})\index{v-negp} $=$ {\it{c\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-ror \\ \index{flags-interpretation-ror}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ {\rm{boolp}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{boolp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{c-set}}\,({\it{set-flags\/}})\index{c-set} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-cc}}\index{cc-cc}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-ror}}\index{op-ror})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{nth}}\,({\tt{0}}, {\it{a\/}})\index{nth}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-cs}}\index{cc-cs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-ror}}\index{op-ror})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{nth}}\,({\tt{0}}, {\it{a\/}})\index{nth})\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{n-set}}\,({\it{set-flags\/}})\index{n-set} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-pl}}\index{cc-pl}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-ror}}\index{op-ror})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-mi}}\index{cc-mi}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-ror}}\index{op-ror})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-lsr \\ \index{flags-interpretation-lsr}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not\simeq {\tt{0}}$) $\wedge$ {\rm{c-set}}\,({\it{set-flags\/}})\index{c-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-cc}}\index{cc-cc}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-lsr}}\index{op-lsr})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{nth}}\,({\tt{0}}, {\it{a\/}})\index{nth}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-cs}}\index{cc-cs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-lsr}}\index{op-lsr})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{nth}}\,({\tt{0}}, {\it{a\/}})\index{nth})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-xor \\ \index{flags-interpretation-xor}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not\simeq {\tt{0}}$) $\wedge$ {\rm{z-set}}\,({\it{set-flags\/}})\index{z-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ne}}\index{cc-ne}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-xor}}\index{op-xor})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\it{a\/}} $\not=$ {\it{b\/}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-eq}}\index{cc-eq}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-xor}}\index{op-xor})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\it{a\/}} $=$ {\it{b\/}}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-nat-move \\ \index{flags-interpretation-nat-move}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ {\rm{z-set}}\,({\it{set-flags\/}})\index{z-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ne}}\index{cc-ne}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-move}}\index{op-move})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $\not=$ {\tt{0}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-eq}}\index{cc-eq}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-move}}\index{op-move})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $=$ {\tt{0}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ne}}\index{cc-ne}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-m15}}\index{op-m15})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $\not=$ {\tt{0}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-eq}}\index{cc-eq}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-m15}}\index{op-m15})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $=$ {\tt{0}}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-nat-inc \\ \index{flags-interpretation-nat-inc}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ {\rm{c-set}}\,({\it{set-flags\/}})\index{c-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-cc}}\index{cc-cc}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-inc}}\index{op-inc})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$(($1\;+$ {\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat}) $<$ {\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{exp}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-cs}}\index{cc-cs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-inc}}\index{op-inc})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$(($1\;+$ {\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat}) $\not<$ {\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{exp}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-nat-addc \\ \index{flags-interpretation-nat-addc}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ {\rm{c-set}}\,({\it{set-flags\/}})\index{c-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-cc}}\index{cc-cc}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-addc}}\index{op-addc})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$(\=\+({\rm{b-to-nat}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{b-to-nat} $+$ {\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $+$ {\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat}) \\ 
$<$$\;\;\;\;${\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{exp})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-cs}}\index{cc-cs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-addc}}\index{op-addc})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$(\=\+(\=\+{\rm{b-to-nat}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{b-to-nat} \\ 
$+$$\;\;\;\;${\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} \\ 
$+$$\;\;\;\;${\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat})\- \\ 
$\not<$$\;\;\;\;${\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{exp})\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-nat-add \\ \index{flags-interpretation-nat-add}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ {\rm{c-set}}\,({\it{set-flags\/}})\index{c-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-cc}}\index{cc-cc}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-add}}\index{op-add})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$(({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $+$ {\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat}) $<$ {\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{exp}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-cs}}\index{cc-cs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-add}}\index{op-add})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$(({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $+$ {\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat}) $\not<$ {\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{exp}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  when-the-mantissa-isnt-0-then-neither-is-the-exponential \\ \index{when-the-mantissa-isnt-0-then-neit!her-is-the-exponential}
({\it{mantissa\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ ({\rm{exp}}\,({\it{mantissa\/}}, {\it{exponent\/}})\index{exp} $\not=$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{double-difference-induction} \\  
\=\+{\rm{double-difference-induction}}\,({\it{n\/}}, {\it{m\/}}, {\it{l\/}})\index{double-difference-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\it{m\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf elseif }{\it{l\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{double-difference-induction}}\,({\it{n\/}} $-$ {\it{l\/}}, {\it{m\/}} $-$ {\it{l\/}}, {\it{l\/}})\index{double-difference-induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-lessp-double-remainder\$help \\ \index{quotient-lessp-double-remainder!\$help}
\=\+(\=\+({\it{n\/}} $<$ {\it{m\/}}) \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$({\it{m\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$({\it{l\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$(({\it{n\/}} ${}${\bf{mod}}${}$ {\it{l\/}}) $=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(({\it{m\/}} ${}${\bf{mod}}${}$ {\it{l\/}}) $=$ {\tt{0}}))\- \\ 
$\rightarrow$$\;\;\;\;$(({\it{n\/}} $\div$ {\it{l\/}}) $<$ ({\it{m\/}} $\div$ {\it{l\/}}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-nzerop-nat-to-v\$help \\ \index{v-nzerop-nat-to-v\$help}
\=\+(({\it{l\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\it{n\/}} $\not\simeq {\tt{0}}$) $\wedge$ (({\it{n\/}} ${}${\bf{mod}}${}$ {\tt{2}}) $=$ {\tt{0}}) $\wedge$ ({\it{n\/}} $<$ {\rm{exp}}\,({\tt{2}}, {\it{l\/}})\index{exp})) \\ 
$\rightarrow$$\;\;\;\;$(({\it{n\/}} $\div$ {\tt{2}}) $<$ {\rm{exp}}\,({\tt{2}}, {\it{l\/}} $-\;1$)\index{exp})\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-nzerop-nat-to-v\$help; name this event `v-nzerop-nat-to-v\$help-off'.\index{v-nzerop-nat-to-v\$help-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-nzerop-nat-to-v \\ \index{v-nzerop-nat-to-v}
({\it{n\/}} $<$ {\rm{exp}}\,({\tt{2}}, {\it{l\/}})\index{exp}) $\rightarrow$ ({\rm{v-nzerop}}\,({\rm{nat-to-v}}\,({\it{n\/}}, {\it{l\/}})\index{nat-to-v})\index{v-nzerop} $=$ ({\it{n\/}} $\not\simeq {\tt{0}}$))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-sub1-plus-a-b-b \\ \index{lessp-sub1-plus-a-b-b}
((({\it{a\/}} $+$ {\it{b\/}}) $-\;1$) $<$ {\it{b\/}}) $=$ (({\it{a\/}} $\simeq {\tt{0}}$) $\wedge$ ({\it{b\/}} $\not\simeq {\tt{0}}$))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-v-to-nat-exp-2-length-a \\ \index{lessp-v-to-nat-exp-2-length-a}
({\it{l\/}} $=$ {\rm{length}}\,({\it{a\/}})\index{length}) $\rightarrow$ (({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $<$ {\rm{exp}}\,({\tt{2}}, {\it{l\/}})\index{exp}) $=$ {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-v-to-nat-exp-2-length-a\$linear \\ \index{lessp-v-to-nat-exp-2-length-a\$!linear}
{\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $<$ {\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{exp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-nat-dec \\ \index{flags-interpretation-nat-dec}
\=\+{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{c-set}}\,({\it{set-flags\/}})\index{c-set} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-cc}}\index{cc-cc}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-dec}}\index{op-dec})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $\not=$ {\tt{0}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-cs}}\index{cc-cs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-dec}}\index{op-dec})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $=$ {\tt{0}}))\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{z-set}}\,({\it{set-flags\/}})\index{z-set} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ne}}\index{cc-ne}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-dec}}\index{op-dec})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $\not=$ {\tt{1}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-eq}}\index{cc-eq}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-dec}}\index{op-dec})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $=$ {\tt{1}}))\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-theorem-for-subb \\ \index{remainder-theorem-for-subb}
(({\it{a\/}} $<$ {\it{b\/}}) $\wedge$ ({\it{b\/}} $<$ {\it{c\/}})) $\rightarrow$ (((({\it{b\/}} $+$ {\it{c\/}}) $-$ {\it{a\/}}) ${}${\bf{mod}}${}$ {\it{c\/}}) $=$ ({\it{b\/}} $-$ {\it{a\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  difference-linear \\ \index{difference-linear}
({\it{a\/}} $<$ {\it{b\/}}) $\rightarrow$ ((({\it{a\/}} $-$ {\it{c\/}}) $<$ {\it{b\/}}) $=$ {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-nat-subb-carry \\ \index{flags-interpretation-nat-subb-c!arry}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ {\rm{c-set}}\,({\it{set-flags\/}})\index{c-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-cc}}\index{cc-cc}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-subb}}\index{op-subb})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat} $\not<$ ({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $+$ {\rm{b-to-nat}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{b-to-nat})))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-cs}}\index{cc-cs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-subb}}\index{op-subb})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$(\=\+{\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat} \\ 
$<$$\;\;\;\;$({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $+$ {\rm{b-to-nat}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{b-to-nat}))\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-nat-subb-higher \\ \index{flags-interpretation-nat-subb-hi!gher}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ {\rm{c-set}}\,({\it{set-flags\/}})\index{c-set} $\wedge$ {\rm{z-set}}\,({\it{set-flags\/}})\index{z-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-hi}}\index{cc-hi}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-subb}}\index{op-subb})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$(({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $+$ {\rm{b-to-nat}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{b-to-nat}) $<$ {\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ls}}\index{cc-ls}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-subb}}\index{op-subb})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$(\=\+({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $+$ {\rm{b-to-nat}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{b-to-nat}) \\ 
$\not<$$\;\;\;\;${\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat})\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  carry-flag-nat-interpretation-for-sub \\ \index{carry-flag-nat-interpretation-f!or-sub}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ {\rm{c-set}}\,({\it{set-flags\/}})\index{c-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{c-flag}}\,({\rm{update-flags}}\,({\it{flags\/}}, {\it{set-flags\/}}, {\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-sub}}\index{op-sub})\index{v-alu})\index{update-flags})\index{c-flag} \\ 
$=$$\;\;\;\;$({\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat} $<$ {\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-nat-sub \\ \index{flags-interpretation-nat-sub}
\=\+{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{c-set}}\,({\it{set-flags\/}})\index{c-set} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-cc}}\index{cc-cc}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-sub}}\index{op-sub})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat} $\not<$ {\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-cs}}\index{cc-cs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-sub}}\index{op-sub})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat} $<$ {\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat}))\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{c-set}}\,({\it{set-flags\/}})\index{c-set} $\wedge$ {\rm{z-set}}\,({\it{set-flags\/}})\index{z-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-hi}}\index{cc-hi}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-sub}}\index{op-sub})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $<$ {\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ls}}\index{cc-ls}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-sub}}\index{op-sub})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $\not<$ {\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat}))\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-nat-lsr-carry \\ \index{flags-interpretation-nat-lsr-ca!rry}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not\simeq {\tt{0}}$) $\wedge$ {\rm{c-set}}\,({\it{set-flags\/}})\index{c-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-cc}}\index{cc-cc}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-lsr}}\index{op-lsr})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$(({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} ${}${\bf{mod}}${}$ {\tt{2}}) $=$ {\tt{0}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-cs}}\index{cc-cs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-lsr}}\index{op-lsr})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$(({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} ${}${\bf{mod}}${}$ {\tt{2}}) $\not=$ {\tt{0}}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-nat-lsr-zero \\ \index{flags-interpretation-nat-lsr-ze!ro}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not\simeq {\tt{0}}$) $\wedge$ {\rm{z-set}}\,({\it{set-flags\/}})\index{z-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ne}}\index{cc-ne}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-lsr}}\index{op-lsr})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$(({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $\div$ {\tt{2}}) $\not=$ {\tt{0}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-eq}}\index{cc-eq}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-lsr}}\index{op-lsr})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$(({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $\div$ {\tt{2}}) $=$ {\tt{0}}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  idifference-0 \\ \index{idifference-0}
({\rm{integerp}}\,({\it{a\/}})\index{integerp} $\wedge$ {\rm{integerp}}\,({\it{b\/}})\index{integerp}) $\rightarrow$ (({\rm{idifference}}\,({\it{a\/}}, {\it{b\/}})\index{idifference} $=$ {\tt{0}}) $=$ ({\it{a\/}} $=$ {\it{b\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-to-nat-lessp-exp-2-length \\ \index{v-to-nat-lessp-exp-2-length}
{\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $<$ {\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{exp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integerp-v-to-int \\ \index{integerp-v-to-int}
{\rm{integerp}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{integerp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-negp-as-bounds \\ \index{v-negp-as-bounds}
{\rm{bvp}}\,({\it{x\/}})\index{bvp} $\rightarrow$ ({\rm{v-negp}}\,({\it{x\/}})\index{v-negp} $=$ ({\rm{v-to-nat}}\,({\it{x\/}})\index{v-to-nat} $\not<$ {\rm{exp}}\,({\tt{2}}, {\rm{length}}\,({\it{x\/}})\index{length} $-\;1$)\index{exp}))
\end{tabbing}


\noindent{\sc Event}:   Enable v-negp-as-bounds; name this event `v-negp-as-bounds-off'.\index{v-negp-as-bounds-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  negativep-idifference-on-numberps \\ \index{negativep-idifference-on-numberp!s}
(({\it{a\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{b\/}} $\in\;${\bf{N}}${}$)) $\rightarrow$ ({\rm{negativep}}\,({\rm{idifference}}\,({\it{a\/}}, {\it{b\/}})\index{idifference}) $=$ ({\it{a\/}} $<$ {\it{b\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-negp-$>$negativep-v-to-int \\ \index{v-negp-$>$negativep-v-to-int}
{\rm{bvp}}\,({\it{a\/}})\index{bvp} $\rightarrow$ ({\rm{v-negp}}\,({\it{a\/}})\index{v-negp} $=$ {\rm{negativep}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}))
\end{tabbing}


\noindent{\sc Event}:   Enable v-negp-$>$negativep-v-to-int; name this event `v-negp-$>$negativep-v-to-int-off'.\index{v-negp-$>$negativep-v-to-int-of!f}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-equal-v-to-int-0 \\ \index{rewrite-equal-v-to-int-0}
({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int} $=$ {\tt{0}}) $=$ {\rm{v-zerop}}\,({\it{a\/}})\index{v-zerop}
\end{tabbing}


\noindent{\sc Event}:   Enable rewrite-equal-v-to-int-0; name this event `rewrite-equal-v-to-int-0-off'.\index{rewrite-equal-v-to-int-0-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  int-to-v-v-to-int-0 \\ \index{int-to-v-v-to-int-0}
{\rm{v-to-int}}\,({\rm{int-to-v}}\,({\tt{0}}, {\it{l\/}})\index{int-to-v})\index{v-to-int} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bvp-int-to-v \\ \index{bvp-int-to-v}
{\rm{bvp}}\,({\rm{int-to-v}}\,({\it{i\/}}, {\it{l\/}})\index{int-to-v})\index{bvp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-to-int-nat-to-v-0 \\ \index{v-to-int-nat-to-v-0}
{\rm{v-to-int}}\,({\rm{nat-to-v}}\,({\tt{0}}, {\it{l\/}})\index{nat-to-v})\index{v-to-int} $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integer-in-rangep-minus-0 \\ \index{integer-in-rangep-minus-0}
{\rm{integer-in-rangep}}\,($-$ {\tt{0}}, {\it{l\/}})\index{integer-in-rangep}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  not-equal-iplus-minus-0 \\ \index{not-equal-iplus-minus-0}
{\rm{iplus}}\,({\it{a\/}}, {\it{b\/}})\index{iplus} $\not=$ ($-$ {\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-1-plus-x-x \\ \index{lessp-1-plus-x-x}
({\tt{1}} $<$ ({\it{x\/}} $+$ {\it{x\/}})) $=$ ({\it{x\/}} $\not\simeq {\tt{0}}$)
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integer-in-rangep-1 \\ \index{integer-in-rangep-1}
(({\it{l\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\it{l\/}} $\not=$ {\tt{1}})) $\rightarrow$ {\rm{integer-in-rangep}}\,({\tt{1}}, {\it{l\/}})\index{integer-in-rangep}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-a-plus-a-a \\ \index{lessp-a-plus-a-a}
({\it{a\/}} $<$ ({\it{a\/}} $+$ {\it{a\/}})) $=$ ({\it{a\/}} $\not\simeq {\tt{0}}$)
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  exp-linear-bounds \\ \index{exp-linear-bounds}
\=\+(\=\+\=\+{\bf if }{\it{v\/}} $<$ {\rm{exp}}\,({\tt{2}}, {\it{n\/}} $-\;1$)\index{exp}$\;\;${\bf then }{\bf{f}} \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$({\it{v\/}} $<$ {\rm{exp}}\,({\tt{2}}, {\it{n\/}})\index{exp}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{exp}}\,({\tt{2}}, {\it{n\/}} $-\;1$)\index{exp} $\not<$ ({\rm{exp}}\,({\tt{2}}, {\it{n\/}})\index{exp} $-$ {\it{v\/}}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integer-in-rangep-v-to-int \\ \index{integer-in-rangep-v-to-int}
({\it{l\/}} $=$ {\rm{length}}\,({\it{a\/}})\index{length}) $\rightarrow$ {\rm{integer-in-rangep}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\it{l\/}})\index{integer-in-rangep}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  addition-cases-for-integer-in-rangep-lemmas \\ \index{addition-cases-for-integer-in-r!angep-lemmas}
\=\+({\rm{integer-in-rangep}}\,({\it{a\/}}, {\it{l\/}})\index{integer-in-rangep} $\wedge$ {\rm{integer-in-rangep}}\,({\it{b\/}}, {\it{l\/}})\index{integer-in-rangep} $\wedge$ ({\it{l\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$({\rm{iplus}}\,({\it{a\/}}, {\it{b\/}})\index{iplus} $<$ {\rm{exp}}\,({\tt{2}}, {\it{l\/}})\index{exp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  subtraction-cases-for-integer-in-rangep-lemmas \\ \index{subtraction-cases-for-integer-i!n-rangep-lemmas}
\=\+({\rm{integer-in-rangep}}\,({\it{a\/}}, {\it{l\/}})\index{integer-in-rangep} $\wedge$ {\rm{integer-in-rangep}}\,({\it{b\/}}, {\it{l\/}})\index{integer-in-rangep} $\wedge$ ({\it{l\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$({\rm{iplus}}\,({\it{b\/}}, {\rm{ineg}}\,({\it{a\/}})\index{ineg})\index{iplus} $<$ {\rm{exp}}\,({\tt{2}}, {\it{l\/}})\index{exp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  exp-2-l-1$<$=exp-2-l \\ \index{exp-2-l-1$<$=exp-2-l}
({\it{l\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ ({\rm{exp}}\,({\tt{2}}, {\it{l\/}} $-\;1$)\index{exp} $<$ {\rm{exp}}\,({\tt{2}}, {\it{l\/}})\index{exp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-remainder-theorem \\ \index{lessp-remainder-theorem}
({\it{n\/}} $<$ {\it{m\/}}) $\rightarrow$ (({\it{n\/}} ${}${\bf{mod}}${}$ {\it{r\/}}) $<$ {\it{m\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integer-in-rangep-the-obvious-way \\ \index{integer-in-rangep-the-obvious-w!ay}
\=\+(({\it{l\/}} $\not\simeq {\tt{0}}$) $\wedge$ {\rm{integerp}}\,({\it{i\/}})\index{integerp} $\wedge$ {\rm{integer-in-rangep}}\,({\it{i\/}}, {\it{l\/}})\index{integer-in-rangep}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{v-negp}}\,({\rm{int-to-v}}\,({\it{i\/}}, {\it{l\/}})\index{int-to-v})\index{v-negp} $=$ {\rm{negativep}}\,({\it{i\/}}))\-
\end{tabbing}


\noindent{\sc Event}:   Enable integer-in-rangep-the-obvious-way; name this event `integer-in-rangep-the-obvious-way-off'.\index{integer-in-rangep-the-obvious-w!ay-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  integer-in-rangep-iplus \\ \index{integer-in-rangep-iplus}
\=\+({\rm{integer-in-rangep}}\,({\it{a\/}}, {\it{l\/}})\index{integer-in-rangep} $\wedge$ {\rm{integer-in-rangep}}\,({\it{b\/}}, {\it{l\/}})\index{integer-in-rangep} $\wedge$ ({\it{l\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{integer-in-rangep}}\,({\rm{iplus}}\,({\it{a\/}}, {\it{b\/}})\index{iplus}, {\it{l\/}})\index{integer-in-rangep} \\ 
$=$$\;\;\;\;$({\rm{v-negp}}\,({\rm{int-to-v}}\,({\rm{iplus}}\,({\it{a\/}}, {\it{b\/}})\index{iplus}, {\it{l\/}})\index{int-to-v})\index{v-negp} $=$ {\rm{negativep}}\,({\rm{iplus}}\,({\it{a\/}}, {\it{b\/}})\index{iplus})))\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable integer-in-rangep-iplus; name this event `integer-in-rangep-iplus-off'.\index{integer-in-rangep-iplus-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  integer-in-rangep-iplus\$commuted \\ \index{integer-in-rangep-iplus\$commute!d}
\=\+({\rm{integer-in-rangep}}\,({\it{a\/}}, {\it{l\/}})\index{integer-in-rangep} $\wedge$ {\rm{integer-in-rangep}}\,({\it{b\/}}, {\it{l\/}})\index{integer-in-rangep} $\wedge$ ({\it{l\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{negativep}}\,({\rm{iplus}}\,({\it{a\/}}, {\it{b\/}})\index{iplus}) \\ 
$=$$\;\;\;\;$(\=\+{\rm{integer-in-rangep}}\,({\rm{iplus}}\,({\it{a\/}}, {\it{b\/}})\index{iplus}, {\it{l\/}})\index{integer-in-rangep} \\ 
$\leftrightarrow$$\;\;\;\;${\rm{v-negp}}\,({\rm{int-to-v}}\,({\rm{iplus}}\,({\it{a\/}}, {\it{b\/}})\index{iplus}, {\it{l\/}})\index{int-to-v})\index{v-negp})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integer-in-rangep-iplus-carry \\ \index{integer-in-rangep-iplus-carry}
\=\+({\rm{integer-in-rangep}}\,({\it{a\/}}, {\it{l\/}})\index{integer-in-rangep} $\wedge$ {\rm{integer-in-rangep}}\,({\it{b\/}}, {\it{l\/}})\index{integer-in-rangep} $\wedge$ ({\it{l\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{integer-in-rangep}}\,({\rm{iplus}}\,({\tt{1}}, {\rm{iplus}}\,({\it{a\/}}, {\it{b\/}})\index{iplus})\index{iplus}, {\it{l\/}})\index{integer-in-rangep} \\ 
$=$$\;\;\;\;$(\=\+{\rm{v-negp}}\,({\rm{int-to-v}}\,({\rm{iplus}}\,({\tt{1}}, {\rm{iplus}}\,({\it{a\/}}, {\it{b\/}})\index{iplus})\index{iplus}, {\it{l\/}})\index{int-to-v})\index{v-negp} \\ 
$=$$\;\;\;\;${\rm{negativep}}\,({\rm{iplus}}\,({\tt{1}}, {\rm{iplus}}\,({\it{a\/}}, {\it{b\/}})\index{iplus})\index{iplus}))\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable integer-in-rangep-iplus-carry; name this event `integer-in-rangep-iplus-carry-off'.\index{integer-in-rangep-iplus-carry-o!ff}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  integer-in-rangep-iplus-carry\$commuted \\ \index{integer-in-rangep-iplus-carry\$!commuted}
\=\+({\rm{integer-in-rangep}}\,({\it{a\/}}, {\it{l\/}})\index{integer-in-rangep} $\wedge$ {\rm{integer-in-rangep}}\,({\it{b\/}}, {\it{l\/}})\index{integer-in-rangep} $\wedge$ ({\it{l\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{negativep}}\,({\rm{iplus}}\,({\tt{1}}, {\rm{iplus}}\,({\it{a\/}}, {\it{b\/}})\index{iplus})\index{iplus}) \\ 
$=$$\;\;\;\;$(\=\+{\rm{integer-in-rangep}}\,({\rm{iplus}}\,({\tt{1}}, {\rm{iplus}}\,({\it{a\/}}, {\it{b\/}})\index{iplus})\index{iplus}, {\it{l\/}})\index{integer-in-rangep} \\ 
$\leftrightarrow$$\;\;\;\;${\rm{v-negp}}\,({\rm{int-to-v}}\,({\rm{iplus}}\,({\tt{1}}, {\rm{iplus}}\,({\it{a\/}}, {\it{b\/}})\index{iplus})\index{iplus}, {\it{l\/}})\index{int-to-v})\index{v-negp})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  not-integerp-minus-zero \\ \index{not-integerp-minus-zero}
{\rm{integerp}}\,($-$ {\it{x\/}})\index{integerp} $=$ ({\it{x\/}} $\not\simeq {\tt{0}}$)
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integer-in-rangep-iplus-ineg \\ \index{integer-in-rangep-iplus-ineg}
\=\+({\rm{integer-in-rangep}}\,({\it{a\/}}, {\it{l\/}})\index{integer-in-rangep} $\wedge$ {\rm{integer-in-rangep}}\,({\it{b\/}}, {\it{l\/}})\index{integer-in-rangep} $\wedge$ ({\it{l\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{integer-in-rangep}}\,({\rm{iplus}}\,({\it{b\/}}, {\rm{ineg}}\,({\it{a\/}})\index{ineg})\index{iplus}, {\it{l\/}})\index{integer-in-rangep} \\ 
$=$$\;\;\;\;$(\=\+{\rm{v-negp}}\,({\rm{int-to-v}}\,({\rm{iplus}}\,({\it{b\/}}, {\rm{ineg}}\,({\it{a\/}})\index{ineg})\index{iplus}, {\it{l\/}})\index{int-to-v})\index{v-negp} \\ 
$=$$\;\;\;\;${\rm{negativep}}\,({\rm{iplus}}\,({\it{b\/}}, {\rm{ineg}}\,({\it{a\/}})\index{ineg})\index{iplus}))\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable integer-in-rangep-iplus-ineg; name this event `integer-in-rangep-iplus-ineg-off'.\index{integer-in-rangep-iplus-ineg-of!f}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  integer-in-rangep-iplus-ineg\$commuted \\ \index{integer-in-rangep-iplus-ineg\$c!ommuted}
\=\+({\rm{integer-in-rangep}}\,({\it{a\/}}, {\it{l\/}})\index{integer-in-rangep} $\wedge$ {\rm{integer-in-rangep}}\,({\it{b\/}}, {\it{l\/}})\index{integer-in-rangep} $\wedge$ ({\it{l\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{negativep}}\,({\rm{iplus}}\,({\it{b\/}}, {\rm{ineg}}\,({\it{a\/}})\index{ineg})\index{iplus}) \\ 
$=$$\;\;\;\;$(\=\+{\rm{integer-in-rangep}}\,({\rm{iplus}}\,({\it{b\/}}, {\rm{ineg}}\,({\it{a\/}})\index{ineg})\index{iplus}, {\it{l\/}})\index{integer-in-rangep} \\ 
$\leftrightarrow$$\;\;\;\;${\rm{v-negp}}\,({\rm{int-to-v}}\,({\rm{iplus}}\,({\it{b\/}}, {\rm{ineg}}\,({\it{a\/}})\index{ineg})\index{iplus}, {\it{l\/}})\index{int-to-v})\index{v-negp})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integer-in-rangep-iplus-ineg-carry \\ \index{integer-in-rangep-iplus-ineg-ca!rry}
\=\+(\=\+{\rm{integer-in-rangep}}\,({\it{a\/}}, {\it{l\/}})\index{integer-in-rangep} \\ 
$\wedge$$\;\;\;\;${\rm{integer-in-rangep}}\,({\it{b\/}}, {\it{l\/}})\index{integer-in-rangep} \\ 
$\wedge$$\;\;\;\;$({\it{l\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$({\it{l\/}} $\not=$ {\tt{1}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{integer-in-rangep}}\,({\rm{iplus}}\,({\it{b\/}}, {\rm{ineg}}\,({\rm{iplus}}\,({\tt{1}}, {\it{a\/}})\index{iplus})\index{ineg})\index{iplus}, {\it{l\/}})\index{integer-in-rangep} \\ 
$=$$\;\;\;\;$(\=\+{\rm{v-negp}}\,({\rm{int-to-v}}\,({\rm{iplus}}\,({\it{b\/}}, {\rm{ineg}}\,({\rm{iplus}}\,({\tt{1}}, {\it{a\/}})\index{iplus})\index{ineg})\index{iplus}, {\it{l\/}})\index{int-to-v})\index{v-negp} \\ 
$=$$\;\;\;\;${\rm{negativep}}\,({\rm{iplus}}\,({\it{b\/}}, {\rm{ineg}}\,({\rm{iplus}}\,({\tt{1}}, {\it{a\/}})\index{iplus})\index{ineg})\index{iplus}))\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Enable integer-in-rangep-iplus-ineg-carry; name this event `integer-in-rangep-iplus-ineg-carry-off'.\index{integer-in-rangep-iplus-ineg-ca!rry-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  integer-in-rangep-iplus-ineg-carry\$commuted \\ \index{integer-in-rangep-iplus-ineg-ca!rry\$commuted}
\=\+(\=\+{\rm{integer-in-rangep}}\,({\it{a\/}}, {\it{l\/}})\index{integer-in-rangep} \\ 
$\wedge$$\;\;\;\;${\rm{integer-in-rangep}}\,({\it{b\/}}, {\it{l\/}})\index{integer-in-rangep} \\ 
$\wedge$$\;\;\;\;$({\it{l\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$({\it{l\/}} $\not=$ {\tt{1}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{negativep}}\,({\rm{iplus}}\,({\it{b\/}}, {\rm{ineg}}\,({\rm{iplus}}\,({\tt{1}}, {\it{a\/}})\index{iplus})\index{ineg})\index{iplus}) \\ 
$=$$\;\;\;\;$(\=\+{\rm{v-negp}}\,({\rm{int-to-v}}\,({\rm{iplus}}\,({\it{b\/}}, {\rm{ineg}}\,({\rm{iplus}}\,({\tt{1}}, {\it{a\/}})\index{iplus})\index{ineg})\index{iplus}, {\it{l\/}})\index{int-to-v})\index{v-negp} \\ 
$\leftrightarrow$$\;\;\;\;${\rm{integer-in-rangep}}\,({\rm{iplus}}\,({\it{b\/}}, {\rm{ineg}}\,({\rm{iplus}}\,({\tt{1}}, {\it{a\/}})\index{iplus})\index{ineg})\index{iplus}, {\it{l\/}})\index{integer-in-rangep})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-1-exp-2 \\ \index{lessp-1-exp-2}
({\it{l\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ ({\tt{1}} $<$ {\rm{exp}}\,({\tt{2}}, {\it{l\/}})\index{exp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-nzerop-int-to-v \\ \index{v-nzerop-int-to-v}
\=\+({\rm{integer-in-rangep}}\,({\it{n\/}}, {\it{l\/}})\index{integer-in-rangep} $\wedge$ ({\it{l\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$({\rm{v-nzerop}}\,({\rm{int-to-v}}\,({\it{n\/}}, {\it{l\/}})\index{int-to-v})\index{v-nzerop} $=$ ($\neg$ {\rm{izerop}}\,({\it{n\/}})\index{izerop}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  izerop-inc-v-nzerop \\ \index{izerop-inc-v-nzerop}
\=\+({\rm{integer-in-rangep}}\,({\it{a\/}}, {\it{l\/}})\index{integer-in-rangep} $\wedge$ ({\it{l\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$({\rm{v-nzerop}}\,({\rm{int-to-v}}\,({\rm{iplus}}\,({\tt{1}}, {\it{a\/}})\index{iplus}, {\it{l\/}})\index{int-to-v})\index{v-nzerop} $=$ ($\neg$ {\rm{izerop}}\,({\rm{iplus}}\,({\tt{1}}, {\it{a\/}})\index{iplus})\index{izerop}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-nzerop-int-to-v-0 \\ \index{v-nzerop-int-to-v-0}
{\rm{izerop}}\,({\it{z\/}})\index{izerop} $\rightarrow$ ($\neg$ {\rm{v-nzerop}}\,({\rm{int-to-v}}\,({\it{z\/}}, {\it{l\/}})\index{int-to-v})\index{v-nzerop})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integer-in-rangep-0 \\ \index{integer-in-rangep-0}
{\rm{izerop}}\,({\it{a\/}})\index{izerop} $\rightarrow$ {\rm{integer-in-rangep}}\,({\it{a\/}}, {\it{l\/}})\index{integer-in-rangep}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  not-v-negp-nat-to-v-0 \\ \index{not-v-negp-nat-to-v-0}
({\it{a\/}} $\simeq {\tt{0}}$) $\rightarrow$ ($\neg$ {\rm{v-negp}}\,({\rm{nat-to-v}}\,({\it{a\/}}, {\it{l\/}})\index{nat-to-v})\index{v-negp})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-int-to-v \\ \index{length-int-to-v}
{\rm{length}}\,({\rm{int-to-v}}\,({\it{i\/}}, {\it{l\/}})\index{int-to-v})\index{length} $=$ {\rm{fix}}\,({\it{l\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integer-in-rangep--1 \\ \index{integer-in-rangep--1}
({\it{l\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ {\rm{integer-in-rangep}}\,({\tt{-1}}, {\it{l\/}})\index{integer-in-rangep}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-move \\ \index{flags-interpretation-int-move}
\=\+{\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{v-set}}\,({\it{set-flags\/}})\index{v-set} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-vc}}\index{cc-vc}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-move}}\index{op-move})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{integer-in-rangep}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{length}}\,({\it{a\/}})\index{length})\index{integer-in-rangep})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-vc}}\index{cc-vc}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-m15}}\index{op-m15})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{integer-in-rangep}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{length}}\,({\it{a\/}})\index{length})\index{integer-in-rangep})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-vs}}\index{cc-vs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-move}}\index{op-move})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{integer-in-rangep}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{length}}\,({\it{a\/}})\index{length})\index{integer-in-rangep}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-vs}}\index{cc-vs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-m15}}\index{op-m15})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{integer-in-rangep}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{length}}\,({\it{a\/}})\index{length})\index{integer-in-rangep}))\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{z-set}}\,({\it{set-flags\/}})\index{z-set} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ne}}\index{cc-ne}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-move}}\index{op-move})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int} $\not=$ {\tt{0}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-eq}}\index{cc-eq}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-move}}\index{op-move})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int} $=$ {\tt{0}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ne}}\index{cc-ne}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-m15}}\index{op-m15})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int} $\not=$ {\tt{0}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-eq}}\index{cc-eq}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-m15}}\index{op-m15})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{izerop}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{izerop})\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{n-set}}\,({\it{set-flags\/}})\index{n-set} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-pl}}\index{cc-pl}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-move}}\index{op-move})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{negativep}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-mi}}\index{cc-mi}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-move}}\index{op-move})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{negativep}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-pl}}\index{cc-pl}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-m15}}\index{op-m15})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{negativep}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-mi}}\index{cc-mi}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-m15}}\index{op-m15})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{negativep}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}))\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{v-set}}\,({\it{set-flags\/}})\index{v-set} $\wedge$ {\rm{n-set}}\,({\it{set-flags\/}})\index{n-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ge}}\index{cc-ge}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-move}}\index{op-move})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{negativep}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-lt}}\index{cc-lt}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-move}}\index{op-move})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{negativep}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ge}}\index{cc-ge}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-m15}}\index{op-m15})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{negativep}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-lt}}\index{cc-lt}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-m15}}\index{op-m15})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{negativep}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}))\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{v-set}}\,({\it{set-flags\/}})\index{v-set} $\wedge$ {\rm{n-set}}\,({\it{set-flags\/}})\index{n-set} $\wedge$ {\rm{z-set}}\,({\it{set-flags\/}})\index{z-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-gt}}\index{cc-gt}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-move}}\index{op-move})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{ilessp}}\,({\tt{0}}, {\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{ilessp})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-le}}\index{cc-le}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-move}}\index{op-move})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{ileq}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{0}})\index{ileq})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-gt}}\index{cc-gt}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-m15}}\index{op-m15})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{ilessp}}\,({\tt{0}}, {\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{ilessp})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-le}}\index{cc-le}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-m15}}\index{op-m15})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{ileq}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{0}})\index{ileq})\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-inc-overflow \\ \index{flags-interpretation-int-inc-ove!rflow}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not\simeq {\tt{0}}$) $\wedge$ {\rm{v-set}}\,({\it{set-flags\/}})\index{v-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-vc}}\index{cc-vc}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-inc}}\index{op-inc})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{integer-in-rangep}}\,({\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{1}})\index{iplus}, {\rm{length}}\,({\it{a\/}})\index{length})\index{integer-in-rangep})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-vs}}\index{cc-vs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-inc}}\index{op-inc})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{integer-in-rangep}}\,(\=\+{\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{1}})\index{iplus}, \\ 
{\rm{length}}\,({\it{a\/}})\index{length})\-\index{integer-in-rangep}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-inc-zero \\ \index{flags-interpretation-int-inc-ze!ro}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}}) $\wedge$ {\rm{z-set}}\,({\it{set-flags\/}})\index{z-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ne}}\index{cc-ne}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-inc}}\index{op-inc})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{1}})\index{iplus} $\not=$ {\tt{0}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-eq}}\index{cc-eq}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-inc}}\index{op-inc})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{1}})\index{iplus} $=$ {\tt{0}}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-inc-negative \\ \index{flags-interpretation-int-inc-ne!gative}
\=\+(\=\+{\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{1}}) \\ 
$\wedge$$\;\;\;\;${\rm{v-set}}\,({\it{set-flags\/}})\index{v-set} \\ 
$\wedge$$\;\;\;\;${\rm{n-set}}\,({\it{set-flags\/}})\index{n-set})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ge}}\index{cc-ge}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-inc}}\index{op-inc})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{negativep}}\,({\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{1}})\index{iplus})))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-lt}}\index{cc-lt}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-inc}}\index{op-inc})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{negativep}}\,({\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{1}})\index{iplus}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-inc-gt-0 \\ \index{flags-interpretation-int-inc-gt!-0}
\=\+(\=\+{\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{1}}) \\ 
$\wedge$$\;\;\;\;${\rm{n-set}}\,({\it{set-flags\/}})\index{n-set} \\ 
$\wedge$$\;\;\;\;${\rm{v-set}}\,({\it{set-flags\/}})\index{v-set} \\ 
$\wedge$$\;\;\;\;${\rm{z-set}}\,({\it{set-flags\/}})\index{z-set})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-gt}}\index{cc-gt}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-inc}}\index{op-inc})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{ilessp}}\,({\tt{0}}, {\rm{iplus}}\,({\tt{1}}, {\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{iplus})\index{ilessp})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-le}}\index{cc-le}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-inc}}\index{op-inc})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{ileq}}\,({\rm{iplus}}\,({\tt{1}}, {\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{iplus}, {\tt{0}})\index{ileq})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-addc-overflow \\ \index{flags-interpretation-int-addc-ove!rflow}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not\simeq {\tt{0}}$) $\wedge$ {\rm{v-set}}\,({\it{set-flags\/}})\index{v-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-vc}}\index{cc-vc}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-addc}}\index{op-addc})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{integer-in-rangep}}\,(\=\+{\rm{iplus}}\,(\=\+{\rm{b-to-nat}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{b-to-nat}, \\ 
{\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int})\index{iplus})\-\index{iplus}, \\ 
{\rm{length}}\,({\it{a\/}})\index{length})\-\index{integer-in-rangep})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-vs}}\index{cc-vs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-addc}}\index{op-addc})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{integer-in-rangep}}\,(\=\+{\rm{iplus}}\,(\=\+{\rm{b-to-nat}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{b-to-nat}, \\ 
{\rm{iplus}}\,(\=\+{\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, \\ 
{\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int})\-\index{iplus})\-\index{iplus}, \\ 
{\rm{length}}\,({\it{a\/}})\index{length})\-\index{integer-in-rangep}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-addc-negative \\ \index{flags-interpretation-int-addc-ne!gative}
\=\+(\=\+{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{1}}) \\ 
$\wedge$$\;\;\;\;${\rm{v-set}}\,({\it{set-flags\/}})\index{v-set} \\ 
$\wedge$$\;\;\;\;${\rm{n-set}}\,({\it{set-flags\/}})\index{n-set})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-lt}}\index{cc-lt}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-addc}}\index{op-addc})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{negativep}}\,({\rm{iplus}}\,(\=\+{\rm{b-to-nat}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{b-to-nat}, \\ 
{\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int})\index{iplus})\-\index{iplus}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ge}}\index{cc-ge}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-addc}}\index{op-addc})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{negativep}}\,({\rm{iplus}}\,(\=\+{\rm{b-to-nat}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{b-to-nat}, \\ 
{\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int})\index{iplus})\-\index{iplus})))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-addc-gt-0 \\ \index{flags-interpretation-int-addc-gt!-0}
\=\+(\=\+{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{1}}) \\ 
$\wedge$$\;\;\;\;${\rm{n-set}}\,({\it{set-flags\/}})\index{n-set} \\ 
$\wedge$$\;\;\;\;${\rm{v-set}}\,({\it{set-flags\/}})\index{v-set} \\ 
$\wedge$$\;\;\;\;${\rm{z-set}}\,({\it{set-flags\/}})\index{z-set})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-gt}}\index{cc-gt}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-addc}}\index{op-addc})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{ilessp}}\,(\=\+{\tt{0}}, \\ 
{\rm{iplus}}\,(\=\+{\rm{b-to-nat}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{b-to-nat}, \\ 
{\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int})\index{iplus})\-\index{iplus})\-\index{ilessp})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-le}}\index{cc-le}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-addc}}\index{op-addc})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{ileq}}\,(\=\+{\rm{iplus}}\,(\=\+{\rm{b-to-nat}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{b-to-nat}, \\ 
{\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int})\index{iplus})\-\index{iplus}, \\ 
{\tt{0}})\-\index{ileq})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-add-overflow \\ \index{flags-interpretation-int-add-ove!rflow}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not\simeq {\tt{0}}$) $\wedge$ {\rm{v-set}}\,({\it{set-flags\/}})\index{v-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-vc}}\index{cc-vc}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-add}}\index{op-add})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{integer-in-rangep}}\,({\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int})\index{iplus}, {\rm{length}}\,({\it{a\/}})\index{length})\index{integer-in-rangep})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-vs}}\index{cc-vs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-add}}\index{op-add})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{integer-in-rangep}}\,(\=\+{\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int})\index{iplus}, \\ 
{\rm{length}}\,({\it{a\/}})\index{length})\-\index{integer-in-rangep}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-add-negative \\ \index{flags-interpretation-int-add-ne!gative}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}}) $\wedge$ {\rm{v-set}}\,({\it{set-flags\/}})\index{v-set} $\wedge$ {\rm{n-set}}\,({\it{set-flags\/}})\index{n-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-lt}}\index{cc-lt}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-add}}\index{op-add})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{negativep}}\,({\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int})\index{iplus}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ge}}\index{cc-ge}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-add}}\index{op-add})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{negativep}}\,({\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int})\index{iplus})))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-add-gt-0 \\ \index{flags-interpretation-int-add-gt!-0}
\=\+(\=\+{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{1}}) \\ 
$\wedge$$\;\;\;\;${\rm{n-set}}\,({\it{set-flags\/}})\index{n-set} \\ 
$\wedge$$\;\;\;\;${\rm{v-set}}\,({\it{set-flags\/}})\index{v-set} \\ 
$\wedge$$\;\;\;\;${\rm{z-set}}\,({\it{set-flags\/}})\index{z-set})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-gt}}\index{cc-gt}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-add}}\index{op-add})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{ilessp}}\,({\tt{0}}, {\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int})\index{iplus})\index{ilessp})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-le}}\index{cc-le}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-add}}\index{op-add})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{ileq}}\,({\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int})\index{iplus}, {\tt{0}})\index{ileq})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  int-neg-range-implications \\ \index{int-neg-range-implications}
\=\+(\=\+(\=\+{\rm{negativep}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{integer-in-rangep}}\,({\rm{negative-guts}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}), {\rm{length}}\,({\it{a\/}})\index{length})\index{integer-in-rangep}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{v-negp}}\,({\rm{int-to-v}}\,({\rm{negative-guts}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}), {\rm{length}}\,({\it{a\/}})\index{length})\index{int-to-v})\index{v-negp})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+($\neg$ {\rm{negativep}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{integer-in-rangep}}\,($-$ {\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{length}}\,({\it{a\/}})\index{length})\index{integer-in-rangep}))\- \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{v-negp}}\,({\rm{int-to-v}}\,($-$ {\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{length}}\,({\it{a\/}})\index{length})\index{int-to-v})\index{v-negp}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+($\neg$ {\rm{negativep}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{integer-in-rangep}}\,($-$ {\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{length}}\,({\it{a\/}})\index{length})\index{integer-in-rangep}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{v-nzerop}}\,({\rm{int-to-v}}\,($-$ {\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{length}}\,({\it{a\/}})\index{length})\index{int-to-v})\index{v-nzerop})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-neg-overflow \\ \index{flags-interpretation-int-neg-ove!rflow}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not\simeq {\tt{0}}$) $\wedge$ {\rm{v-set}}\,({\it{set-flags\/}})\index{v-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-vc}}\index{cc-vc}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-neg}}\index{op-neg})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{integer-in-rangep}}\,({\rm{ineg}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{ineg}, {\rm{length}}\,({\it{a\/}})\index{length})\index{integer-in-rangep})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-vs}}\index{cc-vs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-neg}}\index{op-neg})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{integer-in-rangep}}\,({\rm{ineg}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{ineg}, {\rm{length}}\,({\it{a\/}})\index{length})\index{integer-in-rangep}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-neg-negative \\ \index{flags-interpretation-int-neg-ne!gative}
\=\+(\=\+{\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{1}}) \\ 
$\wedge$$\;\;\;\;${\rm{v-set}}\,({\it{set-flags\/}})\index{v-set} \\ 
$\wedge$$\;\;\;\;${\rm{n-set}}\,({\it{set-flags\/}})\index{n-set})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-lt}}\index{cc-lt}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-neg}}\index{op-neg})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{negativep}}\,({\rm{ineg}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{ineg}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ge}}\index{cc-ge}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-neg}}\index{op-neg})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{negativep}}\,({\rm{ineg}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{ineg})))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-neg-zero \\ \index{flags-interpretation-int-neg-ze!ro}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}}) $\wedge$ {\rm{z-set}}\,({\it{set-flags\/}})\index{z-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ne}}\index{cc-ne}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-neg}}\index{op-neg})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{ineg}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{ineg} $\not=$ {\tt{0}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-eq}}\index{cc-eq}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-neg}}\index{op-neg})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{ineg}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{ineg} $=$ {\tt{0}}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-neg-gt-0 \\ \index{flags-interpretation-int-neg-gt!-0}
\=\+(\=\+{\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{1}}) \\ 
$\wedge$$\;\;\;\;${\rm{n-set}}\,({\it{set-flags\/}})\index{n-set} \\ 
$\wedge$$\;\;\;\;${\rm{v-set}}\,({\it{set-flags\/}})\index{v-set} \\ 
$\wedge$$\;\;\;\;${\rm{z-set}}\,({\it{set-flags\/}})\index{z-set})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-gt}}\index{cc-gt}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-neg}}\index{op-neg})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{ilessp}}\,({\tt{0}}, {\rm{ineg}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{ineg})\index{ilessp})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-le}}\index{cc-le}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-neg}}\index{op-neg})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{ileq}}\,({\rm{ineg}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{ineg}, {\tt{0}})\index{ileq})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  int-dec-rangep-lemmas \\ \index{int-dec-rangep-lemmas}
\=\+(\=\+($\neg$ {\rm{integer-in-rangep}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int} $-\;1$, {\rm{length}}\,({\it{a\/}})\index{length})\index{integer-in-rangep}) \\ 
$\rightarrow$$\;\;\;\;${\rm{v-nzerop}}\,({\rm{int-to-v}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int} $-\;1$, {\rm{length}}\,({\it{a\/}})\index{length})\index{int-to-v})\index{v-nzerop})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{1}}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{integer-in-rangep}}\,(\=\+$-$ ($1\;+$ {\rm{negative-guts}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})), \\ 
{\rm{length}}\,({\it{a\/}})\index{length})\-\index{integer-in-rangep}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{v-nzerop}}\,({\rm{int-to-v}}\,(\=\+$-$ ($1\;+$ {\rm{negative-guts}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})), \\ 
{\rm{length}}\,({\it{a\/}})\index{length})\-\index{int-to-v})\index{v-nzerop})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+($\neg$ {\rm{negativep}}\,({\rm{iplus}}\,({\tt{-1}}, {\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{iplus})) \\ 
$\wedge$$\;\;\;\;${\rm{v-nzerop}}\,({\rm{int-to-v}}\,({\rm{iplus}}\,({\tt{-1}}, {\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{iplus}, {\rm{length}}\,({\it{a\/}})\index{length})\index{int-to-v})\index{v-nzerop})\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{iplus}}\,({\tt{-1}}, {\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{iplus} $\not=$ {\tt{0}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+({\rm{length}}\,({\it{a\/}})\index{length} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{negativep}}\,({\rm{iplus}}\,({\tt{-1}}, {\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{iplus})) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{v-nzerop}}\,({\rm{int-to-v}}\,({\rm{iplus}}\,({\tt{-1}}, {\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{iplus}, {\rm{length}}\,({\it{a\/}})\index{length})\index{int-to-v})\index{v-nzerop}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{iplus}}\,({\tt{-1}}, {\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{iplus} $=$ {\tt{0}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-dec-overflow \\ \index{flags-interpretation-int-dec-ove!rflow}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not\simeq {\tt{0}}$) $\wedge$ {\rm{v-set}}\,({\it{set-flags\/}})\index{v-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-vc}}\index{cc-vc}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-dec}}\index{op-dec})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{integer-in-rangep}}\,({\rm{idifference}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{1}})\index{idifference}, {\rm{length}}\,({\it{a\/}})\index{length})\index{integer-in-rangep})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-vs}}\index{cc-vs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-dec}}\index{op-dec})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{integer-in-rangep}}\,(\=\+{\rm{idifference}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{1}})\index{idifference}, \\ 
{\rm{length}}\,({\it{a\/}})\index{length})\-\index{integer-in-rangep}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-dec-negative \\ \index{flags-interpretation-int-dec-ne!gative}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}}) $\wedge$ {\rm{v-set}}\,({\it{set-flags\/}})\index{v-set} $\wedge$ {\rm{n-set}}\,({\it{set-flags\/}})\index{n-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-lt}}\index{cc-lt}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-dec}}\index{op-dec})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{negativep}}\,({\rm{idifference}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{1}})\index{idifference}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ge}}\index{cc-ge}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-dec}}\index{op-dec})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{negativep}}\,({\rm{idifference}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{1}})\index{idifference})))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-dec-zero \\ \index{flags-interpretation-int-dec-ze!ro}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}}) $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{1}}) $\wedge$ {\rm{z-set}}\,({\it{set-flags\/}})\index{z-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ne}}\index{cc-ne}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-dec}}\index{op-dec})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{idifference}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{1}})\index{idifference} $\not=$ {\tt{0}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-eq}}\index{cc-eq}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-dec}}\index{op-dec})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{idifference}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{1}})\index{idifference} $=$ {\tt{0}}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-dec-gt-0 \\ \index{flags-interpretation-int-dec-gt!-0}
\=\+(\=\+{\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{1}}) \\ 
$\wedge$$\;\;\;\;${\rm{n-set}}\,({\it{set-flags\/}})\index{n-set} \\ 
$\wedge$$\;\;\;\;${\rm{v-set}}\,({\it{set-flags\/}})\index{v-set} \\ 
$\wedge$$\;\;\;\;${\rm{z-set}}\,({\it{set-flags\/}})\index{z-set})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-gt}}\index{cc-gt}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-dec}}\index{op-dec})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{ilessp}}\,({\tt{0}}, {\rm{idifference}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{1}})\index{idifference})\index{ilessp})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-le}}\index{cc-le}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-dec}}\index{op-dec})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{ileq}}\,({\rm{idifference}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{1}})\index{idifference}, {\tt{0}})\index{ileq})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-subb-overflow \\ \index{flags-interpretation-int-subb-ove!rflow}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not\simeq {\tt{0}}$) $\wedge$ {\rm{v-set}}\,({\it{set-flags\/}})\index{v-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-vc}}\index{cc-vc}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-subb}}\index{op-subb})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{integer-in-rangep}}\,(\=\+{\rm{idifference}}\,(\=\+{\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int}, \\ 
{\rm{iplus}}\,(\=\+{\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, \\ 
{\rm{b-to-nat}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{b-to-nat})\-\index{iplus})\-\index{idifference}, \\ 
{\rm{length}}\,({\it{a\/}})\index{length})\-\index{integer-in-rangep})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-vs}}\index{cc-vs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-subb}}\index{op-subb})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{integer-in-rangep}}\,(\=\+{\rm{idifference}}\,(\=\+{\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int}, \\ 
{\rm{iplus}}\,(\=\+{\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, \\ 
{\rm{b-to-nat}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{b-to-nat})\-\index{iplus})\-\index{idifference}, \\ 
{\rm{length}}\,({\it{a\/}})\index{length})\-\index{integer-in-rangep}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-subb-negative \\ \index{flags-interpretation-int-subb-ne!gative}
\=\+(\=\+{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{1}}) \\ 
$\wedge$$\;\;\;\;${\rm{v-set}}\,({\it{set-flags\/}})\index{v-set} \\ 
$\wedge$$\;\;\;\;${\rm{n-set}}\,({\it{set-flags\/}})\index{n-set})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-lt}}\index{cc-lt}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-subb}}\index{op-subb})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{negativep}}\,({\rm{idifference}}\,(\=\+{\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int}, \\ 
{\rm{iplus}}\,(\=\+{\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, \\ 
{\rm{b-to-nat}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{b-to-nat})\-\index{iplus})\-\index{idifference}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ge}}\index{cc-ge}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-subb}}\index{op-subb})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{negativep}}\,({\rm{idifference}}\,(\=\+{\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int}, \\ 
{\rm{iplus}}\,(\=\+{\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, \\ 
{\rm{b-to-nat}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{b-to-nat})\-\index{iplus})\-\index{idifference})))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-subb-gt-0 \\ \index{flags-interpretation-int-subb-gt!-0}
\=\+(\=\+{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{1}}) \\ 
$\wedge$$\;\;\;\;${\rm{n-set}}\,({\it{set-flags\/}})\index{n-set} \\ 
$\wedge$$\;\;\;\;${\rm{v-set}}\,({\it{set-flags\/}})\index{v-set} \\ 
$\wedge$$\;\;\;\;${\rm{z-set}}\,({\it{set-flags\/}})\index{z-set})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-gt}}\index{cc-gt}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-subb}}\index{op-subb})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{ilessp}}\,(\=\+{\tt{0}}, \\ 
{\rm{idifference}}\,(\=\+{\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int}, \\ 
{\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{b-to-nat}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{b-to-nat})\index{iplus})\-\index{idifference})\-\index{ilessp})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-le}}\index{cc-le}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-subb}}\index{op-subb})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{ileq}}\,(\=\+{\rm{idifference}}\,(\=\+{\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int}, \\ 
{\rm{iplus}}\,(\=\+{\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, \\ 
{\rm{b-to-nat}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag})\index{b-to-nat})\-\index{iplus})\-\index{idifference}, \\ 
{\tt{0}})\-\index{ileq})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-sub-overflow \\ \index{flags-interpretation-int-sub-ove!rflow}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not\simeq {\tt{0}}$) $\wedge$ {\rm{v-set}}\,({\it{set-flags\/}})\index{v-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-vc}}\index{cc-vc}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-sub}}\index{op-sub})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{integer-in-rangep}}\,(\=\+{\rm{idifference}}\,({\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int}, {\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{idifference}, \\ 
{\rm{length}}\,({\it{a\/}})\index{length})\-\index{integer-in-rangep})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-vs}}\index{cc-vs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-sub}}\index{op-sub})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{integer-in-rangep}}\,(\=\+{\rm{idifference}}\,(\=\+{\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int}, \\ 
{\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\-\index{idifference}, \\ 
{\rm{length}}\,({\it{a\/}})\index{length})\-\index{integer-in-rangep}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-sub-negative \\ \index{flags-interpretation-int-sub-ne!gative}
\=\+(\=\+{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{1}}) \\ 
$\wedge$$\;\;\;\;${\rm{v-set}}\,({\it{set-flags\/}})\index{v-set} \\ 
$\wedge$$\;\;\;\;${\rm{n-set}}\,({\it{set-flags\/}})\index{n-set})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-lt}}\index{cc-lt}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-sub}}\index{op-sub})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{negativep}}\,({\rm{idifference}}\,({\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int}, {\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{idifference}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ge}}\index{cc-ge}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-sub}}\index{op-sub})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{negativep}}\,({\rm{idifference}}\,({\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int}, {\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{idifference})))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-sub-gt-0 \\ \index{flags-interpretation-int-sub-gt!-0}
\=\+(\=\+{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{1}}) \\ 
$\wedge$$\;\;\;\;${\rm{n-set}}\,({\it{set-flags\/}})\index{n-set} \\ 
$\wedge$$\;\;\;\;${\rm{v-set}}\,({\it{set-flags\/}})\index{v-set} \\ 
$\wedge$$\;\;\;\;${\rm{z-set}}\,({\it{set-flags\/}})\index{z-set})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-gt}}\index{cc-gt}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-sub}}\index{op-sub})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{ilessp}}\,({\tt{0}}, {\rm{idifference}}\,({\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int}, {\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{idifference})\index{ilessp})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-le}}\index{cc-le}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-sub}}\index{op-sub})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{ileq}}\,({\rm{idifference}}\,({\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int}, {\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{idifference}, {\tt{0}})\index{ileq})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-idiv-2-0 \\ \index{equal-idiv-2-0}
({\rm{idiv}}\,({\it{i\/}}, {\tt{2}})\index{idiv} $=$ {\tt{0}}) $=$ ({\rm{izerop}}\,({\it{i\/}})\index{izerop} $\vee$ ({\it{i\/}} $=$ {\tt{1}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integer-in-rangep-idiv \\ \index{integer-in-rangep-idiv}
{\rm{integer-in-rangep}}\,({\it{i\/}}, {\it{l\/}})\index{integer-in-rangep} $\rightarrow$ {\rm{integer-in-rangep}}\,({\rm{idiv}}\,({\it{i\/}}, {\tt{2}})\index{idiv}, {\it{l\/}})\index{integer-in-rangep}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-asr-zero \\ \index{flags-interpretation-int-asr-ze!ro}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not\simeq {\tt{0}}$) $\wedge$ {\rm{z-set}}\,({\it{set-flags\/}})\index{z-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ne}}\index{cc-ne}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-asr}}\index{op-asr})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{idiv}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{2}})\index{idiv} $\not=$ {\tt{0}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-eq}}\index{cc-eq}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-asr}}\index{op-asr})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{idiv}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{2}})\index{idiv} $=$ {\tt{0}}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-sub1-plus-x-x \\ \index{equal-sub1-plus-x-x}
((({\it{x\/}} $+$ {\it{x\/}}) $-\;1$) $=$ {\tt{0}}) $=$ ({\it{x\/}} $\simeq {\tt{0}}$)
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-difference-plus-x-x-plus-y-y \\ \index{remainder-difference-plus-x-x-p!lus-y-y}
((({\it{x\/}} $+$ {\it{x\/}}) $-$ ({\it{y\/}} $+$ {\it{y\/}})) ${}${\bf{mod}}${}$ {\tt{2}}) $=$ {\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-difference-plus-x-x-add1-plus-y-y \\ \index{remainder-difference-plus-x-x-a!dd1-plus-y-y}
\=\+(($1\;+$ ({\it{y\/}} $+$ {\it{y\/}})) $<$ ({\it{x\/}} $+$ {\it{x\/}})) \\ 
$\rightarrow$$\;\;\;\;$(((({\it{x\/}} $+$ {\it{x\/}}) $-$ ($1\;+$ ({\it{y\/}} $+$ {\it{y\/}}))) ${}${\bf{mod}}${}$ {\tt{2}}) $=$ {\tt{1}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-difference-plus-x-x-plus-y-y-2 \\ \index{quotient-difference-plus-x-x-pl!us-y-y-2}
((({\it{x\/}} $+$ {\it{x\/}}) $-$ ({\it{y\/}} $+$ {\it{y\/}})) $\div$ {\tt{2}}) $=$ ({\it{x\/}} $-$ {\it{y\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-difference-plus-x-x-add1-plus-y-y-2 \\ \index{quotient-difference-plus-x-x-ad!d1-plus-y-y-2}
((({\it{x\/}} $+$ {\it{x\/}}) $-$ ($1\;+$ ({\it{y\/}} $+$ {\it{y\/}}))) $\div$ {\tt{2}}) $=$ (({\it{x\/}} $-$ {\it{y\/}}) $-\;1$)
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  quotient-add1-plus-x-x-2 \\ \index{quotient-add1-plus-x-x-2}
(($1\;+$ ({\it{x\/}} $+$ {\it{x\/}})) $\div$ {\tt{2}}) $=$ {\rm{fix}}\,({\it{x\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  imod-v-to-int-2 \\ \index{imod-v-to-int-2}
{\rm{listp}}\,({\it{a\/}}) $\rightarrow$ ({\rm{imod}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{2}})\index{imod} $=$ {\rm{b-to-nat}}\,({\rm{car}}\,({\it{a\/}}))\index{b-to-nat})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-asr-carry \\ \index{flags-interpretation-int-asr-ca!rry}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not\simeq {\tt{0}}$) $\wedge$ {\rm{c-set}}\,({\it{set-flags\/}})\index{c-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-cc}}\index{cc-cc}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-asr}}\index{op-asr})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{imod}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{2}})\index{imod} $=$ {\tt{0}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-cs}}\index{cc-cs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-asr}}\index{op-asr})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$({\rm{imod}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{2}})\index{imod} $\not=$ {\tt{0}}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-asr-negative \\ \index{flags-interpretation-int-asr-ne!gative}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{n-set}}\,({\it{set-flags\/}})\index{n-set} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-pl}}\index{cc-pl}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-asr}}\index{op-asr})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{negativep}}\,({\rm{idiv}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{2}})\index{idiv})))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-mi}}\index{cc-mi}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-asr}}\index{op-asr})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{negativep}}\,({\rm{idiv}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{2}})\index{idiv}))\-)\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{n-set}}\,({\it{set-flags\/}})\index{n-set} $\wedge$ {\rm{v-set}}\,({\it{set-flags\/}})\index{v-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-ge}}\index{cc-ge}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-asr}}\index{op-asr})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{negativep}}\,({\rm{idiv}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{2}})\index{idiv})))\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-lt}}\index{cc-lt}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,(\=\+{\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, \\ 
{\it{a\/}}, \\ 
{\it{b\/}}, \\ 
{\sc{op-asr}}\index{op-asr})\-\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{negativep}}\,({\rm{idiv}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{2}})\index{idiv}))\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-asr-gt-0 \\ \index{flags-interpretation-int-asr-gt!-0}
\=\+(\=\+{\rm{bvp}}\,({\it{a\/}})\index{bvp} \\ 
$\wedge$$\;\;\;\;$({\rm{length}}\,({\it{a\/}})\index{length} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;${\rm{v-set}}\,({\it{set-flags\/}})\index{v-set} \\ 
$\wedge$$\;\;\;\;${\rm{n-set}}\,({\it{set-flags\/}})\index{n-set} \\ 
$\wedge$$\;\;\;\;${\rm{z-set}}\,({\it{set-flags\/}})\index{z-set})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-gt}}\index{cc-gt}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-asr}}\index{op-asr})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{ilessp}}\,({\tt{0}}, {\rm{idiv}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{2}})\index{idiv})\index{ilessp})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-le}}\index{cc-le}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-asr}}\index{op-asr})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{ileq}}\,({\rm{idiv}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{2}})\index{idiv}, {\tt{0}})\index{ileq})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  flags-interpretation-int-asr-overflow \\ \index{flags-interpretation-int-asr-ove!rflow}
\=\+({\rm{bvp}}\,({\it{a\/}})\index{bvp} $\wedge$ {\rm{v-set}}\,({\it{set-flags\/}})\index{v-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-vc}}\index{cc-vc}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-asr}}\index{op-asr})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;${\rm{integer-in-rangep}}\,({\rm{idiv}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{2}})\index{idiv}, {\rm{length}}\,({\it{a\/}})\index{length})\index{integer-in-rangep})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{store-resultp}}\,(\=\+{\sc{cc-vs}}\index{cc-vs}, \\ 
{\rm{update-flags}}\,(\=\+{\it{flags\/}}, \\ 
{\it{set-flags\/}}, \\ 
{\rm{v-alu}}\,({\rm{c-flag}}\,({\it{flags\/}})\index{c-flag}, {\it{a\/}}, {\it{b\/}}, {\sc{op-asr}}\index{op-asr})\index{v-alu})\-\index{update-flags})\-\index{store-resultp} \\ 
$=$$\;\;\;\;$($\neg$ {\rm{integer-in-rangep}}\,({\rm{idiv}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{2}})\index{idiv}, {\rm{length}}\,({\it{a\/}})\index{length})\index{integer-in-rangep}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{v-neg} \\  
{\rm{v-neg}}\,({\it{a\/}})\index{v-neg} $=$ {\rm{v-subtracter-output}}\,({\bf{f}}, {\it{a\/}}, {\rm{nat-to-v}}\,({\tt{0}}, {\rm{length}}\,({\it{a\/}})\index{length})\index{nat-to-v})\index{v-subtracter-output}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bv-cvzbv \\ \index{bv-cvzbv}
{\rm{bv}}\,({\rm{cvzbv}}\,({\it{c\/}}, {\it{v\/}}, {\it{bv\/}})\index{cvzbv})\index{bv} $=$ {\it{bv\/}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  c-cvzbv \\ \index{c-cvzbv}
{\rm{c}}\,({\rm{cvzbv}}\,({\it{c\/}}, {\it{v\/}}, {\it{bv\/}})\index{cvzbv})\index{c} $=$ {\it{c\/}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-cvzbv \\ \index{v-cvzbv}
{\rm{v}}\,({\rm{cvzbv}}\,({\it{c\/}}, {\it{v\/}}, {\it{bv\/}})\index{cvzbv})\index{v} $=$ {\it{v\/}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  zb-cvzbv \\ \index{zb-cvzbv}
{\rm{zb}}\,({\rm{cvzbv}}\,({\it{c\/}}, {\it{v\/}}, {\it{bv\/}})\index{cvzbv})\index{zb} $=$ {\rm{v-zerop}}\,({\it{bv\/}})\index{v-zerop}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bv-v-alu \\ \index{bv-v-alu}
\=\+{\rm{bv}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu})\index{bv} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\rm{v-buf}}\,({\it{a\/}})\index{v-buf} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\rm{v-inc}}\,({\it{a\/}})\index{v-inc} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\rm{v-adder-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-adder-output} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{f}})$\;\;${\bf then }{\rm{v-adder-output}}\,({\bf{f}}, {\it{a\/}}, {\it{b\/}})\index{v-adder-output} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }{\rm{v-neg}}\,({\it{a\/}})\index{v-neg} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }{\rm{v-dec}}\,({\it{a\/}})\index{v-dec} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }{\rm{v-subtracter-output}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}})\index{v-subtracter-output} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{t}}, {\bf{f}})$\;\;${\bf then }{\rm{v-subtracter-output}}\,({\bf{f}}, {\it{a\/}}, {\it{b\/}})\index{v-subtracter-output} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{f}}, {\bf{t}})$\;\;${\bf then }{\rm{v-ror}}\,({\it{a\/}}, {\it{c\/}})\index{v-ror} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{f}}, {\bf{t}})$\;\;${\bf then }{\rm{v-asr}}\,({\it{a\/}})\index{v-asr} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{f}}, {\bf{t}})$\;\;${\bf then }{\rm{v-lsr}}\,({\it{a\/}})\index{v-lsr} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{t}}, {\bf{f}}, {\bf{t}})$\;\;${\bf then }{\rm{v-xor}}\,({\it{a\/}}, {\it{b\/}})\index{v-xor} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{f}}, {\bf{t}}, {\bf{t}})$\;\;${\bf then }{\rm{v-or}}\,({\it{a\/}}, {\it{b\/}})\index{v-or} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{t}}, {\bf{f}}, {\bf{t}}, {\bf{t}})$\;\;${\bf then }{\rm{v-and}}\,({\it{a\/}}, {\it{b\/}})\index{v-and} \\ 
{\bf elseif }{\it{op\/}} $=$ {\rm{list}}\,({\bf{f}}, {\bf{t}}, {\bf{t}}, {\bf{t}})$\;\;${\bf then }{\rm{v-not}}\,({\it{a\/}})\index{v-not} \\ 
{\bf else }{\rm{v-buf}}\,({\it{a\/}})\index{v-buf}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  c-v-alu \\ \index{c-v-alu}
\=\+(\=\+(\=\+({\it{op\/}} $=$ {\sc{op-move}}\index{op-move}) \\ 
$\vee$$\;\;\;\;$({\it{op\/}} $=$ {\sc{op-xor}}\index{op-xor}) \\ 
$\vee$$\;\;\;\;$({\it{op\/}} $=$ {\sc{op-or}}\index{op-or}) \\ 
$\vee$$\;\;\;\;$({\it{op\/}} $=$ {\sc{op-and}}\index{op-and}) \\ 
$\vee$$\;\;\;\;$({\it{op\/}} $=$ {\sc{op-not}}\index{op-not}) \\ 
$\vee$$\;\;\;\;$({\it{op\/}} $=$ {\sc{op-m15}}\index{op-m15}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{c}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu})\index{c} $=$ {\bf{f}}))\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{listp}}\,({\it{a\/}}) \\ 
$\wedge$$\;\;\;\;$(({\it{op\/}} $=$ {\sc{op-ror}}\index{op-ror}) $\vee$ ({\it{op\/}} $=$ {\sc{op-asr}}\index{op-asr}) $\vee$ ({\it{op\/}} $=$ {\sc{op-lsr}}\index{op-lsr})))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{c}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu})\index{c} $=$ {\rm{nth}}\,({\tt{0}}, {\it{a\/}})\index{nth}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-v-alu \\ \index{v-v-alu}
\=\+(\=\+({\it{op\/}} $=$ {\sc{op-move}}\index{op-move}) \\ 
$\vee$$\;\;\;\;$({\it{op\/}} $=$ {\sc{op-ror}}\index{op-ror}) \\ 
$\vee$$\;\;\;\;$({\it{op\/}} $=$ {\sc{op-asr}}\index{op-asr}) \\ 
$\vee$$\;\;\;\;$({\it{op\/}} $=$ {\sc{op-asr}}\index{op-asr}) \\ 
$\vee$$\;\;\;\;$({\it{op\/}} $=$ {\sc{op-lsr}}\index{op-lsr}) \\ 
$\vee$$\;\;\;\;$({\it{op\/}} $=$ {\sc{op-xor}}\index{op-xor}) \\ 
$\vee$$\;\;\;\;$({\it{op\/}} $=$ {\sc{op-or}}\index{op-or}) \\ 
$\vee$$\;\;\;\;$({\it{op\/}} $=$ {\sc{op-and}}\index{op-and}) \\ 
$\vee$$\;\;\;\;$({\it{op\/}} $=$ {\sc{op-not}}\index{op-not}) \\ 
$\vee$$\;\;\;\;$({\it{op\/}} $=$ {\sc{op-m15}}\index{op-m15}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{v}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu})\index{v} $=$ {\bf{f}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-nat-rewrite \\ \index{v-alu-correct-nat-rewrite}
{\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\rightarrow$ ({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu} $=$ {\rm{v-alu-nat}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu-nat})
\end{tabbing}


\noindent{\sc Event}:   Enable v-alu-correct-nat-rewrite; name this event `v-alu-correct-nat-rewrite-off'.\index{v-alu-correct-nat-rewrite-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  v-alu-correct-int-rewrite \\ \index{v-alu-correct-int-rewrite}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu} $=$ {\rm{v-alu-int}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu-int})\-
\end{tabbing}


\noindent{\sc Event}:   Enable v-alu-correct-int-rewrite; name this event `v-alu-correct-int-rewrite-off'.\index{v-alu-correct-int-rewrite-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-quotient-test \\ \index{lessp-quotient-test}
({\it{n\/}} $<$ {\it{m\/}}) $\rightarrow$ ((({\it{n\/}} $\div$ {\it{k\/}}) $<$ {\it{m\/}}) $=$ {\bf{t}})
\end{tabbing}


\noindent{\sc Event}:   Enable lessp-quotient-test; name this event `lessp-quotient-test-off'.\index{lessp-quotient-test-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  nat-to-v-as-remainder \\ \index{nat-to-v-as-remainder}
{\rm{nat-to-v}}\,({\it{n\/}} ${}${\bf{mod}}${}$ {\rm{exp}}\,({\tt{2}}, {\it{l\/}})\index{exp}, {\it{l\/}})\index{nat-to-v} $=$ {\rm{nat-to-v}}\,({\it{n\/}}, {\it{l\/}})\index{nat-to-v}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  nat-to-v-of-v-to-nat* \\ \index{nat-to-v-of-v-to-nat*}
({\rm{bvp}}\,({\it{v\/}})\index{bvp} $\wedge$ ({\it{l\/}} $=$ {\rm{length}}\,({\it{v\/}})\index{length})) $\rightarrow$ ({\rm{nat-to-v}}\,({\rm{v-to-nat}}\,({\it{v\/}})\index{v-to-nat}, {\it{l\/}})\index{nat-to-v} $=$ {\it{v\/}})
\end{tabbing}


\noindent{\sc Event}:   Enable nat-to-v-of-v-to-nat*; name this event `nat-to-v-of-v-to-nat*-off'.\index{nat-to-v-of-v-to-nat*-off}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  bv-v-alu-as-natural \\ \index{bv-v-alu-as-natural}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\tt{32}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{bv}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu})\index{bv} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{op\/}} $=$ {\sc{op-inc}}\index{op-inc}$\;\;${\bf then }{\rm{nat-to-v}}\,({\tt{1}} $+$ {\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat}, {\tt{32}})\index{nat-to-v} \\ 
{\bf elseif }{\it{op\/}} $=$ {\sc{op-addc}}\index{op-addc} \\ 
{\bf then }{\rm{nat-to-v}}\,({\rm{b-to-nat}}\,({\it{c\/}})\index{b-to-nat} $+$ {\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $+$ {\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat}, {\tt{32}})\index{nat-to-v} \\ 
{\bf elseif }{\it{op\/}} $=$ {\sc{op-add}}\index{op-add} \\ 
{\bf then }{\rm{nat-to-v}}\,({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $+$ {\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat}, {\tt{32}})\index{nat-to-v} \\ 
{\bf elseif }{\it{op\/}} $=$ {\sc{op-dec}}\index{op-dec} \\ 
{\bf then }{\rm{nat-to-v}}\,(({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $+$ {\rm{exp}}\,({\tt{2}}, {\tt{32}})\index{exp}) $-$ {\tt{1}}, {\tt{32}})\index{nat-to-v} \\ 
{\bf elseif }{\it{op\/}} $=$ {\sc{op-subb}}\index{op-subb} \\ 
{\bf then }{\rm{nat-to-v}}\,(\=\+\=\+({\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat} $+$ {\rm{exp}}\,({\tt{2}}, {\tt{32}})\index{exp}) \\ 
$-$$\;\;\;\;$({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $+$ {\rm{b-to-nat}}\,({\it{c\/}})\index{b-to-nat})\-, \\ 
{\tt{32}})\-\index{nat-to-v} \\ 
{\bf elseif }{\it{op\/}} $=$ {\sc{op-sub}}\index{op-sub} \\ 
{\bf then }{\rm{nat-to-v}}\,(\=\+({\rm{v-to-nat}}\,({\it{b\/}})\index{v-to-nat} $+$ {\rm{exp}}\,({\tt{2}}, {\tt{32}})\index{exp}) $-$ {\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat}, \\ 
{\tt{32}})\-\index{nat-to-v} \\ 
{\bf elseif }{\it{op\/}} $=$ {\sc{op-lsr}}\index{op-lsr}$\;\;${\bf then }{\rm{nat-to-v}}\,({\rm{v-to-nat}}\,({\it{a\/}})\index{v-to-nat} $\div$ {\tt{2}}, {\tt{32}})\index{nat-to-v} \\ 
{\bf else }{\rm{bv}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu})\index{bv}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  fix-int-int-to-v \\ \index{fix-int-int-to-v}
{\rm{fix-int}}\,({\rm{v-to-int}}\,({\it{v\/}})\index{v-to-int})\index{fix-int} $=$ {\rm{v-to-int}}\,({\it{v\/}})\index{v-to-int}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  int-to-v-of-v-to-int \\ \index{int-to-v-of-v-to-int}
(({\it{l\/}} $=$ {\rm{length}}\,({\it{v\/}})\index{length}) $\wedge$ {\rm{bvp}}\,({\it{v\/}})\index{bvp}) $\rightarrow$ ({\rm{int-to-v}}\,({\rm{v-to-int}}\,({\it{v\/}})\index{v-to-int}, {\it{l\/}})\index{int-to-v} $=$ {\it{v\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ineg-as-idifference \\ \index{ineg-as-idifference}
{\rm{idifference}}\,({\tt{0}}, {\it{i\/}})\index{idifference} $=$ {\rm{ineg}}\,({\it{i\/}})\index{ineg}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bv-v-alu-as-integer \\ \index{bv-v-alu-as-integer}
\=\+({\rm{bv2p}}\,({\it{a\/}}, {\it{b\/}})\index{bv2p} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\tt{32}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{bv}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu})\index{bv} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{op\/}} $=$ {\sc{op-inc}}\index{op-inc}$\;\;${\bf then }{\rm{int-to-v}}\,({\rm{iplus}}\,({\tt{1}}, {\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{iplus}, {\tt{32}})\index{int-to-v} \\ 
{\bf elseif }{\it{op\/}} $=$ {\sc{op-addc}}\index{op-addc} \\ 
{\bf then }{\rm{int-to-v}}\,(\=\+{\rm{iplus}}\,(\=\+{\rm{b-to-nat}}\,({\it{c\/}})\index{b-to-nat}, \\ 
{\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int})\index{iplus})\-\index{iplus}, \\ 
{\tt{32}})\-\index{int-to-v} \\ 
{\bf elseif }{\it{op\/}} $=$ {\sc{op-add}}\index{op-add} \\ 
{\bf then }{\rm{int-to-v}}\,({\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int})\index{iplus}, {\tt{32}})\index{int-to-v} \\ 
{\bf elseif }{\it{op\/}} $=$ {\sc{op-neg}}\index{op-neg}$\;\;${\bf then }{\rm{int-to-v}}\,({\rm{ineg}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{ineg}, {\tt{32}})\index{int-to-v} \\ 
{\bf elseif }{\it{op\/}} $=$ {\sc{op-dec}}\index{op-dec} \\ 
{\bf then }{\rm{int-to-v}}\,({\rm{idifference}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{1}})\index{idifference}, {\tt{32}})\index{int-to-v} \\ 
{\bf elseif }{\it{op\/}} $=$ {\sc{op-subb}}\index{op-subb} \\ 
{\bf then }{\rm{int-to-v}}\,(\=\+{\rm{idifference}}\,(\=\+{\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int}, \\ 
{\rm{iplus}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\rm{b-to-nat}}\,({\it{c\/}})\index{b-to-nat})\index{iplus})\-\index{idifference}, \\ 
{\tt{32}})\-\index{int-to-v} \\ 
{\bf elseif }{\it{op\/}} $=$ {\sc{op-sub}}\index{op-sub} \\ 
{\bf then }{\rm{int-to-v}}\,({\rm{idifference}}\,({\rm{v-to-int}}\,({\it{b\/}})\index{v-to-int}, {\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int})\index{idifference}, {\tt{32}})\index{int-to-v} \\ 
{\bf elseif }{\it{op\/}} $=$ {\sc{op-asr}}\index{op-asr}$\;\;${\bf then }{\rm{int-to-v}}\,({\rm{idiv}}\,({\rm{v-to-int}}\,({\it{a\/}})\index{v-to-int}, {\tt{2}})\index{idiv}, {\tt{32}})\index{int-to-v} \\ 
{\bf else }{\rm{bv}}\,({\rm{v-alu}}\,({\it{c\/}}, {\it{a\/}}, {\it{b\/}}, {\it{op\/}})\index{v-alu})\index{bv}$\;${\bf  endif}\-)\-\-
\end{tabbing}



\noindent{\sc Event}:   Make the library {\tt{"fm9001-replay"}} and compile it.

\addvspace{18pt} 
%\end{list}
\printindex
\end{document}
