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\begin{verbatim}#|
 Copyright (C) 1987, 1994 by William R. Bevier.  All Rights Reserved.

 You may copy and distribute verbatim copies of this Nqthm-1992 event script as
 you receive it, in any medium, including embedding it verbatim in derivative
 works, provided that you conspicuously and appropriately publish on each copy
 a valid copyright notice "Copyright (C) 1987, 1994 by William R. Bevier.  All
 Rights Reserved."

 NO WARRANTY

 William R. Bevier PROVIDES ABSOLUTELY NO WARRANTY.  THE EVENT SCRIPT 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 SCRIPT IS WITH YOU.  SHOULD THE SCRIPT PROVE DEFECTIVE, YOU
 ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.

 IN NO EVENT WILL William R. Bevier 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 THIS SCRIPT (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.''

|#

;
; Kit Script for NQTHM-1992
; Bill Bevier
; Computational Logic, Inc.
; bevier@cli.com
;
; This script is derived from the original Kit proof script. The
; original script contains the events entered by the author, and
; extends over some 62 files. The original runs on a version of NQTHM
; modified by the author to handle deftheory events and hints, and to
; handle opening up of constant functions in a certain way.
;
; This script was derived by replaying the original in PC-NQTHM, and
; simultaneously writing out a translation of each event that would
; allow the script to play in NQTHM-1992. The main differences between
; the events which appear here and those in the original are:
; 
;   1. Constant expressions are expanded in place here. The body of no
;      definition or lemma is modified from the original other than the
;      replacement of a constant expression by its value. 
;   2. A few extra deftheory events and enable-theory hints are
;      required in this script, primarily for controlling *1* functions.
;  


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

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plus-right-id2 \\ \index{plus-right-id2}
({\it{y\/}} $\not\in\;${\bf{N}}${}$) $\rightarrow$ (({\it{x\/}} $+$ {\it{y\/}}) $=$ {\rm{fix}}\,({\it{x\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable plus-right-id2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plus-add1 \\ \index{plus-add1}
\=\+({\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}


\noindent{\sc Event}:   Disable plus-add1.

\addvspace{18pt}

\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}


\noindent{\sc Event}:   Disable commutativity2-of-plus.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable commutativity-of-plus.

\addvspace{18pt}

\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}


\noindent{\sc Event}:   Disable associativity-of-plus.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable plus-equal-0.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable difference-x-x.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-plus \\ \index{difference-plus}
((({\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}:   Disable difference-plus.

\addvspace{18pt}

\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}:   Disable plus-cancellation.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable difference-0.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable equal-difference-0.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-cancellation-0 \\ \index{difference-cancellation-0}
({\it{x\/}} $=$ ({\it{x\/}} $-$ {\it{y\/}})) $=$ (({\it{x\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{x\/}} $=$ {\tt{'}}{\tt{0}}) $\vee$ ({\it{y\/}} $\simeq {\tt{0}}$)))
\end{tabbing}


\noindent{\sc Event}:   Disable difference-cancellation-0.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-cancellation-1 \\ \index{difference-cancellation-1}
\=\+(({\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}:   Disable difference-cancellation-1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  times-zero2 \\ \index{times-zero2}
({\it{y\/}} $\not\in\;${\bf{N}}${}$) $\rightarrow$ (({\it{x\/}} $*$ {\it{y\/}}) $=$ {\tt{'}}{\tt{0}})
\end{tabbing}


\noindent{\sc Event}:   Disable times-zero2.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable distributivity-of-times-over-plus.

\addvspace{18pt}

\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}


\noindent{\sc Event}:   Disable times-add1.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable commutativity-of-times.

\addvspace{18pt}

\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}


\noindent{\sc Event}:   Disable commutativity2-of-times.

\addvspace{18pt}

\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}


\noindent{\sc Event}:   Disable associativity-of-times.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable equal-times-0.

\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{'}}{\tt{1}} \\ 
{\bf else }{\it{i\/}} $*$ {\rm{exp}}\,({\it{i\/}}, {\it{j\/}} $-\;1$)\index{exp}$\;${\bf  endif}\-\-
\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}


\noindent{\sc Event}:   Disable exp-plus.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  equal-lessp \\ \index{equal-lessp}
\=\+(({\it{x\/}} $<$ {\it{y\/}}) $=$ {\it{z\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $<$ {\it{y\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*true}} $=$ {\it{z\/}} \\ 
{\bf else }{\tt{'}}{\tt{*1*false}} $=$ {\it{z\/}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable equal-lessp.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable remainder-quotient.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable remainder-wrt-1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  remainder-wrt-12 \\ \index{remainder-wrt-12}
({\it{x\/}} $\not\in\;${\bf{N}}${}$) $\rightarrow$ (({\it{y\/}} ${}${\bf{mod}}${}$ {\it{x\/}}) $=$ {\rm{fix}}\,({\it{y\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable remainder-wrt-12.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-remainder2 \\ \index{lessp-remainder2}
(({\it{x\/}} ${}${\bf{mod}}${}$ {\it{y\/}}) $<$ {\it{y\/}}) $=$ ({\it{y\/}} $\not\simeq {\tt{0}}$)
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-remainder2.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable remainder-x-x.

\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}:  lessp-times-1 \\ \index{lessp-times-1}
({\it{i\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ (({\it{i\/}} $*$ {\it{j\/}}) $\not<$ {\it{j\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-times-1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-times-2 \\ \index{lessp-times-2}
({\it{i\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ (({\it{j\/}} $*$ {\it{i\/}}) $\not<$ {\it{j\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-times-2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-quotient1 \\ \index{lessp-quotient1}
(({\it{i\/}} $\div$ {\it{j\/}}) $<$ {\it{i\/}}) $=$ (({\it{i\/}} $\not\simeq {\tt{0}}$) $\wedge$ (({\it{j\/}} $\simeq {\tt{0}}$) $\vee$ ({\it{j\/}} $\not=$ {\tt{'}}{\tt{1}})))
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-quotient1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-remainder1 \\ \index{lessp-remainder1}
(({\it{x\/}} ${}${\bf{mod}}${}$ {\it{y\/}}) $<$ {\it{x\/}}) $=$ (({\it{y\/}} $\not\simeq {\tt{0}}$) $\wedge$ (({\it{x\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\it{x\/}} $\not<$ {\it{y\/}})))
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-remainder1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-plus1 \\ \index{difference-plus1}
(({\it{x\/}} $+$ {\it{y\/}}) $-$ {\it{x\/}}) $=$ {\rm{fix}}\,({\it{y\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable difference-plus1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-plus2 \\ \index{difference-plus2}
(({\it{y\/}} $+$ {\it{x\/}}) $-$ {\it{x\/}}) $=$ {\rm{fix}}\,({\it{y\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable difference-plus2.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable difference-plus-cancelation.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  times-difference \\ \index{times-difference}
({\it{x\/}} $*$ ({\it{c\/}} $-$ {\it{w\/}})) $=$ (({\it{c\/}} $*$ {\it{x\/}}) $-$ ({\it{w\/}} $*$ {\it{x\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable times-difference.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{divides}$\;\;$
{\rm{divides}}\,({\it{x\/}}, {\it{y\/}})\index{divides} $=$ (({\it{y\/}} ${}${\bf{mod}}${}$ {\it{x\/}}) $\simeq {\tt{0}}$)
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  divides-times \\ \index{divides-times}
(({\it{x\/}} $*$ {\it{z\/}}) ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{'}}{\tt{0}}
\end{tabbing}


\noindent{\sc Event}:   Disable divides-times.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-plus3 \\ \index{difference-plus3}
(({\it{b\/}} $+$ ({\it{a\/}} $+$ {\it{c\/}})) $-$ {\it{a\/}}) $=$ ({\it{b\/}} $+$ {\it{c\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable difference-plus3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-add1-cancellation \\ \index{difference-add1-cancellation}
(($1\;+$ ({\it{y\/}} $+$ {\it{z\/}})) $-$ {\it{z\/}}) $=$ ($1\;+$ {\it{y\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable difference-add1-cancellation.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  remainder-add1 \\ \index{remainder-add1}
(({\it{y\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\it{y\/}} $\not=$ {\tt{'}}{\tt{1}})) $\rightarrow$ ((($1\;+$ ({\it{x\/}} $*$ {\it{y\/}})) ${}${\bf{mod}}${}$ {\it{y\/}}) $\not=$ {\tt{'}}{\tt{0}})
\end{tabbing}


\noindent{\sc Event}:   Disable remainder-add1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  divides-plus-rewrite1 \\ \index{divides-plus-rewrite1}
\=\+((({\it{x\/}} ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{'}}{\tt{0}}) $\wedge$ (({\it{y\/}} ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{'}}{\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$((({\it{x\/}} $+$ {\it{y\/}}) ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{'}}{\tt{0}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable divides-plus-rewrite1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  divides-plus-rewrite2 \\ \index{divides-plus-rewrite2}
\=\+((({\it{x\/}} ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{'}}{\tt{0}}) $\wedge$ (({\it{y\/}} ${}${\bf{mod}}${}$ {\it{z\/}}) $\not=$ {\tt{'}}{\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$((({\it{x\/}} $+$ {\it{y\/}}) ${}${\bf{mod}}${}$ {\it{z\/}}) $\not=$ {\tt{'}}{\tt{0}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable divides-plus-rewrite2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  divides-plus-rewrite \\ \index{divides-plus-rewrite}
\=\+(({\it{x\/}} ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\rightarrow$$\;\;\;\;$(((({\it{x\/}} $+$ {\it{y\/}}) ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{'}}{\tt{0}}) $=$ (({\it{y\/}} ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{'}}{\tt{0}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable divides-plus-rewrite.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable lessp-plus-cancelation.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  divides-plus-rewrite-commuted \\ \index{divides-plus-rewrite-commuted}
\=\+(({\it{x\/}} ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\rightarrow$$\;\;\;\;$(((({\it{y\/}} $+$ {\it{x\/}}) ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{'}}{\tt{0}}) $=$ (({\it{y\/}} ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{'}}{\tt{0}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable divides-plus-rewrite-commuted.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  euclid \\ \index{euclid}
\=\+(({\it{x\/}} ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+((({\it{y\/}} $-$ {\it{x\/}}) ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $<$ {\it{y\/}}$\;\;${\bf then }({\it{y\/}} ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{'}}{\tt{0}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable euclid.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable lessp-times-cancellation.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-plus-cancellation3 \\ \index{lessp-plus-cancellation3}
({\it{y\/}} $<$ ({\it{x\/}} $+$ {\it{y\/}})) $=$ ({\it{x\/}} $\not\simeq {\tt{0}}$)
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-plus-cancellation3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  quotient-times1 \\ \index{quotient-times1}
\=\+(({\it{y\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{x\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{x\/}} $\not=$ {\tt{'}}{\tt{0}}) $\wedge$ {\rm{divides}}\,({\it{x\/}}, {\it{y\/}})\index{divides}))) \\ 
$\rightarrow$$\;\;\;\;$(({\it{x\/}} $*$ ({\it{y\/}} $\div$ {\it{x\/}})) $=$ {\it{y\/}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable quotient-times1.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable quotient-lessp.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  times-id-iff-1 \\ \index{times-id-iff-1}
({\it{z\/}} $=$ ({\it{w\/}} $*$ {\it{z\/}})) $=$ (({\it{z\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{z\/}} $=$ {\tt{'}}{\tt{0}}) $\vee$ ({\it{w\/}} $=$ {\tt{'}}{\tt{1}})))
\end{tabbing}


\noindent{\sc Event}:   Disable times-id-iff-1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  divides-times1 \\ \index{divides-times1}
({\it{a\/}} $=$ ({\it{z\/}} $*$ {\it{y\/}})) $\rightarrow$ (({\it{a\/}} ${}${\bf{mod}}${}$ {\it{z\/}}) $=$ {\tt{'}}{\tt{0}})
\end{tabbing}


\noindent{\sc Event}:   Disable divides-times1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  times-identity1 \\ \index{times-identity1}
\=\+(({\it{y\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{y\/}} $\not=$ {\tt{'}}{\tt{1}}) $\wedge$ (({\it{y\/}} $\not=$ {\tt{'}}{\tt{0}}) $\wedge$ ({\it{x\/}} $\not=$ {\tt{'}}{\tt{0}})))) \\ 
$\rightarrow$$\;\;\;\;$({\it{x\/}} $\not=$ ({\it{x\/}} $*$ {\it{y\/}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable times-identity1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  times-identity \\ \index{times-identity}
({\it{x\/}} $=$ ({\it{x\/}} $*$ {\it{y\/}})) $=$ (({\it{x\/}} $=$ {\tt{'}}{\tt{0}}) $\vee$ (({\it{x\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{y\/}} $=$ {\tt{'}}{\tt{1}})))
\end{tabbing}


\noindent{\sc Event}:   Disable times-identity.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable quotient-divides.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable remainder-times.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable quotient-times.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  distributivity-of-divides \\ \index{distributivity-of-divides}
(({\it{a\/}} $\not\simeq {\tt{0}}$) $\wedge$ {\rm{divides}}\,({\it{a\/}}, {\it{w\/}})\index{divides}) $\rightarrow$ (({\it{c\/}} $*$ ({\it{w\/}} $\div$ {\it{a\/}})) $=$ (({\it{c\/}} $*$ {\it{w\/}}) $\div$ {\it{a\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable distributivity-of-divides.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  if-times-then-divides \\ \index{if-times-then-divides}
(({\it{c\/}} $\not\simeq {\tt{0}}$) $\wedge$ ($\neg$ {\rm{divides}}\,({\it{c\/}}, {\it{x\/}})\index{divides})) $\rightarrow$ (({\it{c\/}} $*$ {\it{y\/}}) $\not=$ {\it{x\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable if-times-then-divides.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  times-equal-1 \\ \index{times-equal-1}
\=\+(({\it{a\/}} $*$ {\it{b\/}}) $=$ {\tt{'}}{\tt{1}}) \\ 
$=$$\;\;\;\;$(\=\+({\it{a\/}} $\not=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{b\/}} $\not=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{a\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{b\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\it{a\/}} $-\;1$) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(({\it{b\/}} $-\;1$) $=$ {\tt{'}}{\tt{0}}))\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable times-equal-1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  divides-implies-times \\ \index{divides-implies-times}
\=\+(({\it{a\/}} $\not\simeq {\tt{0}}$) $\wedge$ (({\it{c\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{a\/}} $*$ {\it{c\/}}) $=$ {\it{b\/}}))) \\ 
$\rightarrow$$\;\;\;\;$(({\it{c\/}} $=$ ({\it{b\/}} $\div$ {\it{a\/}})) $=$ {\tt{'}}{\tt{*1*true}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable divides-implies-times.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-1 \\ \index{difference-1}
({\it{x\/}} $-$ {\tt{'}}{\tt{1}}) $=$ ({\it{x\/}} $-\;1$)
\end{tabbing}


\noindent{\sc Event}:   Disable difference-1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-2 \\ \index{difference-2}
(($1\;+$ ($1\;+$ {\it{x\/}})) $-$ {\tt{'}}{\tt{2}}) $=$ {\rm{fix}}\,({\it{x\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable difference-2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  half-plus \\ \index{half-plus}
(({\it{x\/}} $+$ ({\it{x\/}} $+$ {\it{y\/}})) $\div$ {\tt{'}}{\tt{2}}) $=$ ({\it{x\/}} $+$ ({\it{y\/}} $\div$ {\tt{'}}{\tt{2}}))
\end{tabbing}


\noindent{\sc Event}:   Disable half-plus.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable times-1.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable exp-of-0.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable exp-of-1.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable exp-by-0.

\addvspace{18pt}

\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}


\noindent{\sc Event}:   Disable exp-times.

\addvspace{18pt}

\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}


\noindent{\sc Event}:   Disable exp-exp.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  remainder-plus-times-1 \\ \index{remainder-plus-times-1}
(({\it{x\/}} $+$ ({\it{i\/}} $*$ {\it{j\/}})) ${}${\bf{mod}}${}$ {\it{j\/}}) $=$ ({\it{x\/}} ${}${\bf{mod}}${}$ {\it{j\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable remainder-plus-times-1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  remainder-plus-times-2 \\ \index{remainder-plus-times-2}
(({\it{x\/}} $+$ ({\it{j\/}} $*$ {\it{i\/}})) ${}${\bf{mod}}${}$ {\it{j\/}}) $=$ ({\it{x\/}} ${}${\bf{mod}}${}$ {\it{j\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable remainder-plus-times-2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  remainder-times-1 \\ \index{remainder-times-1}
(({\it{b\/}} $*$ ({\it{a\/}} $*$ {\it{c\/}})) ${}${\bf{mod}}${}$ {\it{a\/}}) $=$ {\tt{'}}{\tt{0}}
\end{tabbing}


\noindent{\sc Event}:   Disable remainder-times-1.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable remainder-of-1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  remainder-difference-times \\ \index{remainder-difference-times}
((({\it{p\/}} $*$ {\it{x\/}}) $-$ ({\it{p\/}} $*$ {\it{y\/}})) ${}${\bf{mod}}${}$ {\it{p\/}}) $=$ {\tt{'}}{\tt{0}}
\end{tabbing}


\noindent{\sc Event}:   Disable remainder-difference-times.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable lessp-remainder-divisor.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{cl-arithmetic}} to consist of the following events: lessp-remainder-divisor,
remainder-difference-times,
remainder-of-1,
remainder-times-1,
remainder-plus-times-2,
remainder-plus-times-1,
exp-exp,
exp-times,
exp-by-0,
exp-of-1,
exp-of-0,
times-1,
half-plus,
difference-2,
difference-1,
divides-implies-times,
times-equal-1,
if-times-then-divides,
distributivity-of-divides,
quotient-times,
remainder-times,
quotient-divides,
times-identity,
times-identity1,
divides-times1,
times-id-iff-1,
quotient-lessp,
quotient-times1,
lessp-plus-cancellation3,
lessp-times-cancellation,
euclid,
divides-plus-rewrite-commuted,
lessp-plus-cancelation,
divides-plus-rewrite,
divides-plus-rewrite2,
divides-plus-rewrite1,
remainder-add1,
difference-add1-cancellation,
difference-plus3,
divides-times,
divides,
times-difference,
difference-plus-cancelation,
difference-plus2,
difference-plus1,
lessp-remainder1,
lessp-quotient1,
lessp-times-2,
lessp-times-1,
remainder-quotient-elim,
remainder-x-x,
lessp-remainder2,
remainder-wrt-12,
remainder-wrt-1,
remainder-quotient,
difference-elim,
equal-lessp,
exp-plus,
equal-times-0,
associativity-of-times,
commutativity2-of-times,
commutativity-of-times,
times-add1,
distributivity-of-times-over-plus,
times-zero2,
difference-cancellation-1,
difference-cancellation-0,
equal-difference-0,
difference-0,
plus-cancellation,
difference-plus,
difference-x-x,
plus-equal-0,
associativity-of-plus,
commutativity-of-plus,
commutativity2-of-plus,
plus-add1,
plus-right-id2.\index{cl-arithmetic}

\addvspace{18pt}

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

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

\begin{tabbing}{\sc Definition}:\index{double-number-double-list-inducti!on} \\  
\=\+{\rm{double-number-double-list-induction}}\,({\it{i\/}}, {\it{j\/}}, {\it{l1\/}}, {\it{l2\/}})\index{double-number-double-list-inducti!on} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l1\/}}) $\wedge$ {\rm{listp}}\,({\it{l2\/}}) \\ 
{\bf then }\=\+{\bf if }({\it{i\/}} $\simeq {\tt{0}}$) $\vee$ ({\it{j\/}} $\simeq {\tt{0}}$)$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf else }{\rm{double-number-double-list-induction}}\,(\=\+{\it{i\/}} $-\;1$, \\ 
{\it{j\/}} $-\;1$, \\ 
{\rm{cdr}}\,({\it{l1\/}}), \\ 
{\rm{cdr}}\,({\it{l2\/}}))\-\index{double-number-double-list-inducti!on}$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plus-0 \\ \index{plus-0}
({\it{a\/}} $+$ {\tt{'}}{\tt{0}}) $=$ {\rm{fix}}\,({\it{a\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable plus-0.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plus-1 \\ \index{plus-1}
({\tt{'}}{\tt{1}} $+$ {\it{x\/}}) $=$ ($1\;+$ {\it{x\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable plus-1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plus-0-arg1 \\ \index{plus-0-arg1}
({\tt{'}}{\tt{0}} $+$ {\it{x\/}}) $=$ {\rm{fix}}\,({\it{x\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable plus-0-arg1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plus-difference-cancellation \\ \index{plus-difference-cancellation}
\=\+\=\+{\bf if }{\it{b\/}} $<$ {\it{a\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$(({\it{a\/}} $+$ ({\it{b\/}} $-$ {\it{a\/}})) $=$ {\rm{fix}}\,({\it{b\/}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable plus-difference-cancellation.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  canonicalize-plus-terms1 \\ \index{canonicalize-plus-terms1}
($1\;+$ (($1\;+$ {\it{a\/}}) $+$ {\it{b\/}})) $=$ (($1\;+$ ($1\;+$ {\it{a\/}})) $+$ {\it{b\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable canonicalize-plus-terms1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  canonicalize-plus-terms2 \\ \index{canonicalize-plus-terms2}
(($1\;+$ {\it{a\/}}) $+$ (($1\;+$ {\it{b\/}}) $+$ {\it{c\/}})) $=$ ((($1\;+$ {\it{a\/}}) $+$ ($1\;+$ {\it{b\/}})) $+$ {\it{c\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable canonicalize-plus-terms2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  canonicalize-plus-terms3 \\ \index{canonicalize-plus-terms3}
(({\it{a\/}} $*$ {\it{b\/}}) $+$ (($1\;+$ {\it{c\/}}) $+$ {\it{d\/}})) $=$ (($1\;+$ {\it{c\/}}) $+$ ({\it{d\/}} $+$ ({\it{a\/}} $*$ {\it{b\/}})))
\end{tabbing}


\noindent{\sc Event}:   Disable canonicalize-plus-terms3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plus-plus-difference \\ \index{plus-plus-difference}
\=\+(\=\+({\it{i\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $<$ {\it{i\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(({\it{i\/}} $+$ ({\it{j\/}} $+$ ({\it{n\/}} $-$ {\it{i\/}}))) $=$ ({\it{n\/}} $+$ {\it{j\/}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable plus-plus-difference.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable plus-times-reduction.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plus-times-sub1-reduction \\ \index{plus-times-sub1-reduction}
({\it{b\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ (({\it{a\/}} $+$ (({\it{b\/}} $-\;1$) $*$ {\it{a\/}})) $=$ ({\it{b\/}} $*$ {\it{a\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable plus-times-sub1-reduction.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plus-commutativity-associativity-crock \\ \index{plus-commutativity-associativit!y-crock}
({\it{b\/}} $+$ ({\it{a\/}} $+$ {\it{c\/}})) $=$ ({\it{a\/}} $+$ ({\it{b\/}} $+$ {\it{c\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable plus-commutativity-associativity-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  distributivity-of-times-over-plus-backwards \\ \index{distributivity-of-times-over-pl!us-backwards}
(({\it{a\/}} $*$ {\it{b\/}}) $+$ ({\it{a\/}} $*$ {\it{c\/}})) $=$ ({\it{a\/}} $*$ ({\it{b\/}} $+$ {\it{c\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable distributivity-of-times-over-plus-backwards.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable difference-is-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-by-larger-number \\ \index{difference-by-larger-number}
(({\it{x\/}} $-\;1$) $-$ {\it{x\/}}) $=$ {\tt{'}}{\tt{0}}
\end{tabbing}


\noindent{\sc Event}:   Disable difference-by-larger-number.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-add1-arg1 \\ \index{difference-add1-arg1}
\=\+\=\+{\bf if }{\it{a\/}} $<$ {\it{b\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$((($1\;+$ {\it{a\/}}) $-$ {\it{b\/}}) $=$ ($1\;+$ ({\it{a\/}} $-$ {\it{b\/}})))\-
\end{tabbing}


\noindent{\sc Event}:   Disable difference-add1-arg1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-add1-arg2 \\ \index{difference-add1-arg2}
({\it{b\/}} $<$ {\it{a\/}}) $\rightarrow$ (({\it{a\/}} $-$ ($1\;+$ {\it{b\/}})) $=$ (({\it{a\/}} $-$ {\it{b\/}}) $-\;1$))
\end{tabbing}


\noindent{\sc Event}:   Disable difference-add1-arg2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  sub1-difference \\ \index{sub1-difference}
(({\it{a\/}} $-$ {\it{b\/}}) $-\;1$) $=$ (({\it{a\/}} $-\;1$) $-$ {\it{b\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable sub1-difference.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-sub1-arg1 \\ \index{difference-sub1-arg1}
({\it{b\/}} $<$ {\it{a\/}}) $\rightarrow$ ((({\it{a\/}} $-\;1$) $-$ {\it{b\/}}) $=$ (({\it{a\/}} $-$ {\it{b\/}}) $-\;1$))
\end{tabbing}


\noindent{\sc Event}:   Disable difference-sub1-arg1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-sub1-arg2 \\ \index{difference-sub1-arg2}
\=\+(\=\+({\it{b\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $<$ {\it{b\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$(({\it{a\/}} $-$ ({\it{b\/}} $-\;1$)) $=$ ($1\;+$ ({\it{a\/}} $-$ {\it{b\/}})))\-
\end{tabbing}


\noindent{\sc Event}:   Disable difference-sub1-arg2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-plus-cancellation2-instance \\ \index{difference-plus-cancellation2-i!nstance}
\=\+\=\+{\bf if }{\it{a\/}} $<$ {\it{c\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$(((($1\;+$ {\it{a\/}}) $+$ {\it{b\/}}) $-$ ($1\;+$ {\it{c\/}})) $=$ (({\it{a\/}} $-$ {\it{c\/}}) $+$ {\it{b\/}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable difference-plus-cancellation2-instance.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable difference-difference.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  yet-another-difference-plus-crock \\ \index{yet-another-difference-plus-cro!ck}
(({\it{n\/}} $+$ ({\it{b\/}} $+$ {\it{a\/}})) $-$ {\it{a\/}}) $=$ ({\it{n\/}} $+$ {\it{b\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable yet-another-difference-plus-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  non-zero-difference \\ \index{non-zero-difference}
(({\it{a\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{a\/}} $<$ {\it{b\/}})) $\rightarrow$ (({\it{b\/}} $-$ {\it{a\/}}) $\not=$ {\tt{'}}{\tt{0}})
\end{tabbing}


\noindent{\sc Event}:   Disable non-zero-difference.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-non-zero-difference-as-lessp \\ \index{rewrite-non-zero-difference-as-!lessp}
(({\it{a\/}} $-$ {\it{b\/}}) $\not=$ {\tt{'}}{\tt{0}}) $=$ ({\it{b\/}} $<$ {\it{a\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-non-zero-difference-as-lessp.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-zero-difference-as-equality \\ \index{rewrite-zero-difference-as-equa!lity}
\=\+\=\+{\bf if }{\it{a\/}} $<$ {\it{b\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$((({\it{a\/}} $-$ {\it{b\/}}) $=$ {\tt{'}}{\tt{0}}) $=$ ({\rm{fix}}\,({\it{a\/}}) $=$ {\rm{fix}}\,({\it{b\/}})))\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-zero-difference-as-equality.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  regroup-fact \\ \index{regroup-fact}
\=\+(\=\+\=\+{\bf if }{\it{a\/}} $<$ {\it{c\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{b\/}} $<$ {\it{d\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$((({\it{a\/}} $+$ {\it{b\/}}) $-$ ({\it{c\/}} $+$ {\it{d\/}})) $=$ (({\it{a\/}} $-$ {\it{c\/}}) $+$ ({\it{b\/}} $-$ {\it{d\/}})))\-
\end{tabbing}


\noindent{\sc Event}:   Disable regroup-fact.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-equals-0 \\ \index{difference-equals-0}
\=\+(\=\+({\it{a\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{b\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $<$ {\it{b\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$((({\it{a\/}} $-$ {\it{b\/}}) $=$ {\tt{'}}{\tt{0}}) $=$ ({\it{a\/}} $=$ {\it{b\/}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable difference-equals-0.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  times-zero3 \\ \index{times-zero3}
({\it{x\/}} $*$ {\tt{'}}{\tt{0}}) $=$ {\tt{'}}{\tt{0}}
\end{tabbing}


\noindent{\sc Event}:   Disable times-zero3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  distributivity-of-times-over-difference \\ \index{distributivity-of-times-over-di!fference}
(({\it{a\/}} $*$ {\it{b\/}}) $-$ ({\it{a\/}} $*$ {\it{c\/}})) $=$ ({\it{a\/}} $*$ ({\it{b\/}} $-$ {\it{c\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable distributivity-of-times-over-difference.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  exp-2-never-0 \\ \index{exp-2-never-0}
({\tt{'}}{\tt{0}} $<$ {\rm{exp}}\,({\tt{'}}{\tt{2}}, {\it{i\/}})\index{exp}) $=$ {\tt{'}}{\tt{*1*true}}
\end{tabbing}


\noindent{\sc Event}:   Disable exp-2-never-0.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  exp-2-never-0-linear \\ \index{exp-2-never-0-linear}
{\tt{'}}{\tt{0}} $<$ {\rm{exp}}\,({\tt{'}}{\tt{2}}, {\it{i\/}})\index{exp}
\end{tabbing}


\noindent{\sc Event}:   Disable exp-2-never-0-linear.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  remainder-noop \\ \index{remainder-noop}
(({\it{a\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{a\/}} $<$ {\it{b\/}}) $\wedge$ ({\it{b\/}} $\not\simeq {\tt{0}}$))) $\rightarrow$ (({\it{a\/}} ${}${\bf{mod}}${}$ {\it{b\/}}) $=$ {\it{a\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable remainder-noop.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable remainder-add1-casesplit.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable zerop-remainder-difference.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable quotient-x-x.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  remainder-times-other-way \\ \index{remainder-times-other-way}
(({\it{b\/}} $*$ {\it{a\/}}) ${}${\bf{mod}}${}$ {\it{a\/}}) $=$ {\tt{'}}{\tt{0}}
\end{tabbing}


\noindent{\sc Event}:   Disable remainder-times-other-way.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  quotient-times-other-way \\ \index{quotient-times-other-way}
\=\+(({\it{b\/}} $*$ {\it{a\/}}) $\div$ {\it{a\/}}) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf else }{\rm{fix}}\,({\it{b\/}})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable quotient-times-other-way.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  quotient-difference \\ \index{quotient-difference}
({\it{i\/}} $\not<$ {\it{j\/}}) $\rightarrow$ ((({\it{i\/}} $-$ {\it{j\/}}) $\div$ {\it{j\/}}) $=$ (({\it{i\/}} $\div$ {\it{j\/}}) $-\;1$))
\end{tabbing}


\noindent{\sc Event}:   Disable quotient-difference.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable quotient-plus.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable quotient-plus-times.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  leq-times \\ \index{leq-times}
\=\+(\=\+({\it{a\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{c\/}} $<$ {\it{b\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$\=\+{\bf if }({\it{a\/}} $*$ {\it{c\/}}) $<$ ({\it{a\/}} $*$ {\it{b\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-remainder-sub1-crock \\ \index{lessp-remainder-sub1-crock}
({\it{x\/}} $<$ {\it{n\/}}) $\rightarrow$ (({\it{x\/}} $-\;1$) $<$ {\it{n\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  leq-plus \\ \index{leq-plus}
\=\+\=\+{\bf if }{\it{c\/}} $<$ ({\it{a\/}} $+$ {\it{b\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$\=\+{\bf if }{\it{c\/}} $<$ {\it{a\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  leq-plus1 \\ \index{leq-plus1}
\=\+\=\+{\bf if }{\it{c\/}} $<$ ({\it{a\/}} $+$ {\it{b\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+\=\+{\bf if }{\it{c\/}} $<$ {\it{a\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{c\/}} $<$ {\it{b\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  leq-plus2 \\ \index{leq-plus2}
\=\+\=\+{\bf if }{\it{c\/}} $<$ ({\it{a\/}} $+$ {\it{b\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$(({\it{c\/}} $<$ {\it{a\/}}) $=$ {\tt{'}}{\tt{*1*false}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  leq-casesplit \\ \index{leq-casesplit}
\=\+(({\it{a\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{b\/}} $\in\;${\bf{N}}${}$)) \\ 
$\rightarrow$$\;\;\;\;$(\=\+\=\+{\bf if }{\it{b\/}} $<$ {\it{a\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$=$$\;\;\;\;$(({\it{a\/}} $<$ {\it{b\/}}) $\vee$ ({\it{a\/}} $=$ {\it{b\/}})))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integer-inequality-casesplit \\ \index{integer-inequality-casesplit}
(({\it{i\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{j\/}} $\in\;${\bf{N}}${}$)) $\rightarrow$ (({\it{i\/}} $\not=$ {\it{j\/}}) $=$ (({\it{i\/}} $<$ {\it{j\/}}) $\vee$ ({\it{j\/}} $<$ {\it{i\/}})))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  integer-equality-crock \\ \index{integer-equality-crock}
(({\it{a\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{b\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{a\/}} $<$ {\tt{'}}{\tt{1}}) $\wedge$ ({\it{b\/}} $<$ {\tt{'}}{\tt{1}})))) $\rightarrow$ ({\it{a\/}} $=$ {\it{b\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-remainder-remainder \\ \index{lessp-remainder-remainder}
\=\+(({\it{c\/}} $\not\simeq {\tt{0}}$) $\wedge$ (({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}}) $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$((({\it{a\/}} ${}${\bf{mod}}${}$ ({\it{b\/}} ${}${\bf{mod}}${}$ {\it{c\/}})) $<$ {\it{c\/}}) $=$ {\tt{'}}{\tt{*1*true}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-remainder-remainder.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable lessp-times.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  leq-plus-times \\ \index{leq-plus-times}
\=\+(({\it{b\/}} $<$ {\it{c\/}}) $\wedge$ ({\it{a\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$\=\+{\bf if }({\it{a\/}} $*$ {\it{c\/}}) $<$ ({\it{a\/}} $+$ ({\it{a\/}} $*$ {\it{b\/}}))$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-\-
\end{tabbing}

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

\begin{tabbing}{\sc Theorem}:  remainder-difference-non-zero \\ \index{remainder-difference-non-zero}
(({\it{a\/}} $\not\simeq {\tt{0}}$) $\wedge$ (({\it{b\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{a\/}} $<$ {\it{b\/}}))) $\rightarrow$ ((({\it{b\/}} $-$ {\it{a\/}}) ${}${\bf{mod}}${}$ {\it{b\/}}) $\not\simeq {\tt{0}}$)
\end{tabbing}


\noindent{\sc Event}:   Disable remainder-difference-non-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  sum-zero-implies-addends-zero \\ \index{sum-zero-implies-addends-zero}
(({\it{a\/}} $+$ {\it{b\/}}) $=$ {\tt{'}}{\tt{0}}) $\rightarrow$ (({\it{a\/}} $\simeq {\tt{0}}$) $\wedge$ ({\it{b\/}} $\simeq {\tt{0}}$))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-zero-implies-leq-fact \\ \index{remainder-zero-implies-leq-fact}
((({\it{a\/}} ${}${\bf{mod}}${}$ {\it{b\/}}) $=$ {\tt{'}}{\tt{0}}) $\wedge$ ({\it{a\/}} $\not\simeq {\tt{0}}$)) $\rightarrow$ (({\it{a\/}} $<$ {\it{b\/}}) $=$ {\tt{'}}{\tt{*1*false}})
\end{tabbing}


\noindent{\sc Event}:   Disable remainder-zero-implies-leq-fact.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{lessp-quotient-induction} \\  
\=\+{\rm{lessp-quotient-induction}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{lessp-quotient-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{b\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf elseif }{\it{c\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf elseif }{\it{a\/}} $<$ {\it{c\/}}$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf else }{\rm{lessp-quotient-induction}}\,({\it{a\/}} $-$ {\it{c\/}}, {\it{b\/}} $-\;1$, {\it{c\/}})\index{lessp-quotient-induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-quotient-remainder-crock \\ \index{lessp-quotient-remainder-crock}
\=\+(\=\+({\it{a\/}} $<$ ({\it{b\/}} $*$ {\it{c\/}})) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{b\/}} $\not=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(({\it{b\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{c\/}} $\not=$ {\tt{'}}{\tt{0}}) $\wedge$ (({\it{c\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{a\/}} $\in\;${\bf{N}}${}$)))))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(({\it{a\/}} $\div$ {\it{c\/}}) $<$ {\it{b\/}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-quotient-remainder-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-quotient-remainder \\ \index{lessp-quotient-remainder}
(({\it{b\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\it{c\/}} $\not\simeq {\tt{0}}$)) $\rightarrow$ ((({\it{a\/}} ${}${\bf{mod}}${}$ ({\it{b\/}} $*$ {\it{c\/}})) $\div$ {\it{c\/}}) $<$ {\rm{fix}}\,({\it{b\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-quotient-remainder.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-quotient-times \\ \index{lessp-quotient-times}
({\it{a\/}} $<$ ({\it{b\/}} $*$ {\it{c\/}})) $\rightarrow$ ((({\it{a\/}} $\div$ {\it{c\/}}) $<$ {\it{b\/}}) $=$ {\tt{'}}{\tt{*1*true}})
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-quotient-times.

\addvspace{18pt}

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

\begin{tabbing}{\sc Theorem}:  lessp-transitivity \\ \index{lessp-transitivity}
(({\it{a\/}} $<$ {\it{b\/}}) $\wedge$ ({\it{b\/}} $<$ {\it{c\/}})) $\rightarrow$ ({\it{a\/}} $<$ {\it{c\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-plus \\ \index{remainder-plus}
(({\it{a\/}} $+$ {\it{n\/}}) ${}${\bf{mod}}${}$ {\it{a\/}}) $=$ ({\it{n\/}} ${}${\bf{mod}}${}$ {\it{a\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable remainder-plus.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  remainder-divides \\ \index{remainder-divides}
({\rm{divides}}\,({\it{a\/}}, {\it{u\/}})\index{divides} $\wedge$ ({\it{u\/}} $\in\;${\bf{N}}${}$)) $\rightarrow$ ((({\it{u\/}} $+$ {\it{n\/}}) ${}${\bf{mod}}${}$ {\it{a\/}}) $=$ ({\it{n\/}} ${}${\bf{mod}}${}$ {\it{a\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable remainder-divides.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable remainder-remainder.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-quotient \\ \index{lessp-quotient}
({\it{n\/}} $<$ ({\it{a\/}} $*$ {\it{b\/}})) $\rightarrow$ (({\it{n\/}} $\div$ {\it{a\/}}) $<$ {\it{b\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{lessp-quotient-quotient-inducti!on} \\  
\=\+{\rm{lessp-quotient-quotient-induction}}\,({\it{n\/}}, {\it{a\/}}, {\it{b\/}})\index{lessp-quotient-quotient-inducti!on} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf elseif }{\it{a\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf elseif }{\it{b\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf else }{\rm{lessp-quotient-quotient-induction}}\,({\it{n\/}}, {\it{a\/}} $-$ {\it{n\/}}, {\it{b\/}} $-$ {\it{n\/}})\index{lessp-quotient-quotient-inducti!on}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-quotient-quotient \\ \index{lessp-quotient-quotient}
\=\+(({\it{n\/}} $\not\simeq {\tt{0}}$) $\wedge$ ((({\it{b\/}} ${}${\bf{mod}}${}$ {\it{n\/}}) $=$ {\tt{'}}{\tt{0}}) $\wedge$ ({\it{a\/}} $<$ {\it{b\/}}))) \\ 
$\rightarrow$$\;\;\;\;$((({\it{a\/}} $\div$ {\it{n\/}}) $<$ ({\it{b\/}} $\div$ {\it{n\/}})) $=$ {\tt{'}}{\tt{*1*true}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-quotient-quotient.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-times-quotient \\ \index{lessp-times-quotient}
\=\+(({\it{n\/}} $\not\simeq {\tt{0}}$) $\wedge$ (({\it{i\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{i\/}} $<$ {\it{j\/}}) $\wedge$ (({\it{j\/}} ${}${\bf{mod}}${}$ {\it{n\/}}) $=$ {\tt{'}}{\tt{0}})))) \\ 
$\rightarrow$$\;\;\;\;$((({\it{n\/}} $*$ ({\it{i\/}} $\div$ {\it{n\/}})) $<$ {\it{j\/}}) $=$ {\tt{'}}{\tt{*1*true}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-times-quotient.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-lessp-times-plus \\ \index{not-lessp-times-plus}
\=\+(\=\+({\it{a\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{v\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{v\/}} $<$ {\it{n\/}}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{b\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $\not=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{v\/}} $+$ ({\it{a\/}} $*$ {\it{n\/}})) \\ 
$<$$\;\;\;\;$({\it{b\/}} $*$ {\it{n\/}}))\-)\-)\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(({\it{b\/}} $*$ {\it{n\/}}) $\not<$ (({\it{a\/}} $*$ {\it{n\/}}) $+$ {\it{n\/}}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  not-lessp-times-plus-instance \\ \index{not-lessp-times-plus-instance}
\=\+(\=\+({\it{x\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{v\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{v\/}} $<$ {\it{n\/}}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{z\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $\not=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $*$ {\it{z\/}}) \\ 
$<$$\;\;\;\;$({\it{n\/}} $+$ ({\it{n\/}} $*$ {\it{x\/}})))\-)\-)\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$((({\it{v\/}} $+$ ({\it{n\/}} $*$ {\it{x\/}})) $<$ ({\it{n\/}} $*$ {\it{z\/}})) $=$ {\tt{'}}{\tt{*1*false}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable not-lessp-times-plus-instance.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-lessp-plus-times-quotient \\ \index{not-lessp-plus-times-quotient}
\=\+(({\it{n\/}} $\not\simeq {\tt{0}}$) $\wedge$ (({\it{i\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{i\/}} $<$ {\it{j\/}}) $\wedge$ (({\it{j\/}} ${}${\bf{mod}}${}$ {\it{n\/}}) $=$ {\tt{'}}{\tt{0}})))) \\ 
$\rightarrow$$\;\;\;\;$(({\it{j\/}} $<$ (({\it{n\/}} $*$ ({\it{i\/}} $\div$ {\it{n\/}})) $+$ {\it{n\/}})) $=$ {\tt{'}}{\tt{*1*false}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable not-lessp-plus-times-quotient.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  quotient-plus-times-remainder \\ \index{quotient-plus-times-remainder}
({\it{n\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ (((({\it{n\/}} $*$ {\it{a\/}}) $+$ ({\it{b\/}} ${}${\bf{mod}}${}$ {\it{n\/}})) $\div$ {\it{n\/}}) $=$ {\rm{fix}}\,({\it{a\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable quotient-plus-times-remainder.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable remainder-plus-times-remainder.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  remainder-non-zero \\ \index{remainder-non-zero}
(({\it{n\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\it{n\/}} $<$ {\it{m\/}})) $\rightarrow$ ({\tt{'}}{\tt{0}} $<$ ({\it{n\/}} ${}${\bf{mod}}${}$ {\it{m\/}}))
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plus-not-equal \\ \index{plus-not-equal}
({\rm{fix}}\,({\it{b\/}}) $\not=$ {\rm{fix}}\,({\it{c\/}})) $\rightarrow$ (({\it{a\/}} $+$ {\it{b\/}}) $\not=$ ({\it{a\/}} $+$ {\it{c\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable plus-not-equal.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-plus4 \\ \index{difference-plus4}
(({\it{a\/}} $+$ ({\it{b\/}} $+$ {\it{c\/}})) $-$ ({\it{b\/}} $+$ {\it{c\/}})) $=$ {\rm{fix}}\,({\it{a\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable difference-plus4.

\addvspace{18pt}

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

\begin{tabbing}{\sc Theorem}:  associativity-of-plus-inverse \\ \index{associativity-of-plus-inverse}
({\it{a\/}} $+$ ({\it{b\/}} $+$ {\it{c\/}})) $=$ (({\it{a\/}} $+$ {\it{b\/}}) $+$ {\it{c\/}})
\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{'}}{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

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

\begin{tabbing}{\sc Definition}:\index{remove} \\  
\=\+{\rm{remove}}\,({\it{x\/}}, {\it{l\/}})\index{remove} \\ 
$=$$\;\;\;\;$\=\+{\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{remove}}\,({\it{x\/}}, {\rm{cdr}}\,({\it{l\/}}))\index{remove})$\;${\bf  endif}\- \\ 
{\bf else }{\it{l\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{permutation} \\  
\=\+{\rm{permutation}}\,({\it{a\/}}, {\it{b\/}})\index{permutation} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{a\/}}) \\ 
{\bf then }({\rm{car}}\,({\it{a\/}}) $\in$ {\it{b\/}}) $\wedge$ {\rm{permutation}}\,({\rm{cdr}}\,({\it{a\/}}), {\rm{remove}}\,({\rm{car}}\,({\it{a\/}}), {\it{b\/}})\index{remove})\index{permutation} \\ 
{\bf else }{\it{b\/}} $\simeq\;${{\bf{nil}}}${}$$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{plistp} \\  
\=\+{\rm{plistp}}\,({\it{l\/}})\index{plistp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}})$\;\;${\bf then }{\rm{plistp}}\,({\rm{cdr}}\,({\it{l\/}}))\index{plistp} \\ 
{\bf else }{\it{l\/}} $=$ {\tt{'}}{\tt{nil}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{setp} \\  
\=\+{\rm{setp}}\,({\it{l\/}})\index{setp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}})$\;\;${\bf then }({\rm{car}}\,({\it{l\/}}) $\not\in$ {\rm{cdr}}\,({\it{l\/}})) $\wedge$ {\rm{setp}}\,({\rm{cdr}}\,({\it{l\/}}))\index{setp} \\ 
{\bf else }{\it{l\/}} $=$ {\tt{'}}{\tt{nil}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{sorted} \\  
\=\+{\rm{sorted}}\,({\it{l\/}})\index{sorted} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{cdr}}\,({\it{l\/}})) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\rm{cdr}}\,({\it{l\/}})) $<$ {\rm{car}}\,({\it{l\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\rm{sorted}}\,({\rm{cdr}}\,({\it{l\/}}))\index{sorted}$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-\-
\end{tabbing}

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


\noindent{\sc Event}:   Disable not-listp-remove.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-insert \\ \index{length-insert}
{\rm{length}}\,({\rm{insert}}\,({\it{i\/}}, {\it{l\/}})\index{insert})\index{length} $=$ ($1\;+$ {\rm{length}}\,({\it{l\/}})\index{length})
\end{tabbing}


\noindent{\sc Event}:   Disable length-insert.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable length-remove.

\addvspace{18pt}

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

\begin{tabbing}{\sc Theorem}:  number-of-occurrences-of-set-member-is-1 \\ \index{number-of-occurrences-of-set-me!mber-is-1}
({\rm{setp}}\,({\it{l\/}})\index{setp} $\wedge$ ({\it{x\/}} $\in$ {\it{l\/}})) $\rightarrow$ ({\rm{occurrences}}\,({\it{x\/}}, {\it{l\/}})\index{occurrences} $=$ {\tt{'}}{\tt{1}})
\end{tabbing}

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


\noindent{\sc Event}:   Disable plistp-remove.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-set \\ \index{plistp-set}
{\rm{setp}}\,({\it{l\/}})\index{setp} $\rightarrow$ {\rm{plistp}}\,({\it{l\/}})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-set.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  insert-remove \\ \index{insert-remove}
\=\+({\rm{sorted}}\,({\it{l\/}})\index{sorted} $\wedge$ ({\it{x\/}} $\not=$ {\it{y\/}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{insert}}\,({\it{x\/}}, {\rm{remove}}\,({\it{y\/}}, {\it{l\/}})\index{remove})\index{insert} $=$ {\rm{remove}}\,({\it{y\/}}, {\rm{insert}}\,({\it{x\/}}, {\it{l\/}})\index{insert})\index{remove})\-
\end{tabbing}


\noindent{\sc Event}:   Disable insert-remove.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  member-insert \\ \index{member-insert}
({\it{x\/}} $\in$ {\it{l\/}}) $\rightarrow$ ({\it{x\/}} $\in$ {\rm{insert}}\,({\it{i\/}}, {\it{l\/}})\index{insert})
\end{tabbing}


\noindent{\sc Event}:   Disable member-insert.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-member-insert \\ \index{not-member-insert}
(({\it{x\/}} $\not\in$ {\it{l\/}}) $\wedge$ ({\it{i\/}} $\not=$ {\it{x\/}})) $\rightarrow$ ({\it{x\/}} $\not\in$ {\rm{insert}}\,({\it{i\/}}, {\it{l\/}})\index{insert})
\end{tabbing}


\noindent{\sc Event}:   Disable not-member-insert.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  member-remove1 \\ \index{member-remove1}
({\it{x\/}} $\in$ {\rm{remove}}\,({\it{y\/}}, {\it{l\/}})\index{remove}) $\rightarrow$ ({\it{x\/}} $\in$ {\it{l\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  member-remove2 \\ \index{member-remove2}
(({\it{x\/}} $\in$ {\it{l\/}}) $\wedge$ ({\it{x\/}} $\not=$ {\it{y\/}})) $\rightarrow$ ({\it{x\/}} $\in$ {\rm{remove}}\,({\it{y\/}}, {\it{l\/}})\index{remove})
\end{tabbing}


\noindent{\sc Event}:   Disable member-remove2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-member-remove1 \\ \index{not-member-remove1}
{\rm{setp}}\,({\it{l\/}})\index{setp} $\rightarrow$ ({\it{x\/}} $\not\in$ {\rm{remove}}\,({\it{x\/}}, {\it{l\/}})\index{remove})
\end{tabbing}


\noindent{\sc Event}:   Disable not-member-remove1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-member-remove2 \\ \index{not-member-remove2}
({\it{x\/}} $\not\in$ {\it{l\/}}) $\rightarrow$ ({\it{x\/}} $\not\in$ {\rm{remove}}\,({\it{y\/}}, {\it{l\/}})\index{remove})
\end{tabbing}


\noindent{\sc Event}:   Disable not-member-remove2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-member-permutation \\ \index{not-member-permutation}
({\rm{permutation}}\,({\it{a\/}}, {\it{b\/}})\index{permutation} $\wedge$ ({\it{x\/}} $\not\in$ {\it{b\/}})) $\rightarrow$ ({\it{x\/}} $\not\in$ {\it{a\/}})
\end{tabbing}

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

\begin{tabbing}{\sc Theorem}:  remove-remove \\ \index{remove-remove}
({\it{x\/}} $\not=$ {\it{y\/}}) $\rightarrow$ ({\rm{remove}}\,({\it{y\/}}, {\rm{remove}}\,({\it{x\/}}, {\it{l\/}})\index{remove})\index{remove} $=$ {\rm{remove}}\,({\it{x\/}}, {\rm{remove}}\,({\it{y\/}}, {\it{l\/}})\index{remove})\index{remove})
\end{tabbing}


\noindent{\sc Event}:   Disable remove-remove.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  sorted-insert \\ \index{sorted-insert}
({\rm{sorted}}\,({\it{l\/}})\index{sorted} $\wedge$ ({\it{i\/}} $\not\in$ {\it{l\/}})) $\rightarrow$ {\rm{sorted}}\,({\rm{insert}}\,({\it{i\/}}, {\it{l\/}})\index{insert})\index{sorted}
\end{tabbing}


\noindent{\sc Event}:   Disable sorted-insert.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  sorted-remove \\ \index{sorted-remove}
{\rm{sorted}}\,({\it{l\/}})\index{sorted} $\rightarrow$ {\rm{sorted}}\,({\rm{remove}}\,({\it{x\/}}, {\it{l\/}})\index{remove})\index{sorted}
\end{tabbing}


\noindent{\sc Event}:   Disable sorted-remove.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-permutation \\ \index{not-permutation}
({\rm{listp}}\,({\it{b\/}}) $\wedge$ ({\rm{car}}\,({\it{b\/}}) $\not\in$ {\it{a\/}})) $\rightarrow$ ($\neg$ {\rm{permutation}}\,({\it{a\/}}, {\it{b\/}})\index{permutation})
\end{tabbing}


\noindent{\sc Event}:   Disable not-permutation.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-right-cons1 \\ \index{permutation-right-cons1}
\=\+({\rm{listp}}\,({\it{b\/}}) $\wedge$ ({\rm{car}}\,({\it{b\/}}) $\in$ {\it{a\/}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{permutation}}\,({\it{a\/}}, {\it{b\/}})\index{permutation} $=$ {\rm{permutation}}\,({\rm{remove}}\,({\rm{car}}\,({\it{b\/}}), {\it{a\/}})\index{remove}, {\rm{cdr}}\,({\it{b\/}}))\index{permutation})\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-right-cons1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-right-cons \\ \index{permutation-right-cons}
\=\+{\rm{permutation}}\,({\it{a\/}}, {\rm{cons}}\,({\it{x\/}}, {\it{b\/}}))\index{permutation} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{x\/}} $\in$ {\it{a\/}}$\;\;${\bf then }{\rm{permutation}}\,({\rm{remove}}\,({\it{x\/}}, {\it{a\/}})\index{remove}, {\it{b\/}})\index{permutation} \\ 
{\bf else }{\tt{'}}{\tt{*1*false}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-right-cons.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable commutativity-of-permutation.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  member-permutation2 \\ \index{member-permutation2}
({\rm{permutation}}\,({\it{b\/}}, {\it{a\/}})\index{permutation} $\wedge$ ({\it{x\/}} $\in$ {\it{b\/}})) $\rightarrow$ ({\it{x\/}} $\in$ {\it{a\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  permutation-reflexivity \\ \index{permutation-reflexivity}
{\rm{permutation}}\,({\it{l\/}}, {\it{l\/}})\index{permutation}
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-reflexivity.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-append-car \\ \index{permutation-append-car}
{\rm{permutation}}\,({\rm{append}}\,({\it{l\/}}, {\rm{cons}}\,({\it{x\/}}, {\tt{'}}{\tt{nil}})), {\rm{cons}}\,({\it{x\/}}, {\it{l\/}}))\index{permutation}
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-append-car.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-append-insert \\ \index{permutation-append-insert}
\=\+({\rm{permutation}}\,({\it{a\/}}, {\it{b\/}})\index{permutation} $\wedge$ ({\rm{sorted}}\,({\it{b\/}})\index{sorted} $\wedge$ (({\it{x\/}} $\not\in$ {\it{a\/}}) $\wedge$ ({\it{x\/}} $\not\in$ {\it{b\/}})))) \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,({\rm{append}}\,({\it{a\/}}, {\rm{cons}}\,({\it{x\/}}, {\tt{'}}{\tt{nil}})), {\rm{insert}}\,({\it{x\/}}, {\it{b\/}})\index{insert})\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-append-insert.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-remove-remove \\ \index{permutation-remove-remove}
\=\+({\rm{permutation}}\,({\it{a\/}}, {\it{b\/}})\index{permutation} $\wedge$ (({\it{x\/}} $\in$ {\it{a\/}}) $\wedge$ ({\it{x\/}} $\in$ {\it{b\/}}))) \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,({\rm{remove}}\,({\it{x\/}}, {\it{a\/}})\index{remove}, {\rm{remove}}\,({\it{x\/}}, {\it{b\/}})\index{remove})\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-remove-remove.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{transitivity-of-permutation-ind!uction} \\  
\=\+{\rm{transitivity-of-permutation-induction}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}})\index{transitivity-of-permutation-ind!uction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{a\/}}) \\ 
{\bf then }{\rm{transitivity-of-permutation-induction}}\,(\=\+{\rm{cdr}}\,({\it{a\/}}), \\ 
{\rm{remove}}\,({\rm{car}}\,({\it{a\/}}), {\it{b\/}})\index{remove}, \\ 
{\rm{remove}}\,({\rm{car}}\,({\it{a\/}}), {\it{c\/}})\index{remove})\-\index{transitivity-of-permutation-ind!uction} \\ 
{\bf else }{\tt{'}}{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  transitivity-of-permutation-base-case \\ \index{transitivity-of-permutation-base!-case}
(({\it{a\/}} $\simeq\;${{\bf{nil}}}${}$) $\wedge$ ({\rm{permutation}}\,({\it{a\/}}, {\it{b\/}})\index{permutation} $\wedge$ {\rm{permutation}}\,({\it{b\/}}, {\it{c\/}})\index{permutation})) $\rightarrow$ {\rm{permutation}}\,({\it{a\/}}, {\it{c\/}})\index{permutation}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  transitivity-of-permutation-induction-step \\ \index{transitivity-of-permutation-ind!uction-step}
\=\+(\=\+{\rm{listp}}\,({\it{a\/}}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+(\=\+{\rm{permutation}}\,({\rm{cdr}}\,({\it{a\/}}), {\rm{remove}}\,({\rm{car}}\,({\it{a\/}}), {\it{b\/}})\index{remove})\index{permutation} \\ 
$\wedge$$\;\;\;\;${\rm{permutation}}\,({\rm{remove}}\,({\rm{car}}\,({\it{a\/}}), {\it{b\/}})\index{remove}, {\rm{remove}}\,({\rm{car}}\,({\it{a\/}}), {\it{c\/}})\index{remove})\index{permutation})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,({\rm{cdr}}\,({\it{a\/}}), {\rm{remove}}\,({\rm{car}}\,({\it{a\/}}), {\it{c\/}})\index{remove})\index{permutation})\- \\ 
$\wedge$$\;\;\;\;$({\rm{permutation}}\,({\it{a\/}}, {\it{b\/}})\index{permutation} $\wedge$ {\rm{permutation}}\,({\it{b\/}}, {\it{c\/}})\index{permutation}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,({\it{a\/}}, {\it{c\/}})\index{permutation}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  transitivity-of-permutation \\ \index{transitivity-of-permutation}
({\rm{permutation}}\,({\it{a\/}}, {\it{b\/}})\index{permutation} $\wedge$ {\rm{permutation}}\,({\it{b\/}}, {\it{c\/}})\index{permutation}) $\rightarrow$ {\rm{permutation}}\,({\it{a\/}}, {\it{c\/}})\index{permutation}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  setp-remove \\ \index{setp-remove}
{\rm{setp}}\,({\it{a\/}})\index{setp} $\rightarrow$ {\rm{setp}}\,({\rm{remove}}\,({\it{x\/}}, {\it{a\/}})\index{remove})\index{setp}
\end{tabbing}


\noindent{\sc Event}:   Disable setp-remove.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{setp-permutation-induction} \\  
\=\+{\rm{setp-permutation-induction}}\,({\it{a\/}}, {\it{b\/}})\index{setp-permutation-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{a\/}})$\;\;${\bf then }{\rm{setp-permutation-induction}}\,({\rm{cdr}}\,({\it{a\/}}), {\rm{remove}}\,({\rm{car}}\,({\it{a\/}}), {\it{b\/}})\index{remove})\index{setp-permutation-induction} \\ 
{\bf else }{\tt{'}}{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  setp-permutation-base-case \\ \index{setp-permutation-base-case}
(($\neg$ {\rm{listp}}\,({\it{a\/}})) $\wedge$ {\rm{plistp}}\,({\it{a\/}})\index{plistp}) $\rightarrow$ {\rm{setp}}\,({\it{a\/}})\index{setp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  setp-permutation-induction-step \\ \index{setp-permutation-induction-step}
\=\+(\=\+{\rm{listp}}\,({\it{a\/}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{setp}}\,({\it{b\/}})\index{setp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\it{a\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{permutation}}\,({\it{a\/}}, {\it{b\/}})\index{permutation} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{setp}}\,({\rm{remove}}\,({\rm{car}}\,({\it{a\/}}), {\it{b\/}})\index{remove})\index{setp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\rm{cdr}}\,({\it{a\/}}))\index{plistp} \\ 
$\wedge$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{cdr}}\,({\it{a\/}}), \\ 
{\rm{remove}}\,({\rm{car}}\,({\it{a\/}}), {\it{b\/}})\index{remove})\-\index{permutation})\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{setp}}\,({\rm{cdr}}\,({\it{a\/}}))\index{setp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{setp}}\,({\it{a\/}})\index{setp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  setp-permutation \\ \index{setp-permutation}
({\rm{setp}}\,({\it{b\/}})\index{setp} $\wedge$ ({\rm{plistp}}\,({\it{a\/}})\index{plistp} $\wedge$ {\rm{permutation}}\,({\it{a\/}}, {\it{b\/}})\index{permutation})) $\rightarrow$ {\rm{setp}}\,({\it{a\/}})\index{setp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  setp-insert \\ \index{setp-insert}
({\rm{setp}}\,({\it{l\/}})\index{setp} $\wedge$ ({\it{i\/}} $\not\in$ {\it{l\/}})) $\rightarrow$ {\rm{setp}}\,({\rm{insert}}\,({\it{i\/}}, {\it{l\/}})\index{insert})\index{setp}
\end{tabbing}


\noindent{\sc Event}:   Disable setp-insert.

\addvspace{18pt}

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

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

\begin{tabbing}{\sc Definition}:\index{getseg} \\  
\=\+{\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{k\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{'}}{\tt{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{getnth}}\,({\it{n\/}}, {\it{l\/}})\index{getnth}, {\rm{getseg}}\,($1\;+$ {\it{n\/}}, {\it{k\/}} $-\;1$, {\it{l\/}})\index{getseg})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{putseg} \\  
\=\+{\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{s\/}})$\;\;${\bf then }{\rm{putnth}}\,({\rm{car}}\,({\it{s\/}}), {\it{n\/}}, {\rm{putseg}}\,({\rm{cdr}}\,({\it{s\/}}), $1\;+$ {\it{n\/}}, {\it{l\/}})\index{putseg})\index{putnth} \\ 
{\bf else }{\it{l\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{fixlength} \\  
\=\+{\rm{fixlength}}\,({\it{n\/}}, {\it{l\/}}, {\it{default\/}})\index{fixlength} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}}) \\ 
{\bf then }\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{'}}{\tt{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{car}}\,({\it{l\/}}), {\rm{fixlength}}\,({\it{n\/}} $-\;1$, {\rm{cdr}}\,({\it{l\/}}), {\it{default\/}})\index{fixlength})$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{'}}{\tt{nil}} \\ 
{\bf else }{\rm{cons}}\,({\it{default\/}}, {\rm{fixlength}}\,({\it{n\/}} $-\;1$, {\it{l\/}}, {\it{default\/}})\index{fixlength})$\;${\bf  endif}\-\-
\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 }{\tt{'}}{\tt{nil}} \\ 
{\bf else }{\rm{cons}}\,({\rm{car}}\,({\it{l\/}}), {\rm{firstn}}\,({\it{n\/}} $-\;1$, {\rm{cdr}}\,({\it{l\/}}))\index{firstn})$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{nil}}$\;${\bf  endif}\-\-
\end{tabbing}

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

\begin{tabbing}{\sc Theorem}:  non-zero-length-implies-listp \\ \index{non-zero-length-implies-listp}
({\rm{length}}\,({\it{l\/}})\index{length} $\not\simeq {\tt{0}}$) $\rightarrow$ {\rm{listp}}\,({\it{l\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable non-zero-length-implies-listp.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  listp-implies-non-zero-length \\ \index{listp-implies-non-zero-length}
{\rm{listp}}\,({\it{l\/}}) $\rightarrow$ ({\rm{length}}\,({\it{l\/}})\index{length} $\not=$ {\tt{'}}{\tt{0}})
\end{tabbing}


\noindent{\sc Event}:   Disable listp-implies-non-zero-length.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plist-of-non-zero-length-is-a-list \\ \index{plist-of-non-zero-length-is-a-li!st}
({\rm{plistp}}\,({\it{a\/}})\index{plistp} $\wedge$ ({\rm{length}}\,({\it{a\/}})\index{length} $\not=$ {\tt{'}}{\tt{0}})) $\rightarrow$ {\rm{listp}}\,({\it{a\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable plist-of-non-zero-length-is-a-list.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable listp-append.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  listp-append-left \\ \index{listp-append-left}
{\rm{listp}}\,({\it{a\/}}) $\rightarrow$ {\rm{listp}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable listp-append-left.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  listp-getseg \\ \index{listp-getseg}
({\it{k\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ {\rm{listp}}\,({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg})
\end{tabbing}


\noindent{\sc Event}:   Disable listp-getseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  listp-putnth \\ \index{listp-putnth}
{\rm{listp}}\,({\rm{putnth}}\,({\it{v\/}}, {\it{n\/}}, {\it{l\/}})\index{putnth}) $=$ {\rm{listp}}\,({\it{l\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable listp-putnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  listp-putseg \\ \index{listp-putseg}
{\rm{listp}}\,({\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg}) $=$ {\rm{listp}}\,({\it{l\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable listp-putseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-car-to-getnth-0 \\ \index{rewrite-car-to-getnth-0}
{\rm{car}}\,({\it{l\/}}) $=$ {\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{l\/}})\index{getnth}
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-car-to-getnth-0.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  car-append-casesplit \\ \index{car-append-casesplit}
\=\+{\rm{car}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}})) \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{a\/}})$\;\;${\bf then }{\rm{car}}\,({\it{a\/}}) \\ 
{\bf else }{\rm{car}}\,({\it{b\/}})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable car-append-casesplit.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  car-append \\ \index{car-append}
{\rm{listp}}\,({\it{a\/}}) $\rightarrow$ ({\rm{car}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}})) $=$ {\rm{car}}\,({\it{a\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable car-append.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  car-getseg \\ \index{car-getseg}
({\it{k\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ ({\rm{car}}\,({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg}) $=$ {\rm{getnth}}\,({\it{n\/}}, {\it{l\/}})\index{getnth})
\end{tabbing}


\noindent{\sc Event}:   Disable car-getseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  car-putnth-zero \\ \index{car-putnth-zero}
({\rm{listp}}\,({\it{l\/}}) $\wedge$ ({\it{n\/}} $\simeq {\tt{0}}$)) $\rightarrow$ ({\rm{car}}\,({\rm{putnth}}\,({\it{v\/}}, {\it{n\/}}, {\it{l\/}})\index{putnth}) $=$ {\it{v\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable car-putnth-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  car-putseg-zero \\ \index{car-putseg-zero}
(({\it{n\/}} $\simeq {\tt{0}}$) $\wedge$ ({\rm{listp}}\,({\it{s\/}}) $\wedge$ {\rm{listp}}\,({\it{l\/}}))) $\rightarrow$ ({\rm{car}}\,({\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg}) $=$ {\rm{car}}\,({\it{s\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable car-putseg-zero.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable cdr-append.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cdr-getseg \\ \index{cdr-getseg}
({\it{k\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ ({\rm{cdr}}\,({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg}) $=$ {\rm{getseg}}\,($1\;+$ {\it{n\/}}, {\it{k\/}} $-\;1$, {\it{l\/}})\index{getseg})
\end{tabbing}


\noindent{\sc Event}:   Disable cdr-getseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cdr-is-nil-when-length-is-1 \\ \index{cdr-is-nil-when-length-is-1}
\=\+({\rm{plistp}}\,({\it{l\/}})\index{plistp} $\wedge$ ({\rm{length}}\,({\it{l\/}})\index{length} $=$ {\tt{'}}{\tt{1}})) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{cdr}}\,({\it{l\/}}) $=$ {\tt{'}}{\tt{nil}}) $=$ {\tt{'}}{\tt{*1*true}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable cdr-is-nil-when-length-is-1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plist-of-length-0 \\ \index{plist-of-length-0}
({\rm{plistp}}\,({\it{l\/}})\index{plistp} $\wedge$ ({\rm{length}}\,({\it{l\/}})\index{length} $=$ {\tt{'}}{\tt{0}})) $\rightarrow$ (({\it{l\/}} $=$ {\tt{'}}{\tt{nil}}) $=$ {\tt{'}}{\tt{*1*true}})
\end{tabbing}


\noindent{\sc Event}:   Disable plist-of-length-0.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-append \\ \index{plistp-append}
{\rm{plistp}}\,({\it{b\/}})\index{plistp} $\rightarrow$ {\rm{plistp}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-append.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-list1 \\ \index{plistp-list1}
{\rm{plistp}}\,({\rm{cons}}\,({\it{x\/}}, {\tt{'}}{\tt{nil}}))\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-list1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-list2 \\ \index{plistp-list2}
{\rm{plistp}}\,({\rm{cons}}\,({\it{x\/}}, {\rm{cons}}\,({\it{y\/}}, {\tt{'}}{\tt{nil}})))\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-list2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-putnth \\ \index{plistp-putnth}
{\rm{plistp}}\,({\it{l\/}})\index{plistp} $\rightarrow$ {\rm{plistp}}\,({\rm{putnth}}\,({\it{v\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-putnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-getseg \\ \index{plistp-getseg}
{\rm{plistp}}\,({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-getseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-putseg \\ \index{plistp-putseg}
{\rm{plistp}}\,({\it{l\/}})\index{plistp} $\rightarrow$ {\rm{plistp}}\,({\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-putseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-fixlength \\ \index{plistp-fixlength}
{\rm{plistp}}\,({\rm{fixlength}}\,({\it{n\/}}, {\it{l\/}}, {\it{v\/}})\index{fixlength})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-fixlength.

\addvspace{18pt}

\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}


\noindent{\sc Event}:   Disable length-append.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-putnth \\ \index{length-putnth}
{\rm{length}}\,({\rm{putnth}}\,({\it{n\/}}, {\it{v\/}}, {\it{l\/}})\index{putnth})\index{length} $=$ {\rm{length}}\,({\it{l\/}})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-putnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-getseg \\ \index{length-getseg}
{\rm{length}}\,({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg})\index{length} $=$ {\rm{fix}}\,({\it{k\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-getseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-putseg \\ \index{length-putseg}
{\rm{length}}\,({\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg})\index{length} $=$ {\rm{length}}\,({\it{l\/}})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-putseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-fixlength \\ \index{length-fixlength}
{\rm{length}}\,({\rm{fixlength}}\,({\it{n\/}}, {\it{l\/}}, {\it{default\/}})\index{fixlength})\index{length} $=$ {\rm{fix}}\,({\it{n\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-fixlength.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  append-non-list-left \\ \index{append-non-list-left}
($\neg$ {\rm{listp}}\,({\it{a\/}})) $\rightarrow$ ({\rm{append}}\,({\it{a\/}}, {\it{b\/}}) $=$ {\it{b\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable append-non-list-left.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  append-non-list-left-corollary \\ \index{append-non-list-left-corollary}
({\rm{length}}\,({\it{a\/}})\index{length} $=$ {\tt{'}}{\tt{0}}) $\rightarrow$ ({\rm{append}}\,({\it{a\/}}, {\it{b\/}}) $=$ {\it{b\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable append-non-list-left-corollary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  append-nil-on-right \\ \index{append-nil-on-right}
{\rm{plistp}}\,({\it{a\/}})\index{plistp} $\rightarrow$ ({\rm{append}}\,({\it{a\/}}, {\tt{'}}{\tt{nil}}) $=$ {\it{a\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable append-nil-on-right.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  append-cdr \\ \index{append-cdr}
{\rm{listp}}\,({\it{a\/}}) $\rightarrow$ ({\rm{append}}\,({\rm{cdr}}\,({\it{a\/}}), {\it{b\/}}) $=$ {\rm{cdr}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}})))
\end{tabbing}


\noindent{\sc Event}:   Disable append-cdr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  append-crock \\ \index{append-crock}
{\rm{append}}\,({\rm{cons}}\,({\it{a\/}}, {\tt{'}}{\tt{nil}}), {\rm{append}}\,({\it{b\/}}, {\it{c\/}})) $=$ {\rm{append}}\,({\rm{cons}}\,({\it{a\/}}, {\it{b\/}}), {\it{c\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable append-crock.

\addvspace{18pt}

\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}


\noindent{\sc Event}:   Disable associativity-of-append.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  append-fixlength \\ \index{append-fixlength}
\=\+{\rm{append}}\,({\rm{fixlength}}\,({\it{a\/}}, {\tt{'}}{\tt{nil}}, {\it{default\/}})\index{fixlength}, {\rm{fixlength}}\,({\it{b\/}}, {\tt{'}}{\tt{nil}}, {\it{default\/}})\index{fixlength}) \\ 
$=$$\;\;\;\;${\rm{fixlength}}\,({\it{a\/}} $+$ {\it{b\/}}, {\tt{'}}{\tt{nil}}, {\it{default\/}})\index{fixlength}\-
\end{tabbing}


\noindent{\sc Event}:   Disable append-fixlength.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-0-2 \\ \index{getnth-0-2}
{\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{cons}}\,({\it{a\/}}, {\rm{cons}}\,({\it{b\/}}, {\tt{'}}{\tt{nil}})))\index{getnth} $=$ {\it{a\/}}
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-0-2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-1-2 \\ \index{getnth-1-2}
{\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\rm{cons}}\,({\it{a\/}}, {\rm{cons}}\,({\it{b\/}}, {\tt{'}}{\tt{nil}})))\index{getnth} $=$ {\it{b\/}}
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-1-2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  list-getnth-0 \\ \index{list-getnth-0}
({\rm{plistp}}\,({\it{l\/}})\index{plistp} $\wedge$ ({\rm{length}}\,({\it{l\/}})\index{length} $=$ {\tt{'}}{\tt{1}})) $\rightarrow$ ({\rm{cons}}\,({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{l\/}})\index{getnth}, {\tt{'}}{\tt{nil}}) $=$ {\it{l\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable list-getnth-0.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-up-getnth \\ \index{open-up-getnth}
{\rm{getnth}}\,($1\;+$ {\it{n\/}}, {\rm{cons}}\,({\it{a\/}}, {\it{b\/}}))\index{getnth} $=$ {\rm{getnth}}\,({\it{n\/}}, {\it{b\/}})\index{getnth}
\end{tabbing}


\noindent{\sc Event}:   Disable open-up-getnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-up-getnth1 \\ \index{open-up-getnth1}
({\it{n\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ ({\rm{getnth}}\,({\it{n\/}}, {\rm{cons}}\,({\it{a\/}}, {\it{b\/}}))\index{getnth} $=$ {\rm{getnth}}\,({\it{n\/}} $-\;1$, {\it{b\/}})\index{getnth})
\end{tabbing}


\noindent{\sc Event}:   Disable open-up-getnth1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-up-getnth-on-zero \\ \index{open-up-getnth-on-zero}
{\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{cons}}\,({\it{a\/}}, {\it{b\/}}))\index{getnth} $=$ {\it{a\/}}
\end{tabbing}


\noindent{\sc Event}:   Disable open-up-getnth-on-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-with-non-number-index \\ \index{getnth-with-non-number-index}
({\it{n\/}} $\not\in\;${\bf{N}}${}$) $\rightarrow$ ({\rm{getnth}}\,({\it{n\/}}, {\it{l\/}})\index{getnth} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{l\/}})\index{getnth})
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-with-non-number-index.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-append-for-length-left \\ \index{getnth-append-for-length-left}
\=\+{\rm{getnth}}\,({\rm{length}}\,({\it{a\/}})\index{length}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{getnth} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{b\/}})$\;\;${\bf then }{\rm{car}}\,({\it{b\/}}) \\ 
{\bf else }{\tt{'}}{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-append-for-length-left.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-append-casesplit \\ \index{getnth-append-casesplit}
\=\+{\rm{getnth}}\,({\it{n\/}}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{getnth} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $<$ {\rm{length}}\,({\it{a\/}})\index{length}$\;\;${\bf then }{\rm{getnth}}\,({\it{n\/}}, {\it{a\/}})\index{getnth} \\ 
{\bf else }{\rm{getnth}}\,({\it{n\/}} $-$ {\rm{length}}\,({\it{a\/}})\index{length}, {\it{b\/}})\index{getnth}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-append-casesplit.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-append-right \\ \index{getnth-append-right}
\=\+\=\+{\bf if }{\it{n\/}} $<$ {\rm{length}}\,({\it{a\/}})\index{length}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\it{n\/}}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{getnth} $=$ {\rm{getnth}}\,({\it{n\/}} $-$ {\rm{length}}\,({\it{a\/}})\index{length}, {\it{b\/}})\index{getnth})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-append-right.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-append-left \\ \index{getnth-append-left}
({\it{n\/}} $<$ {\rm{length}}\,({\it{a\/}})\index{length}) $\rightarrow$ ({\rm{getnth}}\,({\it{n\/}}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{getnth} $=$ {\rm{getnth}}\,({\it{n\/}}, {\it{a\/}})\index{getnth})
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-append-left.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-putnth-casesplit \\ \index{getnth-putnth-casesplit}
\=\+{\rm{getnth}}\,({\it{i\/}}, {\rm{putnth}}\,({\it{v\/}}, {\it{j\/}}, {\it{l\/}})\index{putnth})\index{getnth} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length} \\ 
{\bf then }\=\+{\bf if }{\rm{fix}}\,({\it{i\/}}) $=$ {\rm{fix}}\,({\it{j\/}})$\;\;${\bf then }{\it{v\/}} \\ 
{\bf else }{\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-putnth-casesplit.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-putnth-coincidence \\ \index{getnth-putnth-coincidence}
({\it{n\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) $\rightarrow$ ({\rm{getnth}}\,({\it{n\/}}, {\rm{putnth}}\,({\it{v\/}}, {\it{n\/}}, {\it{l\/}})\index{putnth})\index{getnth} $=$ {\it{v\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-putnth-coincidence.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-putnth-non-interference \\ \index{getnth-putnth-non-interference}
({\rm{fix}}\,({\it{i\/}}) $\not=$ {\rm{fix}}\,({\it{j\/}})) $\rightarrow$ ({\rm{getnth}}\,({\it{i\/}}, {\rm{putnth}}\,({\it{v\/}}, {\it{j\/}}, {\it{l\/}})\index{putnth})\index{getnth} $=$ {\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-putnth-non-interference.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-getseg-zero-index \\ \index{getnth-getseg-zero-index}
(({\it{k\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\it{i\/}} $\simeq {\tt{0}}$)) $\rightarrow$ ({\rm{getnth}}\,({\it{i\/}}, {\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg})\index{getnth} $=$ {\rm{getnth}}\,({\it{n\/}}, {\it{l\/}})\index{getnth})
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-getseg-zero-index.

\addvspace{18pt}

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

\begin{tabbing}{\sc Theorem}:  getnth-getseg \\ \index{getnth-getseg}
({\it{i\/}} $<$ {\it{k\/}}) $\rightarrow$ ({\rm{getnth}}\,({\it{i\/}}, {\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg})\index{getnth} $=$ {\rm{getnth}}\,({\it{n\/}} $+$ {\it{i\/}}, {\it{l\/}})\index{getnth})
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-getseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-getseg-inverse \\ \index{getnth-getseg-inverse}
({\it{i\/}} $<$ {\it{k\/}}) $\rightarrow$ ({\rm{getnth}}\,({\it{n\/}} $+$ {\it{i\/}}, {\it{l\/}})\index{getnth} $=$ {\rm{getnth}}\,({\it{i\/}}, {\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg})\index{getnth})
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-getseg-inverse.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-after-putseg \\ \index{getnth-after-putseg}
\=\+\=\+{\bf if }{\it{i\/}} $<$ ({\it{n\/}} $+$ {\rm{length}}\,({\it{s\/}})\index{length})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\it{i\/}}, {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg})\index{getnth} $=$ {\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-after-putseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-before-putseg \\ \index{getnth-before-putseg}
({\it{i\/}} $<$ {\it{n\/}}) $\rightarrow$ ({\rm{getnth}}\,({\it{i\/}}, {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg})\index{getnth} $=$ {\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-before-putseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-putseg-coincidence \\ \index{getnth-putseg-coincidence}
\=\+(\=\+\=\+{\bf if }{\it{i\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$((({\it{i\/}} $-$ {\it{n\/}}) $<$ {\rm{length}}\,({\it{s\/}})\index{length}) $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\it{i\/}}, {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg})\index{getnth} $=$ {\rm{getnth}}\,({\it{i\/}} $-$ {\it{n\/}}, {\it{s\/}})\index{getnth})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-putseg-coincidence.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-putnth-casesplit \\ \index{open-putnth-casesplit}
\=\+{\rm{putnth}}\,({\it{v\/}}, {\it{n\/}}, {\rm{cons}}\,({\it{a\/}}, {\it{b\/}}))\index{putnth} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\rm{cons}}\,({\it{v\/}}, {\it{b\/}}) \\ 
{\bf else }{\rm{cons}}\,({\it{a\/}}, {\rm{putnth}}\,({\it{v\/}}, {\it{n\/}} $-\;1$, {\it{b\/}})\index{putnth})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable open-putnth-casesplit.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-up-putnth1 \\ \index{open-up-putnth1}
({\it{n\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ ({\rm{putnth}}\,({\it{v\/}}, {\it{n\/}}, {\rm{cons}}\,({\it{a\/}}, {\it{b\/}}))\index{putnth} $=$ {\rm{cons}}\,({\it{a\/}}, {\rm{putnth}}\,({\it{v\/}}, {\it{n\/}} $-\;1$, {\it{b\/}})\index{putnth}))
\end{tabbing}


\noindent{\sc Event}:   Disable open-up-putnth1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putnth-into-nil \\ \index{putnth-into-nil}
{\rm{putnth}}\,({\it{v\/}}, {\it{i\/}}, {\tt{'}}{\tt{nil}})\index{putnth} $=$ {\tt{'}}{\tt{nil}}
\end{tabbing}


\noindent{\sc Event}:   Disable putnth-into-nil.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-up-putnth-on-zero \\ \index{open-up-putnth-on-zero}
{\rm{putnth}}\,({\it{val\/}}, {\tt{'}}{\tt{0}}, {\rm{cons}}\,({\it{a\/}}, {\it{b\/}}))\index{putnth} $=$ {\rm{cons}}\,({\it{val\/}}, {\it{b\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable open-up-putnth-on-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putnth-with-non-number-index \\ \index{putnth-with-non-number-index}
({\it{i\/}} $\not\in\;${\bf{N}}${}$) $\rightarrow$ ({\rm{putnth}}\,({\it{v\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth} $=$ {\rm{putnth}}\,({\it{v\/}}, {\tt{'}}{\tt{0}}, {\it{l\/}})\index{putnth})
\end{tabbing}


\noindent{\sc Event}:   Disable putnth-with-non-number-index.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putnth-has-no-effect \\ \index{putnth-has-no-effect}
({\it{n\/}} $\not<$ {\rm{length}}\,({\it{l\/}})\index{length}) $\rightarrow$ ({\rm{putnth}}\,({\it{v\/}}, {\it{n\/}}, {\it{l\/}})\index{putnth} $=$ {\it{l\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable putnth-has-no-effect.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putnth-cons1 \\ \index{putnth-cons1}
({\it{n\/}} $\simeq {\tt{0}}$) $\rightarrow$ ({\rm{putnth}}\,({\it{v\/}}, {\it{n\/}}, {\rm{cons}}\,({\it{a\/}}, {\it{b\/}}))\index{putnth} $=$ {\rm{cons}}\,({\it{v\/}}, {\it{b\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable putnth-cons1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putnth-cons2 \\ \index{putnth-cons2}
({\it{n\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ ({\rm{putnth}}\,({\it{v\/}}, {\it{n\/}}, {\rm{cons}}\,({\it{a\/}}, {\it{b\/}}))\index{putnth} $=$ {\rm{cons}}\,({\it{a\/}}, {\rm{putnth}}\,({\it{v\/}}, {\it{n\/}} $-\;1$, {\it{b\/}})\index{putnth}))
\end{tabbing}


\noindent{\sc Event}:   Disable putnth-cons2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putnth-shift \\ \index{putnth-shift}
\=\+({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{putnth}}\,({\it{v\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth} $=$ {\rm{append}}\,({\rm{firstn}}\,({\it{i\/}}, {\it{l\/}})\index{firstn}, {\rm{cons}}\,({\it{v\/}}, {\rm{nthcdr}}\,($1\;+$ {\it{i\/}}, {\it{l\/}})\index{nthcdr})))\-
\end{tabbing}


\noindent{\sc Event}:   Disable putnth-shift.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putnth-append-casesplit \\ \index{putnth-append-casesplit}
\=\+{\rm{putnth}}\,({\it{v\/}}, {\it{n\/}}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{putnth} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $<$ {\rm{length}}\,({\it{a\/}})\index{length}$\;\;${\bf then }{\rm{append}}\,({\rm{putnth}}\,({\it{v\/}}, {\it{n\/}}, {\it{a\/}})\index{putnth}, {\it{b\/}}) \\ 
{\bf else }{\rm{append}}\,({\it{a\/}}, {\rm{putnth}}\,({\it{v\/}}, {\it{n\/}} $-$ {\rm{length}}\,({\it{a\/}})\index{length}, {\it{b\/}})\index{putnth})$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable putnth-append-casesplit.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putnth-append-right \\ \index{putnth-append-right}
\=\+\=\+{\bf if }{\it{n\/}} $<$ {\rm{length}}\,({\it{a\/}})\index{length}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{putnth}}\,({\it{v\/}}, {\it{n\/}}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{putnth} $=$ {\rm{append}}\,({\it{a\/}}, {\rm{putnth}}\,({\it{v\/}}, {\it{n\/}} $-$ {\rm{length}}\,({\it{a\/}})\index{length}, {\it{b\/}})\index{putnth}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable putnth-append-right.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putnth-append-left \\ \index{putnth-append-left}
({\it{n\/}} $<$ {\rm{length}}\,({\it{a\/}})\index{length}) $\rightarrow$ ({\rm{putnth}}\,({\it{v\/}}, {\it{n\/}}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{putnth} $=$ {\rm{append}}\,({\rm{putnth}}\,({\it{v\/}}, {\it{n\/}}, {\it{a\/}})\index{putnth}, {\it{b\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable putnth-append-left.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putnth-getnth-coincidence \\ \index{putnth-getnth-coincidence}
{\rm{putnth}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth}, {\it{i\/}}, {\it{l\/}})\index{putnth} $=$ {\it{l\/}}
\end{tabbing}


\noindent{\sc Event}:   Disable putnth-getnth-coincidence.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putnth-getnth-coincidence1 \\ \index{putnth-getnth-coincidence1}
\=\+({\rm{getnth}}\,({\it{i\/}}, {\it{l1\/}})\index{getnth} $=$ {\rm{getnth}}\,({\it{i\/}}, {\it{l2\/}})\index{getnth}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{putnth}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l1\/}})\index{getnth}, {\it{i\/}}, {\rm{putnth}}\,({\it{v\/}}, {\it{i\/}}, {\it{l2\/}})\index{putnth})\index{putnth} $=$ {\it{l2\/}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable putnth-getnth-coincidence1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putnth-putnth-casesplit \\ \index{putnth-putnth-casesplit}
\=\+(\=\+({\it{i\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{j\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{j\/}} $<$ {\it{i\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{putnth}}\,({\it{b\/}}, {\it{j\/}}, {\rm{putnth}}\,({\it{a\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth})\index{putnth} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{i\/}} $=$ {\it{j\/}}$\;\;${\bf then }{\rm{putnth}}\,({\it{b\/}}, {\it{j\/}}, {\it{l\/}})\index{putnth} \\ 
{\bf else }{\rm{putnth}}\,({\it{a\/}}, {\it{i\/}}, {\rm{putnth}}\,({\it{b\/}}, {\it{j\/}}, {\it{l\/}})\index{putnth})\index{putnth}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable putnth-putnth-casesplit.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putnth-coincidence \\ \index{putnth-coincidence}
({\rm{fix}}\,({\it{i\/}}) $=$ {\rm{fix}}\,({\it{j\/}})) $\rightarrow$ ({\rm{putnth}}\,({\it{b\/}}, {\it{j\/}}, {\rm{putnth}}\,({\it{a\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth})\index{putnth} $=$ {\rm{putnth}}\,({\it{b\/}}, {\it{j\/}}, {\it{l\/}})\index{putnth})
\end{tabbing}


\noindent{\sc Event}:   Disable putnth-coincidence.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putnth-non-interference \\ \index{putnth-non-interference}
\=\+({\rm{fix}}\,({\it{i\/}}) $\not=$ {\rm{fix}}\,({\it{j\/}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{putnth}}\,({\it{b\/}}, {\it{j\/}}, {\rm{putnth}}\,({\it{a\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth})\index{putnth} $=$ {\rm{putnth}}\,({\it{a\/}}, {\it{i\/}}, {\rm{putnth}}\,({\it{b\/}}, {\it{j\/}}, {\it{l\/}})\index{putnth})\index{putnth})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  putnth-non-interference-corollary1 \\ \index{putnth-non-interference-corolla!ry1}
\=\+({\rm{fix}}\,({\it{i\/}}) $<$ ($1\;+$ {\it{j\/}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{putnth}}\,({\it{b\/}}, $1\;+$ {\it{j\/}}, {\rm{putnth}}\,({\it{a\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth})\index{putnth} $=$ {\rm{putnth}}\,({\it{a\/}}, {\it{i\/}}, {\rm{putnth}}\,({\it{b\/}}, $1\;+$ {\it{j\/}}, {\it{l\/}})\index{putnth})\index{putnth})\-
\end{tabbing}


\noindent{\sc Event}:   Disable putnth-non-interference-corollary1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putnth-non-interference-corollary2 \\ \index{putnth-non-interference-corolla!ry2}
\=\+({\rm{fix}}\,({\it{i\/}}) $<$ ({\it{j\/}} $+$ {\it{k\/}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{putnth}}\,({\it{b\/}}, {\it{j\/}} $+$ {\it{k\/}}, {\rm{putnth}}\,({\it{a\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth})\index{putnth} $=$ {\rm{putnth}}\,({\it{a\/}}, {\it{i\/}}, {\rm{putnth}}\,({\it{b\/}}, {\it{j\/}} $+$ {\it{k\/}}, {\it{l\/}})\index{putnth})\index{putnth})\-
\end{tabbing}


\noindent{\sc Event}:   Disable putnth-non-interference-corollary2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putnth-putseg-coincidence-proof \\ \index{putnth-putseg-coincidence-proof}
\=\+(\=\+({\it{n\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{i\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\it{i\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$(({\it{i\/}} $-$ {\it{n\/}}) $<$ {\rm{length}}\,({\it{s\/}})\index{length}))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{putnth}}\,({\it{v\/}}, {\it{i\/}}, {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg})\index{putnth} $=$ {\rm{putseg}}\,({\rm{putnth}}\,({\it{v\/}}, {\it{i\/}} $-$ {\it{n\/}}, {\it{s\/}})\index{putnth}, {\it{n\/}}, {\it{l\/}})\index{putseg})\-
\end{tabbing}


\noindent{\sc Event}:   Disable putnth-putseg-coincidence-proof.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putseg-with-non-number-index \\ \index{putseg-with-non-number-index}
({\it{n\/}} $\not\in\;${\bf{N}}${}$) $\rightarrow$ ({\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg} $=$ {\rm{putseg}}\,({\it{s\/}}, {\tt{'}}{\tt{0}}, {\it{l\/}})\index{putseg})
\end{tabbing}


\noindent{\sc Event}:   Disable putseg-with-non-number-index.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putnth-putseg-coincidence \\ \index{putnth-putseg-coincidence}
\=\+(\=\+\=\+{\bf if }{\it{i\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$(({\it{i\/}} $-$ {\it{n\/}}) $<$ {\rm{length}}\,({\it{s\/}})\index{length}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{putnth}}\,({\it{v\/}}, {\it{i\/}}, {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg})\index{putnth} $=$ {\rm{putseg}}\,({\rm{putnth}}\,({\it{v\/}}, {\it{i\/}} $-$ {\it{n\/}}, {\it{s\/}})\index{putnth}, {\it{n\/}}, {\it{l\/}})\index{putseg})\-
\end{tabbing}


\noindent{\sc Event}:   Disable putnth-putseg-coincidence.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putnth-putseg-coincidence-inverse \\ \index{putnth-putseg-coincidence-inver!se}
\=\+(({\it{i\/}} $<$ {\rm{length}}\,({\it{s\/}})\index{length}) $\wedge$ ({\it{i\/}} $\in\;${\bf{N}}${}$)) \\ 
$\rightarrow$$\;\;\;\;$({\rm{putseg}}\,({\rm{putnth}}\,({\it{v\/}}, {\it{i\/}}, {\it{s\/}})\index{putnth}, {\it{n\/}}, {\it{l\/}})\index{putseg} $=$ {\rm{putnth}}\,({\it{v\/}}, {\it{i\/}} $+$ {\it{n\/}}, {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg})\index{putnth})\-
\end{tabbing}


\noindent{\sc Event}:   Disable putnth-putseg-coincidence-inverse.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putnth-after-putseg-proof \\ \index{putnth-after-putseg-proof}
\=\+(\=\+({\it{i\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\it{i\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }({\it{i\/}} $-$ {\it{n\/}}) $<$ {\rm{length}}\,({\it{s\/}})\index{length}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{putnth}}\,({\it{v\/}}, {\it{i\/}}, {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg})\index{putnth} $=$ {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\rm{putnth}}\,({\it{v\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth})\index{putseg})\-
\end{tabbing}


\noindent{\sc Event}:   Disable putnth-after-putseg-proof.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putnth-after-putseg \\ \index{putnth-after-putseg}
\=\+(\=\+\=\+{\bf if }{\it{i\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }({\it{i\/}} $-$ {\it{n\/}}) $<$ {\rm{length}}\,({\it{s\/}})\index{length}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{putnth}}\,({\it{v\/}}, {\it{i\/}}, {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg})\index{putnth} $=$ {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\rm{putnth}}\,({\it{v\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth})\index{putseg})\-
\end{tabbing}


\noindent{\sc Event}:   Disable putnth-after-putseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-of-length-zero \\ \index{getseg-of-length-zero}
({\it{k\/}} $\simeq {\tt{0}}$) $\rightarrow$ ({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg} $=$ {\tt{'}}{\tt{nil}})
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-of-length-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-add1-length \\ \index{getseg-add1-length}
{\rm{getseg}}\,({\it{n\/}}, $1\;+$ {\it{k\/}}, {\it{l\/}})\index{getseg} $=$ {\rm{append}}\,({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg}, {\rm{cons}}\,({\rm{getnth}}\,({\it{n\/}} $+$ {\it{k\/}}, {\it{l\/}})\index{getnth}, {\tt{'}}{\tt{nil}}))
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-add1-length.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-with-non-number-index \\ \index{getseg-with-non-number-index}
({\it{n\/}} $\not\in\;${\bf{N}}${}$) $\rightarrow$ ({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg} $=$ {\rm{getseg}}\,({\tt{'}}{\tt{0}}, {\it{k\/}}, {\it{l\/}})\index{getseg})
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-with-non-number-index.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable getseg-add1-cons.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-length-1 \\ \index{getseg-length-1}
{\rm{getseg}}\,({\it{n\/}}, {\tt{'}}{\tt{1}}, {\it{l\/}})\index{getseg} $=$ {\rm{cons}}\,({\rm{getnth}}\,({\it{n\/}}, {\it{l\/}})\index{getnth}, {\tt{'}}{\tt{nil}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  getseg-length-1-rule \\ \index{getseg-length-1-rule}
({\it{k\/}} $=$ {\tt{'}}{\tt{1}}) $\rightarrow$ ({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg} $=$ {\rm{cons}}\,({\rm{getnth}}\,({\it{n\/}}, {\it{l\/}})\index{getnth}, {\tt{'}}{\tt{nil}}))
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-length-1-rule.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-add1-length2 \\ \index{getseg-add1-length2}
\=\+(\=\+({\it{n\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ ($1\;+$ {\it{n\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getseg}}\,({\it{n\/}}, $1\;+$ {\it{k\/}}, {\it{l\/}})\index{getseg} $=$ {\rm{cons}}\,({\rm{getnth}}\,({\it{n\/}}, {\it{l\/}})\index{getnth}, {\rm{getseg}}\,($1\;+$ {\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-add1-length2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-append-right \\ \index{getseg-append-right}
\=\+\=\+{\bf if }{\it{n\/}} $<$ {\rm{length}}\,({\it{a\/}})\index{length}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{getseg} $=$ {\rm{getseg}}\,({\it{n\/}} $-$ {\rm{length}}\,({\it{a\/}})\index{length}, {\it{k\/}}, {\it{b\/}})\index{getseg})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-append-right.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-across-append \\ \index{getseg-across-append}
\=\+(\=\+({\it{n\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\rm{length}}\,({\it{a\/}})\index{length} $<$ {\it{n\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }({\it{n\/}} $+$ {\it{k\/}}) $<$ {\rm{length}}\,({\it{a\/}})\index{length}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{getseg} \\ 
$=$$\;\;\;\;${\rm{append}}\,(\=\+{\rm{getseg}}\,({\it{n\/}}, {\rm{length}}\,({\it{a\/}})\index{length} $-$ {\it{n\/}}, {\it{a\/}})\index{getseg}, \\ 
{\rm{getseg}}\,({\tt{'}}{\tt{0}}, {\it{k\/}} $-$ ({\rm{length}}\,({\it{a\/}})\index{length} $-$ {\it{n\/}}), {\it{b\/}})\index{getseg})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-across-append.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-append-left \\ \index{getseg-append-left}
\=\+\=\+{\bf if }{\rm{length}}\,({\it{a\/}})\index{length} $<$ ({\it{n\/}} $+$ {\it{k\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{getseg} $=$ {\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{a\/}})\index{getseg})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-append-left.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-after-putnth \\ \index{getseg-after-putnth}
({\it{n\/}} $<$ {\it{i\/}}) $\rightarrow$ ({\rm{getseg}}\,({\it{i\/}}, {\it{k\/}}, {\rm{putnth}}\,({\it{v\/}}, {\it{n\/}}, {\it{l\/}})\index{putnth})\index{getseg} $=$ {\rm{getseg}}\,({\it{i\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg})
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-after-putnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-before-putnth \\ \index{getseg-before-putnth}
\=\+\=\+{\bf if }{\it{n\/}} $<$ ({\it{i\/}} $+$ {\it{k\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getseg}}\,({\it{i\/}}, {\it{k\/}}, {\rm{putnth}}\,({\it{v\/}}, {\it{n\/}}, {\it{l\/}})\index{putnth})\index{getseg} $=$ {\rm{getseg}}\,({\it{i\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-before-putnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-putnth-coincidence \\ \index{getseg-putnth-coincidence}
\=\+(\=\+\=\+{\bf if }{\it{n\/}} $<$ {\it{i\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$((({\it{n\/}} $-$ {\it{i\/}}) $<$ {\it{k\/}}) $\wedge$ ({\it{n\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getseg}}\,({\it{i\/}}, {\it{k\/}}, {\rm{putnth}}\,({\it{v\/}}, {\it{n\/}}, {\it{l\/}})\index{putnth})\index{getseg} $=$ {\rm{putnth}}\,({\it{v\/}}, {\it{n\/}} $-$ {\it{i\/}}, {\rm{getseg}}\,({\it{i\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg})\index{putnth})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-putnth-coincidence.

\addvspace{18pt}

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

\begin{tabbing}{\sc Theorem}:  getseg-getseg \\ \index{getseg-getseg}
\=\+\=\+{\bf if }{\it{k\/}} $<$ ({\it{i\/}} $+$ {\it{j\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getseg}}\,({\it{i\/}}, {\it{j\/}}, {\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg})\index{getseg} $=$ {\rm{getseg}}\,({\it{n\/}} $+$ {\it{i\/}}, {\it{j\/}}, {\it{l\/}})\index{getseg})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-getseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-after-putseg \\ \index{getseg-after-putseg}
\=\+\=\+{\bf if }{\it{i\/}} $<$ ({\it{n\/}} $+$ {\rm{length}}\,({\it{s\/}})\index{length})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getseg}}\,({\it{i\/}}, {\it{k\/}}, {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg})\index{getseg} $=$ {\rm{getseg}}\,({\it{i\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-after-putseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-before-putseg \\ \index{getseg-before-putseg}
\=\+\=\+{\bf if }{\it{n\/}} $<$ ({\it{i\/}} $+$ {\it{k\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getseg}}\,({\it{i\/}}, {\it{k\/}}, {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg})\index{getseg} $=$ {\rm{getseg}}\,({\it{i\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-before-putseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-within-putseg \\ \index{getseg-within-putseg}
\=\+(\=\+\=\+{\bf if }{\it{i\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ ({\it{n\/}} $+$ {\rm{length}}\,({\it{s\/}})\index{length})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }({\it{n\/}} $+$ {\rm{length}}\,({\it{s\/}})\index{length}) $<$ ({\it{i\/}} $+$ {\it{k\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getseg}}\,({\it{i\/}}, {\it{k\/}}, {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg})\index{getseg} $=$ {\rm{getseg}}\,({\it{i\/}} $-$ {\it{n\/}}, {\it{k\/}}, {\it{s\/}})\index{getseg})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-within-putseg.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{getseg-putseg-induction} \\  
\=\+{\rm{getseg-putseg-induction}}\,({\it{i\/}}, {\it{k\/}}, {\it{s\/}}, {\it{n\/}})\index{getseg-putseg-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{k\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf elseif }{\rm{listp}}\,({\it{s\/}}) \\ 
{\bf then }{\rm{getseg-putseg-induction}}\,($1\;+$ {\it{i\/}}, {\it{k\/}} $-\;1$, {\rm{cdr}}\,({\it{s\/}}), $1\;+$ {\it{n\/}})\index{getseg-putseg-induction} \\ 
{\bf else }{\tt{'}}{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  putseg-has-no-effect \\ \index{putseg-has-no-effect}
({\it{n\/}} $\not<$ {\rm{length}}\,({\it{l\/}})\index{length}) $\rightarrow$ ({\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg} $=$ {\it{l\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable putseg-has-no-effect.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putseg-cons2 \\ \index{putseg-cons2}
({\it{n\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ ({\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\rm{cons}}\,({\it{a\/}}, {\it{b\/}}))\index{putseg} $=$ {\rm{cons}}\,({\it{a\/}}, {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}} $-\;1$, {\it{b\/}})\index{putseg}))
\end{tabbing}


\noindent{\sc Event}:   Disable putseg-cons2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-around-putseg-proof \\ \index{getseg-around-putseg-proof}
\=\+(\=\+({\it{i\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\it{n\/}} $<$ {\it{i\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ ({\it{n\/}} $+$ {\rm{length}}\,({\it{s\/}})\index{length})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }({\it{i\/}} $+$ {\it{k\/}}) $<$ ({\it{n\/}} $+$ {\rm{length}}\,({\it{s\/}})\index{length}) \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getseg}}\,({\it{i\/}}, {\it{k\/}}, {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg})\index{getseg} $=$ {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}} $-$ {\it{i\/}}, {\rm{getseg}}\,({\it{i\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg})\index{putseg})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-around-putseg-proof.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-casesplit \\ \index{numberp-casesplit}
({\it{a\/}} $\in\;${\bf{N}}${}$) $\vee$ ({\it{a\/}} $\not\in\;${\bf{N}}${}$)
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  getseg-around-putseg \\ \index{getseg-around-putseg}
\=\+(\=\+\=\+{\bf if }{\it{n\/}} $<$ {\it{i\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ ({\it{n\/}} $+$ {\rm{length}}\,({\it{s\/}})\index{length})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }({\it{i\/}} $+$ {\it{k\/}}) $<$ ({\it{n\/}} $+$ {\rm{length}}\,({\it{s\/}})\index{length})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getseg}}\,({\it{i\/}}, {\it{k\/}}, {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg})\index{getseg} $=$ {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}} $-$ {\it{i\/}}, {\rm{getseg}}\,({\it{i\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg})\index{putseg})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-around-putseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putseg-nil-segment \\ \index{putseg-nil-segment}
{\rm{putseg}}\,({\tt{'}}{\tt{nil}}, {\it{n\/}}, {\it{l\/}})\index{putseg} $=$ {\it{l\/}}
\end{tabbing}


\noindent{\sc Event}:   Disable putseg-nil-segment.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putseg-non-list-segment \\ \index{putseg-non-list-segment}
($\neg$ {\rm{listp}}\,({\it{s\/}})) $\rightarrow$ ({\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg} $=$ {\it{l\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable putseg-non-list-segment.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-up-putseg-on-segment-cons \\ \index{open-up-putseg-on-segment-cons}
\=\+(\=\+({\it{n\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ ({\it{n\/}} $+$ {\rm{length}}\,({\rm{cons}}\,({\it{a\/}}, {\it{b\/}}))\index{length})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{putseg}}\,({\rm{cons}}\,({\it{a\/}}, {\it{b\/}}), {\it{n\/}}, {\it{l\/}})\index{putseg} $=$ {\rm{putnth}}\,({\it{a\/}}, {\it{n\/}}, {\rm{putseg}}\,({\it{b\/}}, {\tt{'}}{\tt{1}} $+$ {\it{n\/}}, {\it{l\/}})\index{putseg})\index{putnth})\-
\end{tabbing}


\noindent{\sc Event}:   Disable open-up-putseg-on-segment-cons.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putseg-cons1 \\ \index{putseg-cons1}
\=\+(({\it{n\/}} $\simeq {\tt{0}}$) $\wedge$ {\rm{listp}}\,({\it{s\/}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\rm{cons}}\,({\it{a\/}}, {\it{b\/}}))\index{putseg} $=$ {\rm{cons}}\,({\rm{car}}\,({\it{s\/}}), {\rm{putseg}}\,({\rm{cdr}}\,({\it{s\/}}), {\it{n\/}}, {\it{b\/}})\index{putseg}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable putseg-cons1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putseg-getseg-coincidence \\ \index{putseg-getseg-coincidence}
({\it{i\/}} $=$ {\it{n\/}}) $\rightarrow$ ({\rm{putseg}}\,({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg}, {\it{i\/}}, {\it{l\/}})\index{putseg} $=$ {\it{l\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable putseg-getseg-coincidence.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  equality-of-getnth-backchain-proof \\ \index{equality-of-getnth-backchain-pr!oof}
\=\+(\=\+\=\+{\bf if }{\it{i\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$((({\it{i\/}} $-$ {\it{n\/}}) $<$ {\it{k\/}}) $\wedge$ ({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l1\/}})\index{getseg} $=$ {\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l2\/}})\index{getseg})))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\it{i\/}}, {\it{l1\/}})\index{getnth} $=$ {\rm{getnth}}\,({\it{i\/}}, {\it{l2\/}})\index{getnth})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{nested-intervals} \\  
\=\+{\rm{nested-intervals}}\,({\it{n1\/}}, {\it{k1\/}}, {\it{n2\/}}, {\it{k2\/}})\index{nested-intervals} \\ 
$=$$\;\;\;\;$(\=\+\=\+{\bf if }{\it{n2\/}} $<$ {\it{n1\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }({\it{n1\/}} $+$ {\it{k1\/}}) $<$ ({\it{n2\/}} $+$ {\it{k2\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{strange-induction} \\  
\=\+{\rm{strange-induction}}\,({\it{a\/}}, {\it{b\/}}, {\it{c\/}}, {\it{d\/}})\index{strange-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{a\/}} $\simeq {\tt{0}}$) $\vee$ ({\it{b\/}} $\simeq {\tt{0}}$)$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf else }{\rm{strange-induction}}\,({\it{a\/}} $-\;1$, {\it{b\/}} $-\;1$, $1\;+$ {\it{c\/}}, $1\;+$ {\it{d\/}})\index{strange-induction}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plus-arg2-must-be-zero \\ \index{plus-arg2-must-be-zero}
\=\+(\=\+\=\+{\bf if }{\it{i\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $<$ ({\it{i\/}} $+$ {\it{j\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\it{j\/}} $\simeq {\tt{0}}$)\-
\end{tabbing}


\noindent{\sc Event}:   Disable plus-arg2-must-be-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-must-be-nil \\ \index{getseg-must-be-nil}
\=\+(\=\+\=\+{\bf if }{\it{i\/}} $<$ {\it{n\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $<$ ({\it{i\/}} $+$ {\it{j\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getseg}}\,({\it{i\/}}, {\it{j\/}}, {\it{l\/}})\index{getseg} $=$ {\tt{'}}{\tt{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-must-be-nil.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  equality-of-getseg-backchain-base-case \\ \index{equality-of-getseg-backchain-ba!se-case}
\=\+(\=\+(({\it{j\/}} $\simeq {\tt{0}}$) $\vee$ ({\it{k\/}} $\simeq {\tt{0}}$)) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{i\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{nested-intervals}}\,({\it{n\/}}, {\it{k\/}}, {\it{i\/}}, {\it{j\/}})\index{nested-intervals} \\ 
$\wedge$$\;\;\;\;$({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l1\/}})\index{getseg} $=$ {\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l2\/}})\index{getseg}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getseg}}\,({\it{i\/}}, {\it{j\/}}, {\it{l1\/}})\index{getseg} $=$ {\rm{getseg}}\,({\it{i\/}}, {\it{j\/}}, {\it{l2\/}})\index{getseg})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equality-of-getseg-backchain-induction-step-case1 \\ \index{equality-of-getseg-backchain-in!duction-step-case1}
\=\+(\=\+({\it{i\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{j\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{k\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+(\=\+{\rm{nested-intervals}}\,($1\;+$ {\it{n\/}}, {\it{k\/}} $-\;1$, $1\;+$ {\it{i\/}}, {\it{j\/}} $-\;1$)\index{nested-intervals} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getseg}}\,($1\;+$ {\it{n\/}}, {\it{k\/}} $-\;1$, {\it{l1\/}})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,($1\;+$ {\it{n\/}}, {\it{k\/}} $-\;1$, {\it{l2\/}})\index{getseg})\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,($1\;+$ {\it{i\/}}, {\it{j\/}} $-\;1$, {\it{l1\/}})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,($1\;+$ {\it{i\/}}, {\it{j\/}} $-\;1$, {\it{l2\/}})\index{getseg})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{nested-intervals}}\,({\it{n\/}}, {\it{k\/}}, {\it{i\/}}, {\it{j\/}})\index{nested-intervals} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l1\/}})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l2\/}})\index{getseg})\- \\ 
$\wedge$$\;\;\;\;$({\it{i\/}} $=$ {\it{n\/}}))\-)\-)\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getseg}}\,({\it{i\/}}, {\it{j\/}}, {\it{l1\/}})\index{getseg} $=$ {\rm{getseg}}\,({\it{i\/}}, {\it{j\/}}, {\it{l2\/}})\index{getseg})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equality-of-getseg-backchain-induction-step-case2 \\ \index{equality-of-getseg-backchain-in!duction-step-case2}
\=\+(\=\+({\it{i\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{j\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{k\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+(\=\+{\rm{nested-intervals}}\,($1\;+$ {\it{n\/}}, {\it{k\/}} $-\;1$, $1\;+$ {\it{i\/}}, {\it{j\/}} $-\;1$)\index{nested-intervals} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getseg}}\,($1\;+$ {\it{n\/}}, {\it{k\/}} $-\;1$, {\it{l1\/}})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,($1\;+$ {\it{n\/}}, {\it{k\/}} $-\;1$, {\it{l2\/}})\index{getseg})\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,($1\;+$ {\it{i\/}}, {\it{j\/}} $-\;1$, {\it{l1\/}})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,($1\;+$ {\it{i\/}}, {\it{j\/}} $-\;1$, {\it{l2\/}})\index{getseg})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{nested-intervals}}\,({\it{n\/}}, {\it{k\/}}, {\it{i\/}}, {\it{j\/}})\index{nested-intervals} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l1\/}})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l2\/}})\index{getseg})\- \\ 
$\wedge$$\;\;\;\;$({\it{n\/}} $<$ {\it{i\/}}))\-)\-)\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getseg}}\,({\it{i\/}}, {\it{j\/}}, {\it{l1\/}})\index{getseg} $=$ {\rm{getseg}}\,({\it{i\/}}, {\it{j\/}}, {\it{l2\/}})\index{getseg})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equality-of-getseg-backchain-induction-step \\ \index{equality-of-getseg-backchain-in!duction-step}
\=\+(\=\+({\it{i\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{j\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{k\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+(\=\+{\rm{nested-intervals}}\,($1\;+$ {\it{n\/}}, {\it{k\/}} $-\;1$, $1\;+$ {\it{i\/}}, {\it{j\/}} $-\;1$)\index{nested-intervals} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getseg}}\,($1\;+$ {\it{n\/}}, {\it{k\/}} $-\;1$, {\it{l1\/}})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,($1\;+$ {\it{n\/}}, {\it{k\/}} $-\;1$, {\it{l2\/}})\index{getseg})\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,($1\;+$ {\it{i\/}}, {\it{j\/}} $-\;1$, {\it{l1\/}})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,($1\;+$ {\it{i\/}}, {\it{j\/}} $-\;1$, {\it{l2\/}})\index{getseg})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{nested-intervals}}\,({\it{n\/}}, {\it{k\/}}, {\it{i\/}}, {\it{j\/}})\index{nested-intervals} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l1\/}})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l2\/}})\index{getseg})\-)\-)\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getseg}}\,({\it{i\/}}, {\it{j\/}}, {\it{l1\/}})\index{getseg} $=$ {\rm{getseg}}\,({\it{i\/}}, {\it{j\/}}, {\it{l2\/}})\index{getseg})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equality-of-getseg-backchain-proof \\ \index{equality-of-getseg-backchain-pr!oof}
\=\+(\=\+({\it{i\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{nested-intervals}}\,({\it{n\/}}, {\it{k\/}}, {\it{i\/}}, {\it{j\/}})\index{nested-intervals} \\ 
$\wedge$$\;\;\;\;$({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l1\/}})\index{getseg} $=$ {\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l2\/}})\index{getseg}))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getseg}}\,({\it{i\/}}, {\it{j\/}}, {\it{l1\/}})\index{getseg} $=$ {\rm{getseg}}\,({\it{i\/}}, {\it{j\/}}, {\it{l2\/}})\index{getseg})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equality-of-getseg-backchain \\ \index{equality-of-getseg-backchain}
\=\+({\rm{nested-intervals}}\,({\it{n\/}}, {\it{k\/}}, {\it{i\/}}, {\it{j\/}})\index{nested-intervals} $\wedge$ ({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l1\/}})\index{getseg} $=$ {\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l2\/}})\index{getseg})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{getseg}}\,({\it{i\/}}, {\it{j\/}}, {\it{l1\/}})\index{getseg} $=$ {\rm{getseg}}\,({\it{i\/}}, {\it{j\/}}, {\it{l2\/}})\index{getseg})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{getnth2}$\;\;$
{\rm{getnth2}}\,({\it{i\/}}, {\it{j\/}}, {\it{l\/}})\index{getnth2} $=$ {\rm{getnth}}\,({\it{j\/}}, {\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{getnth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{putnth2} \\  
{\rm{putnth2}}\,({\it{v\/}}, {\it{i\/}}, {\it{j\/}}, {\it{l\/}})\index{putnth2} $=$ {\rm{putnth}}\,({\rm{putnth}}\,({\it{v\/}}, {\it{j\/}}, {\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{putnth}, {\it{i\/}}, {\it{l\/}})\index{putnth}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plistp-putnth2 \\ \index{plistp-putnth2}
{\rm{plistp}}\,({\it{l\/}})\index{plistp} $\rightarrow$ {\rm{plistp}}\,({\rm{putnth2}}\,({\it{v\/}}, {\it{i\/}}, {\it{j\/}}, {\it{l\/}})\index{putnth2})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-putnth2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-putnth2 \\ \index{length-putnth2}
{\rm{length}}\,({\rm{putnth2}}\,({\it{v\/}}, {\it{i\/}}, {\it{j\/}}, {\it{l\/}})\index{putnth2})\index{length} $=$ {\rm{length}}\,({\it{l\/}})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-putnth2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-putnth-coincidence1 \\ \index{getnth-putnth-coincidence1}
\=\+(({\rm{fix}}\,({\it{i\/}}) $=$ {\rm{fix}}\,({\it{j\/}})) $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\it{i\/}}, {\rm{putnth}}\,({\it{v\/}}, {\it{j\/}}, {\it{l\/}})\index{putnth})\index{getnth} $=$ {\it{v\/}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-putnth-coincidence1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth2-putnth2-coincidence \\ \index{getnth2-putnth2-coincidence}
\=\+(({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) $\wedge$ ({\it{j\/}} $<$ {\rm{length}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{length})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth2}}\,({\it{i\/}}, {\it{j\/}}, {\rm{putnth2}}\,({\it{v\/}}, {\it{i\/}}, {\it{j\/}}, {\it{l\/}})\index{putnth2})\index{getnth2} $=$ {\it{v\/}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getnth2-putnth2-coincidence.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth2-putnth2-non-interference1 \\ \index{getnth2-putnth2-non-interference!1}
({\rm{fix}}\,({\it{i\/}}) $\not=$ {\rm{fix}}\,({\it{x\/}})) $\rightarrow$ ({\rm{getnth2}}\,({\it{i\/}}, {\it{j\/}}, {\rm{putnth2}}\,({\it{v\/}}, {\it{x\/}}, {\it{y\/}}, {\it{l\/}})\index{putnth2})\index{getnth2} $=$ {\rm{getnth2}}\,({\it{i\/}}, {\it{j\/}}, {\it{l\/}})\index{getnth2})
\end{tabbing}


\noindent{\sc Event}:   Disable getnth2-putnth2-non-interference1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth2-putnth2-non-interference2 \\ \index{getnth2-putnth2-non-interference!2}
\=\+(({\rm{fix}}\,({\it{i\/}}) $=$ {\rm{fix}}\,({\it{x\/}})) $\wedge$ (({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) $\wedge$ ({\rm{fix}}\,({\it{j\/}}) $\not=$ {\rm{fix}}\,({\it{y\/}})))) \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth2}}\,({\it{i\/}}, {\it{j\/}}, {\rm{putnth2}}\,({\it{v\/}}, {\it{x\/}}, {\it{y\/}}, {\it{l\/}})\index{putnth2})\index{getnth2} $=$ {\rm{getnth2}}\,({\it{i\/}}, {\it{j\/}}, {\it{l\/}})\index{getnth2})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getnth2-putnth2-non-interference2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  fixlength-of-length-0 \\ \index{fixlength-of-length-0}
({\it{n\/}} $\simeq {\tt{0}}$) $\rightarrow$ ({\rm{fixlength}}\,({\it{n\/}}, {\it{l\/}}, {\it{x\/}})\index{fixlength} $=$ {\tt{'}}{\tt{nil}})
\end{tabbing}


\noindent{\sc Event}:   Disable fixlength-of-length-0.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  fixlength-idempotence \\ \index{fixlength-idempotence}
{\rm{fixlength}}\,({\it{n\/}}, {\rm{fixlength}}\,({\it{n\/}}, {\it{l\/}}, {\it{a\/}})\index{fixlength}, {\it{b\/}})\index{fixlength} $=$ {\rm{fixlength}}\,({\it{n\/}}, {\it{l\/}}, {\it{a\/}})\index{fixlength}
\end{tabbing}


\noindent{\sc Event}:   Disable fixlength-idempotence.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  fixlength-noop \\ \index{fixlength-noop}
({\rm{plistp}}\,({\it{l\/}})\index{plistp} $\wedge$ ({\it{n\/}} $=$ {\rm{length}}\,({\it{l\/}})\index{length})) $\rightarrow$ ({\rm{fixlength}}\,({\it{n\/}}, {\it{l\/}}, {\it{default\/}})\index{fixlength} $=$ {\it{l\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable fixlength-noop.

\addvspace{18pt}

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

\begin{tabbing}{\sc Theorem}:  plistp-reverse \\ \index{plistp-reverse}
{\rm{plistp}}\,({\rm{reverse}}\,({\it{a\/}})\index{reverse})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-reverse.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable reverse-append.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  reverse-list1 \\ \index{reverse-list1}
{\rm{reverse}}\,({\rm{cons}}\,({\it{a\/}}, {\tt{'}}{\tt{nil}}))\index{reverse} $=$ {\rm{cons}}\,({\it{a\/}}, {\tt{'}}{\tt{nil}})
\end{tabbing}


\noindent{\sc Event}:   Disable reverse-list1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  reverse-list2 \\ \index{reverse-list2}
{\rm{reverse}}\,({\rm{cons}}\,({\it{a\/}}, {\rm{cons}}\,({\it{a\/}}, {\tt{'}}{\tt{nil}})))\index{reverse} $=$ {\rm{cons}}\,({\it{a\/}}, {\rm{cons}}\,({\it{a\/}}, {\tt{'}}{\tt{nil}}))
\end{tabbing}


\noindent{\sc Event}:   Disable reverse-list2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  reverse-reverse \\ \index{reverse-reverse}
{\rm{plistp}}\,({\it{l\/}})\index{plistp} $\rightarrow$ ({\rm{reverse}}\,({\rm{reverse}}\,({\it{l\/}})\index{reverse})\index{reverse} $=$ {\it{l\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable reverse-reverse.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{finite-numberp}$\;\;$
{\rm{finite-numberp}}\,({\it{n\/}}, {\it{lub\/}})\index{finite-numberp} $=$ (({\it{n\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{n\/}} $<$ {\it{lub\/}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{number-listp} \\  
\=\+{\rm{number-listp}}\,({\it{l\/}})\index{number-listp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}})$\;\;${\bf then }({\rm{car}}\,({\it{l\/}}) $\in\;${\bf{N}}${}$) $\wedge$ {\rm{number-listp}}\,({\rm{cdr}}\,({\it{l\/}}))\index{number-listp} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{finite-number-listp} \\  
\=\+{\rm{finite-number-listp}}\,({\it{l\/}}, {\it{lub\/}})\index{finite-number-listp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}}) \\ 
{\bf then }{\rm{finite-numberp}}\,({\rm{car}}\,({\it{l\/}}), {\it{lub\/}})\index{finite-numberp} $\wedge$ {\rm{finite-number-listp}}\,({\rm{cdr}}\,({\it{l\/}}), {\it{lub\/}})\index{finite-number-listp} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{non-zero-listp} \\  
\=\+{\rm{non-zero-listp}}\,({\it{l\/}})\index{non-zero-listp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}})$\;\;${\bf then }({\rm{car}}\,({\it{l\/}}) $\not\simeq {\tt{0}}$) $\wedge$ {\rm{non-zero-listp}}\,({\rm{cdr}}\,({\it{l\/}}))\index{non-zero-listp} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  non-1-finite-number-is-zero \\ \index{non-1-finite-number-is-zero}
({\rm{finite-numberp}}\,({\it{a\/}}, {\tt{'}}{\tt{2}})\index{finite-numberp} $\wedge$ ({\it{a\/}} $\not=$ {\tt{'}}{\tt{1}})) $\rightarrow$ ({\it{a\/}} $=$ {\tt{'}}{\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-numberp-member \\ \index{finite-numberp-member}
({\rm{finite-number-listp}}\,({\it{b\/}}, {\it{lub\/}})\index{finite-number-listp} $\wedge$ ({\it{x\/}} $\in$ {\it{b\/}})) $\rightarrow$ {\rm{finite-numberp}}\,({\it{x\/}}, {\it{lub\/}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-member.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  a-finite-number-is-lessp-than-its-lub \\ \index{a-finite-number-is-lessp-than-it!s-lub}
{\rm{finite-numberp}}\,({\it{n\/}}, {\it{lub\/}})\index{finite-numberp} $\rightarrow$ (({\it{n\/}} $<$ {\it{lub\/}}) $=$ {\tt{'}}{\tt{*1*true}})
\end{tabbing}


\noindent{\sc Event}:   Disable a-finite-number-is-lessp-than-its-lub.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  a-finite-number-is-a-number \\ \index{a-finite-number-is-a-number}
{\rm{finite-numberp}}\,({\it{n\/}}, {\it{lub\/}})\index{finite-numberp} $\rightarrow$ ({\it{n\/}} $\in\;${\bf{N}}${}$)
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-numberp-from-smaller-lub \\ \index{finite-numberp-from-smaller-lub}
({\rm{finite-numberp}}\,({\it{n\/}}, {\it{i\/}})\index{finite-numberp} $\wedge$ ({\it{i\/}} $<$ {\it{j\/}})) $\rightarrow$ {\rm{finite-numberp}}\,({\it{n\/}}, {\it{j\/}})\index{finite-numberp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-number-sub1 \\ \index{finite-number-sub1}
{\rm{finite-numberp}}\,({\it{a\/}}, {\it{b\/}})\index{finite-numberp} $\rightarrow$ {\rm{finite-numberp}}\,({\it{a\/}} $-\;1$, {\it{b\/}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-sub1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-remainder \\ \index{finite-numberp-remainder}
({\it{b\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ {\rm{finite-numberp}}\,({\it{a\/}} ${}${\bf{mod}}${}$ {\it{b\/}}, {\it{b\/}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-remainder.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  a-finite-number-list-is-a-number-list \\ \index{a-finite-number-list-is-a-numbe!r-list}
{\rm{finite-number-listp}}\,({\it{l\/}}, {\it{lub\/}})\index{finite-number-listp} $\rightarrow$ {\rm{number-listp}}\,({\it{l\/}})\index{number-listp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-numberp-getnth \\ \index{finite-numberp-getnth}
\=\+({\rm{finite-number-listp}}\,({\it{l\/}}, {\it{lub\/}})\index{finite-number-listp} $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth}, {\it{lub\/}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-getnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-getnth \\ \index{numberp-getnth}
({\rm{finite-number-listp}}\,({\it{l\/}}, {\it{lub\/}})\index{finite-number-listp} $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) $\rightarrow$ ({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth} $\in\;${\bf{N}}${}$)
\end{tabbing}


\noindent{\sc Event}:   Disable numberp-getnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-getnth \\ \index{lessp-getnth}
\=\+({\rm{finite-number-listp}}\,({\it{l\/}}, {\it{lub\/}})\index{finite-number-listp} $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth} $<$ {\it{lub\/}}) $=$ {\tt{'}}{\tt{*1*true}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-getnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-getnth-linear \\ \index{lessp-getnth-linear}
\=\+({\rm{finite-number-listp}}\,({\it{l\/}}, {\it{lub\/}})\index{finite-number-listp} $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth} $<$ {\it{lub\/}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-getnth-linear.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  element-of-non-zero-list-is-a-number \\ \index{element-of-non-zero-list-is-a-n!umber}
({\rm{non-zero-listp}}\,({\it{l\/}})\index{non-zero-listp} $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) $\rightarrow$ ({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth} $\in\;${\bf{N}}${}$)
\end{tabbing}


\noindent{\sc Event}:   Disable element-of-non-zero-list-is-a-number.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  element-of-non-zero-list-is-non-zero \\ \index{element-of-non-zero-list-is-non!-zero}
({\rm{non-zero-listp}}\,({\it{l\/}})\index{non-zero-listp} $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) $\rightarrow$ ({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth} $\not=$ {\tt{'}}{\tt{0}})
\end{tabbing}


\noindent{\sc Event}:   Disable element-of-non-zero-list-is-non-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-list \\ \index{finite-number-listp-list}
{\rm{finite-numberp}}\,({\it{n\/}}, {\it{lub\/}})\index{finite-numberp} $\rightarrow$ {\rm{finite-number-listp}}\,({\rm{cons}}\,({\it{n\/}}, {\tt{'}}{\tt{nil}}), {\it{lub\/}})\index{finite-number-listp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-list.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-append \\ \index{finite-number-listp-append}
\=\+({\rm{finite-number-listp}}\,({\it{a\/}}, {\it{lub\/}})\index{finite-number-listp} $\wedge$ {\rm{finite-number-listp}}\,({\it{b\/}}, {\it{lub\/}})\index{finite-number-listp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-listp}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}), {\it{lub\/}})\index{finite-number-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-append.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-remove \\ \index{finite-number-listp-remove}
{\rm{finite-number-listp}}\,({\it{l\/}}, {\it{lub\/}})\index{finite-number-listp} $\rightarrow$ {\rm{finite-number-listp}}\,({\rm{remove}}\,({\it{x\/}}, {\it{l\/}})\index{remove}, {\it{lub\/}})\index{finite-number-listp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-remove.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-permutation \\ \index{finite-number-listp-permutation}
\=\+({\rm{finite-number-listp}}\,({\it{b\/}}, {\it{lub\/}})\index{finite-number-listp} $\wedge$ {\rm{permutation}}\,({\it{a\/}}, {\it{b\/}})\index{permutation}) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-listp}}\,({\it{a\/}}, {\it{lub\/}})\index{finite-number-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-permutation.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-putnth \\ \index{finite-number-listp-putnth}
\=\+({\rm{finite-number-listp}}\,({\it{l\/}}, {\it{lub\/}})\index{finite-number-listp} $\wedge$ {\rm{finite-numberp}}\,({\it{v\/}}, {\it{lub\/}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-listp}}\,({\rm{putnth}}\,({\it{v\/}}, {\it{n\/}}, {\it{l\/}})\index{putnth}, {\it{lub\/}})\index{finite-number-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-putnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-getseg \\ \index{finite-number-listp-getseg}
\=\+(\=\+{\rm{finite-number-listp}}\,({\it{l\/}}, {\it{lub\/}})\index{finite-number-listp} \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ ({\it{n\/}} $+$ {\it{k\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-listp}}\,({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg}, {\it{lub\/}})\index{finite-number-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-getseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-putseg \\ \index{finite-number-listp-putseg}
\=\+({\rm{finite-number-listp}}\,({\it{l\/}}, {\it{lub\/}})\index{finite-number-listp} $\wedge$ {\rm{finite-number-listp}}\,({\it{s\/}}, {\it{lub\/}})\index{finite-number-listp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-listp}}\,({\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg}, {\it{lub\/}})\index{finite-number-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-putseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-fixlength \\ \index{finite-number-listp-fixlength}
\=\+({\rm{finite-number-listp}}\,({\it{l\/}}, {\it{lub\/}})\index{finite-number-listp} $\wedge$ {\rm{finite-numberp}}\,({\it{default\/}}, {\it{lub\/}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-listp}}\,({\rm{fixlength}}\,({\it{n\/}}, {\it{l\/}}, {\it{default\/}})\index{fixlength}, {\it{lub\/}})\index{finite-number-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-fixlength.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-for-zero-list \\ \index{finite-number-listp-for-zero-li!st}
({\it{lub\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ {\rm{finite-number-listp}}\,({\rm{fixlength}}\,({\it{n\/}}, {\tt{'}}{\tt{nil}}, {\tt{'}}{\tt{0}})\index{fixlength}, {\it{lub\/}})\index{finite-number-listp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-for-zero-list.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-from-smaller-lub \\ \index{finite-number-listp-from-smalle!r-lub}
({\rm{finite-number-listp}}\,({\it{l\/}}, {\it{i\/}})\index{finite-number-listp} $\wedge$ ({\it{i\/}} $<$ {\it{j\/}})) $\rightarrow$ {\rm{finite-number-listp}}\,({\it{l\/}}, {\it{j\/}})\index{finite-number-listp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  non-zero-listp-list \\ \index{non-zero-listp-list}
({\it{a\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ {\rm{non-zero-listp}}\,({\rm{cons}}\,({\it{a\/}}, {\tt{'}}{\tt{nil}}))\index{non-zero-listp}
\end{tabbing}


\noindent{\sc Event}:   Disable non-zero-listp-list.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  non-zero-listp-append \\ \index{non-zero-listp-append}
({\rm{non-zero-listp}}\,({\it{a\/}})\index{non-zero-listp} $\wedge$ {\rm{non-zero-listp}}\,({\it{b\/}})\index{non-zero-listp}) $\rightarrow$ {\rm{non-zero-listp}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{non-zero-listp}
\end{tabbing}


\noindent{\sc Event}:   Disable non-zero-listp-append.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  non-zero-listp-putnth \\ \index{non-zero-listp-putnth}
({\rm{non-zero-listp}}\,({\it{l\/}})\index{non-zero-listp} $\wedge$ ({\it{v\/}} $\not\simeq {\tt{0}}$)) $\rightarrow$ {\rm{non-zero-listp}}\,({\rm{putnth}}\,({\it{v\/}}, {\it{n\/}}, {\it{l\/}})\index{putnth})\index{non-zero-listp}
\end{tabbing}


\noindent{\sc Event}:   Disable non-zero-listp-putnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  non-zero-listp-getseg \\ \index{non-zero-listp-getseg}
\=\+(\=\+{\rm{non-zero-listp}}\,({\it{l\/}})\index{non-zero-listp} \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ ({\it{n\/}} $+$ {\it{k\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{non-zero-listp}}\,({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg})\index{non-zero-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable non-zero-listp-getseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  non-zero-listp-putseg \\ \index{non-zero-listp-putseg}
({\rm{non-zero-listp}}\,({\it{l\/}})\index{non-zero-listp} $\wedge$ {\rm{non-zero-listp}}\,({\it{s\/}})\index{non-zero-listp}) $\rightarrow$ {\rm{non-zero-listp}}\,({\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg})\index{non-zero-listp}
\end{tabbing}


\noindent{\sc Event}:   Disable non-zero-listp-putseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  non-zero-listp-fixlength \\ \index{non-zero-listp-fixlength}
\=\+({\rm{non-zero-listp}}\,({\it{l\/}})\index{non-zero-listp} $\wedge$ ({\it{default\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;${\rm{non-zero-listp}}\,({\rm{fixlength}}\,({\it{n\/}}, {\it{l\/}}, {\it{default\/}})\index{fixlength})\index{non-zero-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable non-zero-listp-fixlength.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  car-nthcdr \\ \index{car-nthcdr}
({\it{n\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) $\rightarrow$ ({\rm{car}}\,({\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr}) $=$ {\rm{getnth}}\,({\it{n\/}}, {\it{l\/}})\index{getnth})
\end{tabbing}


\noindent{\sc Event}:   Disable car-nthcdr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cdr-nthcdr \\ \index{cdr-nthcdr}
({\it{n\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) $\rightarrow$ ({\rm{cdr}}\,({\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr}) $=$ {\rm{nthcdr}}\,($1\;+$ {\it{n\/}}, {\it{l\/}})\index{nthcdr})
\end{tabbing}


\noindent{\sc Event}:   Disable cdr-nthcdr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  listp-nthcdr \\ \index{listp-nthcdr}
({\it{n\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) $\rightarrow$ {\rm{listp}}\,({\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr})
\end{tabbing}


\noindent{\sc Event}:   Disable listp-nthcdr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-firstn \\ \index{plistp-firstn}
{\rm{plistp}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{l\/}})\index{firstn})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-firstn.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-nthcdr \\ \index{plistp-nthcdr}
{\rm{plistp}}\,({\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr})\index{plistp} $=$ {\rm{plistp}}\,({\it{l\/}})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-nthcdr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-firstn \\ \index{length-firstn}
\=\+\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ {\it{n\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{length}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{l\/}})\index{firstn})\index{length} $=$ {\rm{fix}}\,({\it{n\/}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-firstn.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-nthcdr \\ \index{length-nthcdr}
{\rm{length}}\,({\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr})\index{length} $=$ ({\rm{length}}\,({\it{l\/}})\index{length} $-$ {\it{n\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-nthcdr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  firstn-zero \\ \index{firstn-zero}
({\it{k\/}} $\simeq {\tt{0}}$) $\rightarrow$ ({\rm{firstn}}\,({\it{k\/}}, {\it{l\/}})\index{firstn} $=$ {\tt{'}}{\tt{nil}})
\end{tabbing}


\noindent{\sc Event}:   Disable firstn-zero.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable nthcdr-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  nthcdr-with-large-n \\ \index{nthcdr-with-large-n}
\=\+(\=\+{\rm{plistp}}\,({\it{l\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr} $=$ {\tt{'}}{\tt{nil}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable nthcdr-with-large-n.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  firstn-for-length \\ \index{firstn-for-length}
({\rm{plistp}}\,({\it{l\/}})\index{plistp} $\wedge$ ({\it{n\/}} $=$ {\rm{length}}\,({\it{l\/}})\index{length})) $\rightarrow$ ({\rm{firstn}}\,({\it{n\/}}, {\it{l\/}})\index{firstn} $=$ {\it{l\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable firstn-for-length.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  append-firstn-nthcdr \\ \index{append-firstn-nthcdr}
{\rm{append}}\,({\rm{firstn}}\,({\it{i\/}}, {\it{l\/}})\index{firstn}, {\rm{nthcdr}}\,({\it{i\/}}, {\it{l\/}})\index{nthcdr}) $=$ {\it{l\/}}
\end{tabbing}


\noindent{\sc Event}:   Disable append-firstn-nthcdr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  firstn-firstn \\ \index{firstn-firstn}
({\it{i\/}} $<$ {\it{n\/}}) $\rightarrow$ ({\rm{firstn}}\,({\it{i\/}}, {\rm{firstn}}\,({\it{n\/}}, {\it{l\/}})\index{firstn})\index{firstn} $=$ {\rm{firstn}}\,({\it{i\/}}, {\it{l\/}})\index{firstn})
\end{tabbing}


\noindent{\sc Event}:   Disable firstn-firstn.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  firstn-nthcdr \\ \index{firstn-nthcdr}
{\rm{plistp}}\,({\it{l\/}})\index{plistp} $\rightarrow$ ({\rm{firstn}}\,({\rm{length}}\,({\it{l\/}})\index{length} $-$ {\it{k\/}}, {\rm{nthcdr}}\,({\it{k\/}}, {\it{l\/}})\index{nthcdr})\index{firstn} $=$ {\rm{nthcdr}}\,({\it{k\/}}, {\it{l\/}})\index{nthcdr})
\end{tabbing}


\noindent{\sc Event}:   Disable firstn-nthcdr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  nthcdr-append-right \\ \index{nthcdr-append-right}
\=\+\=\+{\bf if }{\it{n\/}} $<$ {\rm{length}}\,({\it{a\/}})\index{length}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{nthcdr}}\,({\it{n\/}}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{nthcdr} $=$ {\rm{nthcdr}}\,({\it{n\/}} $-$ {\rm{length}}\,({\it{a\/}})\index{length}, {\it{b\/}})\index{nthcdr})\-
\end{tabbing}


\noindent{\sc Event}:   Disable nthcdr-append-right.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  nthcdr-append-left \\ \index{nthcdr-append-left}
\=\+\=\+{\bf if }{\rm{length}}\,({\it{a\/}})\index{length} $<$ {\it{n\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{nthcdr}}\,({\it{n\/}}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{nthcdr} $=$ {\rm{append}}\,({\rm{nthcdr}}\,({\it{n\/}}, {\it{a\/}})\index{nthcdr}, {\it{b\/}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable nthcdr-append-left.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tablep} \\  
\=\+{\rm{tablep}}\,({\it{n\/}}, {\it{l\/}})\index{tablep} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}}) \\ 
{\bf then }\=\+{\rm{plistp}}\,({\rm{car}}\,({\it{l\/}}))\index{plistp} \\ 
$\wedge$$\;\;\;\;$(({\rm{length}}\,({\rm{car}}\,({\it{l\/}}))\index{length} $=$ {\it{n\/}}) $\wedge$ {\rm{tablep}}\,({\it{n\/}}, {\rm{cdr}}\,({\it{l\/}}))\index{tablep})\- \\ 
{\bf else }{\it{l\/}} $=$ {\tt{'}}{\tt{nil}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-of-nthcdr-goes-down \\ \index{length-of-nthcdr-goes-down}
\=\+({\rm{listp}}\,({\it{l\/}}) $\wedge$ ({\it{n\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{length}}\,({\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr})\index{length} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) $=$ {\tt{'}}{\tt{*1*true}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-of-nthcdr-goes-down.

\addvspace{18pt}


\noindent{\sc Event}:   Enable length-of-nthcdr-goes-down.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{table} \\  
\=\+{\rm{table}}\,({\it{n\/}}, {\it{l\/}})\index{table} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\it{l\/}} \\ 
{\bf elseif }{\rm{listp}}\,({\it{l\/}})$\;\;${\bf then }{\rm{cons}}\,({\rm{getseg}}\,({\tt{'}}{\tt{0}}, {\it{n\/}}, {\it{l\/}})\index{getseg}, {\rm{table}}\,({\it{n\/}}, {\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr})\index{table}) \\ 
{\bf else }{\tt{'}}{\tt{nil}}$\;${\bf  endif}\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-of-nthcdr-goes-down.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{flatten} \\  
\=\+{\rm{flatten}}\,({\it{table\/}})\index{flatten} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{table\/}})$\;\;${\bf then }{\rm{append}}\,({\rm{car}}\,({\it{table\/}}), {\rm{flatten}}\,({\rm{cdr}}\,({\it{table\/}}))\index{flatten}) \\ 
{\bf else }{\tt{'}}{\tt{nil}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plistp-table \\ \index{plistp-table}
{\rm{plistp}}\,({\it{l\/}})\index{plistp} $\rightarrow$ {\rm{plistp}}\,({\rm{table}}\,({\it{n\/}}, {\it{l\/}})\index{table})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-table \\ \index{length-table}
\=\+(({\it{n\/}} $\not\simeq {\tt{0}}$) $\wedge$ (({\rm{length}}\,({\it{l\/}})\index{length} ${}${\bf{mod}}${}$ {\it{n\/}}) $=$ {\tt{'}}{\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{length}}\,({\rm{table}}\,({\it{n\/}}, {\it{l\/}})\index{table})\index{length} $=$ ({\rm{length}}\,({\it{l\/}})\index{length} $\div$ {\it{n\/}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tablep-table \\ \index{tablep-table}
({\it{n\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ {\rm{tablep}}\,({\it{n\/}}, {\rm{table}}\,({\it{n\/}}, {\it{l\/}})\index{table})\index{tablep}
\end{tabbing}


\noindent{\sc Event}:   Disable tablep-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-getnth-from-table \\ \index{length-getnth-from-table}
({\rm{tablep}}\,({\it{n\/}}, {\it{l\/}})\index{tablep} $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) $\rightarrow$ ({\rm{length}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{length} $=$ {\it{n\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plistp-getnth-from-table \\ \index{plistp-getnth-from-table}
({\rm{tablep}}\,({\it{n\/}}, {\it{l\/}})\index{tablep} $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) $\rightarrow$ {\rm{plistp}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{plistp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-getnth-table \\ \index{length-getnth-table}
\=\+(({\it{n\/}} $\not\simeq {\tt{0}}$) $\wedge$ ((({\rm{length}}\,({\it{l\/}})\index{length} ${}${\bf{mod}}${}$ {\it{n\/}}) $=$ {\tt{'}}{\tt{0}}) $\wedge$ ({\it{i\/}} $<$ ({\rm{length}}\,({\it{l\/}})\index{length} $\div$ {\it{n\/}})))) \\ 
$\rightarrow$$\;\;\;\;$({\rm{length}}\,({\rm{getnth}}\,({\it{i\/}}, {\rm{table}}\,({\it{n\/}}, {\it{l\/}})\index{table})\index{getnth})\index{length} $=$ {\it{n\/}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-getnth-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-getnth-table \\ \index{plistp-getnth-table}
\=\+(({\it{n\/}} $\not\simeq {\tt{0}}$) $\wedge$ ((({\rm{length}}\,({\it{l\/}})\index{length} ${}${\bf{mod}}${}$ {\it{n\/}}) $=$ {\tt{'}}{\tt{0}}) $\wedge$ ({\it{i\/}} $<$ ({\rm{length}}\,({\it{l\/}})\index{length} $\div$ {\it{n\/}})))) \\ 
$\rightarrow$$\;\;\;\;${\rm{plistp}}\,({\rm{getnth}}\,({\it{i\/}}, {\rm{table}}\,({\it{n\/}}, {\it{l\/}})\index{table})\index{getnth})\index{plistp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-getnth-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-equals-firstn-nthcdr \\ \index{getseg-equals-firstn-nthcdr}
\=\+(\=\+\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ {\it{n\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }({\rm{length}}\,({\it{l\/}})\index{length} $-$ {\it{n\/}}) $<$ {\it{k\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg} $=$ {\rm{firstn}}\,({\it{k\/}}, {\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr})\index{firstn})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-equals-firstn-nthcdr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-for-length \\ \index{getseg-for-length}
({\rm{plistp}}\,({\it{l\/}})\index{plistp} $\wedge$ ({\it{k\/}} $=$ {\rm{length}}\,({\it{l\/}})\index{length})) $\rightarrow$ ({\rm{getseg}}\,({\tt{'}}{\tt{0}}, {\it{k\/}}, {\it{l\/}})\index{getseg} $=$ {\it{l\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-for-length.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-flatten \\ \index{plistp-flatten}
{\rm{plistp}}\,({\rm{flatten}}\,({\it{table\/}})\index{flatten})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-flatten.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-flatten \\ \index{length-flatten}
(({\it{n\/}} $\not\simeq {\tt{0}}$) $\wedge$ {\rm{tablep}}\,({\it{n\/}}, {\it{l\/}})\index{tablep}) $\rightarrow$ ({\rm{length}}\,({\rm{flatten}}\,({\it{l\/}})\index{flatten})\index{length} $=$ ({\rm{length}}\,({\it{l\/}})\index{length} $*$ {\it{n\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable length-flatten.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  table-append \\ \index{table-append}
\=\+(({\it{n\/}} $\not\simeq {\tt{0}}$) $\wedge$ (({\rm{length}}\,({\it{a\/}})\index{length} ${}${\bf{mod}}${}$ {\it{n\/}}) $=$ {\tt{'}}{\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{table}}\,({\it{n\/}}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{table} $=$ {\rm{append}}\,({\rm{table}}\,({\it{n\/}}, {\it{a\/}})\index{table}, {\rm{table}}\,({\it{n\/}}, {\it{b\/}})\index{table}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable table-append.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  nthcdr-for-length \\ \index{nthcdr-for-length}
{\rm{plistp}}\,({\it{l\/}})\index{plistp} $\rightarrow$ ({\rm{nthcdr}}\,({\rm{length}}\,({\it{l\/}})\index{length}, {\it{l\/}})\index{nthcdr} $=$ {\tt{'}}{\tt{nil}})
\end{tabbing}


\noindent{\sc Event}:   Disable nthcdr-for-length.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  table-for-length \\ \index{table-for-length}
({\rm{plistp}}\,({\it{l\/}})\index{plistp} $\wedge$ ({\rm{length}}\,({\it{l\/}})\index{length} $\not\simeq {\tt{0}}$)) $\rightarrow$ ({\rm{table}}\,({\rm{length}}\,({\it{l\/}})\index{length}, {\it{l\/}})\index{table} $=$ {\rm{cons}}\,({\it{l\/}}, {\tt{'}}{\tt{nil}}))
\end{tabbing}


\noindent{\sc Event}:   Disable table-for-length.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  table-flatten \\ \index{table-flatten}
(({\it{n\/}} $\not\simeq {\tt{0}}$) $\wedge$ {\rm{tablep}}\,({\it{n\/}}, {\it{table\/}})\index{tablep}) $\rightarrow$ ({\rm{table}}\,({\it{n\/}}, {\rm{flatten}}\,({\it{table\/}})\index{flatten})\index{table} $=$ {\it{table\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable table-flatten.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  listp-table \\ \index{listp-table}
({\it{n\/}} $\not\simeq {\tt{0}}$) $\rightarrow$ ({\rm{listp}}\,({\rm{table}}\,({\it{n\/}}, {\it{l\/}})\index{table}) $=$ {\rm{listp}}\,({\it{l\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable listp-table.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{integer-nthcdr-induction} \\  
\=\+{\rm{integer-nthcdr-induction}}\,({\it{i\/}}, {\it{n\/}}, {\it{l\/}})\index{integer-nthcdr-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf elseif }{\rm{listp}}\,({\it{l\/}}) \\ 
{\bf then }\=\+{\bf if }{\it{i\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf else }{\rm{integer-nthcdr-induction}}\,({\it{i\/}} $-\;1$, {\it{n\/}}, {\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr})\index{integer-nthcdr-induction}$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  getnth-nthcdr \\ \index{getnth-nthcdr}
{\rm{getnth}}\,({\it{i\/}}, {\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr})\index{getnth} $=$ {\rm{getnth}}\,({\it{n\/}} $+$ {\it{i\/}}, {\it{l\/}})\index{getnth}
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-nthcdr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-nthcdr-proof \\ \index{getseg-nthcdr-proof}
({\it{i\/}} $\in\;${\bf{N}}${}$) $\rightarrow$ ({\rm{getseg}}\,({\it{i\/}}, {\it{k\/}}, {\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr})\index{getseg} $=$ {\rm{getseg}}\,({\it{n\/}} $+$ {\it{i\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg})
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-nthcdr-proof.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-nthcdr \\ \index{getseg-nthcdr}
{\rm{getseg}}\,({\it{i\/}}, {\it{k\/}}, {\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr})\index{getseg} $=$ {\rm{getseg}}\,({\it{n\/}} $+$ {\it{i\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg}
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-nthcdr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-table \\ \index{getnth-table}
\=\+((({\it{i\/}} $*$ {\it{n\/}}) $<$ {\rm{length}}\,({\it{l\/}})\index{length}) $\wedge$ ({\it{n\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\it{i\/}}, {\rm{table}}\,({\it{n\/}}, {\it{l\/}})\index{table})\index{getnth} $=$ {\rm{getseg}}\,({\it{i\/}} $*$ {\it{n\/}}, {\it{n\/}}, {\it{l\/}})\index{getseg})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-table-inverse \\ \index{getnth-table-inverse}
\=\+((({\it{i\/}} $*$ {\it{n\/}}) $<$ {\rm{length}}\,({\it{l\/}})\index{length}) $\wedge$ ({\it{n\/}} $\not\simeq {\tt{0}}$)) \\ 
$\rightarrow$$\;\;\;\;$({\rm{getseg}}\,({\it{i\/}} $*$ {\it{n\/}}, {\it{n\/}}, {\it{l\/}})\index{getseg} $=$ {\rm{getnth}}\,({\it{i\/}}, {\rm{table}}\,({\it{n\/}}, {\it{l\/}})\index{table})\index{getnth})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-table-inverse.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-getnth-from-table \\ \index{rewrite-getnth-from-table}
\=\+(\=\+({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{i\/}} $<$ {\it{n\/}}) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ ({\it{n\/}} $+$ ({\it{n\/}} $*$ {\it{j\/}}))$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\it{i\/}} $+$ ({\it{n\/}} $*$ {\it{j\/}}), {\it{l\/}})\index{getnth} $=$ {\rm{getnth}}\,({\it{i\/}}, {\rm{getnth}}\,({\it{j\/}}, {\rm{table}}\,({\it{n\/}}, {\it{l\/}})\index{table})\index{getnth})\index{getnth})\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-getnth-from-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-getnth-from-table0 \\ \index{rewrite-getnth-from-table0}
\=\+(\=\+({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ ({\it{n\/}} $+$ ({\it{n\/}} $*$ {\it{j\/}}))$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\it{n\/}} $*$ {\it{j\/}}, {\it{l\/}})\index{getnth} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{getnth}}\,({\it{j\/}}, {\rm{table}}\,({\it{n\/}}, {\it{l\/}})\index{table})\index{getnth})\index{getnth})\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-getnth-from-table0.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  nthcdr-nthcdr \\ \index{nthcdr-nthcdr}
{\rm{nthcdr}}\,({\it{i\/}}, {\rm{nthcdr}}\,({\it{j\/}}, {\it{l\/}})\index{nthcdr})\index{nthcdr} $=$ {\rm{nthcdr}}\,({\it{j\/}} $+$ {\it{i\/}}, {\it{l\/}})\index{nthcdr}
\end{tabbing}


\noindent{\sc Event}:   Disable nthcdr-nthcdr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putnth-nthcdr \\ \index{putnth-nthcdr}
{\rm{putnth}}\,({\it{v\/}}, {\it{i\/}}, {\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr})\index{putnth} $=$ {\rm{nthcdr}}\,({\it{n\/}}, {\rm{putnth}}\,({\it{v\/}}, {\it{n\/}} $+$ {\it{i\/}}, {\it{l\/}})\index{putnth})\index{nthcdr}
\end{tabbing}


\noindent{\sc Event}:   Disable putnth-nthcdr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putseg-nthcdr-proof \\ \index{putseg-nthcdr-proof}
({\it{i\/}} $\in\;${\bf{N}}${}$) $\rightarrow$ ({\rm{putseg}}\,({\it{s\/}}, {\it{i\/}}, {\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr})\index{putseg} $=$ {\rm{nthcdr}}\,({\it{n\/}}, {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}} $+$ {\it{i\/}}, {\it{l\/}})\index{putseg})\index{nthcdr})
\end{tabbing}


\noindent{\sc Event}:   Disable putseg-nthcdr-proof.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  putseg-nthcdr \\ \index{putseg-nthcdr}
{\rm{putseg}}\,({\it{s\/}}, {\it{i\/}}, {\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr})\index{putseg} $=$ {\rm{nthcdr}}\,({\it{n\/}}, {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}} $+$ {\it{i\/}}, {\it{l\/}})\index{putseg})\index{nthcdr}
\end{tabbing}


\noindent{\sc Event}:   Disable putseg-nthcdr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  nthcdr-putnth \\ \index{nthcdr-putnth}
({\it{n\/}} $<$ {\it{i\/}}) $\rightarrow$ ({\rm{nthcdr}}\,({\it{i\/}}, {\rm{putnth}}\,({\it{v\/}}, {\it{n\/}}, {\it{l\/}})\index{putnth})\index{nthcdr} $=$ {\rm{nthcdr}}\,({\it{i\/}}, {\it{l\/}})\index{nthcdr})
\end{tabbing}


\noindent{\sc Event}:   Disable nthcdr-putnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  nthcdr-putseg \\ \index{nthcdr-putseg}
\=\+\=\+{\bf if }{\it{i\/}} $<$ ({\it{n\/}} $+$ {\rm{length}}\,({\it{s\/}})\index{length})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{nthcdr}}\,({\it{i\/}}, {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}}, {\it{l\/}})\index{putseg})\index{nthcdr} $=$ {\rm{nthcdr}}\,({\it{i\/}}, {\it{l\/}})\index{nthcdr})\-
\end{tabbing}


\noindent{\sc Event}:   Disable nthcdr-putseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  table-putseg-subcase \\ \index{table-putseg-subcase}
\=\+(\=\+{\rm{plistp}}\,({\it{s\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\it{s\/}})\index{length} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ {\rm{length}}\,({\it{s\/}})\index{length}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\rm{length}}\,({\it{s\/}})\index{length}, {\rm{putseg}}\,({\it{s\/}}, {\tt{'}}{\tt{0}}, {\it{l\/}})\index{putseg})\index{table} \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\it{s\/}}, {\rm{table}}\,({\rm{length}}\,({\it{s\/}})\index{length}, {\rm{nthcdr}}\,({\rm{length}}\,({\it{s\/}})\index{length}, {\it{l\/}})\index{nthcdr})\index{table}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable table-putseg-subcase.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  table-putseg \\ \index{table-putseg}
\=\+(\=\+{\rm{plistp}}\,({\it{s\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\it{s\/}})\index{length} $=$ {\it{n\/}}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ (({\it{n\/}} $*$ {\it{i\/}}) $+$ {\rm{length}}\,({\it{s\/}})\index{length}) \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{table}}\,({\it{n\/}}, {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}} $*$ {\it{i\/}}, {\it{l\/}})\index{putseg})\index{table} $=$ {\rm{putnth}}\,({\it{s\/}}, {\it{i\/}}, {\rm{table}}\,({\it{n\/}}, {\it{l\/}})\index{table})\index{putnth})\-
\end{tabbing}


\noindent{\sc Event}:   Disable table-putseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  table-putseg-inverse \\ \index{table-putseg-inverse}
\=\+(\=\+{\rm{plistp}}\,({\it{s\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\it{s\/}})\index{length} $=$ {\it{n\/}}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ (({\it{n\/}} $*$ {\it{i\/}}) $+$ {\rm{length}}\,({\it{s\/}})\index{length}) \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{putnth}}\,({\it{s\/}}, {\it{i\/}}, {\rm{table}}\,({\it{n\/}}, {\it{l\/}})\index{table})\index{putnth} $=$ {\rm{table}}\,({\it{n\/}}, {\rm{putseg}}\,({\it{s\/}}, {\it{n\/}} $*$ {\it{i\/}}, {\it{l\/}})\index{putseg})\index{table})\-
\end{tabbing}


\noindent{\sc Event}:   Disable table-putseg-inverse.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  table-putnth \\ \index{table-putnth}
\=\+(\=\+({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$(({\it{i\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) $\wedge$ (({\rm{length}}\,({\it{l\/}})\index{length} ${}${\bf{mod}}${}$ {\it{n\/}}) $=$ {\tt{'}}{\tt{0}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\it{n\/}}, {\rm{putnth}}\,({\it{v\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{putnth}}\,({\it{v\/}}, {\it{i\/}} ${}${\bf{mod}}${}$ {\it{n\/}}, {\rm{getnth}}\,({\it{i\/}} $\div$ {\it{n\/}}, {\rm{table}}\,({\it{n\/}}, {\it{l\/}})\index{table})\index{getnth})\index{putnth}, \\ 
{\it{i\/}} $\div$ {\it{n\/}}, \\ 
{\rm{table}}\,({\it{n\/}}, {\it{l\/}})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable table-putnth.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{finite-number-tablep} \\  
\=\+{\rm{finite-number-tablep}}\,({\it{n\/}}, {\it{l\/}}, {\it{lub\/}})\index{finite-number-tablep} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}}) \\ 
{\bf then }\=\+{\rm{plistp}}\,({\rm{car}}\,({\it{l\/}}))\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-number-listp}}\,({\rm{car}}\,({\it{l\/}}), {\it{lub\/}})\index{finite-number-listp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\rm{car}}\,({\it{l\/}}))\index{length} $=$ {\it{n\/}}) \\ 
$\wedge$$\;\;\;\;${\rm{finite-number-tablep}}\,({\it{n\/}}, {\rm{cdr}}\,({\it{l\/}}), {\it{lub\/}})\index{finite-number-tablep})\-)\-\- \\ 
{\bf else }{\it{l\/}} $=$ {\tt{'}}{\tt{nil}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  a-finite-number-table-is-a-table \\ \index{a-finite-number-table-is-a-table}
{\rm{finite-number-tablep}}\,({\it{n\/}}, {\it{l\/}}, {\it{lub\/}})\index{finite-number-tablep} $\rightarrow$ {\rm{tablep}}\,({\it{n\/}}, {\it{l\/}})\index{tablep}
\end{tabbing}


\noindent{\sc Event}:   Disable a-finite-number-table-is-a-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-nil \\ \index{finite-number-listp-nil}
{\rm{finite-number-listp}}\,({\tt{'}}{\tt{nil}}, {\it{lub\/}})\index{finite-number-listp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-nil.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-flatten \\ \index{finite-number-listp-flatten}
\=\+(({\it{n\/}} $\not\simeq {\tt{0}}$) $\wedge$ {\rm{finite-number-tablep}}\,({\it{n\/}}, {\it{l\/}}, {\it{lub\/}})\index{finite-number-tablep}) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-listp}}\,({\rm{flatten}}\,({\it{l\/}})\index{flatten}, {\it{lub\/}})\index{finite-number-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-flatten.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-tablep-list \\ \index{finite-number-tablep-list}
\=\+({\rm{plistp}}\,({\it{l\/}})\index{plistp} $\wedge$ (({\rm{length}}\,({\it{l\/}})\index{length} $=$ {\it{n\/}}) $\wedge$ {\rm{finite-number-listp}}\,({\it{l\/}}, {\it{lub\/}})\index{finite-number-listp})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-tablep}}\,({\it{n\/}}, {\rm{cons}}\,({\it{l\/}}, {\tt{'}}{\tt{nil}}), {\it{lub\/}})\index{finite-number-tablep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-tablep-list.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-tablep-append \\ \index{finite-number-tablep-append}
\=\+({\rm{finite-number-tablep}}\,({\it{n\/}}, {\it{l1\/}}, {\it{lub\/}})\index{finite-number-tablep} $\wedge$ {\rm{finite-number-tablep}}\,({\it{n\/}}, {\it{l2\/}}, {\it{lub\/}})\index{finite-number-tablep}) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-tablep}}\,({\it{n\/}}, {\rm{append}}\,({\it{l1\/}}, {\it{l2\/}}), {\it{lub\/}})\index{finite-number-tablep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-tablep-append.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-plus-1-is-cadr-nthcdr \\ \index{getnth-plus-1-is-cadr-nthcdr}
{\rm{getnth}}\,({\tt{'}}{\tt{1}} $+$ {\it{n\/}}, {\it{l\/}})\index{getnth} $=$ {\rm{car}}\,({\rm{cdr}}\,({\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr}))
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-plus-1-is-cadr-nthcdr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cadr-firstn \\ \index{cadr-firstn}
({\tt{'}}{\tt{1}} $<$ {\it{n\/}}) $\rightarrow$ ({\rm{car}}\,({\rm{cdr}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{l\/}})\index{firstn})) $=$ {\rm{car}}\,({\rm{cdr}}\,({\it{l\/}})))
\end{tabbing}


\noindent{\sc Event}:   Disable cadr-firstn.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-plus-1-is-cadr-getseg \\ \index{getnth-plus-1-is-cadr-getseg}
\=\+(\=\+({\tt{'}}{\tt{1}} $<$ {\it{k\/}}) \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ {\it{n\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }({\rm{length}}\,({\it{l\/}})\index{length} $-$ {\it{n\/}}) $<$ {\it{k\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{1}} $+$ {\it{n\/}}, {\it{l\/}})\index{getnth} $=$ {\rm{car}}\,({\rm{cdr}}\,({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg})))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  getnth-plus-1-is-cadr-getseg-inverse \\ \index{getnth-plus-1-is-cadr-getseg-inve!rse}
\=\+(\=\+({\tt{'}}{\tt{1}} $<$ {\it{k\/}}) \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ {\it{n\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }({\rm{length}}\,({\it{l\/}})\index{length} $-$ {\it{n\/}}) $<$ {\it{k\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{car}}\,({\rm{cdr}}\,({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg})) $=$ {\rm{getnth}}\,({\tt{'}}{\tt{1}} $+$ {\it{n\/}}, {\it{l\/}})\index{getnth})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-plus-1-is-cadr-getseg-inverse.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  firstn-fixlength \\ \index{firstn-fixlength}
\=\+(\=\+\=\+{\bf if }{\it{n\/}} $<$ {\it{i\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ {\it{i\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{firstn}}\,({\it{i\/}}, {\rm{fixlength}}\,({\it{n\/}}, {\it{l\/}}, {\it{default\/}})\index{fixlength})\index{firstn} $=$ {\rm{firstn}}\,({\it{i\/}}, {\it{l\/}})\index{firstn})\-
\end{tabbing}


\noindent{\sc Event}:   Disable firstn-fixlength.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-fixlength \\ \index{getseg-fixlength}
\=\+({\rm{plistp}}\,({\it{l\/}})\index{plistp} $\wedge$ (({\it{n\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\rm{length}}\,({\it{l\/}})\index{length} $<$ {\it{n\/}}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\tt{'}}{\tt{0}}, {\rm{length}}\,({\it{l\/}})\index{length}, {\rm{fixlength}}\,({\it{n\/}}, {\it{l\/}}, {\it{default\/}})\index{fixlength})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\tt{'}}{\tt{0}}, {\rm{length}}\,({\it{l\/}})\index{length}, {\it{l\/}})\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-fixlength.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  number-listp-finite-number-listp \\ \index{number-listp-finite-number-listp}
{\rm{finite-number-listp}}\,({\it{l\/}}, {\it{lub\/}})\index{finite-number-listp} $\rightarrow$ {\rm{number-listp}}\,({\it{l\/}})\index{number-listp}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{nonlast}$\;\;$
{\rm{nonlast}}\,({\it{l\/}})\index{nonlast} $=$ {\rm{getseg}}\,({\tt{'}}{\tt{0}}, {\rm{length}}\,({\it{l\/}})\index{length} $-\;1$, {\it{l\/}})\index{getseg}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-nonlast \\ \index{length-nonlast}
{\rm{length}}\,({\rm{nonlast}}\,({\it{l\/}})\index{nonlast})\index{length} $=$ ({\rm{length}}\,({\it{l\/}})\index{length} $-\;1$)
\end{tabbing}


\noindent{\sc Event}:   Disable length-nonlast.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-nonlast \\ \index{plistp-nonlast}
{\rm{plistp}}\,({\rm{nonlast}}\,({\it{l\/}})\index{nonlast})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-nonlast.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-nonlast \\ \index{finite-number-listp-nonlast}
{\rm{finite-number-listp}}\,({\it{l\/}}, {\it{lub\/}})\index{finite-number-listp} $\rightarrow$ {\rm{finite-number-listp}}\,({\rm{nonlast}}\,({\it{l\/}})\index{nonlast}, {\it{lub\/}})\index{finite-number-listp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-nonlast.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-sub1-plus-crock \\ \index{difference-sub1-plus-crock}
(({\it{a\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\it{b\/}} $\not\simeq {\tt{0}}$)) $\rightarrow$ (((({\it{a\/}} $+$ {\it{b\/}}) $-\;1$) $-$ {\it{a\/}}) $=$ ({\it{b\/}} $-\;1$))
\end{tabbing}


\noindent{\sc Event}:   Disable difference-sub1-plus-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  nonlast-append \\ \index{nonlast-append}
\=\+{\rm{plistp}}\,({\it{a\/}})\index{plistp} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{nonlast}}\,({\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{nonlast} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{b\/}})\index{length} $=$ {\tt{'}}{\tt{0}}$\;\;${\bf then }{\rm{nonlast}}\,({\it{a\/}})\index{nonlast} \\ 
{\bf else }{\rm{append}}\,({\it{a\/}}, {\rm{nonlast}}\,({\it{b\/}})\index{nonlast})$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable nonlast-append.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{incr-mod} \\  
\=\+{\rm{incr-mod}}\,({\it{n\/}}, {\it{lub\/}})\index{incr-mod} \\ 
$=$$\;\;\;\;$\=\+{\bf if }($1\;+$ {\it{n\/}}) $<$ {\it{lub\/}}$\;\;${\bf then }$1\;+$ {\it{n\/}} \\ 
{\bf else }{\tt{'}}{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

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

\begin{tabbing}{\sc Theorem}:  decr-mod-size \\ \index{decr-mod-size}
(({\it{n\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\it{a\/}} $<$ {\it{n\/}})) $\rightarrow$ ({\rm{decr-mod}}\,({\it{a\/}}, {\it{n\/}})\index{decr-mod} $<$ {\it{n\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable decr-mod-size.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  incr-mod-equals-remainder-add1 \\ \index{incr-mod-equals-remainder-add1}
({\it{n\/}} $<$ {\it{lub\/}}) $\rightarrow$ ({\rm{incr-mod}}\,({\it{n\/}}, {\it{lub\/}})\index{incr-mod} $=$ (($1\;+$ {\it{n\/}}) ${}${\bf{mod}}${}$ {\it{lub\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable incr-mod-equals-remainder-add1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  incr-mod-decr-mod \\ \index{incr-mod-decr-mod}
({\it{n\/}} $<$ {\it{lub\/}}) $\rightarrow$ ({\rm{incr-mod}}\,({\rm{decr-mod}}\,({\it{n\/}}, {\it{lub\/}})\index{decr-mod}, {\it{lub\/}})\index{incr-mod} $=$ {\rm{fix}}\,({\it{n\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable incr-mod-decr-mod.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-incr-mod \\ \index{lessp-incr-mod}
({\it{n\/}} $<$ {\it{lub\/}}) $\rightarrow$ ({\rm{incr-mod}}\,({\it{n\/}}, {\it{lub\/}})\index{incr-mod} $<$ {\it{lub\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-incr-mod.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{qfirst}$\;\;$
{\rm{qfirst}}\,({\it{table\/}})\index{qfirst} $=$ {\rm{car}}\,({\it{table\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{enq}$\;\;$
{\rm{enq}}\,({\it{item\/}}, {\it{table\/}})\index{enq} $=$ {\rm{append}}\,({\it{table\/}}, {\rm{cons}}\,({\it{item\/}}, {\tt{'}}{\tt{nil}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{deq}$\;\;$
{\rm{deq}}\,({\it{table\/}})\index{deq} $=$ {\rm{cdr}}\,({\it{table\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{qemptyp}$\;\;$
{\rm{qemptyp}}\,({\it{table\/}})\index{qemptyp} $=$ ({\rm{length}}\,({\it{table\/}})\index{length} $=$ {\tt{'}}{\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{qfullp}$\;\;$
{\rm{qfullp}}\,({\it{table\/}}, {\it{max\/}})\index{qfullp} $=$ ({\rm{length}}\,({\it{table\/}})\index{length} $\not<$ {\it{max\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{qreplace}$\;\;$
{\rm{qreplace}}\,({\it{item\/}}, {\it{queue\/}})\index{qreplace} $=$ {\rm{enq}}\,({\it{item\/}}, {\rm{nonlast}}\,({\it{queue\/}})\index{nonlast})\index{enq}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plistp-enq \\ \index{plistp-enq}
{\rm{plistp}}\,({\rm{enq}}\,({\it{item\/}}, {\it{l\/}})\index{enq})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-enq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-deq \\ \index{plistp-deq}
({\rm{plistp}}\,({\it{queue\/}})\index{plistp} $\wedge$ ($\neg$ {\rm{qemptyp}}\,({\it{queue\/}})\index{qemptyp})) $\rightarrow$ {\rm{plistp}}\,({\rm{deq}}\,({\it{queue\/}})\index{deq})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-deq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-qreplace \\ \index{plistp-qreplace}
{\rm{plistp}}\,({\rm{qreplace}}\,({\it{item\/}}, {\it{queue\/}})\index{qreplace})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-qreplace.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-enq \\ \index{length-enq}
{\rm{length}}\,({\rm{enq}}\,({\it{item\/}}, {\it{queue\/}})\index{enq})\index{length} $=$ ($1\;+$ {\rm{length}}\,({\it{queue\/}})\index{length})
\end{tabbing}


\noindent{\sc Event}:   Disable length-enq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-non-empty-queue \\ \index{length-non-empty-queue}
($\neg$ {\rm{qemptyp}}\,({\it{queue\/}})\index{qemptyp}) $\rightarrow$ ({\rm{length}}\,({\it{queue\/}})\index{length} $\not=$ {\tt{'}}{\tt{0}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-non-empty-queue.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-deq \\ \index{length-deq}
($\neg$ {\rm{qemptyp}}\,({\it{queue\/}})\index{qemptyp}) $\rightarrow$ ({\rm{length}}\,({\rm{deq}}\,({\it{queue\/}})\index{deq})\index{length} $=$ ({\rm{length}}\,({\it{queue\/}})\index{length} $-\;1$))
\end{tabbing}


\noindent{\sc Event}:   Disable length-deq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-qreplace \\ \index{length-qreplace}
($\neg$ {\rm{qemptyp}}\,({\it{queue\/}})\index{qemptyp}) $\rightarrow$ ({\rm{length}}\,({\rm{qreplace}}\,({\it{item\/}}, {\it{queue\/}})\index{qreplace})\index{length} $=$ {\rm{length}}\,({\it{queue\/}})\index{length})
\end{tabbing}


\noindent{\sc Event}:   Disable length-qreplace.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-qemptyp-enq \\ \index{not-qemptyp-enq}
$\neg$ {\rm{qemptyp}}\,({\rm{enq}}\,({\it{item\/}}, {\it{queue\/}})\index{enq})\index{qemptyp}
\end{tabbing}


\noindent{\sc Event}:   Disable not-qemptyp-enq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-qfullp-deq \\ \index{not-qfullp-deq}
\=\+(\=\+\=\+{\bf if }{\it{n\/}} $<$ {\rm{length}}\,({\it{queue\/}})\index{length}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{qemptyp}}\,({\it{queue\/}})\index{qemptyp}))\- \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{qfullp}}\,({\rm{deq}}\,({\it{queue\/}})\index{deq}, {\it{n\/}})\index{qfullp})\-
\end{tabbing}


\noindent{\sc Event}:   Disable not-qfullp-deq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  qfirst-enq \\ \index{qfirst-enq}
($\neg$ {\rm{qemptyp}}\,({\it{queue\/}})\index{qemptyp}) $\rightarrow$ ({\rm{qfirst}}\,({\rm{enq}}\,({\it{x\/}}, {\it{queue\/}})\index{enq})\index{qfirst} $=$ {\rm{qfirst}}\,({\it{queue\/}})\index{qfirst})
\end{tabbing}


\noindent{\sc Event}:   Disable qfirst-enq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-enq \\ \index{finite-number-listp-enq}
\=\+({\rm{finite-number-listp}}\,({\it{queue\/}}, {\it{lub\/}})\index{finite-number-listp} $\wedge$ {\rm{finite-numberp}}\,({\it{item\/}}, {\it{lub\/}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-listp}}\,({\rm{enq}}\,({\it{item\/}}, {\it{queue\/}})\index{enq}, {\it{lub\/}})\index{finite-number-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-enq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-deq \\ \index{finite-number-listp-deq}
\=\+({\rm{finite-number-listp}}\,({\it{queue\/}}, {\it{lub\/}})\index{finite-number-listp} $\wedge$ ($\neg$ {\rm{qemptyp}}\,({\it{queue\/}})\index{qemptyp})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-listp}}\,({\rm{deq}}\,({\it{queue\/}})\index{deq}, {\it{lub\/}})\index{finite-number-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-deq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-qreplace \\ \index{finite-number-listp-qreplace}
\=\+({\rm{finite-number-listp}}\,({\it{queue\/}}, {\it{lub\/}})\index{finite-number-listp} $\wedge$ {\rm{finite-numberp}}\,({\it{item\/}}, {\it{lub\/}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-listp}}\,({\rm{qreplace}}\,({\it{item\/}}, {\it{queue\/}})\index{qreplace}, {\it{lub\/}})\index{finite-number-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-qreplace.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-qfirst \\ \index{finite-numberp-qfirst}
\=\+({\rm{finite-number-listp}}\,({\it{queue\/}}, {\it{lub\/}})\index{finite-number-listp} $\wedge$ ($\neg$ {\rm{qemptyp}}\,({\it{queue\/}})\index{qemptyp})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{qfirst}}\,({\it{queue\/}})\index{qfirst}, {\it{lub\/}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-qfirst.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-qfirst \\ \index{numberp-qfirst}
(($\neg$ {\rm{qemptyp}}\,({\it{queue\/}})\index{qemptyp}) $\wedge$ {\rm{number-listp}}\,({\it{queue\/}})\index{number-listp}) $\rightarrow$ ({\rm{qfirst}}\,({\it{queue\/}})\index{qfirst} $\in\;${\bf{N}}${}$)
\end{tabbing}


\noindent{\sc Event}:   Disable numberp-qfirst.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  deq-is-remove \\ \index{deq-is-remove}
({\rm{setp}}\,({\it{l\/}})\index{setp} $\wedge$ ({\tt{'}}{\tt{0}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) $\rightarrow$ ({\rm{deq}}\,({\it{l\/}})\index{deq} $=$ {\rm{remove}}\,({\rm{qfirst}}\,({\it{l\/}})\index{qfirst}, {\it{l\/}})\index{remove})
\end{tabbing}


\noindent{\sc Event}:   Disable deq-is-remove.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  member-qfirst-queue \\ \index{member-qfirst-queue}
($\neg$ {\rm{qemptyp}}\,({\it{queue\/}})\index{qemptyp}) $\rightarrow$ ({\rm{qfirst}}\,({\it{queue\/}})\index{qfirst} $\in$ {\it{queue\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable member-qfirst-queue.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-enq-deq \\ \index{permutation-enq-deq}
($\neg$ {\rm{qemptyp}}\,({\it{queue\/}})\index{qemptyp}) $\rightarrow$ {\rm{permutation}}\,({\rm{enq}}\,({\rm{qfirst}}\,({\it{queue\/}})\index{qfirst}, {\rm{deq}}\,({\it{queue\/}})\index{deq})\index{enq}, {\it{queue\/}})\index{permutation}
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-enq-deq.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{qhead-field}$\;\;$
{\sc{qhead-field}}\index{qhead-field} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{qtail-field}$\;\;$
{\sc{qtail-field}}\index{qtail-field} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{qcurrlength-field}$\;\;$
{\sc{qcurrlength-field}}\index{qcurrlength-field} $=$ {\tt{'}}{\tt{2}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{qmaxlength-field}$\;\;$
{\sc{qmaxlength-field}}\index{qmaxlength-field} $=$ {\tt{'}}{\tt{3}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{qarray-field}$\;\;$
{\sc{qarray-field}}\index{qarray-field} $=$ {\tt{'}}{\tt{4}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{delta} \\  
\=\+{\rm{delta}}\,({\it{a\/}}, {\it{b\/}}, {\it{max\/}})\index{delta} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\bf if }{\it{a\/}} $<$ {\it{b\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-$\;\;${\bf then }({\it{max\/}} $-$ {\it{a\/}}) $+$ {\it{b\/}} \\ 
{\bf else }{\it{b\/}} $-$ {\it{a\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  delta-a-a \\ \index{delta-a-a}
({\it{a\/}} $<$ {\it{max\/}}) $\rightarrow$ ({\rm{delta}}\,({\it{a\/}}, {\it{a\/}}, {\it{max\/}})\index{delta} $=$ {\it{max\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable delta-a-a.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  delta-incr-mod-a \\ \index{delta-incr-mod-a}
\=\+(({\it{a\/}} $<$ {\it{max\/}}) $\wedge$ ({\it{b\/}} $<$ {\it{max\/}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{delta}}\,({\rm{incr-mod}}\,({\it{a\/}}, {\it{max\/}})\index{incr-mod}, {\it{b\/}}, {\it{max\/}})\index{delta} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{delta}}\,({\it{a\/}}, {\it{b\/}}, {\it{max\/}})\index{delta} $=$ {\tt{'}}{\tt{1}}$\;\;${\bf then }{\it{max\/}} \\ 
{\bf else }{\rm{delta}}\,({\it{a\/}}, {\it{b\/}}, {\it{max\/}})\index{delta} $-\;1$$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable delta-incr-mod-a.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  delta-incr-mod-b \\ \index{delta-incr-mod-b}
\=\+(({\it{a\/}} $<$ {\it{max\/}}) $\wedge$ ({\it{b\/}} $<$ {\it{max\/}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{delta}}\,({\it{a\/}}, {\rm{incr-mod}}\,({\it{b\/}}, {\it{max\/}})\index{incr-mod}, {\it{max\/}})\index{delta} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{fix}}\,({\it{a\/}}) $=$ {\rm{fix}}\,({\it{b\/}})$\;\;${\bf then }{\tt{'}}{\tt{1}} \\ 
{\bf else }$1\;+$ {\rm{delta}}\,({\it{a\/}}, {\it{b\/}}, {\it{max\/}})\index{delta}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable delta-incr-mod-b.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  delta-equals-max-iff-a-equals-b \\ \index{delta-equals-max-iff-a-equals-b}
\=\+(({\it{a\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{b\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{a\/}} $<$ {\it{max\/}}) $\wedge$ ({\it{b\/}} $<$ {\it{max\/}})))) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{delta}}\,({\it{a\/}}, {\it{b\/}}, {\it{max\/}})\index{delta} $=$ {\it{max\/}}) $=$ ({\it{a\/}} $=$ {\it{b\/}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable delta-equals-max-iff-a-equals-b.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  leq-delta \\ \index{leq-delta}
\=\+(({\it{a\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{b\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{a\/}} $<$ {\it{max\/}}) $\wedge$ ({\it{b\/}} $<$ {\it{max\/}})))) \\ 
$\rightarrow$$\;\;\;\;$\=\+{\bf if }{\it{max\/}} $<$ {\rm{delta}}\,({\it{a\/}}, {\it{b\/}}, {\it{max\/}})\index{delta}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{array-qindex-relation} \\  
\=\+{\rm{array-qindex-relation}}\,({\it{queue\/}})\index{array-qindex-relation} \\ 
$=$$\;\;\;\;$(\=\+{\rm{delta}}\,({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth}, {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})\index{delta} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $\simeq {\tt{0}}$$\;\;${\bf then }{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth} \\ 
{\bf else }{\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{array-queuep} \\  
\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$=$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\it{queue\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\it{queue\/}})\index{length} $=$ ({\tt{'}}{\tt{4}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth} \\ 
$<$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{3}}, \\ 
{\it{queue\/}})\-\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\it{queue\/}})\-\index{getnth} \\ 
$<$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{3}}, \\ 
{\it{queue\/}})\-\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\it{queue\/}})\-\index{getnth} \\ 
$<$$\;\;\;\;$($1\;+$ {\rm{getnth}}\,(\=\+{\tt{'}}{\tt{3}}, \\ 
{\it{queue\/}})\-\index{getnth}))\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qindex-relation}}\,({\it{queue\/}})\index{array-qindex-relation})\-)\-)\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plistp-array-queue \\ \index{plistp-array-queue}
{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\rightarrow$ {\rm{plistp}}\,({\it{queue\/}})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-array-queue.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-array-queue \\ \index{length-array-queue}
{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\rightarrow$ ({\rm{length}}\,({\it{queue\/}})\index{length} $=$ ({\tt{'}}{\tt{4}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}))
\end{tabbing}


\noindent{\sc Event}:   Disable length-array-queue.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-qhead \\ \index{numberp-qhead}
{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\rightarrow$ ({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$)
\end{tabbing}


\noindent{\sc Event}:   Disable numberp-qhead.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-qtail \\ \index{numberp-qtail}
{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\rightarrow$ ({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$)
\end{tabbing}


\noindent{\sc Event}:   Disable numberp-qtail.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-qcurrlength \\ \index{numberp-qcurrlength}
{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\rightarrow$ ({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$)
\end{tabbing}


\noindent{\sc Event}:   Disable numberp-qcurrlength.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-qmaxlength \\ \index{numberp-qmaxlength}
{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\rightarrow$ ({\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$)
\end{tabbing}


\noindent{\sc Event}:   Disable numberp-qmaxlength.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  qmaxlength-non-zero \\ \index{qmaxlength-non-zero}
{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\rightarrow$ ({\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth} $\not=$ {\tt{'}}{\tt{0}})
\end{tabbing}


\noindent{\sc Event}:   Disable qmaxlength-non-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  qmaxlength-greater-than-zero \\ \index{qmaxlength-greater-than-zero}
{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\rightarrow$ ({\tt{'}}{\tt{0}} $<$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})
\end{tabbing}


\noindent{\sc Event}:   Disable qmaxlength-greater-than-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-qhead-qmaxlength \\ \index{lessp-qhead-qmaxlength}
{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\rightarrow$ ({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth} $<$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-qhead-qmaxlength.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-qtail-qmaxlength \\ \index{lessp-qtail-qmaxlength}
{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\rightarrow$ ({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth} $<$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-qtail-qmaxlength.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-qcurrlength-add1-qmaxlength \\ \index{lessp-qcurrlength-add1-qmaxlengt!h}
{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\rightarrow$ ({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $<$ ($1\;+$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}))
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-qcurrlength-add1-qmaxlength.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-array-qarray \\ \index{plistp-array-qarray}
{\rm{plistp}}\,({\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\rm{length}}\,({\it{queue\/}})\index{length} $-$ {\tt{'}}{\tt{4}}, {\it{queue\/}})\index{getseg})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-array-qarray.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-array-qarray \\ \index{length-array-qarray}
\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\rightarrow$$\;\;\;\;$({\rm{length}}\,({\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\rm{length}}\,({\it{queue\/}})\index{length} $-$ {\tt{'}}{\tt{4}}, {\it{queue\/}})\index{getseg})\index{length} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-array-qarray.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{array-enq} \\  
\=\+{\rm{array-enq}}\,({\it{item\/}}, {\it{queue\/}})\index{array-enq} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{incr-mod}}\,({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})\index{incr-mod}, \\ 
{\tt{'}}{\tt{1}}, \\ 
{\rm{putnth}}\,(\=\+$1\;+$ {\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth}, \\ 
{\tt{'}}{\tt{2}}, \\ 
{\rm{putnth}}\,({\it{item\/}}, {\tt{'}}{\tt{4}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, {\it{queue\/}})\index{putnth})\-\index{putnth})\-\index{putnth}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{array-deq} \\  
\=\+{\rm{array-deq}}\,({\it{queue\/}})\index{array-deq} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{incr-mod}}\,({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})\index{incr-mod}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $-\;1$, {\tt{'}}{\tt{2}}, {\it{queue\/}})\index{putnth})\-\index{putnth}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{array-qfirst} \\  
{\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{4}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth}, {\it{queue\/}})\index{getnth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{array-qfullp} \\  
{\rm{array-qfullp}}\,({\it{queue\/}})\index{array-qfullp} $=$ ({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{array-qemptyp}$\;\;$
{\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp} $=$ ({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $\simeq {\tt{0}}$)
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-array-enq \\ \index{length-array-enq}
{\rm{length}}\,({\rm{array-enq}}\,({\it{item\/}}, {\it{queue\/}})\index{array-enq})\index{length} $=$ {\rm{length}}\,({\it{queue\/}})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-array-enq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-array-enq \\ \index{plistp-array-enq}
{\rm{plistp}}\,({\it{queue\/}})\index{plistp} $\rightarrow$ {\rm{plistp}}\,({\rm{array-enq}}\,({\it{item\/}}, {\it{queue\/}})\index{array-enq})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-array-enq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qhead-array-enq \\ \index{array-qhead-array-enq}
{\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{array-enq}}\,({\it{item\/}}, {\it{queue\/}})\index{array-enq})\index{getnth} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth}
\end{tabbing}


\noindent{\sc Event}:   Disable array-qhead-array-enq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qtail-array-enq \\ \index{array-qtail-array-enq}
\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\rm{array-enq}}\,({\it{item\/}}, {\it{queue\/}})\index{array-enq})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{incr-mod}}\,({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})\index{incr-mod})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qtail-array-enq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qcurrlength-array-enq \\ \index{array-qcurrlength-array-enq}
\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\rm{array-enq}}\,({\it{item\/}}, {\it{queue\/}})\index{array-enq})\index{getnth} $=$ ($1\;+$ {\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qcurrlength-array-enq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qmaxlength-array-enq \\ \index{array-qmaxlength-array-enq}
{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{array-enq}}\,({\it{item\/}}, {\it{queue\/}})\index{array-enq})\index{getnth} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}
\end{tabbing}


\noindent{\sc Event}:   Disable array-qmaxlength-array-enq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qarray-array-enq \\ \index{array-qarray-array-enq}
\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}, {\rm{array-enq}}\,({\it{item\/}}, {\it{queue\/}})\index{array-enq})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\it{item\/}}, \\ 
{\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, \\ 
{\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}, {\it{queue\/}})\index{getseg})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qarray-array-enq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-queuep-array-enq \\ \index{array-queuep-array-enq}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ ($\neg$ {\rm{array-qfullp}}\,({\it{queue\/}})\index{array-qfullp})) \\ 
$\rightarrow$$\;\;\;\;${\rm{array-queuep}}\,({\rm{array-enq}}\,({\it{item\/}}, {\it{queue\/}})\index{array-enq})\index{array-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-queuep-array-enq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-array-deq \\ \index{length-array-deq}
{\rm{length}}\,({\rm{array-deq}}\,({\it{queue\/}})\index{array-deq})\index{length} $=$ {\rm{length}}\,({\it{queue\/}})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-array-deq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-array-deq \\ \index{plistp-array-deq}
{\rm{plistp}}\,({\it{queue\/}})\index{plistp} $\rightarrow$ {\rm{plistp}}\,({\rm{array-deq}}\,({\it{queue\/}})\index{array-deq})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-array-deq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qhead-array-deq \\ \index{array-qhead-array-deq}
\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{array-deq}}\,({\it{queue\/}})\index{array-deq})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{incr-mod}}\,({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})\index{incr-mod})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qhead-array-deq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qtail-array-deq \\ \index{array-qtail-array-deq}
{\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\rm{array-deq}}\,({\it{queue\/}})\index{array-deq})\index{getnth} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}
\end{tabbing}


\noindent{\sc Event}:   Disable array-qtail-array-deq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qcurrlength-array-deq \\ \index{array-qcurrlength-array-deq}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\rm{array-deq}}\,({\it{queue\/}})\index{array-deq})\index{getnth} $=$ ({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $-\;1$))\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qcurrlength-array-deq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qmaxlength-array-deq \\ \index{array-qmaxlength-array-deq}
{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{array-deq}}\,({\it{queue\/}})\index{array-deq})\index{getnth} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}
\end{tabbing}


\noindent{\sc Event}:   Disable array-qmaxlength-array-deq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qarray-array-deq \\ \index{array-qarray-array-deq}
\=\+{\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}, {\rm{array-deq}}\,({\it{queue\/}})\index{array-deq})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}, {\it{queue\/}})\index{getseg}\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qarray-array-deq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-queuep-array-deq \\ \index{array-queuep-array-deq}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;${\rm{array-queuep}}\,({\rm{array-deq}}\,({\it{queue\/}})\index{array-deq})\index{array-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-queuep-array-deq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-array-qemptyp-array-enq \\ \index{not-array-qemptyp-array-enq}
{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\rightarrow$ ($\neg$ {\rm{array-qemptyp}}\,({\rm{array-enq}}\,({\it{item\/}}, {\it{queue\/}})\index{array-enq})\index{array-qemptyp})
\end{tabbing}


\noindent{\sc Event}:   Disable not-array-qemptyp-array-enq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-array-qfullp-array-deq \\ \index{not-array-qfullp-array-deq}
{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\rightarrow$ ($\neg$ {\rm{array-qfullp}}\,({\rm{array-deq}}\,({\it{queue\/}})\index{array-deq})\index{array-qfullp})
\end{tabbing}


\noindent{\sc Event}:   Disable not-array-qfullp-array-deq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qcurrlength-in-a-full-queue \\ \index{array-qcurrlength-in-a-full-que!ue}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ {\rm{array-qfullp}}\,({\it{queue\/}})\index{array-qfullp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qcurrlength-in-a-full-queue.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qcurrlength-in-a-non-full-queue \\ \index{array-qcurrlength-in-a-non-full!-queue}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ ($\neg$ {\rm{array-qfullp}}\,({\it{queue\/}})\index{array-qfullp})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $<$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qcurrlength-in-a-non-full-queue.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qcurrlength-in-an-empty-queue \\ \index{array-qcurrlength-in-an-empty-q!ueue}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $=$ {\tt{'}}{\tt{0}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qcurrlength-in-an-empty-queue.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qcurrlength-in-a-non-empty-queue \\ \index{array-qcurrlength-in-a-non-empt!y-queue}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $\not=$ {\tt{'}}{\tt{0}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qcurrlength-in-a-non-empty-queue.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{array-nonlast} \\  
\=\+{\rm{array-nonlast}}\,({\it{queue\/}})\index{array-nonlast} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{decr-mod}}\,({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})\index{decr-mod}, \\ 
{\tt{'}}{\tt{1}}, \\ 
{\rm{putnth}}\,({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $-\;1$, {\tt{'}}{\tt{2}}, {\it{queue\/}})\index{putnth})\-\index{putnth}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-array-nonlast \\ \index{length-array-nonlast}
{\rm{length}}\,({\rm{array-nonlast}}\,({\it{queue\/}})\index{array-nonlast})\index{length} $=$ {\rm{length}}\,({\it{queue\/}})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-array-nonlast.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-array-nonlast \\ \index{plistp-array-nonlast}
{\rm{plistp}}\,({\it{queue\/}})\index{plistp} $\rightarrow$ {\rm{plistp}}\,({\rm{array-nonlast}}\,({\it{queue\/}})\index{array-nonlast})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-array-nonlast.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qhead-array-nonlast \\ \index{array-qhead-array-nonlast}
{\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{array-nonlast}}\,({\it{queue\/}})\index{array-nonlast})\index{getnth} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth}
\end{tabbing}


\noindent{\sc Event}:   Disable array-qhead-array-nonlast.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qtail-array-nonlast \\ \index{array-qtail-array-nonlast}
\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\rm{array-nonlast}}\,({\it{queue\/}})\index{array-nonlast})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{decr-mod}}\,({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})\index{decr-mod})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qtail-array-nonlast.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qcurrlength-array-nonlast \\ \index{array-qcurrlength-array-nonlast}
\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\rm{array-nonlast}}\,({\it{queue\/}})\index{array-nonlast})\index{getnth} $=$ ({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $-\;1$))\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qcurrlength-array-nonlast.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qmaxlength-array-nonlast \\ \index{array-qmaxlength-array-nonlast}
{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{array-nonlast}}\,({\it{queue\/}})\index{array-nonlast})\index{getnth} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}
\end{tabbing}


\noindent{\sc Event}:   Disable array-qmaxlength-array-nonlast.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qarray-array-nonlast \\ \index{array-qarray-array-nonlast}
\=\+{\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}, {\rm{array-nonlast}}\,({\it{queue\/}})\index{array-nonlast})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}, {\it{queue\/}})\index{getseg}\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qarray-array-nonlast.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  delta-sub1-b-case1 \\ \index{delta-sub1-b-case1}
\=\+(\=\+({\it{a\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{b\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{b\/}} $\not=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{a\/}} $<$ {\it{max\/}}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{b\/}} $<$ {\it{max\/}}) \\ 
$\wedge$$\;\;\;\;$(({\rm{delta}}\,({\it{a\/}}, {\it{b\/}}, {\it{max\/}})\index{delta} $-\;1$) $\not=$ {\tt{'}}{\tt{0}}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{delta}}\,({\it{a\/}}, {\it{b\/}} $-\;1$, {\it{max\/}})\index{delta} $=$ ({\rm{delta}}\,({\it{a\/}}, {\it{b\/}}, {\it{max\/}})\index{delta} $-\;1$))\-
\end{tabbing}


\noindent{\sc Event}:   Disable delta-sub1-b-case1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  delta-sub1-b-case2 \\ \index{delta-sub1-b-case2}
\=\+(({\it{a\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{a\/}} $<$ {\it{max\/}}) $\wedge$ (({\rm{delta}}\,({\it{a\/}}, {\tt{'}}{\tt{0}}, {\it{max\/}})\index{delta} $-\;1$) $\not=$ {\tt{'}}{\tt{0}}))) \\ 
$\rightarrow$$\;\;\;\;$({\rm{delta}}\,({\it{a\/}}, {\it{max\/}} $-\;1$, {\it{max\/}})\index{delta} $=$ ({\rm{delta}}\,({\it{a\/}}, {\tt{'}}{\tt{0}}, {\it{max\/}})\index{delta} $-\;1$))\-
\end{tabbing}


\noindent{\sc Event}:   Disable delta-sub1-b-case2.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 ARRAY-QUEUEP-ARRAY-NONLAST-CROCK1
 (REWRITE)
 (IMPLIES
  (AND
   (PLISTP QUEUE)
   (AND
    (EQUAL (LENGTH QUEUE)
           (PLUS '4 (GETNTH '3 QUEUE)))
    (AND
     (NUMBERP (GETNTH '0 QUEUE))
     (AND
      (NUMBERP (GETNTH '1 QUEUE))
      (AND
       (NOT (EQUAL (GETNTH '3 QUEUE) '0))
       (AND (NUMBERP (GETNTH '3 QUEUE))
            (AND (LESSP (GETNTH '0 QUEUE)
                        (GETNTH '3 QUEUE))
                 (AND (LESSP (GETNTH '1 QUEUE)
                             (GETNTH '3 QUEUE))
                      (AND (LESSP (SUB1 (GETNTH '2 QUEUE))
                                  (GETNTH '3 QUEUE))
                           (AND (EQUAL (DELTA (GETNTH '0 QUEUE)
                                              (GETNTH '1 QUEUE)
                                              (GETNTH '3 QUEUE))
                                       (GETNTH '2 QUEUE))
                                (AND (NOT (EQUAL (GETNTH '2 QUEUE) '0))
                                     (AND (EQUAL (SUB1 (GETNTH '2 QUEUE)) '0)
                                          (NOT (EQUAL (GETNTH '1 QUEUE)
                                                      '0))))))))))))))
  (EQUAL (GETNTH '0 QUEUE)
         (SUB1 (GETNTH '1 QUEUE))))
 ((ENABLE DELTA)
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable array-queuep-array-nonlast-crock1.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 ARRAY-QUEUEP-ARRAY-NONLAST-CROCK2
 (REWRITE)
 (IMPLIES
  (AND
   (PLISTP QUEUE)
   (AND
    (EQUAL (LENGTH QUEUE)
           (PLUS '4 (GETNTH '3 QUEUE)))
    (AND
     (NUMBERP (GETNTH '0 QUEUE))
     (AND
      (NUMBERP (GETNTH '1 QUEUE))
      (AND
       (NOT (EQUAL (GETNTH '3 QUEUE) '0))
       (AND (NUMBERP (GETNTH '3 QUEUE))
            (AND (LESSP (GETNTH '0 QUEUE)
                        (GETNTH '3 QUEUE))
                 (AND (LESSP (GETNTH '1 QUEUE)
                             (GETNTH '3 QUEUE))
                      (AND (LESSP (SUB1 (GETNTH '2 QUEUE))
                                  (GETNTH '3 QUEUE))
                           (AND (EQUAL (DELTA (GETNTH '0 QUEUE)
                                              (GETNTH '1 QUEUE)
                                              (GETNTH '3 QUEUE))
                                       (GETNTH '2 QUEUE))
                                (AND (NOT (EQUAL (GETNTH '2 QUEUE) '0))
                                     (AND (EQUAL (SUB1 (GETNTH '2 QUEUE)) '0)
                                          (EQUAL (GETNTH '1 QUEUE)
                                                 '0)))))))))))))
  (EQUAL (GETNTH '0 QUEUE)
         (SUB1 (GETNTH '3 QUEUE))))
 ((ENABLE LENGTH DELTA)
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable array-queuep-array-nonlast-crock2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-queuep-array-nonlast \\ \index{array-queuep-array-nonlast}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;${\rm{array-queuep}}\,({\rm{array-nonlast}}\,({\it{queue\/}})\index{array-nonlast})\index{array-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-queuep-array-nonlast.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{array-qreplace} \\  
{\rm{array-qreplace}}\,({\it{item\/}}, {\it{queue\/}})\index{array-qreplace} $=$ {\rm{array-enq}}\,({\it{item\/}}, {\rm{array-nonlast}}\,({\it{queue\/}})\index{array-nonlast})\index{array-enq}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-array-qreplace \\ \index{length-array-qreplace}
{\rm{length}}\,({\rm{array-qreplace}}\,({\it{item\/}}, {\it{queue\/}})\index{array-qreplace})\index{length} $=$ {\rm{length}}\,({\it{queue\/}})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-array-qreplace.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-array-qreplace \\ \index{plistp-array-qreplace}
{\rm{plistp}}\,({\it{queue\/}})\index{plistp} $\rightarrow$ {\rm{plistp}}\,({\rm{array-qreplace}}\,({\it{item\/}}, {\it{queue\/}})\index{array-qreplace})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-array-qreplace.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qhead-array-qreplace \\ \index{array-qhead-array-qreplace}
{\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{array-qreplace}}\,({\it{item\/}}, {\it{queue\/}})\index{array-qreplace})\index{getnth} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth}
\end{tabbing}


\noindent{\sc Event}:   Disable array-qhead-array-qreplace.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qtail-array-qreplace \\ \index{array-qtail-array-qreplace}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\rm{array-qreplace}}\,({\it{item\/}}, {\it{queue\/}})\index{array-qreplace})\index{getnth} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth})\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qtail-array-qreplace.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qcurrlength-array-qreplace \\ \index{array-qcurrlength-array-qreplace}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\rm{array-qreplace}}\,({\it{item\/}}, {\it{queue\/}})\index{array-qreplace})\index{getnth} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth})\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qcurrlength-array-qreplace.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qmaxlength-array-qreplace \\ \index{array-qmaxlength-array-qreplace}
{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{array-qreplace}}\,({\it{item\/}}, {\it{queue\/}})\index{array-qreplace})\index{getnth} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}
\end{tabbing}


\noindent{\sc Event}:   Disable array-qmaxlength-array-qreplace.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qarray-array-qreplace \\ \index{array-qarray-array-qreplace}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}, {\rm{array-qreplace}}\,({\it{item\/}}, {\it{queue\/}})\index{array-qreplace})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\it{item\/}}, \\ 
{\rm{decr-mod}}\,({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})\index{decr-mod}, \\ 
{\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}, {\it{queue\/}})\index{getseg})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qarray-array-qreplace.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-array-qfullp-array-nonlast \\ \index{not-array-qfullp-array-nonlast}
{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\rightarrow$ ($\neg$ {\rm{array-qfullp}}\,({\rm{array-nonlast}}\,({\it{queue\/}})\index{array-nonlast})\index{array-qfullp})
\end{tabbing}


\noindent{\sc Event}:   Disable not-array-qfullp-array-nonlast.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-queuep-array-qreplace \\ \index{array-queuep-array-qreplace}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;${\rm{array-queuep}}\,({\rm{array-qreplace}}\,({\it{item\/}}, {\it{queue\/}})\index{array-qreplace})\index{array-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-queuep-array-qreplace.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{array-queue-facts}} to consist of the following events: array-qcurrlength-in-an-empty-queue,
array-qcurrlength-in-a-non-empty-queue,
array-qcurrlength-in-a-non-full-queue,
array-qcurrlength-in-a-full-queue,
not-array-qfullp-array-deq,
not-array-qemptyp-array-enq,
array-queuep-array-qreplace,
array-qmaxlength-array-qreplace,
array-qcurrlength-array-qreplace,
array-qtail-array-qreplace,
array-qhead-array-qreplace,
plistp-array-qreplace,
length-array-qreplace,
array-queuep-array-deq,
array-qmaxlength-array-deq,
array-qcurrlength-array-deq,
array-qtail-array-deq,
array-qhead-array-deq,
plistp-array-deq,
length-array-deq,
array-queuep-array-enq,
array-qmaxlength-array-enq,
array-qcurrlength-array-enq,
array-qtail-array-enq,
array-qhead-array-enq,
plistp-array-enq,
length-array-enq,
length-array-qarray,
plistp-array-qarray,
lessp-qcurrlength-add1-qmaxlength,
lessp-qtail-qmaxlength,
lessp-qhead-qmaxlength,
qmaxlength-greater-than-zero,
qmaxlength-non-zero,
numberp-qmaxlength,
numberp-qcurrlength,
numberp-qtail,
numberp-qhead.\index{array-queue-facts}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qfullp-implies-not-array-qemptyp \\ \index{array-qfullp-implies-not-array-qe!mptyp}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ {\rm{array-qfullp}}\,({\it{queue\/}})\index{array-qfullp}) \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  array-qhead-equals-array-qtail-in-an-empty-queue \\ \index{array-qhead-equals-array-qtail-i!n-an-empty-queue}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth})\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qhead-equals-array-qtail-in-an-empty-queue.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qhead-equals-array-qtail-iff-qfull-or-qempty \\ \index{array-qhead-equals-array-qtail-i!ff-qfull-or-qempty}
\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}) \\ 
$=$$\;\;\;\;$({\rm{array-qfullp}}\,({\it{queue\/}})\index{array-qfullp} $\vee$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qhead-equals-array-qtail-iff-qfull-or-qempty.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{delta-segment} \\  
\=\+{\rm{delta-segment}}\,({\it{a\/}}, {\it{b\/}}, {\it{s\/}})\index{delta-segment} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\bf if }{\it{a\/}} $<$ {\it{b\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
{\bf then }{\rm{append}}\,({\rm{getseg}}\,({\it{a\/}}, {\rm{length}}\,({\it{s\/}})\index{length} $-$ {\it{a\/}}, {\it{s\/}})\index{getseg}, {\rm{getseg}}\,({\tt{'}}{\tt{0}}, {\it{b\/}}, {\it{s\/}})\index{getseg}) \\ 
{\bf else }{\rm{getseg}}\,({\it{a\/}}, {\it{b\/}} $-$ {\it{a\/}}, {\it{s\/}})\index{getseg}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  delta-equals-length-delta-segment \\ \index{delta-equals-length-delta-segme!nt}
\=\+(({\it{a\/}} $<$ {\rm{length}}\,({\it{s\/}})\index{length}) $\wedge$ ({\it{b\/}} $<$ {\rm{length}}\,({\it{s\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{length}}\,({\rm{delta-segment}}\,({\it{a\/}}, {\it{b\/}}, {\it{s\/}})\index{delta-segment})\index{length} $=$ {\rm{delta}}\,({\it{a\/}}, {\it{b\/}}, {\rm{length}}\,({\it{s\/}})\index{length})\index{delta})\-
\end{tabbing}


\noindent{\sc Event}:   Disable delta-equals-length-delta-segment.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-delta-segment \\ \index{plistp-delta-segment}
{\rm{plistp}}\,({\rm{delta-segment}}\,({\it{a\/}}, {\it{b\/}}, {\it{s\/}})\index{delta-segment})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-delta-segment.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-delta-segment \\ \index{finite-number-listp-delta-segme!nt}
\=\+(\=\+{\rm{finite-number-listp}}\,({\it{s\/}}, {\it{lub\/}})\index{finite-number-listp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{b\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\rm{length}}\,({\it{s\/}})\index{length} $<$ {\it{b\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{a\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{s\/}})\index{length} $<$ {\it{a\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-listp}}\,({\rm{delta-segment}}\,({\it{a\/}}, {\it{b\/}}, {\it{s\/}})\index{delta-segment}, {\it{lub\/}})\index{finite-number-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-delta-segment.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-delta-segment \\ \index{length-delta-segment}
\=\+(({\it{a\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{b\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{a\/}} $<$ {\rm{length}}\,({\it{s\/}})\index{length}) $\wedge$ ({\it{b\/}} $<$ {\rm{length}}\,({\it{s\/}})\index{length})))) \\ 
$\rightarrow$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{s\/}})\index{length} $<$ {\rm{length}}\,({\rm{delta-segment}}\,({\it{a\/}}, {\it{b\/}}, {\it{s\/}})\index{delta-segment})\index{length}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{mapup-queue} \\  
\=\+{\rm{mapup-queue}}\,({\it{queue\/}})\index{mapup-queue} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp}$\;\;${\bf then }{\tt{'}}{\tt{nil}} \\ 
{\bf else }{\rm{delta-segment}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth}, \\ 
{\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, \\ 
{\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}, {\it{queue\/}})\index{getseg})\-\index{delta-segment}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-mapup-queue \\ \index{finite-number-listp-mapup-queue}
\=\+(\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\wedge$$\;\;\;\;${\rm{finite-number-listp}}\,({\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}, {\it{queue\/}})\index{getseg}, {\it{lub\/}})\index{finite-number-listp})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-listp}}\,({\rm{mapup-queue}}\,({\it{queue\/}})\index{mapup-queue}, {\it{lub\/}})\index{finite-number-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-mapup-queue.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-mapup-queue \\ \index{plistp-mapup-queue}
{\rm{plistp}}\,({\rm{mapup-queue}}\,({\it{queue\/}})\index{mapup-queue})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-mapup-queue.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-mapup-queue \\ \index{length-mapup-queue}
\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\rightarrow$$\;\;\;\;$\=\+{\bf if }{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth} $<$ {\rm{length}}\,({\rm{mapup-queue}}\,({\it{queue\/}})\index{mapup-queue})\index{length}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  delta-segment-incr-mod-b \\ \index{delta-segment-incr-mod-b}
\=\+(\=\+{\rm{plistp}}\,({\it{s\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{a\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{b\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(({\it{a\/}} $<$ {\it{n\/}}) $\wedge$ (({\it{b\/}} $<$ {\it{n\/}}) $\wedge$ ({\it{n\/}} $=$ {\rm{length}}\,({\it{s\/}})\index{length}))))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{delta-segment}}\,({\it{a\/}}, {\rm{incr-mod}}\,({\it{b\/}}, {\it{n\/}})\index{incr-mod}, {\it{s\/}})\index{delta-segment} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $=$ {\it{b\/}}$\;\;${\bf then }{\rm{cons}}\,({\rm{getnth}}\,({\it{a\/}}, {\it{s\/}})\index{getnth}, {\tt{'}}{\tt{nil}}) \\ 
{\bf else }{\rm{append}}\,(\=\+{\rm{delta-segment}}\,({\it{a\/}}, {\it{b\/}}, {\it{s\/}})\index{delta-segment}, \\ 
{\rm{cons}}\,({\rm{getnth}}\,({\it{b\/}}, {\it{s\/}})\index{getnth}, {\tt{'}}{\tt{nil}}))\-$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable delta-segment-incr-mod-b.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  delta-segment-putnth-non-interference \\ \index{delta-segment-putnth-non-interfe!rence}
\=\+(\=\+({\it{a\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{b\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(({\it{a\/}} $<$ {\rm{length}}\,({\it{s\/}})\index{length}) $\wedge$ (({\it{b\/}} $<$ {\rm{length}}\,({\it{s\/}})\index{length}) $\wedge$ ({\it{a\/}} $\not=$ {\it{b\/}}))))\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{delta-segment}}\,({\it{a\/}}, {\it{b\/}}, {\rm{putnth}}\,({\it{v\/}}, {\it{b\/}}, {\it{s\/}})\index{putnth})\index{delta-segment} $=$ {\rm{delta-segment}}\,({\it{a\/}}, {\it{b\/}}, {\it{s\/}})\index{delta-segment})\-
\end{tabbing}


\noindent{\sc Event}:   Disable delta-segment-putnth-non-interference.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-array-enq \\ \index{correctness-of-array-enq}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ ($\neg$ {\rm{array-qfullp}}\,({\it{queue\/}})\index{array-qfullp})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{mapup-queue}}\,({\rm{array-enq}}\,({\it{item\/}}, {\it{queue\/}})\index{array-enq})\index{mapup-queue} $=$ {\rm{enq}}\,({\it{item\/}}, {\rm{mapup-queue}}\,({\it{queue\/}})\index{mapup-queue})\index{enq})\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-array-enq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  delta-segment-incr-mod-a \\ \index{delta-segment-incr-mod-a}
\=\+(\=\+{\rm{plistp}}\,({\it{s\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{a\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{b\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(({\it{a\/}} $<$ {\it{n\/}}) $\wedge$ (({\it{b\/}} $<$ {\it{n\/}}) $\wedge$ ({\it{n\/}} $=$ {\rm{length}}\,({\it{s\/}})\index{length}))))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{delta-segment}}\,({\rm{incr-mod}}\,({\it{a\/}}, {\it{n\/}})\index{incr-mod}, {\it{b\/}}, {\it{s\/}})\index{delta-segment} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{delta}}\,({\it{a\/}}, {\it{b\/}}, {\it{n\/}})\index{delta} $=$ {\tt{'}}{\tt{1}}$\;\;${\bf then }{\rm{delta-segment}}\,({\it{b\/}}, {\it{b\/}}, {\it{s\/}})\index{delta-segment} \\ 
{\bf else }{\rm{cdr}}\,({\rm{delta-segment}}\,({\it{a\/}}, {\it{b\/}}, {\it{s\/}})\index{delta-segment})$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable delta-segment-incr-mod-a.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qemtpyp-array-deq-when-delta-is-1 \\ \index{array-qemtpyp-array-deq-when-de!lta-is-1}
\=\+(\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{delta}}\,({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth}, {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})\index{delta} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{1}})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\it{queue\/}})\index{array-deq})\index{array-qemptyp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qemtpyp-array-deq-when-delta-is-1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qemtpyp-array-deq-when-delta-is-1-alternative \\ \index{array-qemtpyp-array-deq-when-de!lta-is-1-alternative}
\=\+(\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp}) $\wedge$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\it{queue\/}})\index{array-deq})\index{array-qemptyp}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{delta}}\,({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth}, {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})\index{delta} $=$ {\tt{'}}{\tt{1}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qemtpyp-array-deq-when-delta-is-1-alternative.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-array-deq-case-3 \\ \index{correctness-of-array-deq-case-3}
\=\+(\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp}) $\wedge$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\it{queue\/}})\index{array-deq})\index{array-qemptyp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{cdr}}\,({\rm{delta-segment}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth}, \\ 
{\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, \\ 
{\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}, {\it{queue\/}})\index{getseg})\-\index{delta-segment}) \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{nil}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-array-deq-case-3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qmaxlength-must-be-1 \\ \index{array-qmaxlength-must-be-1}
\=\+(\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\wedge$$\;\;\;\;$({\rm{array-qfullp}}\,({\it{queue\/}})\index{array-qfullp} $\wedge$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\it{queue\/}})\index{array-deq})\index{array-qemptyp}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth} $=$ {\tt{'}}{\tt{1}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qmaxlength-must-be-1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-delta-segment-a-a \\ \index{length-delta-segment-a-a}
\=\+(\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\wedge$$\;\;\;\;$({\rm{array-qfullp}}\,({\it{queue\/}})\index{array-qfullp} $\wedge$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\it{queue\/}})\index{array-deq})\index{array-qemptyp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{length}}\,({\rm{delta-segment}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth}, \\ 
{\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth}, \\ 
{\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}, {\it{queue\/}})\index{getseg})\-\index{delta-segment})\index{length} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{1}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-delta-segment-a-a.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-array-deq-case-1 \\ \index{correctness-of-array-deq-case-1}
\=\+(\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\wedge$$\;\;\;\;$({\rm{array-qfullp}}\,({\it{queue\/}})\index{array-qfullp} $\wedge$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\it{queue\/}})\index{array-deq})\index{array-qemptyp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{cdr}}\,({\rm{delta-segment}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth}, \\ 
{\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth}, \\ 
{\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}, {\it{queue\/}})\index{getseg})\-\index{delta-segment}) \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{nil}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-array-deq-case-1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-array-deq \\ \index{correctness-of-array-deq}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{mapup-queue}}\,({\rm{array-deq}}\,({\it{queue\/}})\index{array-deq})\index{mapup-queue} $=$ {\rm{deq}}\,({\rm{mapup-queue}}\,({\it{queue\/}})\index{mapup-queue})\index{deq})\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-array-deq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-array-qfirst \\ \index{correctness-of-array-qfirst}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst} $=$ {\rm{qfirst}}\,({\rm{mapup-queue}}\,({\it{queue\/}})\index{mapup-queue})\index{qfirst})\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-array-qfirst.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-array-qemptyp \\ \index{correctness-of-array-qemptyp}
\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\rightarrow$$\;\;\;\;$({\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp} $=$ {\rm{qemptyp}}\,({\rm{mapup-queue}}\,({\it{queue\/}})\index{mapup-queue})\index{qemptyp})\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-array-qemptyp.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-array-qfullp \\ \index{correctness-of-array-qfullp}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ ({\it{max\/}} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{array-qfullp}}\,({\it{queue\/}})\index{array-qfullp} $=$ {\rm{qfullp}}\,({\rm{mapup-queue}}\,({\it{queue\/}})\index{mapup-queue}, {\it{max\/}})\index{qfullp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-delta-segment-decr-mod-arg1 \\ \index{length-delta-segment-decr-mod-a!rg1}
\=\+(({\it{a\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{b\/}} $=$ {\rm{length}}\,({\it{s\/}})\index{length}) $\wedge$ ({\it{a\/}} $<$ {\rm{length}}\,({\it{s\/}})\index{length}))) \\ 
$\rightarrow$$\;\;\;\;$({\rm{length}}\,({\rm{delta-segment}}\,({\rm{decr-mod}}\,({\it{a\/}}, {\it{b\/}})\index{decr-mod}, {\it{a\/}}, {\it{s\/}})\index{delta-segment})\index{length} $=$ {\tt{'}}{\tt{1}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-delta-segment-decr-mod-arg1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  nonlast-of-length-1 \\ \index{nonlast-of-length-1}
({\rm{length}}\,({\it{l\/}})\index{length} $=$ {\tt{'}}{\tt{1}}) $\rightarrow$ ({\rm{nonlast}}\,({\it{l\/}})\index{nonlast} $=$ {\tt{'}}{\tt{nil}})
\end{tabbing}


\noindent{\sc Event}:   Disable nonlast-of-length-1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-array-nonlast-case1 \\ \index{correctness-of-array-nonlast-ca!se1}
\=\+(\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp}) $\wedge$ {\rm{array-qemptyp}}\,({\rm{array-nonlast}}\,({\it{queue\/}})\index{array-nonlast})\index{array-qemptyp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{nonlast}}\,({\rm{delta-segment}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth}, \\ 
{\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, \\ 
{\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}, {\it{queue\/}})\index{getseg})\-\index{delta-segment})\index{nonlast} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{nil}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-array-nonlast-case1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  delta-segment-decr-mod-arg2 \\ \index{delta-segment-decr-mod-arg2}
\=\+(\=\+({\it{a\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{a\/}} $<$ {\rm{length}}\,({\it{s\/}})\index{length}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{b\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(({\it{b\/}} $<$ {\rm{length}}\,({\it{s\/}})\index{length}) $\wedge$ ({\it{a\/}} $\not=$ {\rm{decr-mod}}\,({\it{b\/}}, {\rm{length}}\,({\it{s\/}})\index{length})\index{decr-mod})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{delta-segment}}\,({\it{a\/}}, {\rm{decr-mod}}\,({\it{b\/}}, {\rm{length}}\,({\it{s\/}})\index{length})\index{decr-mod}, {\it{s\/}})\index{delta-segment} \\ 
$=$$\;\;\;\;${\rm{nonlast}}\,({\rm{delta-segment}}\,({\it{a\/}}, {\it{b\/}}, {\it{s\/}})\index{delta-segment})\index{nonlast})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable delta-segment-decr-mod-arg2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-array-nonlast-case2 \\ \index{correctness-of-array-nonlast-ca!se2}
\=\+(\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-nonlast}}\,({\it{queue\/}})\index{array-nonlast})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{delta-segment}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth}, \\ 
{\rm{decr-mod}}\,({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})\index{decr-mod}, \\ 
{\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}, {\it{queue\/}})\index{getseg})\-\index{delta-segment} \\ 
$=$$\;\;\;\;${\rm{nonlast}}\,({\rm{delta-segment}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth}, \\ 
{\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, \\ 
{\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}, {\it{queue\/}})\index{getseg})\-\index{delta-segment})\index{nonlast})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-array-nonlast-case2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-array-nonlast \\ \index{correctness-of-array-nonlast}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{mapup-queue}}\,({\rm{array-nonlast}}\,({\it{queue\/}})\index{array-nonlast})\index{mapup-queue} $=$ {\rm{nonlast}}\,({\rm{mapup-queue}}\,({\it{queue\/}})\index{mapup-queue})\index{nonlast})\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-array-nonlast.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-array-qreplace \\ \index{correctness-of-array-qreplace}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{array-qreplace}}\,({\it{item\/}}, {\it{queue\/}})\index{array-qreplace})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{qreplace}}\,({\it{item\/}}, {\rm{mapup-queue}}\,({\it{queue\/}})\index{mapup-queue})\index{qreplace})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-array-qreplace.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-mapup-queue-is-qcurrlength \\ \index{length-mapup-queue-is-qcurrlengt!h}
{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\rightarrow$ ({\rm{length}}\,({\rm{mapup-queue}}\,({\it{queue\/}})\index{mapup-queue})\index{length} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth})
\end{tabbing}


\noindent{\sc Event}:   Disable length-mapup-queue-is-qcurrlength.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{qfirst2}$\;\;$
{\rm{qfirst2}}\,({\it{i\/}}, {\it{j\/}}, {\it{qtable\/}})\index{qfirst2} $=$ {\rm{qfirst}}\,({\rm{getnth2}}\,({\it{i\/}}, {\it{j\/}}, {\it{qtable\/}})\index{getnth2})\index{qfirst}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{enq2} \\  
{\rm{enq2}}\,({\it{msg\/}}, {\it{i\/}}, {\it{j\/}}, {\it{qtable\/}})\index{enq2} $=$ {\rm{putnth2}}\,({\rm{enq}}\,({\it{msg\/}}, {\rm{getnth2}}\,({\it{i\/}}, {\it{j\/}}, {\it{qtable\/}})\index{getnth2})\index{enq}, {\it{i\/}}, {\it{j\/}}, {\it{qtable\/}})\index{putnth2}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{deq2} \\  
{\rm{deq2}}\,({\it{i\/}}, {\it{j\/}}, {\it{qtable\/}})\index{deq2} $=$ {\rm{putnth2}}\,({\rm{deq}}\,({\rm{getnth2}}\,({\it{i\/}}, {\it{j\/}}, {\it{qtable\/}})\index{getnth2})\index{deq}, {\it{i\/}}, {\it{j\/}}, {\it{qtable\/}})\index{putnth2}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{qfullp2} \\  
{\rm{qfullp2}}\,({\it{i\/}}, {\it{j\/}}, {\it{qtable\/}}, {\it{max\/}})\index{qfullp2} $=$ {\rm{qfullp}}\,({\rm{getnth2}}\,({\it{i\/}}, {\it{j\/}}, {\it{qtable\/}})\index{getnth2}, {\it{max\/}})\index{qfullp}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{qemptyp2}$\;\;$
{\rm{qemptyp2}}\,({\it{i\/}}, {\it{j\/}}, {\it{qtable\/}})\index{qemptyp2} $=$ {\rm{qemptyp}}\,({\rm{getnth2}}\,({\it{i\/}}, {\it{j\/}}, {\it{qtable\/}})\index{getnth2})\index{qemptyp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  array-qemptyp-implies-not-array-qfullp \\ \index{array-qemptyp-implies-not-array!-qfullp}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp}) \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\it{queue\/}})\index{array-qfullp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  array-qfirst-array-enq \\ \index{array-qfirst-array-enq}
\=\+(\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp}) $\wedge$ ($\neg$ {\rm{array-qfullp}}\,({\it{queue\/}})\index{array-qfullp})))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{array-qfirst}}\,({\rm{array-enq}}\,({\it{item\/}}, {\it{queue\/}})\index{array-enq})\index{array-qfirst} $=$ {\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst})\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qfirst-array-enq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qfirst-array-enq1 \\ \index{array-qfirst-array-enq1}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{array-qfirst}}\,({\rm{array-enq}}\,({\it{item\/}}, {\it{queue\/}})\index{array-enq})\index{array-qfirst} $=$ {\it{item\/}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qfirst-array-enq1.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tm-wordsize}$\;\;$
{\sc{tm-wordsize}}\index{tm-wordsize} $=$ {\tt{'}}{\tt{16}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-wordlub}$\;\;$
{\sc{tm-wordlub}}\index{tm-wordlub} $=$ {\tt{'}}{\tt{65536}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{alu-result} \\  
{\rm{alu-result}}\,({\it{value\/}}, {\it{carry\/}})\index{alu-result} $=$ {\rm{cons}}\,({\it{value\/}}, {\rm{cons}}\,({\it{carry\/}}, {\tt{'}}{\tt{nil}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{alu-value}$\;\;$
{\rm{alu-value}}\,({\it{alu-result\/}})\index{alu-value} $=$ {\rm{car}}\,({\it{alu-result\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{alu-carry}$\;\;$
{\rm{alu-carry}}\,({\it{alu-result\/}})\index{alu-carry} $=$ {\rm{car}}\,({\rm{cdr}}\,({\it{alu-result\/}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-alu-decr} \\  
\=\+{\rm{tm-alu-decr}}\,({\it{a\/}})\index{tm-alu-decr} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{'}}{\tt{(}}{\tt{65535}}{\tt{ }}{\tt{*1*true}}{\tt{)}} \\ 
{\bf else }{\rm{alu-result}}\,(({\it{a\/}} $-\;1$) ${}${\bf{mod}}${}$ {\tt{'}}{\tt{65536}}, {\tt{'}}{\tt{*1*false}})\index{alu-result}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-alu-decr-mod} \\  
\=\+{\rm{tm-alu-decr-mod}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-decr-mod} \\ 
$=$$\;\;\;\;${\rm{alu-result}}\,({\rm{decr-mod}}\,({\it{a\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{65536}}, {\it{b\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{65536}})\index{decr-mod}, {\tt{'}}{\tt{*1*false}})\index{alu-result}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-alu-difference} \\  
\=\+{\rm{tm-alu-difference}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-difference} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{b\/}} $<$ {\it{a\/}} \\ 
{\bf then }{\rm{alu-result}}\,(({\tt{'}}{\tt{65536}} $-$ ({\it{a\/}} $-$ {\it{b\/}})) ${}${\bf{mod}}${}$ {\tt{'}}{\tt{65536}}, {\tt{'}}{\tt{*1*true}})\index{alu-result} \\ 
{\bf else }{\rm{alu-result}}\,(({\it{b\/}} $-$ {\it{a\/}}) ${}${\bf{mod}}${}$ {\tt{'}}{\tt{65536}}, {\tt{'}}{\tt{*1*false}})\index{alu-result}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-alu-incr} \\  
\=\+{\rm{tm-alu-incr}}\,({\it{a\/}})\index{tm-alu-incr} \\ 
$=$$\;\;\;\;$\=\+{\bf if }($1\;+$ {\it{a\/}}) $<$ {\tt{'}}{\tt{65536}}$\;\;${\bf then }{\rm{alu-result}}\,($1\;+$ {\it{a\/}}, {\tt{'}}{\tt{*1*false}})\index{alu-result} \\ 
{\bf else }{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{*1*true}}{\tt{)}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-alu-incr-mod} \\  
\=\+{\rm{tm-alu-incr-mod}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-incr-mod} \\ 
$=$$\;\;\;\;${\rm{alu-result}}\,({\rm{incr-mod}}\,({\it{a\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{65536}}, {\it{b\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{65536}})\index{incr-mod}, {\tt{'}}{\tt{*1*false}})\index{alu-result}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-alu-mod} \\  
\=\+{\rm{tm-alu-mod}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-mod} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{b\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{65536}}) $\simeq {\tt{0}}$$\;\;${\bf then }{\rm{alu-result}}\,({\it{a\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{65536}}, {\tt{'}}{\tt{*1*false}})\index{alu-result} \\ 
{\bf else }{\rm{alu-result}}\,({\it{a\/}} ${}${\bf{mod}}${}$ ({\it{b\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{65536}}), {\tt{'}}{\tt{*1*false}})\index{alu-result}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-alu-mult} \\  
\=\+{\rm{tm-alu-mult}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-mult} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{a\/}} $*$ {\it{b\/}}) $<$ {\tt{'}}{\tt{65536}}$\;\;${\bf then }{\rm{alu-result}}\,({\it{a\/}} $*$ {\it{b\/}}, {\tt{'}}{\tt{*1*false}})\index{alu-result} \\ 
{\bf else }{\rm{alu-result}}\,(({\it{a\/}} $*$ {\it{b\/}}) ${}${\bf{mod}}${}$ {\tt{'}}{\tt{65536}}, {\tt{'}}{\tt{*1*true}})\index{alu-result}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-alu-plus} \\  
\=\+{\rm{tm-alu-plus}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-plus} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{a\/}} $+$ {\it{b\/}}) $<$ {\tt{'}}{\tt{65536}}$\;\;${\bf then }{\rm{alu-result}}\,({\it{a\/}} $+$ {\it{b\/}}, {\tt{'}}{\tt{*1*false}})\index{alu-result} \\ 
{\bf else }{\rm{alu-result}}\,(({\it{a\/}} $+$ {\it{b\/}}) ${}${\bf{mod}}${}$ {\tt{'}}{\tt{65536}}, {\tt{'}}{\tt{*1*true}})\index{alu-result}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-numberp-alu-value-tm-alu-decr \\ \index{finite-numberp-alu-value-tm-alu!-decr}
{\rm{finite-numberp}}\,({\rm{alu-value}}\,({\rm{tm-alu-decr}}\,({\it{a\/}})\index{tm-alu-decr})\index{alu-value}, {\tt{'}}{\tt{65536}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-alu-value-tm-alu-decr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-alu-value-tm-alu-decr-wordsize \\ \index{lessp-alu-value-tm-alu-decr-wor!dsize}
({\rm{alu-value}}\,({\rm{tm-alu-decr}}\,({\it{a\/}})\index{tm-alu-decr})\index{alu-value} $<$ {\tt{'}}{\tt{65536}}) $=$ {\tt{'}}{\tt{*1*true}}
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-alu-value-tm-alu-decr-wordsize.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-alu-value-tm-alu-decr-wordsize-linear \\ \index{lessp-alu-value-tm-alu-decr-wor!dsize-linear}
{\rm{alu-value}}\,({\rm{tm-alu-decr}}\,({\it{a\/}})\index{tm-alu-decr})\index{alu-value} $<$ {\tt{'}}{\tt{65536}}
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-alu-value-tm-alu-decr-wordsize-linear.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-alu-value-tm-alu-decr \\ \index{numberp-alu-value-tm-alu-decr}
{\rm{alu-value}}\,({\rm{tm-alu-decr}}\,({\it{a\/}})\index{tm-alu-decr})\index{alu-value} $\in\;${\bf{N}}${}$
\end{tabbing}


\noindent{\sc Event}:   Disable numberp-alu-value-tm-alu-decr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-alu-decr-value-identical-to-ideal-result \\ \index{tm-alu-decr-value-identical-to-i!deal-result}
(({\it{a\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\it{a\/}} $<$ {\tt{'}}{\tt{65536}})) $\rightarrow$ ({\rm{alu-value}}\,({\rm{tm-alu-decr}}\,({\it{a\/}})\index{tm-alu-decr})\index{alu-value} $=$ ({\it{a\/}} $-\;1$))
\end{tabbing}


\noindent{\sc Event}:   Disable tm-alu-decr-value-identical-to-ideal-result.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-alu-value-tm-alu-decr-mod \\ \index{finite-numberp-alu-value-tm-alu!-decr-mod}
{\rm{finite-numberp}}\,({\rm{alu-value}}\,({\rm{tm-alu-decr-mod}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-decr-mod})\index{alu-value}, {\tt{'}}{\tt{65536}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-alu-value-tm-alu-decr-mod.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-alu-value-tm-alu-decr-mod-wordsize \\ \index{lessp-alu-value-tm-alu-decr-mod!-wordsize}
({\rm{alu-value}}\,({\rm{tm-alu-decr-mod}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-decr-mod})\index{alu-value} $<$ {\tt{'}}{\tt{65536}}) $=$ {\tt{'}}{\tt{*1*true}}
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-alu-value-tm-alu-decr-mod-wordsize.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-alu-value-tm-alu-decr-mod-wordsize-linear \\ \index{lessp-alu-value-tm-alu-decr-mod!-wordsize-linear}
{\rm{alu-value}}\,({\rm{tm-alu-decr-mod}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-decr-mod})\index{alu-value} $<$ {\tt{'}}{\tt{65536}}
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-alu-value-tm-alu-decr-mod-wordsize-linear.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-alu-value-tm-alu-decr-mod \\ \index{numberp-alu-value-tm-alu-decr-m!od}
{\rm{alu-value}}\,({\rm{tm-alu-decr-mod}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-decr-mod})\index{alu-value} $\in\;${\bf{N}}${}$
\end{tabbing}


\noindent{\sc Event}:   Disable numberp-alu-value-tm-alu-decr-mod.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-alu-decr-mod-value-identical-to-ideal-result \\ \index{tm-alu-decr-mod-value-identical!-to-ideal-result}
\=\+(({\it{a\/}} $<$ {\tt{'}}{\tt{65536}}) $\wedge$ ({\it{b\/}} $<$ {\tt{'}}{\tt{65536}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{alu-value}}\,({\rm{tm-alu-decr-mod}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-decr-mod})\index{alu-value} $=$ {\rm{decr-mod}}\,({\it{a\/}}, {\it{b\/}})\index{decr-mod})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-alu-decr-mod-value-identical-to-ideal-result.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-alu-value-tm-alu-incr \\ \index{finite-numberp-alu-value-tm-alu!-incr}
{\rm{finite-numberp}}\,({\rm{alu-value}}\,({\rm{tm-alu-incr}}\,({\it{a\/}})\index{tm-alu-incr})\index{alu-value}, {\tt{'}}{\tt{65536}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-alu-value-tm-alu-incr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-alu-value-tm-alu-incr-wordsize \\ \index{lessp-alu-value-tm-alu-incr-wor!dsize}
({\rm{alu-value}}\,({\rm{tm-alu-incr}}\,({\it{a\/}})\index{tm-alu-incr})\index{alu-value} $<$ {\tt{'}}{\tt{65536}}) $=$ {\tt{'}}{\tt{*1*true}}
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-alu-value-tm-alu-incr-wordsize.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-alu-value-tm-alu-incr-wordsize-linear \\ \index{lessp-alu-value-tm-alu-incr-wor!dsize-linear}
{\rm{alu-value}}\,({\rm{tm-alu-incr}}\,({\it{a\/}})\index{tm-alu-incr})\index{alu-value} $<$ {\tt{'}}{\tt{65536}}
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-alu-value-tm-alu-incr-wordsize-linear.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-alu-value-tm-alu-incr \\ \index{numberp-alu-value-tm-alu-incr}
{\rm{alu-value}}\,({\rm{tm-alu-incr}}\,({\it{a\/}})\index{tm-alu-incr})\index{alu-value} $\in\;${\bf{N}}${}$
\end{tabbing}


\noindent{\sc Event}:   Disable numberp-alu-value-tm-alu-incr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-alu-incr-value-identical-to-ideal-result \\ \index{tm-alu-incr-value-identical-to-i!deal-result}
(($1\;+$ {\it{a\/}}) $<$ {\tt{'}}{\tt{65536}}) $\rightarrow$ ({\rm{alu-value}}\,({\rm{tm-alu-incr}}\,({\it{a\/}})\index{tm-alu-incr})\index{alu-value} $=$ ($1\;+$ {\it{a\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable tm-alu-incr-value-identical-to-ideal-result.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-alu-value-tm-alu-incr-mod \\ \index{finite-numberp-alu-value-tm-alu!-incr-mod}
{\rm{finite-numberp}}\,({\rm{alu-value}}\,({\rm{tm-alu-incr-mod}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-incr-mod})\index{alu-value}, {\tt{'}}{\tt{65536}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-alu-value-tm-alu-incr-mod.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-alu-value-tm-alu-incr-mod-wordsize \\ \index{lessp-alu-value-tm-alu-incr-mod!-wordsize}
({\rm{alu-value}}\,({\rm{tm-alu-incr-mod}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-incr-mod})\index{alu-value} $<$ {\tt{'}}{\tt{65536}}) $=$ {\tt{'}}{\tt{*1*true}}
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-alu-value-tm-alu-incr-mod-wordsize.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-alu-value-tm-alu-incr-mod-wordsize-linear \\ \index{lessp-alu-value-tm-alu-incr-mod!-wordsize-linear}
{\rm{alu-value}}\,({\rm{tm-alu-incr-mod}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-incr-mod})\index{alu-value} $<$ {\tt{'}}{\tt{65536}}
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-alu-value-tm-alu-incr-mod-wordsize-linear.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-alu-value-tm-alu-incr-mod \\ \index{numberp-alu-value-tm-alu-incr-m!od}
{\rm{alu-value}}\,({\rm{tm-alu-incr-mod}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-incr-mod})\index{alu-value} $\in\;${\bf{N}}${}$
\end{tabbing}


\noindent{\sc Event}:   Disable numberp-alu-value-tm-alu-incr-mod.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-alu-incr-mod-value-identical-to-ideal-result \\ \index{tm-alu-incr-mod-value-identical!-to-ideal-result}
\=\+(({\it{a\/}} $<$ {\tt{'}}{\tt{65536}}) $\wedge$ ({\it{b\/}} $<$ {\tt{'}}{\tt{65536}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{alu-value}}\,({\rm{tm-alu-incr-mod}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-incr-mod})\index{alu-value} $=$ {\rm{incr-mod}}\,({\it{a\/}}, {\it{b\/}})\index{incr-mod})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-alu-incr-mod-value-identical-to-ideal-result.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-alu-value-tm-alu-mod \\ \index{finite-numberp-alu-value-tm-alu!-mod}
{\rm{finite-numberp}}\,({\rm{alu-value}}\,({\rm{tm-alu-mod}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-mod})\index{alu-value}, {\tt{'}}{\tt{65536}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-alu-value-tm-alu-mod.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-alu-value-tm-alu-mod-wordsize \\ \index{lessp-alu-value-tm-alu-mod-word!size}
({\rm{alu-value}}\,({\rm{tm-alu-mod}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-mod})\index{alu-value} $<$ {\tt{'}}{\tt{65536}}) $=$ {\tt{'}}{\tt{*1*true}}
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-alu-value-tm-alu-mod-wordsize.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-alu-value-tm-alu-mod-wordsize-linear \\ \index{lessp-alu-value-tm-alu-mod-word!size-linear}
{\rm{alu-value}}\,({\rm{tm-alu-mod}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-mod})\index{alu-value} $<$ {\tt{'}}{\tt{65536}}
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-alu-value-tm-alu-mod-wordsize-linear.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-alu-value-tm-alu-mod \\ \index{numberp-alu-value-tm-alu-mod}
{\rm{alu-value}}\,({\rm{tm-alu-mod}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-mod})\index{alu-value} $\in\;${\bf{N}}${}$
\end{tabbing}


\noindent{\sc Event}:   Disable numberp-alu-value-tm-alu-mod.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-alu-mod-value-identical-to-ideal-result \\ \index{tm-alu-mod-value-identical-to-i!deal-result}
\=\+(({\it{b\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\it{b\/}} $<$ {\tt{'}}{\tt{65536}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{alu-value}}\,({\rm{tm-alu-mod}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-mod})\index{alu-value} $=$ ({\it{a\/}} ${}${\bf{mod}}${}$ {\it{b\/}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-alu-mod-value-identical-to-ideal-result.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-alu-value-tm-alu-mult \\ \index{finite-numberp-alu-value-tm-alu!-mult}
{\rm{finite-numberp}}\,({\rm{alu-value}}\,({\rm{tm-alu-mult}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-mult})\index{alu-value}, {\tt{'}}{\tt{65536}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-alu-value-tm-alu-mult.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-alu-value-tm-alu-mult-wordsize \\ \index{lessp-alu-value-tm-alu-mult-wor!dsize}
({\rm{alu-value}}\,({\rm{tm-alu-mult}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-mult})\index{alu-value} $<$ {\tt{'}}{\tt{65536}}) $=$ {\tt{'}}{\tt{*1*true}}
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-alu-value-tm-alu-mult-wordsize.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-alu-value-tm-alu-mult-wordsize-linear \\ \index{lessp-alu-value-tm-alu-mult-wor!dsize-linear}
{\rm{alu-value}}\,({\rm{tm-alu-mult}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-mult})\index{alu-value} $<$ {\tt{'}}{\tt{65536}}
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-alu-value-tm-alu-mult-wordsize-linear.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-alu-value-tm-alu-mult \\ \index{numberp-alu-value-tm-alu-mult}
{\rm{alu-value}}\,({\rm{tm-alu-mult}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-mult})\index{alu-value} $\in\;${\bf{N}}${}$
\end{tabbing}


\noindent{\sc Event}:   Disable numberp-alu-value-tm-alu-mult.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-alu-mult-value-identical-to-ideal-result \\ \index{tm-alu-mult-value-identical-to-i!deal-result}
(({\it{a\/}} $*$ {\it{b\/}}) $<$ {\tt{'}}{\tt{65536}}) $\rightarrow$ ({\rm{alu-value}}\,({\rm{tm-alu-mult}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-mult})\index{alu-value} $=$ ({\it{a\/}} $*$ {\it{b\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable tm-alu-mult-value-identical-to-ideal-result.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-alu-value-tm-alu-plus \\ \index{finite-numberp-alu-value-tm-alu!-plus}
{\rm{finite-numberp}}\,({\rm{alu-value}}\,({\rm{tm-alu-plus}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-plus})\index{alu-value}, {\tt{'}}{\tt{65536}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-alu-value-tm-alu-plus.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-alu-value-tm-alu-plus-wordsize \\ \index{lessp-alu-value-tm-alu-plus-wor!dsize}
({\rm{alu-value}}\,({\rm{tm-alu-plus}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-plus})\index{alu-value} $<$ {\tt{'}}{\tt{65536}}) $=$ {\tt{'}}{\tt{*1*true}}
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-alu-value-tm-alu-plus-wordsize.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-alu-value-tm-alu-plus-wordsize-linear \\ \index{lessp-alu-value-tm-alu-plus-wor!dsize-linear}
{\rm{alu-value}}\,({\rm{tm-alu-plus}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-plus})\index{alu-value} $<$ {\tt{'}}{\tt{65536}}
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-alu-value-tm-alu-plus-wordsize-linear.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-alu-value-tm-alu-plus \\ \index{numberp-alu-value-tm-alu-plus}
{\rm{alu-value}}\,({\rm{tm-alu-plus}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-plus})\index{alu-value} $\in\;${\bf{N}}${}$
\end{tabbing}


\noindent{\sc Event}:   Disable numberp-alu-value-tm-alu-plus.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-alu-plus-value-identical-to-ideal-result \\ \index{tm-alu-plus-value-identical-to-i!deal-result}
(({\it{a\/}} $+$ {\it{b\/}}) $<$ {\tt{'}}{\tt{65536}}) $\rightarrow$ ({\rm{alu-value}}\,({\rm{tm-alu-plus}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-plus})\index{alu-value} $=$ ({\it{a\/}} $+$ {\it{b\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable tm-alu-plus-value-identical-to-ideal-result.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{tm-alu-arithmetic}} to consist of the following events: tm-alu-plus-value-identical-to-ideal-result,
numberp-alu-value-tm-alu-plus,
lessp-alu-value-tm-alu-plus-wordsize-linear,
lessp-alu-value-tm-alu-plus-wordsize,
finite-numberp-alu-value-tm-alu-plus,
tm-alu-mult-value-identical-to-ideal-result,
numberp-alu-value-tm-alu-mult,
lessp-alu-value-tm-alu-mult-wordsize-linear,
lessp-alu-value-tm-alu-mult-wordsize,
finite-numberp-alu-value-tm-alu-mult,
tm-alu-mod-value-identical-to-ideal-result,
numberp-alu-value-tm-alu-mod,
lessp-alu-value-tm-alu-mod-wordsize-linear,
lessp-alu-value-tm-alu-mod-wordsize,
finite-numberp-alu-value-tm-alu-mod,
tm-alu-incr-mod-value-identical-to-ideal-result,
numberp-alu-value-tm-alu-incr-mod,
lessp-alu-value-tm-alu-incr-mod-wordsize-linear,
lessp-alu-value-tm-alu-incr-mod-wordsize,
finite-numberp-alu-value-tm-alu-incr-mod,
tm-alu-incr-value-identical-to-ideal-result,
numberp-alu-value-tm-alu-incr,
lessp-alu-value-tm-alu-incr-wordsize-linear,
lessp-alu-value-tm-alu-incr-wordsize,
finite-numberp-alu-value-tm-alu-incr,
tm-alu-decr-mod-value-identical-to-ideal-result,
numberp-alu-value-tm-alu-decr-mod,
lessp-alu-value-tm-alu-decr-mod-wordsize-linear,
lessp-alu-value-tm-alu-decr-mod-wordsize,
finite-numberp-alu-value-tm-alu-decr-mod,
tm-alu-decr-value-identical-to-ideal-result,
numberp-alu-value-tm-alu-decr,
lessp-alu-value-tm-alu-decr-wordsize-linear,
lessp-alu-value-tm-alu-decr-wordsize,
finite-numberp-alu-value-tm-alu-decr.\index{tm-alu-arithmetic}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tm-incr}$\;\;$
{\rm{tm-incr}}\,({\it{a\/}})\index{tm-incr} $=$ (($1\;+$ {\it{a\/}}) ${}${\bf{mod}}${}$ {\tt{'}}{\tt{65536}})
\end{tabbing}

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

\begin{tabbing}{\sc Definition}:\index{tm-decr} \\  
\=\+{\rm{tm-decr}}\,({\it{a\/}})\index{tm-decr} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{a\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{'}}{\tt{65535}} \\ 
{\bf else }{\it{a\/}} $-\;1$$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-incr \\ \index{finite-numberp-tm-incr}
{\rm{finite-numberp}}\,({\rm{tm-incr}}\,({\it{a\/}})\index{tm-incr}, {\tt{'}}{\tt{65536}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-incr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-incrn \\ \index{finite-numberp-tm-incrn}
{\rm{finite-numberp}}\,({\it{a\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp} $\rightarrow$ {\rm{finite-numberp}}\,({\rm{tm-incrn}}\,({\it{n\/}}, {\it{a\/}})\index{tm-incrn}, {\tt{'}}{\tt{65536}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-incrn.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-decr \\ \index{finite-numberp-tm-decr}
{\rm{finite-numberp}}\,({\it{a\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp} $\rightarrow$ {\rm{finite-numberp}}\,({\rm{tm-decr}}\,({\it{a\/}})\index{tm-decr}, {\tt{'}}{\tt{65536}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-decr.

\addvspace{18pt}


\noindent{\sc Event}:   Add the shell {\it{tm\/}}\index{tm}, with recognizer function symbol {\it{tm-shellp\/}} and 14 accessors: {\it{tm-memory\/}}, with type restriction (none-of) and default value zero; {\it{tm-regs\/}}, with type restriction (none-of) and default value zero; {\it{tm-cc\/}}, with type restriction (none-of) and default value zero; {\it{tm-error\/}}, with type restriction (none-of) and default value zero; {\it{tm-svcflag\/}}, with type restriction (none-of) and default value zero; {\it{tm-svcid\/}}, with type restriction (none-of) and default value zero; {\it{tm-base\/}}, with type restriction (none-of) and default value zero; {\it{tm-limit\/}}, with type restriction (none-of) and default value zero; {\it{tm-slimit\/}}, with type restriction (none-of) and default value zero; {\it{tm-svmode\/}}, with type restriction (none-of) and default value zero; {\it{tm-rwstate\/}}, with type restriction (none-of) and default value zero; {\it{tm-clock\/}}, with type restriction (none-of) and default value zero; {\it{tm-iports\/}}, with type restriction (none-of) and default value zero; {\it{tm-oports\/}}, with type restriction (none-of) and default value zero.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tm-regsize}$\;\;$
{\sc{tm-regsize}}\index{tm-regsize} $=$ {\tt{'}}{\tt{3}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-charsize}$\;\;$
{\sc{tm-charsize}}\index{tm-charsize} $=$ {\tt{'}}{\tt{8}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-ccsize}$\;\;$
{\sc{tm-ccsize}}\index{tm-ccsize} $=$ {\tt{'}}{\tt{2}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-errorsize}$\;\;$
{\sc{tm-errorsize}}\index{tm-errorsize} $=$ {\tt{'}}{\tt{6}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-svcflagsize}$\;\;$
{\sc{tm-svcflagsize}}\index{tm-svcflagsize} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-svcidsize}$\;\;$
{\sc{tm-svcidsize}}\index{tm-svcidsize} $=$ {\tt{'}}{\tt{7}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-cclub}$\;\;$
{\sc{tm-cclub}}\index{tm-cclub} $=$ {\tt{'}}{\tt{4}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-errorlub}$\;\;$
{\sc{tm-errorlub}}\index{tm-errorlub} $=$ {\tt{'}}{\tt{64}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-svcflaglub}$\;\;$
{\sc{tm-svcflaglub}}\index{tm-svcflaglub} $=$ {\tt{'}}{\tt{2}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-svcidlub}$\;\;$
{\sc{tm-svcidlub}}\index{tm-svcidlub} $=$ {\tt{'}}{\tt{128}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-reglength}$\;\;$
{\sc{tm-reglength}}\index{tm-reglength} $=$ {\tt{'}}{\tt{8}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-memlength}$\;\;$
{\sc{tm-memlength}}\index{tm-memlength} $=$ {\tt{'}}{\tt{65536}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-charlub}$\;\;$
{\sc{tm-charlub}}\index{tm-charlub} $=$ {\tt{'}}{\tt{256}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-port-length}$\;\;$
{\sc{tm-port-length}}\index{tm-port-length} $=$ {\tt{'}}{\tt{16}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-pc-address}$\;\;$
{\sc{tm-pc-address}}\index{tm-pc-address} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-sp-address}$\;\;$
{\sc{tm-sp-address}}\index{tm-sp-address} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-set-memory} \\  
\=\+{\rm{tm-set-memory}}\,({\it{memory\/}}, {\it{tm\/}})\index{tm-set-memory} \\ 
$=$$\;\;\;\;${\rm{tm}}\,(\=\+{\it{memory\/}}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}, \\ 
{\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit}, \\ 
{\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode}, \\ 
{\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate}, \\ 
{\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock}, \\ 
{\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports}, \\ 
{\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-\index{tm}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-set-regs} \\  
\=\+{\rm{tm-set-regs}}\,({\it{regs\/}}, {\it{tm\/}})\index{tm-set-regs} \\ 
$=$$\;\;\;\;${\rm{tm}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\it{regs\/}}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}, \\ 
{\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit}, \\ 
{\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode}, \\ 
{\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate}, \\ 
{\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock}, \\ 
{\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports}, \\ 
{\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-\index{tm}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-set-cc} \\  
\=\+{\rm{tm-set-cc}}\,({\it{cc\/}}, {\it{tm\/}})\index{tm-set-cc} \\ 
$=$$\;\;\;\;${\rm{tm}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\it{cc\/}}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}, \\ 
{\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit}, \\ 
{\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode}, \\ 
{\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate}, \\ 
{\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock}, \\ 
{\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports}, \\ 
{\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-\index{tm}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-set-error} \\  
\=\+{\rm{tm-set-error}}\,({\it{error\/}}, {\it{tm\/}})\index{tm-set-error} \\ 
$=$$\;\;\;\;${\rm{tm}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\it{error\/}}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}, \\ 
{\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit}, \\ 
{\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode}, \\ 
{\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate}, \\ 
{\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock}, \\ 
{\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports}, \\ 
{\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-\index{tm}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-set-svcflag} \\  
\=\+{\rm{tm-set-svcflag}}\,({\it{svcflag\/}}, {\it{tm\/}})\index{tm-set-svcflag} \\ 
$=$$\;\;\;\;${\rm{tm}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\it{svcflag\/}}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}, \\ 
{\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit}, \\ 
{\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode}, \\ 
{\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate}, \\ 
{\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock}, \\ 
{\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports}, \\ 
{\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-\index{tm}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-set-svcid} \\  
\=\+{\rm{tm-set-svcid}}\,({\it{svcid\/}}, {\it{tm\/}})\index{tm-set-svcid} \\ 
$=$$\;\;\;\;${\rm{tm}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\it{svcid\/}}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}, \\ 
{\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit}, \\ 
{\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode}, \\ 
{\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate}, \\ 
{\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock}, \\ 
{\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports}, \\ 
{\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-\index{tm}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-set-base} \\  
\=\+{\rm{tm-set-base}}\,({\it{base\/}}, {\it{tm\/}})\index{tm-set-base} \\ 
$=$$\;\;\;\;${\rm{tm}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\it{base\/}}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}, \\ 
{\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit}, \\ 
{\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode}, \\ 
{\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate}, \\ 
{\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock}, \\ 
{\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports}, \\ 
{\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-\index{tm}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-set-limit} \\  
\=\+{\rm{tm-set-limit}}\,({\it{limit\/}}, {\it{tm\/}})\index{tm-set-limit} \\ 
$=$$\;\;\;\;${\rm{tm}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\it{limit\/}}, \\ 
{\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit}, \\ 
{\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode}, \\ 
{\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate}, \\ 
{\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock}, \\ 
{\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports}, \\ 
{\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-\index{tm}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-set-slimit} \\  
\=\+{\rm{tm-set-slimit}}\,({\it{slimit\/}}, {\it{tm\/}})\index{tm-set-slimit} \\ 
$=$$\;\;\;\;${\rm{tm}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}, \\ 
{\it{slimit\/}}, \\ 
{\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode}, \\ 
{\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate}, \\ 
{\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock}, \\ 
{\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports}, \\ 
{\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-\index{tm}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-set-svmode} \\  
\=\+{\rm{tm-set-svmode}}\,({\it{svmode\/}}, {\it{tm\/}})\index{tm-set-svmode} \\ 
$=$$\;\;\;\;${\rm{tm}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}, \\ 
{\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit}, \\ 
{\it{svmode\/}}, \\ 
{\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate}, \\ 
{\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock}, \\ 
{\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports}, \\ 
{\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-\index{tm}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-set-rwstate} \\  
\=\+{\rm{tm-set-rwstate}}\,({\it{rwstate\/}}, {\it{tm\/}})\index{tm-set-rwstate} \\ 
$=$$\;\;\;\;${\rm{tm}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}, \\ 
{\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit}, \\ 
{\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode}, \\ 
{\it{rwstate\/}}, \\ 
{\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock}, \\ 
{\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports}, \\ 
{\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-\index{tm}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-set-clock} \\  
\=\+{\rm{tm-set-clock}}\,({\it{clock\/}}, {\it{tm\/}})\index{tm-set-clock} \\ 
$=$$\;\;\;\;${\rm{tm}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}, \\ 
{\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit}, \\ 
{\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode}, \\ 
{\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate}, \\ 
{\it{clock\/}}, \\ 
{\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports}, \\ 
{\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-\index{tm}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-set-iports} \\  
\=\+{\rm{tm-set-iports}}\,({\it{iports\/}}, {\it{tm\/}})\index{tm-set-iports} \\ 
$=$$\;\;\;\;${\rm{tm}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}, \\ 
{\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit}, \\ 
{\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode}, \\ 
{\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate}, \\ 
{\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock}, \\ 
{\it{iports\/}}, \\ 
{\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-\index{tm}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-set-oports} \\  
\=\+{\rm{tm-set-oports}}\,({\it{oports\/}}, {\it{tm\/}})\index{tm-set-oports} \\ 
$=$$\;\;\;\;${\rm{tm}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}, \\ 
{\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit}, \\ 
{\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode}, \\ 
{\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate}, \\ 
{\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock}, \\ 
{\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports}, \\ 
{\it{oports\/}})\-\index{tm}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-pc}$\;\;$
{\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs})\index{getnth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-set-pc} \\  
{\rm{tm-set-pc}}\,({\it{pc\/}}, {\it{tm\/}})\index{tm-set-pc} $=$ {\rm{tm-set-regs}}\,({\rm{putnth}}\,({\it{pc\/}}, {\tt{'}}{\tt{0}}, {\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs})\index{putnth}, {\it{tm\/}})\index{tm-set-regs}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-sp}$\;\;$
{\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs})\index{getnth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-set-sp} \\  
{\rm{tm-set-sp}}\,({\it{sp\/}}, {\it{tm\/}})\index{tm-set-sp} $=$ {\rm{tm-set-regs}}\,({\rm{putnth}}\,({\it{sp\/}}, {\tt{'}}{\tt{1}}, {\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs})\index{putnth}, {\it{tm\/}})\index{tm-set-regs}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-non-zero-no-carry-condition}$\;\;$
{\sc{tm-non-zero-no-carry-condition}}\index{tm-non-zero-no-carry-condition} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-zero-no-carry-condition}$\;\;$
{\sc{tm-zero-no-carry-condition}}\index{tm-zero-no-carry-condition} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-non-zero-carry-condition}$\;\;$
{\sc{tm-non-zero-carry-condition}}\index{tm-non-zero-carry-condition} $=$ {\tt{'}}{\tt{2}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-zero-carry-condition}$\;\;$
{\sc{tm-zero-carry-condition}}\index{tm-zero-carry-condition} $=$ {\tt{'}}{\tt{3}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-cc-value} \\  
\=\+{\rm{tm-cc-value}}\,({\it{alu-result\/}})\index{tm-cc-value} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{alu-value}}\,({\it{alu-result\/}})\index{alu-value} $\simeq {\tt{0}}$ \\ 
{\bf then }\=\+{\bf if }{\rm{falsep}}\,({\rm{alu-carry}}\,({\it{alu-result\/}})\index{alu-carry})$\;\;${\bf then }{\tt{'}}{\tt{1}} \\ 
{\bf else }{\tt{'}}{\tt{3}}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{falsep}}\,({\rm{alu-carry}}\,({\it{alu-result\/}})\index{alu-carry})$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf else }{\tt{'}}{\tt{2}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-cc-divisor}$\;\;$
{\sc{tm-cc-divisor}}\index{tm-cc-divisor} $=$ {\tt{'}}{\tt{4}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-error-divisor}$\;\;$
{\sc{tm-error-divisor}}\index{tm-error-divisor} $=$ {\tt{'}}{\tt{256}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-svcflag-divisor}$\;\;$
{\sc{tm-svcflag-divisor}}\index{tm-svcflag-divisor} $=$ {\tt{'}}{\tt{512}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-pack-psw} \\  
\=\+{\rm{tm-pack-psw}}\,({\it{cc\/}}, {\it{error\/}}, {\it{svcflag\/}}, {\it{svcid\/}})\index{tm-pack-psw} \\ 
$=$$\;\;\;\;$({\it{cc\/}} $+$ (\=\+({\it{error\/}} $*$ {\tt{'}}{\tt{4}}) \\ 
$+$$\;\;\;\;$(({\it{svcflag\/}} $*$ {\tt{'}}{\tt{256}}) $+$ ({\it{svcid\/}} $*$ {\tt{'}}{\tt{512}})))\-)\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-pack-psw1 \\ \index{finite-numberp-tm-pack-psw1}
\=\+(\=\+{\rm{finite-numberp}}\,({\it{cc\/}}, {\tt{'}}{\tt{4}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{error\/}}, {\tt{'}}{\tt{64}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$({\rm{finite-numberp}}\,({\it{svcflag\/}}, {\tt{'}}{\tt{2}})\index{finite-numberp} $\wedge$ {\rm{finite-numberp}}\,({\it{svcid\/}}, {\tt{'}}{\tt{128}})\index{finite-numberp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-pack-psw}}\,({\it{cc\/}}, {\it{error\/}}, {\it{svcflag\/}}, {\it{svcid\/}})\index{tm-pack-psw}, {\tt{'}}{\tt{65536}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-pack-psw1.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tm-unpack-cc}$\;\;$
{\rm{tm-unpack-cc}}\,({\it{psw\/}})\index{tm-unpack-cc} $=$ ({\it{psw\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-unpack-error}$\;\;$
{\rm{tm-unpack-error}}\,({\it{psw\/}})\index{tm-unpack-error} $=$ (({\it{psw\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{256}}) $\div$ {\tt{'}}{\tt{4}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-unpack-svcflag} \\  
{\rm{tm-unpack-svcflag}}\,({\it{psw\/}})\index{tm-unpack-svcflag} $=$ (({\it{psw\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{512}}) $\div$ {\tt{'}}{\tt{256}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-unpack-svcid}$\;\;$
{\rm{tm-unpack-svcid}}\,({\it{psw\/}})\index{tm-unpack-svcid} $=$ ({\it{psw\/}} $\div$ {\tt{'}}{\tt{512}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-unpack-cc \\ \index{finite-numberp-tm-unpack-cc}
{\rm{finite-numberp}}\,({\rm{tm-unpack-cc}}\,({\it{psw\/}})\index{tm-unpack-cc}, {\tt{'}}{\tt{4}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-unpack-cc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-unpack-error \\ \index{finite-numberp-tm-unpack-error}
{\rm{finite-numberp}}\,({\rm{tm-unpack-error}}\,({\it{psw\/}})\index{tm-unpack-error}, {\tt{'}}{\tt{64}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-unpack-error.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-unpack-svcflag \\ \index{finite-numberp-tm-unpack-svcfla!g}
{\rm{finite-numberp}}\,({\rm{tm-unpack-svcflag}}\,({\it{psw\/}})\index{tm-unpack-svcflag}, {\tt{'}}{\tt{2}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-unpack-svcflag.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-unpack-svcid \\ \index{finite-numberp-tm-unpack-svcid}
{\rm{finite-numberp}}\,({\it{psw\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp} $\rightarrow$ {\rm{finite-numberp}}\,({\rm{tm-unpack-svcid}}\,({\it{psw\/}})\index{tm-unpack-svcid}, {\tt{'}}{\tt{128}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-unpack-svcid.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tm-register-save-area-addr}$\;\;$
{\sc{tm-register-save-area-addr}}\index{tm-register-save-area-addr} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-clock-new-pc-addr}$\;\;$
{\sc{tm-clock-new-pc-addr}}\index{tm-clock-new-pc-addr} $=$ {\tt{'}}{\tt{3}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-error-new-pc-addr}$\;\;$
{\sc{tm-error-new-pc-addr}}\index{tm-error-new-pc-addr} $=$ {\tt{'}}{\tt{4}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-svc-new-pc-addr}$\;\;$
{\sc{tm-svc-new-pc-addr}}\index{tm-svc-new-pc-addr} $=$ {\tt{'}}{\tt{5}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-input-new-pc-addr}$\;\;$
{\sc{tm-input-new-pc-addr}}\index{tm-input-new-pc-addr} $=$ {\tt{'}}{\tt{6}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-output-new-pc-addr}$\;\;$
{\sc{tm-output-new-pc-addr}}\index{tm-output-new-pc-addr} $=$ {\tt{'}}{\tt{7}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-svcid-addr}$\;\;$
{\sc{tm-svcid-addr}}\index{tm-svcid-addr} $=$ {\tt{'}}{\tt{8}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-input-devid-addr}$\;\;$
{\sc{tm-input-devid-addr}}\index{tm-input-devid-addr} $=$ {\tt{'}}{\tt{8}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-input-char-addr}$\;\;$
{\sc{tm-input-char-addr}}\index{tm-input-char-addr} $=$ {\tt{'}}{\tt{9}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-output-devid-addr}$\;\;$
{\sc{tm-output-devid-addr}}\index{tm-output-devid-addr} $=$ {\tt{'}}{\tt{9}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-no-error}$\;\;$
{\sc{tm-no-error}}\index{tm-no-error} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-halt-status}$\;\;$
{\sc{tm-halt-status}}\index{tm-halt-status} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-opcode-error}$\;\;$
{\sc{tm-opcode-error}}\index{tm-opcode-error} $=$ {\tt{'}}{\tt{2}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-privilege-error}$\;\;$
{\sc{tm-privilege-error}}\index{tm-privilege-error} $=$ {\tt{'}}{\tt{3}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-stack-overflow-error}$\;\;$
{\sc{tm-stack-overflow-error}}\index{tm-stack-overflow-error} $=$ {\tt{'}}{\tt{4}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-stack-underflow-error}$\;\;$
{\sc{tm-stack-underflow-error}}\index{tm-stack-underflow-error} $=$ {\tt{'}}{\tt{5}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-address-error}$\;\;$
{\sc{tm-address-error}}\index{tm-address-error} $=$ {\tt{'}}{\tt{6}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-pc-address-error}$\;\;$
{\sc{tm-pc-address-error}}\index{tm-pc-address-error} $=$ {\tt{'}}{\tt{7}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-supervisor-mode}$\;\;$
{\sc{tm-supervisor-mode}}\index{tm-supervisor-mode} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-user-mode}$\;\;$
{\sc{tm-user-mode}}\index{tm-user-mode} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-in-supervisor-mode}$\;\;$
{\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode} $=$ ({\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode} $=$ {\tt{'}}{\tt{1}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-wait-state}$\;\;$
{\sc{tm-wait-state}}\index{tm-wait-state} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-run-state}$\;\;$
{\sc{tm-run-state}}\index{tm-run-state} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-waiting}$\;\;$
{\rm{tm-waiting}}\,({\it{tm\/}})\index{tm-waiting} $=$ ({\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate} $=$ {\tt{'}}{\tt{1}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-svc}$\;\;$
{\sc{tm-svc}}\index{tm-svc} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-no-svc}$\;\;$
{\sc{tm-no-svc}}\index{tm-no-svc} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-cleared-svcflag}$\;\;$
{\sc{tm-cleared-svcflag}}\index{tm-cleared-svcflag} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}


\noindent{\sc Event}:   Add the shell {\it{tm-iport\/}}\index{tm-iport}, with recognizer function symbol {\it{tm-iportp\/}} and 3 accessors: {\it{tm-iinterrupt-flag\/}}, with type restriction (none-of) and default value zero; {\it{tm-ierror-flag\/}}, with type restriction (none-of) and default value zero; {\it{tm-ichar\/}}, with type restriction (none-of) and default value zero.

\addvspace{18pt}


\noindent{\sc Event}:   Add the shell {\it{tm-oport\/}}\index{tm-oport}, with recognizer function symbol {\it{tm-oportp\/}} and 3 accessors: {\it{tm-ointerrupt-flag\/}}, with type restriction (none-of) and default value zero; {\it{tm-obusy-flag\/}}, with type restriction (none-of) and default value zero; {\it{tm-ochar\/}}, with type restriction (none-of) and default value zero.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tm-iport-errorp} \\  
{\rm{tm-iport-errorp}}\,({\it{id\/}}, {\it{ports\/}})\index{tm-iport-errorp} $=$ ({\rm{tm-ierror-flag}}\,({\rm{getnth}}\,({\it{id\/}}, {\it{ports\/}})\index{getnth})\index{tm-ierror-flag} $=$ {\tt{'}}{\tt{1}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-clear-input-interrupt} \\  
\=\+{\rm{tm-clear-input-interrupt}}\,({\it{id\/}}, {\it{ports\/}})\index{tm-clear-input-interrupt} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-iport}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-ierror-flag}}\,({\rm{getnth}}\,({\it{id\/}}, {\it{ports\/}})\index{getnth})\index{tm-ierror-flag}, \\ 
{\rm{tm-ichar}}\,({\rm{getnth}}\,({\it{id\/}}, {\it{ports\/}})\index{getnth})\index{tm-ichar})\-\index{tm-iport}, \\ 
{\it{id\/}}, \\ 
{\it{ports\/}})\-\index{putnth}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-post-input-interrupt} \\  
\=\+{\rm{tm-post-input-interrupt}}\,({\it{char\/}}, {\it{id\/}}, {\it{ports\/}})\index{tm-post-input-interrupt} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-iport}}\,({\tt{'}}{\tt{1}}, {\rm{tm-iinterrupt-flag}}\,({\rm{getnth}}\,({\it{id\/}}, {\it{ports\/}})\index{getnth})\index{tm-iinterrupt-flag}, {\it{char\/}})\index{tm-iport}, \\ 
{\it{id\/}}, \\ 
{\it{ports\/}})\-\index{putnth}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-oport-idlep} \\  
{\rm{tm-oport-idlep}}\,({\it{id\/}}, {\it{ports\/}})\index{tm-oport-idlep} $=$ ({\rm{tm-obusy-flag}}\,({\rm{getnth}}\,({\it{id\/}}, {\it{ports\/}})\index{getnth})\index{tm-obusy-flag} $=$ {\tt{'}}{\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-start-output} \\  
\=\+{\rm{tm-start-output}}\,({\it{char\/}}, {\it{id\/}}, {\it{ports\/}})\index{tm-start-output} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,({\rm{tm-oport}}\,({\tt{'}}{\tt{0}}, {\tt{'}}{\tt{1}}, {\it{char\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{256}})\index{tm-oport}, {\it{id\/}}, {\it{ports\/}})\index{putnth}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-post-output-interrupt} \\  
\=\+{\rm{tm-post-output-interrupt}}\,({\it{id\/}}, {\it{ports\/}})\index{tm-post-output-interrupt} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,({\tt{'}}{\tt{(}}{\tt{*1*quote}}{\tt{ }}{\tt{tm-oport}}{\tt{ }}{\tt{1}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, {\it{id\/}}, {\it{ports\/}})\index{putnth}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-clear-output-interrupt} \\  
\=\+{\rm{tm-clear-output-interrupt}}\,({\it{id\/}}, {\it{ports\/}})\index{tm-clear-output-interrupt} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-oport}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-obusy-flag}}\,({\rm{getnth}}\,({\it{id\/}}, {\it{ports\/}})\index{getnth})\index{tm-obusy-flag}, \\ 
{\rm{tm-ochar}}\,({\rm{getnth}}\,({\it{id\/}}, {\it{ports\/}})\index{getnth})\index{tm-ochar})\-\index{tm-oport}, \\ 
{\it{id\/}}, \\ 
{\it{ports\/}})\-\index{putnth}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{real-addr} \\  
{\rm{real-addr}}\,({\it{source\/}}, {\it{num\/}})\index{real-addr} $=$ {\rm{cons}}\,({\it{source\/}}, {\rm{cons}}\,({\it{num\/}}, {\tt{'}}{\tt{nil}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{real-addr-source}$\;\;$
{\rm{real-addr-source}}\,({\it{real-addr\/}})\index{real-addr-source} $=$ {\rm{car}}\,({\it{real-addr\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{real-addr-num}$\;\;$
{\rm{real-addr-num}}\,({\it{real-addr\/}})\index{real-addr-num} $=$ {\rm{car}}\,({\rm{cdr}}\,({\it{real-addr\/}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-arg-mode}$\;\;$
{\rm{tm-arg-mode}}\,({\it{x\/}})\index{tm-arg-mode} $=$ {\rm{car}}\,({\it{x\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-arg-datum}$\;\;$
{\rm{tm-arg-datum}}\,({\it{x\/}})\index{tm-arg-datum} $=$ {\rm{car}}\,({\rm{cdr}}\,({\it{x\/}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-arg-index}$\;\;$
{\rm{tm-arg-index}}\,({\it{x\/}})\index{tm-arg-index} $=$ {\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{x\/}})))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-fix-word}$\;\;$
{\rm{tm-fix-word}}\,({\it{n\/}})\index{tm-fix-word} $=$ ({\it{n\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{65536}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-fix-reg-address}$\;\;$
{\rm{tm-fix-reg-address}}\,({\it{n\/}})\index{tm-fix-reg-address} $=$ ({\it{n\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{8}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-compute-address} \\  
\=\+{\rm{tm-compute-address}}\,({\it{arg\/}}, {\it{tm\/}})\index{tm-compute-address} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-arg-mode}}\,({\it{arg\/}})\index{tm-arg-mode} $\simeq {\tt{0}}$ \\ 
{\bf then }{\rm{real-addr}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-fix-word}}\,({\rm{tm-arg-datum}}\,({\it{arg\/}})\index{tm-arg-datum} $+$ {\rm{tm-arg-index}}\,({\it{arg\/}})\index{tm-arg-index})\index{tm-fix-word})\-\index{real-addr} \\ 
{\bf elseif }{\rm{tm-arg-mode}}\,({\it{arg\/}})\index{tm-arg-mode} $=$ {\tt{'}}{\tt{1}} \\ 
{\bf then }{\rm{real-addr}}\,({\tt{'}}{\tt{1}}, {\rm{tm-fix-reg-address}}\,({\rm{tm-arg-datum}}\,({\it{arg\/}})\index{tm-arg-datum})\index{tm-fix-reg-address})\index{real-addr} \\ 
{\bf elseif }{\rm{tm-arg-mode}}\,({\it{arg\/}})\index{tm-arg-mode} $=$ {\tt{'}}{\tt{2}} \\ 
{\bf then }{\rm{real-addr}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{tm-fix-word}}\,({\rm{tm-arg-datum}}\,({\it{arg\/}})\index{tm-arg-datum} $+$ {\rm{tm-arg-index}}\,({\it{arg\/}})\index{tm-arg-index})\index{tm-fix-word})\-\index{real-addr} \\ 
{\bf else }{\rm{real-addr}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{tm-fix-word}}\,(\=\+{\rm{getnth}}\,(\=\+{\rm{tm-fix-reg-address}}\,({\rm{tm-arg-datum}}\,({\it{arg\/}})\index{tm-arg-datum})\index{tm-fix-reg-address}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs})\-\index{getnth} \\ 
$+$$\;\;\;\;${\rm{tm-arg-index}}\,({\it{arg\/}})\index{tm-arg-index}\-)\index{tm-fix-word})\-\index{real-addr}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-good-address} \\  
\=\+{\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} $\simeq {\tt{0}}$ \\ 
{\bf then }{\rm{finite-numberp}}\,({\rm{real-addr-num}}\,({\it{addr\/}})\index{real-addr-num}, {\tt{'}}{\tt{65536}})\index{finite-numberp} \\ 
{\bf elseif }{\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} $=$ {\tt{'}}{\tt{1}} \\ 
{\bf then }{\rm{finite-numberp}}\,({\rm{real-addr-num}}\,({\it{addr\/}})\index{real-addr-num}, {\tt{'}}{\tt{8}})\index{finite-numberp} \\ 
{\bf elseif }{\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode} \\ 
{\bf then }{\rm{finite-numberp}}\,({\rm{real-addr-num}}\,({\it{addr\/}})\index{real-addr-num}, {\tt{'}}{\tt{65536}})\index{finite-numberp} \\ 
{\bf else }{\rm{finite-numberp}}\,(\=\+{\rm{real-addr-num}}\,({\it{addr\/}})\index{real-addr-num}, \\ 
{\rm{min}}\,({\tt{'}}{\tt{65536}} $-$ {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\index{min})\-\index{finite-numberp}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-incr-address} \\  
\=\+{\rm{tm-incr-address}}\,({\it{addr\/}})\index{tm-incr-address} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} $\simeq {\tt{0}}$ \\ 
{\bf then }{\rm{real-addr}}\,({\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source}, {\rm{tm-incr}}\,({\rm{real-addr-num}}\,({\it{addr\/}})\index{real-addr-num})\index{tm-incr})\index{real-addr} \\ 
{\bf elseif }{\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} $=$ {\tt{'}}{\tt{1}} \\ 
{\bf then }{\rm{real-addr}}\,(\=\+{\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source}, \\ 
($1\;+$ {\rm{real-addr-num}}\,({\it{addr\/}})\index{real-addr-num}) ${}${\bf{mod}}${}$ {\tt{'}}{\tt{8}})\-\index{real-addr} \\ 
{\bf else }{\rm{real-addr}}\,(\=\+{\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source}, \\ 
{\rm{tm-incr}}\,({\rm{real-addr-num}}\,({\it{addr\/}})\index{real-addr-num})\index{tm-incr})\-\index{real-addr}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-incrn-address} \\  
\=\+{\rm{tm-incrn-address}}\,({\it{n\/}}, {\it{a\/}})\index{tm-incrn-address} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\it{a\/}} \\ 
{\bf else }{\rm{tm-incr-address}}\,({\rm{tm-incrn-address}}\,({\it{n\/}} $-\;1$, {\it{a\/}})\index{tm-incrn-address})\index{tm-incr-address}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-fetch-from-memory} \\  
\=\+{\rm{tm-fetch-from-memory}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch-from-memory} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}$\;\;${\bf then }{\rm{getnth}}\,({\it{addr\/}}, {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{getnth} \\ 
{\bf else }{\rm{getnth}}\,({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\it{addr\/}}, {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{getnth}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-store-in-memory} \\  
\=\+{\rm{tm-store-in-memory}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store-in-memory} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode} \\ 
{\bf then }{\rm{tm-set-memory}}\,({\rm{putnth}}\,({\it{value\/}}, {\it{addr\/}}, {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{putnth}, {\it{tm\/}})\index{tm-set-memory} \\ 
{\bf else }{\rm{tm-set-memory}}\,(\=\+{\rm{putnth}}\,(\=\+{\it{value\/}}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\it{addr\/}}, \\ 
{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\-\index{putnth}, \\ 
{\it{tm\/}})\-\index{tm-set-memory}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-fetch-from-regmem} \\  
{\rm{tm-fetch-from-regmem}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch-from-regmem} $=$ {\rm{getnth}}\,({\it{addr\/}}, {\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs})\index{getnth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-store-in-regmem} \\  
\=\+{\rm{tm-store-in-regmem}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store-in-regmem} \\ 
$=$$\;\;\;\;${\rm{tm-set-regs}}\,({\rm{putnth}}\,({\it{value\/}}, {\it{addr\/}}, {\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs})\index{putnth}, {\it{tm\/}})\index{tm-set-regs}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-fetch} \\  
\=\+{\rm{tm-fetch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} $\simeq {\tt{0}}$$\;\;${\bf then }{\rm{real-addr-num}}\,({\it{addr\/}})\index{real-addr-num} \\ 
{\bf elseif }{\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} $=$ {\tt{'}}{\tt{1}} \\ 
{\bf then }{\rm{tm-fetch-from-regmem}}\,({\rm{real-addr-num}}\,({\it{addr\/}})\index{real-addr-num}, {\it{tm\/}})\index{tm-fetch-from-regmem} \\ 
{\bf else }{\rm{tm-fetch-from-memory}}\,({\rm{real-addr-num}}\,({\it{addr\/}})\index{real-addr-num}, {\it{tm\/}})\index{tm-fetch-from-memory}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-store} \\  
\=\+{\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} $\simeq {\tt{0}}$$\;\;${\bf then }{\it{tm\/}} \\ 
{\bf elseif }{\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} $=$ {\tt{'}}{\tt{1}} \\ 
{\bf then }{\rm{tm-store-in-regmem}}\,({\it{value\/}}, {\rm{real-addr-num}}\,({\it{addr\/}})\index{real-addr-num}, {\it{tm\/}})\index{tm-store-in-regmem} \\ 
{\bf else }{\rm{tm-store-in-memory}}\,({\it{value\/}}, {\rm{real-addr-num}}\,({\it{addr\/}})\index{real-addr-num}, {\it{tm\/}})\index{tm-store-in-memory}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-stack-overflowp}$\;\;$
{\rm{tm-stack-overflowp}}\,({\it{tm\/}})\index{tm-stack-overflowp} $=$ ({\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp} $\simeq {\tt{0}}$)
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-stack-underflowp} \\  
\=\+{\rm{tm-stack-underflowp}}\,({\it{tm\/}})\index{tm-stack-underflowp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}$\;\;${\bf then }($1\;+$ {\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp}) $\not<$ {\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit} \\ 
{\bf else }\=\+($1\;+$ {\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp}) \\ 
$\not<$$\;\;\;\;${\rm{min}}\,({\tt{'}}{\tt{65536}} $-$ {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\index{min}\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tm-stack-underflowp-guards-good-address \\ \index{tm-stack-underflowp-guards-good!-address}
\=\+(($\neg$ {\rm{tm-stack-underflowp}}\,({\it{tm\/}})\index{tm-stack-underflowp}) $\wedge$ {\rm{finite-numberp}}\,({\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit}, {\tt{'}}{\tt{65536}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{tm-good-address}}\,({\rm{real-addr}}\,({\tt{'}}{\tt{2}}, $1\;+$ {\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp})\index{real-addr}, {\it{tm\/}})\index{tm-good-address}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-stack-underflowp-guards-good-address.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tm-execute-add} \\  
\=\+{\rm{tm-execute-add}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-add} \\ 
$=$$\;\;\;\;${\rm{tm-store}}\,(\=\+{\rm{alu-value}}\,({\rm{tm-alu-plus}}\,({\rm{tm-fetch}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-fetch}, {\rm{tm-fetch}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-fetch})\index{tm-alu-plus})\index{alu-value}, \\ 
{\it{addr1\/}}, \\ 
{\rm{tm-set-cc}}\,(\=\+{\rm{tm-cc-value}}\,({\rm{tm-alu-plus}}\,(\=\+{\rm{tm-fetch}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-fetch}, \\ 
{\rm{tm-fetch}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-fetch})\-\index{tm-alu-plus})\index{tm-cc-value}, \\ 
{\it{tm\/}})\-\index{tm-set-cc})\-\index{tm-store}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-branch} \\  
{\rm{tm-execute-branch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch} $=$ {\rm{tm-set-pc}}\,({\rm{tm-fetch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch}, {\it{tm\/}})\index{tm-set-pc}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-branch-on-zero} \\  
\=\+{\rm{tm-execute-branch-on-zero}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch-on-zero} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc} $=$ {\tt{'}}{\tt{1}}$\;\;${\bf then }{\rm{tm-set-pc}}\,({\rm{tm-fetch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch}, {\it{tm\/}})\index{tm-set-pc} \\ 
{\bf else }{\it{tm\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-branch-not-zero} \\  
\=\+{\rm{tm-execute-branch-not-zero}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch-not-zero} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc} $=$ {\tt{'}}{\tt{1}}$\;\;${\bf then }{\it{tm\/}} \\ 
{\bf else }{\rm{tm-set-pc}}\,({\rm{tm-fetch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch}, {\it{tm\/}})\index{tm-set-pc}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-call} \\  
\=\+{\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-call} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-stack-overflowp}}\,({\it{tm\/}})\index{tm-stack-overflowp}$\;\;${\bf then }{\rm{tm-set-error}}\,({\tt{'}}{\tt{4}}, {\it{tm\/}})\index{tm-set-error} \\ 
{\bf elseif }{\rm{tm-good-address}}\,({\rm{real-addr}}\,({\tt{'}}{\tt{2}}, {\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp})\index{real-addr}, {\it{tm\/}})\index{tm-good-address} \\ 
{\bf then }{\rm{tm-store}}\,(\=\+{\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc}, \\ 
{\rm{real-addr}}\,({\tt{'}}{\tt{2}}, {\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp})\index{real-addr}, \\ 
{\rm{tm-set-pc}}\,(\=\+{\rm{tm-fetch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch}, \\ 
{\rm{tm-set-sp}}\,({\rm{tm-decr}}\,({\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp})\index{tm-decr}, {\it{tm\/}})\index{tm-set-sp})\-\index{tm-set-pc})\-\index{tm-store} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{6}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-compare} \\  
\=\+{\rm{tm-execute-compare}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-compare} \\ 
$=$$\;\;\;\;${\rm{tm-set-cc}}\,(\=\+{\rm{tm-cc-value}}\,({\rm{tm-alu-difference}}\,(\=\+{\rm{tm-fetch}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-fetch}, \\ 
{\rm{tm-fetch}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-fetch})\-\index{tm-alu-difference})\index{tm-cc-value}, \\ 
{\it{tm\/}})\-\index{tm-set-cc}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-decr} \\  
\=\+{\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-decr} \\ 
$=$$\;\;\;\;${\rm{tm-store}}\,(\=\+{\rm{alu-value}}\,({\rm{tm-alu-decr}}\,({\rm{tm-fetch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch})\index{tm-alu-decr})\index{alu-value}, \\ 
{\it{addr\/}}, \\ 
{\rm{tm-set-cc}}\,({\rm{tm-cc-value}}\,({\rm{tm-alu-decr}}\,({\rm{tm-fetch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch})\index{tm-alu-decr})\index{tm-cc-value}, {\it{tm\/}})\index{tm-set-cc})\-\index{tm-store}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-decr-mod} \\  
\=\+{\rm{tm-execute-decr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-decr-mod} \\ 
$=$$\;\;\;\;${\rm{tm-store}}\,(\=\+{\rm{alu-value}}\,({\rm{tm-alu-decr-mod}}\,(\=\+{\rm{tm-fetch}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-fetch}, \\ 
{\rm{tm-fetch}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-fetch})\-\index{tm-alu-decr-mod})\index{alu-value}, \\ 
{\it{addr1\/}}, \\ 
{\rm{tm-set-cc}}\,(\=\+{\rm{tm-cc-value}}\,({\rm{tm-alu-decr-mod}}\,(\=\+{\rm{tm-fetch}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-fetch}, \\ 
{\rm{tm-fetch}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-fetch})\-\index{tm-alu-decr-mod})\index{tm-cc-value}, \\ 
{\it{tm\/}})\-\index{tm-set-cc})\-\index{tm-store}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-incr} \\  
\=\+{\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-incr} \\ 
$=$$\;\;\;\;${\rm{tm-store}}\,(\=\+{\rm{alu-value}}\,({\rm{tm-alu-incr}}\,({\rm{tm-fetch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch})\index{tm-alu-incr})\index{alu-value}, \\ 
{\it{addr\/}}, \\ 
{\rm{tm-set-cc}}\,({\rm{tm-cc-value}}\,({\rm{tm-alu-incr}}\,({\rm{tm-fetch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch})\index{tm-alu-incr})\index{tm-cc-value}, {\it{tm\/}})\index{tm-set-cc})\-\index{tm-store}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-incr-mod} \\  
\=\+{\rm{tm-execute-incr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-incr-mod} \\ 
$=$$\;\;\;\;${\rm{tm-store}}\,(\=\+{\rm{alu-value}}\,({\rm{tm-alu-incr-mod}}\,(\=\+{\rm{tm-fetch}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-fetch}, \\ 
{\rm{tm-fetch}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-fetch})\-\index{tm-alu-incr-mod})\index{alu-value}, \\ 
{\it{addr1\/}}, \\ 
{\rm{tm-set-cc}}\,(\=\+{\rm{tm-cc-value}}\,({\rm{tm-alu-incr-mod}}\,(\=\+{\rm{tm-fetch}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-fetch}, \\ 
{\rm{tm-fetch}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-fetch})\-\index{tm-alu-incr-mod})\index{tm-cc-value}, \\ 
{\it{tm\/}})\-\index{tm-set-cc})\-\index{tm-store}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-load-base} \\  
\=\+{\rm{tm-execute-load-base}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-base} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}$\;\;${\bf then }{\rm{tm-set-base}}\,({\rm{tm-fetch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch}, {\it{tm\/}})\index{tm-set-base} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{3}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-load-limit} \\  
\=\+{\rm{tm-execute-load-limit}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-limit} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}$\;\;${\bf then }{\rm{tm-set-limit}}\,({\rm{tm-fetch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch}, {\it{tm\/}})\index{tm-set-limit} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{3}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-load-psw} \\  
\=\+{\rm{tm-execute-load-psw}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-psw} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode} \\ 
{\bf then }{\rm{tm-set-svmode}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-set-pc}}\,(\=\+{\rm{tm-fetch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch}, \\ 
{\rm{tm-set-sp}}\,(\=\+{\rm{tm-fetch}}\,(\=\+{\rm{tm-incrn-address}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\it{addr\/}})\-\index{tm-incrn-address}, \\ 
{\it{tm\/}})\-\index{tm-fetch}, \\ 
{\rm{tm-set-cc}}\,(\=\+{\rm{tm-unpack-cc}}\,({\rm{tm-fetch}}\,(\=\+{\rm{tm-incrn-address}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\it{addr\/}})\-\index{tm-incrn-address}, \\ 
{\it{tm\/}})\-\index{tm-fetch})\index{tm-unpack-cc}, \\ 
{\rm{tm-set-error}}\,(\=\+{\rm{tm-unpack-error}}\,({\rm{tm-fetch}}\,(\=\+{\rm{tm-incrn-address}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\it{addr\/}})\-\index{tm-incrn-address}, \\ 
{\it{tm\/}})\-\index{tm-fetch})\index{tm-unpack-error}, \\ 
{\rm{tm-set-svcflag}}\,(\=\+{\rm{tm-unpack-svcflag}}\,({\rm{tm-fetch}}\,(\=\+{\rm{tm-incrn-address}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\it{addr\/}})\-\index{tm-incrn-address}, \\ 
{\it{tm\/}})\-\index{tm-fetch})\index{tm-unpack-svcflag}, \\ 
{\rm{tm-set-svcid}}\,(\=\+{\rm{tm-unpack-svcid}}\,({\rm{tm-fetch}}\,(\=\+{\rm{tm-incrn-address}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\it{addr\/}})\-\index{tm-incrn-address}, \\ 
{\it{tm\/}})\-\index{tm-fetch})\index{tm-unpack-svcid}, \\ 
{\it{tm\/}})\-\index{tm-set-svcid})\-\index{tm-set-svcflag})\-\index{tm-set-error})\-\index{tm-set-cc})\-\index{tm-set-sp})\-\index{tm-set-pc})\-\index{tm-set-svmode} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{3}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-mod} \\  
\=\+{\rm{tm-execute-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-mod} \\ 
$=$$\;\;\;\;${\rm{tm-store}}\,(\=\+{\rm{alu-value}}\,({\rm{tm-alu-mod}}\,({\rm{tm-fetch}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-fetch}, {\rm{tm-fetch}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-fetch})\index{tm-alu-mod})\index{alu-value}, \\ 
{\it{addr1\/}}, \\ 
{\rm{tm-set-cc}}\,(\=\+{\rm{tm-cc-value}}\,({\rm{tm-alu-mod}}\,(\=\+{\rm{tm-fetch}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-fetch}, \\ 
{\rm{tm-fetch}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-fetch})\-\index{tm-alu-mod})\index{tm-cc-value}, \\ 
{\it{tm\/}})\-\index{tm-set-cc})\-\index{tm-store}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-move} \\  
{\rm{tm-execute-move}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-move} $=$ {\rm{tm-store}}\,({\rm{tm-fetch}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-fetch}, {\it{addr1\/}}, {\it{tm\/}})\index{tm-store}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-multiply} \\  
\=\+{\rm{tm-execute-multiply}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-multiply} \\ 
$=$$\;\;\;\;${\rm{tm-store}}\,(\=\+{\rm{alu-value}}\,({\rm{tm-alu-mult}}\,({\rm{tm-fetch}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-fetch}, {\rm{tm-fetch}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-fetch})\index{tm-alu-mult})\index{alu-value}, \\ 
{\it{addr1\/}}, \\ 
{\rm{tm-set-cc}}\,(\=\+{\rm{tm-cc-value}}\,({\rm{tm-alu-mult}}\,(\=\+{\rm{tm-fetch}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-fetch}, \\ 
{\rm{tm-fetch}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-fetch})\-\index{tm-alu-mult})\index{tm-cc-value}, \\ 
{\it{tm\/}})\-\index{tm-set-cc})\-\index{tm-store}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-post-output-interrupt} \\  
\=\+{\rm{tm-execute-post-output-interrupt}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-post-output-interrupt} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode} \\ 
{\bf then }{\rm{tm-set-oports}}\,(\=\+{\rm{tm-post-output-interrupt}}\,(\=\+{\rm{tm-fetch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch}, \\ 
{\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-\index{tm-post-output-interrupt}, \\ 
{\it{tm\/}})\-\index{tm-set-oports} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{3}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-return} \\  
\=\+{\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-stack-underflowp}}\,({\it{tm\/}})\index{tm-stack-underflowp}$\;\;${\bf then }{\rm{tm-set-error}}\,({\tt{'}}{\tt{5}}, {\it{tm\/}})\index{tm-set-error} \\ 
{\bf else }{\rm{tm-set-pc}}\,(\=\+{\rm{tm-fetch}}\,({\rm{real-addr}}\,({\tt{'}}{\tt{2}}, {\rm{tm-incr}}\,({\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp})\index{tm-incr})\index{real-addr}, {\it{tm\/}})\index{tm-fetch}, \\ 
{\rm{tm-set-sp}}\,({\rm{tm-incr}}\,({\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp})\index{tm-incr}, {\it{tm\/}})\index{tm-set-sp})\-\index{tm-set-pc}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-run} \\  
\=\+{\rm{tm-execute-run}}\,({\it{tm\/}})\index{tm-execute-run} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}$\;\;${\bf then }{\rm{tm-set-rwstate}}\,({\tt{'}}{\tt{0}}, {\it{tm\/}})\index{tm-set-rwstate} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{3}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-set-clock} \\  
\=\+{\rm{tm-execute-set-clock}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-set-clock} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}$\;\;${\bf then }{\rm{tm-set-clock}}\,({\rm{tm-fetch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch}, {\it{tm\/}})\index{tm-set-clock} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{3}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-start-output} \\  
\=\+{\rm{tm-execute-start-output}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-start-output} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode} \\ 
{\bf then }{\rm{tm-set-oports}}\,(\=\+{\rm{tm-start-output}}\,(\=\+{\rm{tm-fetch}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-fetch}, \\ 
{\rm{tm-fetch}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-fetch}, \\ 
{\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-\index{tm-start-output}, \\ 
{\it{tm\/}})\-\index{tm-set-oports} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{3}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-svc} \\  
\=\+{\rm{tm-execute-svc}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}$\;\;${\bf then }{\it{tm\/}} \\ 
{\bf else }{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{tm-set-svcid}}\,(\=\+{\rm{tm-fetch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{128}}, \\ 
{\it{tm\/}})\-\index{tm-set-svcid})\-\index{tm-set-svcflag}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-svc-return} \\  
\=\+{\rm{tm-execute-svc-return}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc-return} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode} \\ 
{\bf then }{\rm{tm-set-svmode}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-set-pc}}\,(\=\+{\rm{tm-fetch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch}, \\ 
{\rm{tm-set-sp}}\,(\=\+{\rm{tm-fetch}}\,(\=\+{\rm{tm-incrn-address}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\it{addr\/}})\-\index{tm-incrn-address}, \\ 
{\it{tm\/}})\-\index{tm-fetch}, \\ 
{\rm{tm-set-cc}}\,(\=\+{\rm{tm-unpack-cc}}\,({\rm{tm-fetch}}\,(\=\+{\rm{tm-incrn-address}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\it{addr\/}})\-\index{tm-incrn-address}, \\ 
{\it{tm\/}})\-\index{tm-fetch})\index{tm-unpack-cc}, \\ 
{\rm{tm-set-error}}\,(\=\+{\rm{tm-unpack-error}}\,({\rm{tm-fetch}}\,(\=\+{\rm{tm-incrn-address}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\it{addr\/}})\-\index{tm-incrn-address}, \\ 
{\it{tm\/}})\-\index{tm-fetch})\index{tm-unpack-error}, \\ 
{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-set-svcid}}\,(\=\+{\rm{tm-unpack-svcid}}\,({\rm{tm-fetch}}\,(\=\+{\rm{tm-incrn-address}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\it{addr\/}})\-\index{tm-incrn-address}, \\ 
{\it{tm\/}})\-\index{tm-fetch})\index{tm-unpack-svcid}, \\ 
{\it{tm\/}})\-\index{tm-set-svcid})\-\index{tm-set-svcflag})\-\index{tm-set-error})\-\index{tm-set-cc})\-\index{tm-set-sp})\-\index{tm-set-pc})\-\index{tm-set-svmode} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{3}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-test-iport} \\  
\=\+{\rm{tm-execute-test-iport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-iport} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode} \\ 
{\bf then }\=\+{\bf if }{\rm{tm-iport-errorp}}\,({\rm{tm-fetch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{16}}, {\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{tm-iport-errorp} \\ 
{\bf then }{\rm{tm-set-cc}}\,({\tt{'}}{\tt{1}}, {\it{tm\/}})\index{tm-set-cc} \\ 
{\bf else }{\rm{tm-set-cc}}\,({\tt{'}}{\tt{0}}, {\it{tm\/}})\index{tm-set-cc}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{3}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-test-oport} \\  
\=\+{\rm{tm-execute-test-oport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-oport} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode} \\ 
{\bf then }\=\+{\bf if }{\rm{tm-oport-idlep}}\,({\rm{tm-fetch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{16}}, {\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\index{tm-oport-idlep} \\ 
{\bf then }{\rm{tm-set-cc}}\,({\tt{'}}{\tt{1}}, {\it{tm\/}})\index{tm-set-cc} \\ 
{\bf else }{\rm{tm-set-cc}}\,({\tt{'}}{\tt{0}}, {\it{tm\/}})\index{tm-set-cc}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{3}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-wait} \\  
\=\+{\rm{tm-execute-wait}}\,({\it{tm\/}})\index{tm-execute-wait} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode} \\ 
{\bf then }{\rm{tm-set-rwstate}}\,({\tt{'}}{\tt{1}}, {\rm{tm-set-svmode}}\,({\tt{'}}{\tt{0}}, {\it{tm\/}})\index{tm-set-svmode})\index{tm-set-rwstate} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{3}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-opcode-size}$\;\;$
{\sc{tm-opcode-size}}\index{tm-opcode-size} $=$ {\tt{'}}{\tt{6}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-mode-size}$\;\;$
{\sc{tm-mode-size}}\index{tm-mode-size} $=$ {\tt{'}}{\tt{2}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-index-size}$\;\;$
{\sc{tm-index-size}}\index{tm-index-size} $=$ {\tt{'}}{\tt{3}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-opcode-divisor}$\;\;$
{\sc{tm-opcode-divisor}}\index{tm-opcode-divisor} $=$ {\tt{'}}{\tt{64}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-mode1-divisor}$\;\;$
{\sc{tm-mode1-divisor}}\index{tm-mode1-divisor} $=$ {\tt{'}}{\tt{256}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-index1-divisor}$\;\;$
{\sc{tm-index1-divisor}}\index{tm-index1-divisor} $=$ {\tt{'}}{\tt{2048}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-mode2-divisor}$\;\;$
{\sc{tm-mode2-divisor}}\index{tm-mode2-divisor} $=$ {\tt{'}}{\tt{8192}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-opcode}$\;\;$
{\rm{tm-opcode}}\,({\it{instruction\/}})\index{tm-opcode} $=$ ({\it{instruction\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{64}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-mode1} \\  
{\rm{tm-mode1}}\,({\it{instruction\/}})\index{tm-mode1} $=$ (({\it{instruction\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{256}}) $\div$ {\tt{'}}{\tt{64}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-index1} \\  
{\rm{tm-index1}}\,({\it{instruction\/}})\index{tm-index1} $=$ (({\it{instruction\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{2048}}) $\div$ {\tt{'}}{\tt{256}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-mode2} \\  
{\rm{tm-mode2}}\,({\it{instruction\/}})\index{tm-mode2} $=$ (({\it{instruction\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{8192}}) $\div$ {\tt{'}}{\tt{2048}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-index2}$\;\;$
{\rm{tm-index2}}\,({\it{instruction\/}})\index{tm-index2} $=$ ({\it{instruction\/}} $\div$ {\tt{'}}{\tt{8192}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-nullary-instructionp} \\  
\=\+{\rm{tm-nullary-instructionp}}\,({\it{instruction\/}})\index{tm-nullary-instructionp} \\ 
$=$$\;\;\;\;$(({\rm{tm-opcode}}\,({\it{instruction\/}})\index{tm-opcode} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-unary-instructionp} \\  
\=\+{\rm{tm-unary-instructionp}}\,({\it{instruction\/}})\index{tm-unary-instructionp} \\ 
$=$$\;\;\;\;$(({\rm{tm-opcode}}\,({\it{instruction\/}})\index{tm-opcode} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{2}}) $=$ {\tt{'}}{\tt{0}})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-datum1} \\  
{\rm{tm-datum1}}\,({\it{instruction-list\/}})\index{tm-datum1} $=$ {\rm{car}}\,({\rm{cdr}}\,({\it{instruction-list\/}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-datum2} \\  
{\rm{tm-datum2}}\,({\it{instruction-list\/}})\index{tm-datum2} $=$ {\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{instruction-list\/}})))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-arg1} \\  
\=\+{\rm{tm-arg1}}\,({\it{instruction-list\/}})\index{tm-arg1} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{tm-mode1}}\,({\rm{car}}\,({\it{instruction-list\/}}))\index{tm-mode1}, \\ 
{\rm{cons}}\,(\=\+{\rm{tm-datum1}}\,({\it{instruction-list\/}})\index{tm-datum1}, \\ 
{\rm{cons}}\,({\rm{tm-index1}}\,({\rm{car}}\,({\it{instruction-list\/}}))\index{tm-index1}, {\tt{'}}{\tt{nil}}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-arg2} \\  
\=\+{\rm{tm-arg2}}\,({\it{instruction-list\/}})\index{tm-arg2} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{tm-mode2}}\,({\rm{car}}\,({\it{instruction-list\/}}))\index{tm-mode2}, \\ 
{\rm{cons}}\,(\=\+{\rm{tm-datum2}}\,({\it{instruction-list\/}})\index{tm-datum2}, \\ 
{\rm{cons}}\,({\rm{tm-index2}}\,({\rm{car}}\,({\it{instruction-list\/}}))\index{tm-index2}, {\tt{'}}{\tt{nil}}))\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-return-opcode}$\;\;$
{\sc{tm-return-opcode}}\index{tm-return-opcode} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-wait-opcode}$\;\;$
{\sc{tm-wait-opcode}}\index{tm-wait-opcode} $=$ {\tt{'}}{\tt{4}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-run-opcode}$\;\;$
{\sc{tm-run-opcode}}\index{tm-run-opcode} $=$ {\tt{'}}{\tt{8}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-nullary} \\  
\=\+{\rm{tm-execute-nullary}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{opcode\/}} $=$ {\tt{'}}{\tt{0}}$\;\;${\bf then }{\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{8}}$\;\;${\bf then }{\rm{tm-execute-run}}\,({\it{tm\/}})\index{tm-execute-run} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{4}}$\;\;${\bf then }{\rm{tm-execute-wait}}\,({\it{tm\/}})\index{tm-execute-wait} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{2}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-br-opcode}$\;\;$
{\sc{tm-br-opcode}}\index{tm-br-opcode} $=$ {\tt{'}}{\tt{2}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-brnz-opcode}$\;\;$
{\sc{tm-brnz-opcode}}\index{tm-brnz-opcode} $=$ {\tt{'}}{\tt{6}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-brz-opcode}$\;\;$
{\sc{tm-brz-opcode}}\index{tm-brz-opcode} $=$ {\tt{'}}{\tt{10}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-call-opcode}$\;\;$
{\sc{tm-call-opcode}}\index{tm-call-opcode} $=$ {\tt{'}}{\tt{14}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-decr-opcode}$\;\;$
{\sc{tm-decr-opcode}}\index{tm-decr-opcode} $=$ {\tt{'}}{\tt{18}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-incr-opcode}$\;\;$
{\sc{tm-incr-opcode}}\index{tm-incr-opcode} $=$ {\tt{'}}{\tt{22}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-lbase-opcode}$\;\;$
{\sc{tm-lbase-opcode}}\index{tm-lbase-opcode} $=$ {\tt{'}}{\tt{26}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-llimit-opcode}$\;\;$
{\sc{tm-llimit-opcode}}\index{tm-llimit-opcode} $=$ {\tt{'}}{\tt{30}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-lpsw-opcode}$\;\;$
{\sc{tm-lpsw-opcode}}\index{tm-lpsw-opcode} $=$ {\tt{'}}{\tt{34}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-post-opcode}$\;\;$
{\sc{tm-post-opcode}}\index{tm-post-opcode} $=$ {\tt{'}}{\tt{38}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-svc-opcode}$\;\;$
{\sc{tm-svc-opcode}}\index{tm-svc-opcode} $=$ {\tt{'}}{\tt{42}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-svc-return-opcode}$\;\;$
{\sc{tm-svc-return-opcode}}\index{tm-svc-return-opcode} $=$ {\tt{'}}{\tt{46}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-testi-opcode}$\;\;$
{\sc{tm-testi-opcode}}\index{tm-testi-opcode} $=$ {\tt{'}}{\tt{50}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-testo-opcode}$\;\;$
{\sc{tm-testo-opcode}}\index{tm-testo-opcode} $=$ {\tt{'}}{\tt{54}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-time-opcode}$\;\;$
{\sc{tm-time-opcode}}\index{tm-time-opcode} $=$ {\tt{'}}{\tt{58}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-unary} \\  
\=\+{\rm{tm-execute-unary}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary} \\ 
$=$$\;\;\;\;$\=\+{\bf if }$\neg$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}$\;\;${\bf then }{\rm{tm-set-error}}\,({\tt{'}}{\tt{6}}, {\it{tm\/}})\index{tm-set-error} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{2}}$\;\;${\bf then }{\rm{tm-execute-branch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{10}}$\;\;${\bf then }{\rm{tm-execute-branch-on-zero}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch-on-zero} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{6}}$\;\;${\bf then }{\rm{tm-execute-branch-not-zero}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch-not-zero} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{14}}$\;\;${\bf then }{\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-call} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{18}}$\;\;${\bf then }{\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-decr} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{22}}$\;\;${\bf then }{\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-incr} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{26}}$\;\;${\bf then }{\rm{tm-execute-load-base}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-base} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{30}}$\;\;${\bf then }{\rm{tm-execute-load-limit}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-limit} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{34}}$\;\;${\bf then }{\rm{tm-execute-load-psw}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-psw} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{58}}$\;\;${\bf then }{\rm{tm-execute-set-clock}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-set-clock} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{50}}$\;\;${\bf then }{\rm{tm-execute-test-iport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-iport} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{54}}$\;\;${\bf then }{\rm{tm-execute-test-oport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-oport} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{42}}$\;\;${\bf then }{\rm{tm-execute-svc}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{46}}$\;\;${\bf then }{\rm{tm-execute-svc-return}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc-return} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{38}}$\;\;${\bf then }{\rm{tm-execute-post-output-interrupt}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-post-output-interrupt} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{2}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-add-opcode}$\;\;$
{\sc{tm-add-opcode}}\index{tm-add-opcode} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-compare-opcode}$\;\;$
{\sc{tm-compare-opcode}}\index{tm-compare-opcode} $=$ {\tt{'}}{\tt{3}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-decr-mod-opcode}$\;\;$
{\sc{tm-decr-mod-opcode}}\index{tm-decr-mod-opcode} $=$ {\tt{'}}{\tt{5}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-incr-mod-opcode}$\;\;$
{\sc{tm-incr-mod-opcode}}\index{tm-incr-mod-opcode} $=$ {\tt{'}}{\tt{7}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-mod-opcode}$\;\;$
{\sc{tm-mod-opcode}}\index{tm-mod-opcode} $=$ {\tt{'}}{\tt{9}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-move-opcode}$\;\;$
{\sc{tm-move-opcode}}\index{tm-move-opcode} $=$ {\tt{'}}{\tt{11}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-mult-opcode}$\;\;$
{\sc{tm-mult-opcode}}\index{tm-mult-opcode} $=$ {\tt{'}}{\tt{13}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-stout-opcode}$\;\;$
{\sc{tm-stout-opcode}}\index{tm-stout-opcode} $=$ {\tt{'}}{\tt{15}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-binary} \\  
\=\+{\rm{tm-execute-binary}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-binary} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+($\neg$ {\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address}) \\ 
$\vee$$\;\;\;\;$($\neg$ {\rm{tm-good-address}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-good-address})\-$\;\;${\bf then }{\rm{tm-set-error}}\,({\tt{'}}{\tt{6}}, {\it{tm\/}})\index{tm-set-error} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{1}}$\;\;${\bf then }{\rm{tm-execute-add}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-add} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{3}}$\;\;${\bf then }{\rm{tm-execute-compare}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-compare} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{5}}$\;\;${\bf then }{\rm{tm-execute-decr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-decr-mod} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{7}}$\;\;${\bf then }{\rm{tm-execute-incr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-incr-mod} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{9}}$\;\;${\bf then }{\rm{tm-execute-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-mod} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{11}}$\;\;${\bf then }{\rm{tm-execute-move}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-move} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{13}}$\;\;${\bf then }{\rm{tm-execute-multiply}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-multiply} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{15}}$\;\;${\bf then }{\rm{tm-execute-start-output}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-start-output} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{2}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-instruction} \\  
\=\+{\rm{tm-execute-instruction}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute-instruction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{instruction\/}})\index{length} $=$ {\tt{'}}{\tt{1}} \\ 
{\bf then }{\rm{tm-execute-nullary}}\,({\rm{tm-opcode}}\,({\rm{car}}\,({\it{instruction\/}}))\index{tm-opcode}, {\it{tm\/}})\index{tm-execute-nullary} \\ 
{\bf elseif }{\rm{length}}\,({\it{instruction\/}})\index{length} $=$ {\tt{'}}{\tt{2}} \\ 
{\bf then }{\rm{tm-execute-unary}}\,(\=\+{\rm{tm-opcode}}\,({\rm{car}}\,({\it{instruction\/}}))\index{tm-opcode}, \\ 
{\rm{tm-compute-address}}\,({\rm{tm-arg1}}\,({\it{instruction\/}})\index{tm-arg1}, {\it{tm\/}})\index{tm-compute-address}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary} \\ 
{\bf elseif }{\rm{length}}\,({\it{instruction\/}})\index{length} $=$ {\tt{'}}{\tt{3}} \\ 
{\bf then }{\rm{tm-execute-binary}}\,(\=\+{\rm{tm-opcode}}\,({\rm{car}}\,({\it{instruction\/}}))\index{tm-opcode}, \\ 
{\rm{tm-compute-address}}\,({\rm{tm-arg1}}\,({\it{instruction\/}})\index{tm-arg1}, {\it{tm\/}})\index{tm-compute-address}, \\ 
{\rm{tm-compute-address}}\,({\rm{tm-arg2}}\,({\it{instruction\/}})\index{tm-arg2}, {\it{tm\/}})\index{tm-compute-address}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{2}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-fetch-opcode} \\  
{\rm{tm-fetch-opcode}}\,({\it{tm\/}})\index{tm-fetch-opcode} $=$ {\rm{tm-fetch}}\,({\rm{real-addr}}\,({\tt{'}}{\tt{2}}, {\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc})\index{real-addr}, {\it{tm\/}})\index{tm-fetch}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-fetch-arg1} \\  
{\rm{tm-fetch-arg1}}\,({\it{tm\/}})\index{tm-fetch-arg1} $=$ {\rm{tm-fetch}}\,({\rm{real-addr}}\,({\tt{'}}{\tt{2}}, {\rm{tm-incrn}}\,({\tt{'}}{\tt{1}}, {\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc})\index{tm-incrn})\index{real-addr}, {\it{tm\/}})\index{tm-fetch}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-fetch-arg2} \\  
{\rm{tm-fetch-arg2}}\,({\it{tm\/}})\index{tm-fetch-arg2} $=$ {\rm{tm-fetch}}\,({\rm{real-addr}}\,({\tt{'}}{\tt{2}}, {\rm{tm-incrn}}\,({\tt{'}}{\tt{2}}, {\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc})\index{tm-incrn})\index{real-addr}, {\it{tm\/}})\index{tm-fetch}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute} \\  
\=\+{\rm{tm-execute}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-nullary-instructionp}}\,({\it{opcode\/}})\index{tm-nullary-instructionp} \\ 
{\bf then }{\rm{tm-execute-instruction}}\,(\=\+{\rm{cons}}\,({\it{opcode\/}}, {\tt{'}}{\tt{nil}}), \\ 
{\rm{tm-set-pc}}\,({\rm{tm-incrn}}\,({\tt{'}}{\tt{1}}, {\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc})\index{tm-incrn}, {\it{tm\/}})\index{tm-set-pc})\-\index{tm-execute-instruction} \\ 
{\bf elseif }{\rm{tm-good-address}}\,({\rm{real-addr}}\,({\tt{'}}{\tt{2}}, {\rm{tm-incrn}}\,({\tt{'}}{\tt{1}}, {\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc})\index{tm-incrn})\index{real-addr}, {\it{tm\/}})\index{tm-good-address} \\ 
{\bf then }\=\+{\bf if }{\rm{tm-unary-instructionp}}\,({\it{opcode\/}})\index{tm-unary-instructionp} \\ 
{\bf then }{\rm{tm-execute-instruction}}\,(\=\+{\rm{cons}}\,(\=\+{\it{opcode\/}}, \\ 
{\rm{cons}}\,({\rm{tm-fetch-arg1}}\,({\it{tm\/}})\index{tm-fetch-arg1}, {\tt{'}}{\tt{nil}}))\-, \\ 
{\rm{tm-set-pc}}\,({\rm{tm-incrn}}\,({\tt{'}}{\tt{2}}, {\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc})\index{tm-incrn}, {\it{tm\/}})\index{tm-set-pc})\-\index{tm-execute-instruction} \\ 
{\bf elseif }{\rm{tm-good-address}}\,({\rm{real-addr}}\,({\tt{'}}{\tt{2}}, {\rm{tm-incrn}}\,({\tt{'}}{\tt{2}}, {\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc})\index{tm-incrn})\index{real-addr}, {\it{tm\/}})\index{tm-good-address} \\ 
{\bf then }{\rm{tm-execute-instruction}}\,(\=\+{\rm{cons}}\,(\=\+{\it{opcode\/}}, \\ 
{\rm{cons}}\,(\=\+{\rm{tm-fetch-arg1}}\,({\it{tm\/}})\index{tm-fetch-arg1}, \\ 
{\rm{cons}}\,(\=\+{\rm{tm-fetch-arg2}}\,({\it{tm\/}})\index{tm-fetch-arg2}, \\ 
{\tt{'}}{\tt{nil}})\-)\-)\-, \\ 
{\rm{tm-set-pc}}\,({\rm{tm-incrn}}\,({\tt{'}}{\tt{3}}, {\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc})\index{tm-incrn}, {\it{tm\/}})\index{tm-set-pc})\-\index{tm-execute-instruction} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{7}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{7}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-decrement-clock} \\  
\=\+{\rm{tm-decrement-clock}}\,({\it{tm\/}})\index{tm-decrement-clock} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock} $\simeq {\tt{0}}$$\;\;${\bf then }{\it{tm\/}} \\ 
{\bf elseif }$\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode} \\ 
{\bf then }{\rm{tm-set-clock}}\,({\rm{tm-decr}}\,({\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock})\index{tm-decr}, {\it{tm\/}})\index{tm-set-clock} \\ 
{\bf else }{\it{tm\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-good-pc-address} \\  
{\rm{tm-good-pc-address}}\,({\it{tm\/}})\index{tm-good-pc-address} $=$ {\rm{tm-good-address}}\,({\rm{real-addr}}\,({\tt{'}}{\tt{2}}, {\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc})\index{real-addr}, {\it{tm\/}})\index{tm-good-address}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-fetch-execute} \\  
\=\+{\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-good-pc-address}}\,({\it{tm\/}})\index{tm-good-pc-address} \\ 
{\bf then }{\rm{tm-execute}}\,({\rm{tm-fetch-opcode}}\,({\it{tm\/}})\index{tm-fetch-opcode}, {\rm{tm-decrement-clock}}\,({\it{tm\/}})\index{tm-decrement-clock})\index{tm-execute} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{7}}, {\rm{tm-decrement-clock}}\,({\it{tm\/}})\index{tm-decrement-clock})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-fetch-new-pc-on-interrupt} \\  
\=\+{\rm{tm-fetch-new-pc-on-interrupt}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch-new-pc-on-interrupt} \\ 
$=$$\;\;\;\;${\rm{tm-set-pc}}\,({\rm{tm-fetch-from-memory}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch-from-memory}, {\it{tm\/}})\index{tm-set-pc}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-store-old-psw-on-interrupt} \\  
\=\+{\rm{tm-store-old-psw-on-interrupt}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-store-old-psw-on-interrupt} \\ 
$=$$\;\;\;\;${\rm{tm-store}}\,(\=\+{\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc}, \\ 
{\rm{real-addr}}\,({\tt{'}}{\tt{2}}, {\it{addr\/}})\index{real-addr}, \\ 
{\rm{tm-store}}\,(\=\+{\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp}, \\ 
{\rm{tm-incrn-address}}\,({\tt{'}}{\tt{1}}, {\rm{real-addr}}\,({\tt{'}}{\tt{2}}, {\it{addr\/}})\index{real-addr})\index{tm-incrn-address}, \\ 
{\rm{tm-store}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\-\index{tm-pack-psw}, \\ 
{\rm{tm-incrn-address}}\,({\tt{'}}{\tt{2}}, {\rm{real-addr}}\,({\tt{'}}{\tt{2}}, {\it{addr\/}})\index{real-addr})\index{tm-incrn-address}, \\ 
{\it{tm\/}})\-\index{tm-store})\-\index{tm-store})\-\index{tm-store}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-clock-interruptp} \\  
\=\+{\rm{tm-clock-interruptp}}\,({\it{tm\/}})\index{tm-clock-interruptp} \\ 
$=$$\;\;\;\;$(($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) $\wedge$ ({\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock} $\simeq {\tt{0}}$))\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-clock-interrupt} \\  
\=\+{\rm{tm-execute-clock-interrupt}}\,({\it{tm\/}})\index{tm-execute-clock-interrupt} \\ 
$=$$\;\;\;\;${\rm{tm-set-sp}}\,(\=\+{\rm{tm-decr}}\,({\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit})\index{tm-decr}, \\ 
{\rm{tm-fetch-new-pc-on-interrupt}}\,(\=\+{\tt{'}}{\tt{3}}, \\ 
{\rm{tm-store-old-psw-on-interrupt}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-set-svmode}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\it{tm\/}})\-\index{tm-set-svmode})\-\index{tm-store-old-psw-on-interrupt})\-\index{tm-fetch-new-pc-on-interrupt})\-\index{tm-set-sp}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-errorp}$\;\;$
{\rm{tm-errorp}}\,({\it{tm\/}})\index{tm-errorp} $=$ ({\rm{tm-error}}\,({\it{tm\/}})\index{tm-error} $\not=$ {\tt{'}}{\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-error-interrupt} \\  
\=\+{\rm{tm-execute-error-interrupt}}\,({\it{tm\/}})\index{tm-execute-error-interrupt} \\ 
$=$$\;\;\;\;${\rm{tm-set-sp}}\,(\=\+{\rm{tm-decr}}\,({\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit})\index{tm-decr}, \\ 
{\rm{tm-set-error}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-fetch-new-pc-on-interrupt}}\,(\=\+{\tt{'}}{\tt{4}}, \\ 
{\rm{tm-store-old-psw-on-interrupt}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-set-svmode}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\it{tm\/}})\-\index{tm-set-svmode})\-\index{tm-store-old-psw-on-interrupt})\-\index{tm-fetch-new-pc-on-interrupt})\-\index{tm-set-error})\-\index{tm-set-sp}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-svc-interruptp} \\  
\=\+{\rm{tm-svc-interruptp}}\,({\it{tm\/}})\index{tm-svc-interruptp} \\ 
$=$$\;\;\;\;$(($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) $\wedge$ ({\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag} $=$ {\tt{'}}{\tt{1}}))\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-store-svcid-on-interrupt} \\  
{\rm{tm-store-svcid-on-interrupt}}\,({\it{tm\/}})\index{tm-store-svcid-on-interrupt} $=$ {\rm{tm-store}}\,({\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, {\tt{'}}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{8}}{\tt{)}}, {\it{tm\/}})\index{tm-store}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-svc-interrupt} \\  
\=\+{\rm{tm-execute-svc-interrupt}}\,({\it{tm\/}})\index{tm-execute-svc-interrupt} \\ 
$=$$\;\;\;\;${\rm{tm-set-sp}}\,(\=\+{\rm{tm-decr}}\,({\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit})\index{tm-decr}, \\ 
{\rm{tm-fetch-new-pc-on-interrupt}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-store-svcid-on-interrupt}}\,({\rm{tm-store-old-psw-on-interrupt}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-set-svmode}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\it{tm\/}})\-\index{tm-set-svmode})\-\index{tm-store-old-psw-on-interrupt})\index{tm-store-svcid-on-interrupt})\-\index{tm-fetch-new-pc-on-interrupt})\-\index{tm-set-sp}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-overflow-char}$\;\;$
{\rm{tm-overflow-char}}\,({\it{char\/}})\index{tm-overflow-char} $=$ ({\tt{'}}{\tt{256}} $+$ {\it{char\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-some-input-interruptp} \\  
\=\+{\rm{tm-some-input-interruptp}}\,({\it{ports\/}})\index{tm-some-input-interruptp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{ports\/}}) \\ 
{\bf then }\=\+({\rm{tm-iinterrupt-flag}}\,({\rm{car}}\,({\it{ports\/}}))\index{tm-iinterrupt-flag} $=$ {\tt{'}}{\tt{1}}) \\ 
$\vee$$\;\;\;\;${\rm{tm-some-input-interruptp}}\,({\rm{cdr}}\,({\it{ports\/}}))\index{tm-some-input-interruptp}\- \\ 
{\bf else }{\tt{'}}{\tt{*1*false}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-input-interruptp} \\  
\=\+{\rm{tm-input-interruptp}}\,({\it{tm\/}})\index{tm-input-interruptp} \\ 
$=$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{tm-some-input-interruptp})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-interrupting-input-port} \\  
\=\+{\rm{tm-interrupting-input-port}}\,({\it{ports\/}})\index{tm-interrupting-input-port} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{ports\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{tm-iinterrupt-flag}}\,({\rm{car}}\,({\it{ports\/}}))\index{tm-iinterrupt-flag} $=$ {\tt{'}}{\tt{1}}$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf else }$1\;+$ {\rm{tm-interrupting-input-port}}\,({\rm{cdr}}\,({\it{ports\/}}))\index{tm-interrupting-input-port}$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-store-interrupting-input-devi!ce} \\  
\=\+{\rm{tm-store-interrupting-input-device}}\,({\it{id\/}}, {\it{tm\/}})\index{tm-store-interrupting-input-devi!ce} \\ 
$=$$\;\;\;\;${\rm{tm-store}}\,(\=\+{\it{id\/}}, \\ 
{\tt{'}}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{8}}{\tt{)}}, \\ 
{\rm{tm-store}}\,({\rm{tm-ichar}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{getnth})\index{tm-ichar}, {\tt{'}}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{9}}{\tt{)}}, {\it{tm\/}})\index{tm-store})\-\index{tm-store}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-input-interrupt} \\  
\=\+{\rm{tm-execute-input-interrupt}}\,({\it{tm\/}})\index{tm-execute-input-interrupt} \\ 
$=$$\;\;\;\;${\rm{tm-set-sp}}\,(\=\+{\rm{tm-decr}}\,({\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit})\index{tm-decr}, \\ 
{\rm{tm-set-error}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-fetch-new-pc-on-interrupt}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-set-iports}}\,(\=\+{\rm{tm-clear-input-interrupt}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\-\index{tm-clear-input-interrupt}, \\ 
{\rm{tm-store-interrupting-input-device}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-store-old-psw-on-interrupt}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-set-svmode}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{tm-set-rwstate}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\it{tm\/}})\-\index{tm-set-rwstate})\-\index{tm-set-svmode})\-\index{tm-store-old-psw-on-interrupt})\-\index{tm-store-interrupting-input-devi!ce})\-\index{tm-set-iports})\-\index{tm-fetch-new-pc-on-interrupt})\-\index{tm-set-error})\-\index{tm-set-sp}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-some-output-interruptp} \\  
\=\+{\rm{tm-some-output-interruptp}}\,({\it{ports\/}})\index{tm-some-output-interruptp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{ports\/}}) \\ 
{\bf then }\=\+({\rm{tm-ointerrupt-flag}}\,({\rm{car}}\,({\it{ports\/}}))\index{tm-ointerrupt-flag} $=$ {\tt{'}}{\tt{1}}) \\ 
$\vee$$\;\;\;\;${\rm{tm-some-output-interruptp}}\,({\rm{cdr}}\,({\it{ports\/}}))\index{tm-some-output-interruptp}\- \\ 
{\bf else }{\tt{'}}{\tt{*1*false}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-output-interruptp} \\  
\=\+{\rm{tm-output-interruptp}}\,({\it{tm\/}})\index{tm-output-interruptp} \\ 
$=$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\index{tm-some-output-interruptp})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-interrupting-output-port} \\  
\=\+{\rm{tm-interrupting-output-port}}\,({\it{ports\/}})\index{tm-interrupting-output-port} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{ports\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{tm-ointerrupt-flag}}\,({\rm{car}}\,({\it{ports\/}}))\index{tm-ointerrupt-flag} $=$ {\tt{'}}{\tt{1}}$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf else }$1\;+$ {\rm{tm-interrupting-output-port}}\,({\rm{cdr}}\,({\it{ports\/}}))\index{tm-interrupting-output-port}$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-store-interrupting-output-devi!ce} \\  
{\rm{tm-store-interrupting-output-device}}\,({\it{id\/}}, {\it{tm\/}})\index{tm-store-interrupting-output-devi!ce} $=$ {\rm{tm-store}}\,({\it{id\/}}, {\tt{'}}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{9}}{\tt{)}}, {\it{tm\/}})\index{tm-store}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-output-interrupt} \\  
\=\+{\rm{tm-execute-output-interrupt}}\,({\it{tm\/}})\index{tm-execute-output-interrupt} \\ 
$=$$\;\;\;\;${\rm{tm-set-sp}}\,(\=\+{\rm{tm-decr}}\,({\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit})\index{tm-decr}, \\ 
{\rm{tm-set-error}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-fetch-new-pc-on-interrupt}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-set-oports}}\,(\=\+{\rm{tm-clear-output-interrupt}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-\index{tm-clear-output-interrupt}, \\ 
{\rm{tm-store-interrupting-output-device}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{tm-store-old-psw-on-interrupt}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-set-svmode}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{tm-set-rwstate}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\it{tm\/}})\-\index{tm-set-rwstate})\-\index{tm-set-svmode})\-\index{tm-store-old-psw-on-interrupt})\-\index{tm-store-interrupting-output-devi!ce})\-\index{tm-set-oports})\-\index{tm-fetch-new-pc-on-interrupt})\-\index{tm-set-error})\-\index{tm-set-sp}\-
\end{tabbing}


\noindent{\sc Event}:   Add the shell {\it{tm-device-input-event\/}}\index{tm-device-input-event}, with recognizer function symbol {\it{tm-device-input-eventp\/}} and 2 accessors: {\it{tm-idevid\/}}, with type restriction (none-of) and default value zero; {\it{tm-idatum\/}}, with type restriction (none-of) and default value zero.

\addvspace{18pt}


\noindent{\sc Event}:   Add the shell {\it{tm-device-output-event\/}}\index{tm-device-output-event}, with recognizer function symbol {\it{tm-device-output-eventp\/}} and 1 accessor: {\it{tm-odevid\/}}, with type restriction (none-of) and default value zero.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tm-post-interrupt} \\  
\=\+{\rm{tm-post-interrupt}}\,({\it{event\/}}, {\it{tm\/}})\index{tm-post-interrupt} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-device-input-eventp}}\,({\it{event\/}})\index{tm-device-input-eventp} \\ 
{\bf then }{\rm{tm-set-iports}}\,(\=\+{\rm{tm-post-input-interrupt}}\,(\=\+\=\+{\rm{tm-idatum}}\,({\it{event\/}})\index{tm-idatum} \\ 
${}${\bf{mod}}${}$$\;\;\;\;${\tt{'}}{\tt{256}}\-, \\ 
{\rm{tm-idevid}}\,({\it{event\/}})\index{tm-idevid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{16}}, \\ 
{\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\-\index{tm-post-input-interrupt}, \\ 
{\it{tm\/}})\-\index{tm-set-iports} \\ 
{\bf elseif }{\rm{tm-device-output-eventp}}\,({\it{event\/}})\index{tm-device-output-eventp} \\ 
{\bf then }{\rm{tm-set-oports}}\,(\=\+{\rm{tm-post-output-interrupt}}\,(\=\+\=\+{\rm{tm-odevid}}\,({\it{event\/}})\index{tm-odevid} \\ 
${}${\bf{mod}}${}$$\;\;\;\;${\tt{'}}{\tt{16}}\-, \\ 
{\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-\index{tm-post-output-interrupt}, \\ 
{\it{tm\/}})\-\index{tm-set-oports} \\ 
{\bf else }{\it{tm\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-step} \\  
\=\+{\rm{tm-step}}\,({\it{tm\/}})\index{tm-step} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-input-interruptp}}\,({\it{tm\/}})\index{tm-input-interruptp}$\;\;${\bf then }{\rm{tm-execute-input-interrupt}}\,({\it{tm\/}})\index{tm-execute-input-interrupt} \\ 
{\bf elseif }{\rm{tm-output-interruptp}}\,({\it{tm\/}})\index{tm-output-interruptp}$\;\;${\bf then }{\rm{tm-execute-output-interrupt}}\,({\it{tm\/}})\index{tm-execute-output-interrupt} \\ 
{\bf elseif }{\rm{tm-waiting}}\,({\it{tm\/}})\index{tm-waiting}$\;\;${\bf then }{\it{tm\/}} \\ 
{\bf elseif }{\rm{tm-errorp}}\,({\it{tm\/}})\index{tm-errorp}$\;\;${\bf then }{\rm{tm-execute-error-interrupt}}\,({\it{tm\/}})\index{tm-execute-error-interrupt} \\ 
{\bf elseif }{\rm{tm-clock-interruptp}}\,({\it{tm\/}})\index{tm-clock-interruptp}$\;\;${\bf then }{\rm{tm-execute-clock-interrupt}}\,({\it{tm\/}})\index{tm-execute-clock-interrupt} \\ 
{\bf elseif }{\rm{tm-svc-interruptp}}\,({\it{tm\/}})\index{tm-svc-interruptp}$\;\;${\bf then }{\rm{tm-execute-svc-interrupt}}\,({\it{tm\/}})\index{tm-execute-svc-interrupt} \\ 
{\bf else }{\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-processor} \\  
\=\+{\rm{tm-processor}}\,({\it{tm\/}}, {\it{oracle\/}})\index{tm-processor} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{oracle\/}}) \\ 
{\bf then }{\rm{tm-processor}}\,(\=\+{\rm{tm-step}}\,({\rm{tm-post-interrupt}}\,({\rm{car}}\,({\it{oracle\/}}), {\it{tm\/}})\index{tm-post-interrupt})\index{tm-step}, \\ 
{\rm{cdr}}\,({\it{oracle\/}}))\-\index{tm-processor} \\ 
{\bf else }{\it{tm\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tm-processor-with-null-oracle \\ \index{tm-processor-with-null-oracle}
{\rm{tm-processor}}\,({\it{tm\/}}, {\tt{'}}{\tt{nil}})\index{tm-processor} $=$ {\it{tm\/}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-processor-with-null-oracle.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  open-up-tm-processor \\ \index{open-up-tm-processor}
\=\+{\rm{tm-processor}}\,({\it{tm\/}}, {\rm{cons}}\,({\it{a\/}}, {\it{b\/}}))\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,({\rm{tm-step}}\,({\rm{tm-post-interrupt}}\,({\it{a\/}}, {\it{tm\/}})\index{tm-post-interrupt})\index{tm-step}, {\it{b\/}})\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable open-up-tm-processor.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-processor-append-oracle \\ \index{tm-processor-append-oracle}
{\rm{tm-processor}}\,({\it{tm\/}}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{tm-processor} $=$ {\rm{tm-processor}}\,({\rm{tm-processor}}\,({\it{tm\/}}, {\it{a\/}})\index{tm-processor}, {\it{b\/}})\index{tm-processor}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-processor-append-oracle.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-cc-value \\ \index{finite-numberp-tm-cc-value}
{\rm{finite-numberp}}\,({\rm{tm-cc-value}}\,({\it{x\/}})\index{tm-cc-value}, {\tt{'}}{\tt{4}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-cc-value.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-tm-cc-value-tm-cclub \\ \index{lessp-tm-cc-value-tm-cclub}
({\rm{tm-cc-value}}\,({\it{x\/}})\index{tm-cc-value} $<$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{*1*true}}
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-tm-cc-value-tm-cclub.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-tm-cc-value-tm-cclub-linear \\ \index{lessp-tm-cc-value-tm-cclub-line!ar}
{\rm{tm-cc-value}}\,({\it{x\/}})\index{tm-cc-value} $<$ {\tt{'}}{\tt{4}}
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-tm-cc-value-tm-cclub-linear.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cc-value-on-compare-equal \\ \index{tm-cc-value-on-compare-equal}
\=\+({\rm{finite-numberp}}\,({\it{a\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp} $\wedge$ ({\rm{finite-numberp}}\,({\it{b\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp} $\wedge$ ({\it{a\/}} $=$ {\it{b\/}}))) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-cc-value}}\,({\rm{tm-alu-difference}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-difference})\index{tm-cc-value} $=$ {\tt{'}}{\tt{1}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cc-value-on-compare-equal.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cc-value-on-compare-greaterp \\ \index{tm-cc-value-on-compare-greaterp}
\=\+(({\it{b\/}} $<$ {\it{a\/}}) $\wedge$ ({\it{a\/}} $<$ {\tt{'}}{\tt{65536}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-cc-value}}\,({\rm{tm-alu-difference}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-difference})\index{tm-cc-value} $=$ {\tt{'}}{\tt{2}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cc-value-on-compare-greaterp.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cc-value-on-compare-lessp \\ \index{tm-cc-value-on-compare-lessp}
\=\+(({\it{a\/}} $<$ {\it{b\/}}) $\wedge$ ({\it{b\/}} $<$ {\tt{'}}{\tt{65536}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-cc-value}}\,({\rm{tm-alu-difference}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-difference})\index{tm-cc-value} $=$ {\tt{'}}{\tt{0}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cc-value-on-compare-lessp.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cc-value-on-compare-not-equal \\ \index{tm-cc-value-on-compare-not-equa!l}
\=\+({\rm{finite-numberp}}\,({\it{a\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp} $\wedge$ ({\rm{finite-numberp}}\,({\it{b\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp} $\wedge$ ({\it{a\/}} $\not=$ {\it{b\/}}))) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{tm-cc-value}}\,({\rm{tm-alu-difference}}\,({\it{a\/}}, {\it{b\/}})\index{tm-alu-difference})\index{tm-cc-value} $=$ {\tt{'}}{\tt{1}}) $=$ {\tt{'}}{\tt{*1*false}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cc-value-on-compare-not-equal.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cc-value-on-compare-not-equal-to-zero \\ \index{tm-cc-value-on-compare-not-equa!l-to-zero}
\=\+({\rm{finite-numberp}}\,({\it{a\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp} $\wedge$ ({\it{a\/}} $\not=$ {\tt{'}}{\tt{0}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-cc-value}}\,({\rm{tm-alu-difference}}\,({\it{a\/}}, {\tt{'}}{\tt{0}})\index{tm-alu-difference})\index{tm-cc-value} $=$ {\tt{'}}{\tt{2}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cc-value-on-compare-not-equal-to-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-tm-fix-word \\ \index{numberp-tm-fix-word}
{\rm{tm-fix-word}}\,({\it{n\/}})\index{tm-fix-word} $\in\;${\bf{N}}${}$
\end{tabbing}


\noindent{\sc Event}:   Disable numberp-tm-fix-word.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-fix-word-size \\ \index{tm-fix-word-size}
({\rm{tm-fix-word}}\,({\it{n\/}})\index{tm-fix-word} $<$ {\tt{'}}{\tt{65536}}) $=$ {\tt{'}}{\tt{*1*true}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-fix-word-size.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-fix-word-size-linear \\ \index{tm-fix-word-size-linear}
{\rm{tm-fix-word}}\,({\it{n\/}})\index{tm-fix-word} $<$ {\tt{'}}{\tt{65536}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-fix-word-size-linear.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-fix-word-noop \\ \index{tm-fix-word-noop}
({\it{n\/}} $<$ {\tt{'}}{\tt{65536}}) $\rightarrow$ ({\rm{tm-fix-word}}\,({\it{n\/}})\index{tm-fix-word} $=$ {\rm{fix}}\,({\it{n\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable tm-fix-word-noop.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-tm-fix-reg-address \\ \index{numberp-tm-fix-reg-address}
{\rm{tm-fix-reg-address}}\,({\it{n\/}})\index{tm-fix-reg-address} $\in\;${\bf{N}}${}$
\end{tabbing}


\noindent{\sc Event}:   Disable numberp-tm-fix-reg-address.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-fix-reg-address-size \\ \index{tm-fix-reg-address-size}
({\rm{tm-fix-reg-address}}\,({\it{n\/}})\index{tm-fix-reg-address} $<$ {\tt{'}}{\tt{8}}) $=$ {\tt{'}}{\tt{*1*true}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-fix-reg-address-size.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-fix-reg-address-size-linear \\ \index{tm-fix-reg-address-size-linear}
{\rm{tm-fix-reg-address}}\,({\it{n\/}})\index{tm-fix-reg-address} $<$ {\tt{'}}{\tt{8}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-fix-reg-address-size-linear.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-fix-reg-address-noop \\ \index{tm-fix-reg-address-noop}
({\it{n\/}} $<$ {\tt{'}}{\tt{8}}) $\rightarrow$ ({\rm{tm-fix-reg-address}}\,({\it{n\/}})\index{tm-fix-reg-address} $=$ {\rm{fix}}\,({\it{n\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable tm-fix-reg-address-noop.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{good-tm-iport} \\  
\=\+{\rm{good-tm-iport}}\,({\it{x\/}})\index{good-tm-iport} \\ 
$=$$\;\;\;\;$(\=\+{\rm{tm-iportp}}\,({\it{x\/}})\index{tm-iportp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\rm{tm-iinterrupt-flag}}\,({\it{x\/}})\index{tm-iinterrupt-flag}, {\tt{'}}{\tt{2}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\rm{tm-ierror-flag}}\,({\it{x\/}})\index{tm-ierror-flag}, {\tt{'}}{\tt{2}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-ichar}}\,({\it{x\/}})\index{tm-ichar}, {\tt{'}}{\tt{256}})\index{finite-numberp})\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{good-tm-iport-array} \\  
\=\+{\rm{good-tm-iport-array}}\,({\it{l\/}})\index{good-tm-iport-array} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}}) \\ 
{\bf then }{\rm{good-tm-iport}}\,({\rm{car}}\,({\it{l\/}}))\index{good-tm-iport} $\wedge$ {\rm{good-tm-iport-array}}\,({\rm{cdr}}\,({\it{l\/}}))\index{good-tm-iport-array} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{good-tm-oport} \\  
\=\+{\rm{good-tm-oport}}\,({\it{x\/}})\index{good-tm-oport} \\ 
$=$$\;\;\;\;$(\=\+{\rm{tm-oportp}}\,({\it{x\/}})\index{tm-oportp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\rm{tm-ointerrupt-flag}}\,({\it{x\/}})\index{tm-ointerrupt-flag}, {\tt{'}}{\tt{2}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\rm{tm-obusy-flag}}\,({\it{x\/}})\index{tm-obusy-flag}, {\tt{'}}{\tt{2}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-ochar}}\,({\it{x\/}})\index{tm-ochar}, {\tt{'}}{\tt{256}})\index{finite-numberp})\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{good-tm-oport-array} \\  
\=\+{\rm{good-tm-oport-array}}\,({\it{l\/}})\index{good-tm-oport-array} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}}) \\ 
{\bf then }{\rm{good-tm-oport}}\,({\rm{car}}\,({\it{l\/}}))\index{good-tm-oport} $\wedge$ {\rm{good-tm-oport-array}}\,({\rm{cdr}}\,({\it{l\/}}))\index{good-tm-oport-array} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN GOOD-TM
 (TM)
 (AND
  (TM-SHELLP TM)
  (AND
   (PLISTP (TM-MEMORY TM))
   (AND
    (EQUAL (LENGTH (TM-MEMORY TM))
           '65536)
    (AND
     (FINITE-NUMBER-LISTP (TM-MEMORY TM)
                          '65536)
     (AND
      (PLISTP (TM-REGS TM))
      (AND
       (EQUAL (LENGTH (TM-REGS TM)) '8)
       (AND
        (FINITE-NUMBER-LISTP (TM-REGS TM)
                             '65536)
        (AND
         (FINITE-NUMBERP (TM-CC TM) '4)
         (AND
          (FINITE-NUMBERP (TM-ERROR TM) '64)
          (AND
           (FINITE-NUMBERP (TM-SVCFLAG TM) '2)
           (AND
            (FINITE-NUMBERP (TM-SVCID TM) '128)
            (AND
             (FINITE-NUMBERP (TM-BASE TM) '65536)
             (AND
              (FINITE-NUMBERP (TM-LIMIT TM) '65536)
              (AND
               (FINITE-NUMBERP (TM-SLIMIT TM)
                               '65536)
               (AND
                (FINITE-NUMBERP (TM-SVMODE TM) '2)
                (AND
                 (FINITE-NUMBERP (TM-RWSTATE TM) '2)
                 (AND
                  (FINITE-NUMBERP (TM-CLOCK TM) '65536)
                  (AND
                   (PLISTP (TM-IPORTS TM))
                   (AND
                    (EQUAL (LENGTH (TM-IPORTS TM)) '16)
                    (AND
                     (GOOD-TM-IPORT-ARRAY (TM-IPORTS TM))
                     (AND
                      (PLISTP (TM-OPORTS TM))
                      (AND
                       (EQUAL (LENGTH (TM-OPORTS TM)) '16)
                       (GOOD-TM-OPORT-ARRAY
                                          (TM-OPORTS TM))))))))))))))))))))))))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  tm-shellp-tm \\ \index{tm-shellp-tm}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{tm-shellp}}\,({\it{tm\/}})\index{tm-shellp}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-shellp-tm.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-tm-memory \\ \index{plistp-tm-memory}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{plistp}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-tm-memory.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory \\ \index{length-tm-memory}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ ({\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length} $=$ {\tt{'}}{\tt{65536}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-tm-memory \\ \index{finite-number-listp-tm-memory}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{finite-number-listp}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, {\tt{'}}{\tt{65536}})\index{finite-number-listp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-tm-memory.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-getnth-from-tm-memory \\ \index{numberp-getnth-from-tm-memory}
({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ ({\it{i\/}} $<$ {\tt{'}}{\tt{65536}})) $\rightarrow$ ({\rm{getnth}}\,({\it{i\/}}, {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{getnth} $\in\;${\bf{N}}${}$)
\end{tabbing}


\noindent{\sc Event}:   Disable numberp-getnth-from-tm-memory.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-tm-regs \\ \index{plistp-tm-regs}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{plistp}}\,({\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-tm-regs.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-regs \\ \index{length-tm-regs}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ ({\rm{length}}\,({\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs})\index{length} $=$ {\tt{'}}{\tt{8}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-regs.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-tm-regs \\ \index{finite-number-listp-tm-regs}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{finite-number-listp}}\,({\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, {\tt{'}}{\tt{65536}})\index{finite-number-listp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-tm-regs.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-getnth-from-tm-regs \\ \index{numberp-getnth-from-tm-regs}
({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ ({\it{i\/}} $<$ {\tt{'}}{\tt{8}})) $\rightarrow$ ({\rm{getnth}}\,({\it{i\/}}, {\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs})\index{getnth} $\in\;${\bf{N}}${}$)
\end{tabbing}


\noindent{\sc Event}:   Disable numberp-getnth-from-tm-regs.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-cc \\ \index{finite-numberp-tm-cc}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{finite-numberp}}\,({\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, {\tt{'}}{\tt{4}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-cc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-error \\ \index{finite-numberp-tm-error}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{finite-numberp}}\,({\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, {\tt{'}}{\tt{64}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-error.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-base \\ \index{finite-numberp-tm-base}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{finite-numberp}}\,({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, {\tt{'}}{\tt{65536}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-base.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-limit \\ \index{finite-numberp-tm-limit}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{finite-numberp}}\,({\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}, {\tt{'}}{\tt{65536}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-limit.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-slimit \\ \index{finite-numberp-tm-slimit}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{finite-numberp}}\,({\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit}, {\tt{'}}{\tt{65536}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-slimit.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-svmode \\ \index{finite-numberp-tm-svmode}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{finite-numberp}}\,({\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode}, {\tt{'}}{\tt{2}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-svmode.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-clock \\ \index{finite-numberp-tm-clock}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{finite-numberp}}\,({\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock}, {\tt{'}}{\tt{65536}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-clock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-pc \\ \index{finite-numberp-tm-pc}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{finite-numberp}}\,({\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc}, {\tt{'}}{\tt{65536}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-pc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-sp \\ \index{finite-numberp-tm-sp}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{finite-numberp}}\,({\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp}, {\tt{'}}{\tt{65536}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-sp.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-pack-psw \\ \index{finite-numberp-tm-pack-psw}
\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-pack-psw.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-svcflag \\ \index{finite-numberp-tm-svcflag}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{finite-numberp}}\,({\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, {\tt{'}}{\tt{2}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-svcflag.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-svcid \\ \index{finite-numberp-tm-svcid}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{finite-numberp}}\,({\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, {\tt{'}}{\tt{128}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-svcid.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-rwstate \\ \index{finite-numberp-tm-rwstate}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{finite-numberp}}\,({\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate}, {\tt{'}}{\tt{2}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-rwstate.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-tm-iports \\ \index{plistp-tm-iports}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{plistp}}\,({\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-tm-iports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-iports \\ \index{length-tm-iports}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ ({\rm{length}}\,({\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{length} $=$ {\tt{'}}{\tt{16}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-iports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-iport-array-tm-iports \\ \index{good-tm-iport-array-tm-iports}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm-iport-array}}\,({\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{good-tm-iport-array}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-iport-array-tm-iports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-tm-oports \\ \index{plistp-tm-oports}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{plistp}}\,({\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-tm-oports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-oports \\ \index{length-tm-oports}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ ({\rm{length}}\,({\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\index{length} $=$ {\tt{'}}{\tt{16}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-oports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-oport-array-tm-oports \\ \index{good-tm-oport-array-tm-oports}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm-oport-array}}\,({\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\index{good-tm-oport-array}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-oport-array-tm-oports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-iport-getnth \\ \index{good-tm-iport-getnth}
\=\+({\rm{good-tm-iport-array}}\,({\it{l\/}})\index{good-tm-iport-array} $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm-iport}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{good-tm-iport}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-iport-getnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-iport-array-putnth \\ \index{good-tm-iport-array-putnth}
\=\+({\rm{good-tm-iport-array}}\,({\it{l\/}})\index{good-tm-iport-array} $\wedge$ {\rm{good-tm-iport}}\,({\it{iport\/}})\index{good-tm-iport}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm-iport-array}}\,({\rm{putnth}}\,({\it{iport\/}}, {\it{n\/}}, {\it{l\/}})\index{putnth})\index{good-tm-iport-array}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-iport-array-putnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-iport-getnth-from-tm-iports \\ \index{good-tm-iport-getnth-from-tm-ip!orts}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm-iport}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{getnth})\index{good-tm-iport}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-iport-getnth-from-tm-iports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-iport-array-putnth-into-tm-iports \\ \index{good-tm-iport-array-putnth-into!-tm-iports}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{good-tm-iport}}\,({\it{iport\/}})\index{good-tm-iport}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm-iport-array}}\,({\rm{putnth}}\,({\it{iport\/}}, {\it{n\/}}, {\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{putnth})\index{good-tm-iport-array}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-iport-array-putnth-into-tm-iports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-oport-getnth \\ \index{good-tm-oport-getnth}
\=\+({\rm{good-tm-oport-array}}\,({\it{l\/}})\index{good-tm-oport-array} $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm-oport}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{good-tm-oport}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-oport-getnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-oport-array-putnth \\ \index{good-tm-oport-array-putnth}
\=\+({\rm{good-tm-oport-array}}\,({\it{l\/}})\index{good-tm-oport-array} $\wedge$ {\rm{good-tm-oport}}\,({\it{oport\/}})\index{good-tm-oport}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm-oport-array}}\,({\rm{putnth}}\,({\it{oport\/}}, {\it{n\/}}, {\it{l\/}})\index{putnth})\index{good-tm-oport-array}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-oport-array-putnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-oport-getnth-from-tm-oports \\ \index{good-tm-oport-getnth-from-tm-op!orts}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm-oport}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\index{getnth})\index{good-tm-oport}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-oport-getnth-from-tm-oports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-oport-array-putnth-into-tm-oports \\ \index{good-tm-oport-array-putnth-into!-tm-oports}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{good-tm-oport}}\,({\it{oport\/}})\index{good-tm-oport}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm-oport-array}}\,({\rm{putnth}}\,({\it{oport\/}}, {\it{n\/}}, {\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\index{putnth})\index{good-tm-oport-array}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-oport-array-putnth-into-tm-oports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  size-of-tm-interrupting-input-port \\ \index{size-of-tm-interrupting-input-p!ort}
\=\+{\rm{tm-some-input-interruptp}}\,({\it{l\/}})\index{tm-some-input-interruptp} \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-interrupting-input-port}}\,({\it{l\/}})\index{tm-interrupting-input-port} $<$ {\rm{length}}\,({\it{l\/}})\index{length})\-
\end{tabbing}


\noindent{\sc Event}:   Disable size-of-tm-interrupting-input-port.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-interrupting-input-port \\ \index{finite-numberp-tm-interrupting-i!nput-port}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{tm-interrupting-input-port}, {\tt{'}}{\tt{16}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-interrupting-input-port.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-interrupting-input-port-tm-wordlub \\ \index{finite-numberp-tm-interrupting-i!nput-port-tm-wordlub}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{tm-interrupting-input-port}, {\tt{'}}{\tt{65536}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-interrupting-input-port-tm-wordlub.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-iport-getnth-properties \\ \index{good-tm-iport-getnth-properties}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-iportp}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{getnth})\index{tm-iportp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,(\=\+{\rm{tm-iinterrupt-flag}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{getnth})\index{tm-iinterrupt-flag}, \\ 
{\tt{'}}{\tt{2}})\-\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,(\=\+{\rm{tm-ierror-flag}}\,({\rm{getnth}}\,(\=\+{\it{id\/}}, \\ 
{\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\-\index{getnth})\index{tm-ierror-flag}, \\ 
{\tt{'}}{\tt{2}})\-\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,(\=\+{\rm{tm-ichar}}\,({\rm{getnth}}\,(\=\+{\it{id\/}}, \\ 
{\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\-\index{getnth})\index{tm-ichar}, \\ 
{\tt{'}}{\tt{256}})\-\index{finite-numberp})\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-iport-getnth-properties.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  size-of-tm-interrupting-output-port \\ \index{size-of-tm-interrupting-output-p!ort}
\=\+{\rm{tm-some-output-interruptp}}\,({\it{l\/}})\index{tm-some-output-interruptp} \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-interrupting-output-port}}\,({\it{l\/}})\index{tm-interrupting-output-port} $<$ {\rm{length}}\,({\it{l\/}})\index{length})\-
\end{tabbing}


\noindent{\sc Event}:   Disable size-of-tm-interrupting-output-port.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-interrupting-output-port \\ \index{finite-numberp-tm-interrupting-!output-port}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\index{tm-interrupting-output-port}, {\tt{'}}{\tt{16}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-interrupting-output-port.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-interrupting-output-port-tm-wordlub \\ \index{finite-numberp-tm-interrupting-!output-port-tm-wordlub}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\index{tm-interrupting-output-port}, {\tt{'}}{\tt{65536}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-interrupting-output-port-tm-wordlub.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-oport-getnth-properties \\ \index{good-tm-oport-getnth-properties}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-oportp}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\index{getnth})\index{tm-oportp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,(\=\+{\rm{tm-ointerrupt-flag}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\index{getnth})\index{tm-ointerrupt-flag}, \\ 
{\tt{'}}{\tt{2}})\-\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,(\=\+{\rm{tm-obusy-flag}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\index{getnth})\index{tm-obusy-flag}, \\ 
{\tt{'}}{\tt{2}})\-\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,(\=\+{\rm{tm-ochar}}\,({\rm{getnth}}\,(\=\+{\it{id\/}}, \\ 
{\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-\index{getnth})\index{tm-ochar}, \\ 
{\tt{'}}{\tt{256}})\-\index{finite-numberp})\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-oport-getnth-properties.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{tm-shells}} to consist of the following events: tm-device-output-event,
tm-device-input-event,
tm-oport,
tm-iport,
tm.\index{tm-shells}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-iports-tm-clear-input-interrupt \\ \index{good-tm-iports-tm-clear-input-i!nterrupt}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\rm{tm-clear-input-interrupt}}\,({\it{id\/}}, {\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{tm-clear-input-interrupt})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\rm{tm-clear-input-interrupt}}\,({\it{id\/}}, {\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{tm-clear-input-interrupt})\index{length} $=$ {\tt{'}}{\tt{16}}) \\ 
$\wedge$$\;\;\;\;${\rm{good-tm-iport-array}}\,({\rm{tm-clear-input-interrupt}}\,(\=\+{\it{id\/}}, \\ 
{\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\-\index{tm-clear-input-interrupt})\index{good-tm-iport-array})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-iports-tm-clear-input-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-oports-tm-clear-output-interrupt \\ \index{good-tm-oports-tm-clear-output-i!nterrupt}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\rm{tm-clear-output-interrupt}}\,({\it{id\/}}, {\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\index{tm-clear-output-interrupt})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{length}}\,({\rm{tm-clear-output-interrupt}}\,({\it{id\/}}, {\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\index{tm-clear-output-interrupt})\index{length} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{16}})\- \\ 
$\wedge$$\;\;\;\;${\rm{good-tm-oport-array}}\,({\rm{tm-clear-output-interrupt}}\,(\=\+{\it{id\/}}, \\ 
{\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-\index{tm-clear-output-interrupt})\index{good-tm-oport-array})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-oports-tm-clear-output-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-ichar-getnth-crock \\ \index{finite-numberp-tm-ichar-getnth-!crock}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-ichar}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{getnth})\index{tm-ichar}, {\tt{'}}{\tt{65536}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-ichar-getnth-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-overflow-char \\ \index{finite-numberp-tm-overflow-char}
\=\+{\rm{finite-numberp}}\,({\it{char\/}}, {\tt{'}}{\tt{256}})\index{finite-numberp} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-overflow-char}}\,({\it{char\/}})\index{tm-overflow-char}, {\tt{'}}{\tt{512}})\index{finite-numberp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-overflow-char-tm-wordlub \\ \index{finite-numberp-tm-overflow-char!-tm-wordlub}
\=\+{\rm{finite-numberp}}\,({\it{char\/}}, {\tt{'}}{\tt{256}})\index{finite-numberp} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-overflow-char}}\,({\it{char\/}})\index{tm-overflow-char}, {\tt{'}}{\tt{65536}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-overflow-char-tm-wordlub.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iport-error-flag-is-zero \\ \index{tm-iport-error-flag-is-zero}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{id\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(({\it{id\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ($\neg$ {\rm{tm-iport-errorp}}\,({\it{id\/}}, {\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{tm-iport-errorp})))\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-ierror-flag}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{getnth})\index{tm-ierror-flag} $=$ {\tt{'}}{\tt{0}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iport-error-flag-is-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-interrupting-input-port-crock \\ \index{finite-numberp-tm-interrupting-i!nput-port-crock}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$({\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port} $<$ {\tt{'}}{\tt{16}}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-interrupting-input-port-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-ichar-facts \\ \index{tm-ichar-facts}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+(\=\+{\tt{'}}{\tt{256}} \\ 
$+$$\;\;\;\;${\rm{tm-ichar}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{getnth})\index{tm-ichar})\- \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{65536}})\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-ichar-facts.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-interrupting-output-port-crock \\ \index{finite-numberp-tm-interrupting-!output-port-crock}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$({\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port} $<$ {\tt{'}}{\tt{16}}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-interrupting-output-port-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tm-cpu-length}$\;\;$
{\sc{tm-cpu-length}}\index{tm-cpu-length} $=$ {\tt{'}}{\tt{9}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-r0}$\;\;$
{\rm{tm-r0}}\,({\it{tm\/}})\index{tm-r0} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs})\index{getnth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-r1}$\;\;$
{\rm{tm-r1}}\,({\it{tm\/}})\index{tm-r1} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs})\index{getnth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-r2}$\;\;$
{\rm{tm-r2}}\,({\it{tm\/}})\index{tm-r2} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs})\index{getnth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-r3}$\;\;$
{\rm{tm-r3}}\,({\it{tm\/}})\index{tm-r3} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs})\index{getnth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-r4}$\;\;$
{\rm{tm-r4}}\,({\it{tm\/}})\index{tm-r4} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs})\index{getnth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-r5}$\;\;$
{\rm{tm-r5}}\,({\it{tm\/}})\index{tm-r5} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs})\index{getnth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-r6}$\;\;$
{\rm{tm-r6}}\,({\it{tm\/}})\index{tm-r6} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs})\index{getnth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-r7}$\;\;$
{\rm{tm-r7}}\,({\it{tm\/}})\index{tm-r7} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs})\index{getnth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-cpu} \\  
\=\+{\rm{tm-cpu}}\,({\it{tm\/}})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{tm-r0}}\,({\it{tm\/}})\index{tm-r0}, \\ 
{\rm{cons}}\,(\=\+{\rm{tm-r1}}\,({\it{tm\/}})\index{tm-r1}, \\ 
{\rm{cons}}\,(\=\+{\rm{tm-r2}}\,({\it{tm\/}})\index{tm-r2}, \\ 
{\rm{cons}}\,(\=\+{\rm{tm-r3}}\,({\it{tm\/}})\index{tm-r3}, \\ 
{\rm{cons}}\,(\=\+{\rm{tm-r4}}\,({\it{tm\/}})\index{tm-r4}, \\ 
{\rm{cons}}\,(\=\+{\rm{tm-r5}}\,({\it{tm\/}})\index{tm-r5}, \\ 
{\rm{cons}}\,(\=\+{\rm{tm-r6}}\,({\it{tm\/}})\index{tm-r6}, \\ 
{\rm{cons}}\,(\=\+{\rm{tm-r7}}\,({\it{tm\/}})\index{tm-r7}, \\ 
{\rm{cons}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{nil}})\-)\-)\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{good-cpu} \\  
\=\+{\rm{good-cpu}}\,({\it{cpu\/}})\index{good-cpu} \\ 
$=$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\it{cpu\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(({\rm{length}}\,({\it{cpu\/}})\index{length} $=$ {\tt{'}}{\tt{9}}) $\wedge$ {\rm{finite-number-listp}}\,({\it{cpu\/}}, {\tt{'}}{\tt{65536}})\index{finite-number-listp}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{good-cpu-list} \\  
\=\+{\rm{good-cpu-list}}\,({\it{l\/}})\index{good-cpu-list} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}})$\;\;${\bf then }{\rm{good-cpu}}\,({\rm{car}}\,({\it{l\/}}))\index{good-cpu} $\wedge$ {\rm{good-cpu-list}}\,({\rm{cdr}}\,({\it{l\/}}))\index{good-cpu-list} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  open-up-finite-number-listp \\ \index{open-up-finite-number-listp}
\=\+{\rm{finite-number-listp}}\,({\rm{cons}}\,({\it{a\/}}, {\it{b\/}}), {\it{lub\/}})\index{finite-number-listp} \\ 
$=$$\;\;\;\;$({\rm{finite-numberp}}\,({\it{a\/}}, {\it{lub\/}})\index{finite-numberp} $\wedge$ {\rm{finite-number-listp}}\,({\it{b\/}}, {\it{lub\/}})\index{finite-number-listp})\-
\end{tabbing}


\noindent{\sc Event}:   Disable open-up-finite-number-listp.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-on-non-list \\ \index{finite-number-listp-on-non-list}
($\neg$ {\rm{listp}}\,({\it{x\/}})) $\rightarrow$ ({\rm{finite-number-listp}}\,({\it{x\/}}, {\it{lub\/}})\index{finite-number-listp} $=$ {\tt{'}}{\tt{*1*true}})
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-on-non-list.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-cpu \\ \index{length-tm-cpu}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ ({\rm{length}}\,({\rm{tm-cpu}}\,({\it{tm\/}})\index{tm-cpu})\index{length} $=$ {\tt{'}}{\tt{9}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-cpu.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-tm-cpu \\ \index{plistp-tm-cpu}
{\rm{plistp}}\,({\rm{tm-cpu}}\,({\it{tm\/}})\index{tm-cpu})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-tm-cpu.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-tm-cpu \\ \index{finite-number-listp-tm-cpu}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{finite-number-listp}}\,({\rm{tm-cpu}}\,({\it{tm\/}})\index{tm-cpu}, {\tt{'}}{\tt{65536}})\index{finite-number-listp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-tm-cpu.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-cpu-tm-cpu \\ \index{good-cpu-tm-cpu}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-cpu}}\,({\rm{tm-cpu}}\,({\it{tm\/}})\index{tm-cpu})\index{good-cpu}
\end{tabbing}


\noindent{\sc Event}:   Disable good-cpu-tm-cpu.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-cpu-getnth \\ \index{good-cpu-getnth}
({\rm{good-cpu-list}}\,({\it{l\/}})\index{good-cpu-list} $\wedge$ ({\it{n\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) $\rightarrow$ {\rm{good-cpu}}\,({\rm{getnth}}\,({\it{n\/}}, {\it{l\/}})\index{getnth})\index{good-cpu}
\end{tabbing}


\noindent{\sc Event}:   Disable good-cpu-getnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-cpu-list-putnth \\ \index{good-cpu-list-putnth}
({\rm{good-cpu-list}}\,({\it{l\/}})\index{good-cpu-list} $\wedge$ {\rm{good-cpu}}\,({\it{cpu\/}})\index{good-cpu}) $\rightarrow$ {\rm{good-cpu-list}}\,({\rm{putnth}}\,({\it{cpu\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth})\index{good-cpu-list}
\end{tabbing}


\noindent{\sc Event}:   Disable good-cpu-list-putnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  list-of-getnths8 \\ \index{list-of-getnths8}
\=\+({\rm{plistp}}\,({\it{l\/}})\index{plistp} $\wedge$ ({\rm{length}}\,({\it{l\/}})\index{length} $=$ {\tt{'}}{\tt{8}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,({\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\it{l\/}})\index{getnth}, {\tt{'}}{\tt{nil}}))\-)\-)\-)\-)\-)\-)\- \\ 
$=$$\;\;\;\;${\it{l\/}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable list-of-getnths8.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  cpu-regs-segment \\ \index{cpu-regs-segment}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ ({\rm{getseg}}\,({\tt{'}}{\tt{0}}, {\tt{'}}{\tt{8}}, {\rm{tm-cpu}}\,({\it{tm\/}})\index{tm-cpu})\index{getseg} $=$ {\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs})
\end{tabbing}


\noindent{\sc Event}:   Disable cpu-regs-segment.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{good-tm-properties}} to consist of the following events: cpu-regs-segment,
good-cpu-list-putnth,
good-cpu-getnth,
good-cpu-tm-cpu,
finite-numberp-tm-pack-psw,
finite-number-listp-tm-cpu,
numberp-getnth-from-tm-regs,
numberp-getnth-from-tm-memory,
finite-numberp-tm-pc,
finite-numberp-tm-sp,
finite-numberp-tm-cc,
finite-numberp-tm-error,
finite-numberp-tm-svcflag,
finite-numberp-tm-svcid,
finite-numberp-tm-rwstate,
plistp-tm-iports,
length-tm-iports,
good-tm-iport-array-tm-iports,
plistp-tm-oports,
length-tm-oports,
good-tm-oport-array-tm-oports,
good-tm-iport-getnth-from-tm-iports,
good-tm-iport-array-putnth-into-tm-iports,
good-tm-oport-getnth-from-tm-oports,
good-tm-oport-array-putnth-into-tm-oports,
finite-numberp-tm-clock,
finite-numberp-tm-svmode,
finite-numberp-tm-slimit,
finite-numberp-tm-limit,
finite-numberp-tm-base,
finite-number-listp-tm-regs,
length-tm-regs,
plistp-tm-regs,
finite-number-listp-tm-memory,
length-tm-memory,
plistp-tm-memory,
tm-shellp-tm,
tm-fix-reg-address-noop,
tm-fix-reg-address-size-linear,
tm-fix-reg-address-size,
numberp-tm-fix-reg-address,
tm-fix-word-noop,
tm-fix-word-size-linear,
tm-fix-word-size,
numberp-tm-fix-word,
tm-cc-value-on-compare-lessp,
tm-cc-value-on-compare-greaterp,
finite-numberp-tm-pack-psw,
finite-numberp-tm-overflow-char-tm-wordlub,
finite-numberp-tm-ichar-getnth-crock,
finite-numberp-tm-interrupting-input-port,
finite-numberp-tm-interrupting-input-port-tm-wordlub,
good-tm-iport-getnth-properties,
finite-numberp-tm-interrupting-output-port,
finite-numberp-tm-interrupting-output-port-tm-wordlub,
good-tm-oport-getnth-properties.\index{good-tm-properties}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{tm-definition}} to consist of the following events: tm-processor,
tm-step,
tm-post-interrupt,
tm-execute-output-interrupt,
tm-store-interrupting-output-device,
tm-output-interruptp,
tm-execute-input-interrupt,
tm-store-interrupting-input-device,
tm-input-interruptp,
tm-overflow-char,
tm-execute-svc-interrupt,
tm-store-svcid-on-interrupt,
tm-svc-interruptp,
tm-execute-error-interrupt,
tm-errorp,
tm-execute-clock-interrupt,
tm-clock-interruptp,
tm-store-old-psw-on-interrupt,
tm-fetch-new-pc-on-interrupt,
tm-fetch-execute,
tm-good-pc-address,
tm-decrement-clock,
tm-execute,
tm-fetch-arg2,
tm-fetch-arg1,
tm-fetch-opcode,
tm-execute-instruction,
tm-execute-binary,
tm-execute-unary,
tm-execute-nullary,
tm-arg2,
tm-arg1,
tm-datum2,
tm-datum1,
tm-unary-instructionp,
tm-nullary-instructionp,
tm-index2,
tm-mode2,
tm-index1,
tm-mode1,
tm-opcode,
tm-execute-svc-return,
tm-execute-svc,
tm-execute-start-output,
tm-execute-test-iport,
tm-execute-test-oport,
tm-execute-post-output-interrupt,
tm-execute-wait,
tm-execute-set-clock,
tm-execute-run,
tm-execute-return,
tm-execute-multiply,
tm-execute-move,
tm-execute-mod,
tm-execute-load-psw,
tm-execute-load-limit,
tm-execute-load-base,
tm-execute-incr-mod,
tm-execute-incr,
tm-execute-decr-mod,
tm-execute-decr,
tm-execute-compare,
tm-execute-call,
tm-execute-branch-not-zero,
tm-execute-branch-on-zero,
tm-execute-branch,
tm-execute-add,
tm-stack-underflowp,
tm-stack-overflowp,
tm-store,
tm-fetch,
tm-store-in-regmem,
tm-fetch-from-regmem,
tm-store-in-memory,
tm-fetch-from-memory,
tm-incrn-address,
tm-incr-address,
tm-good-address,
tm-compute-address,
tm-arg-index,
tm-arg-datum,
tm-arg-mode,
real-addr-num,
real-addr-source,
real-addr,
tm-clear-output-interrupt,
tm-post-output-interrupt,
tm-start-output,
tm-oport-idlep,
tm-post-input-interrupt,
tm-clear-input-interrupt,
tm-iport-errorp,
tm-no-svc,
tm-svc,
tm-waiting,
tm-in-supervisor-mode,
tm-user-mode,
tm-supervisor-mode,
tm-pc-address-error,
tm-address-error,
tm-stack-underflow-error,
tm-stack-overflow-error,
tm-privilege-error,
tm-opcode-error,
tm-halt-status,
tm-no-error,
tm-unpack-svcid,
tm-unpack-svcflag,
tm-unpack-error,
tm-unpack-cc,
tm-pack-psw,
tm-zero-carry-condition,
tm-non-zero-carry-condition,
tm-zero-no-carry-condition,
tm-non-zero-no-carry-condition,
tm-set-sp,
tm-sp,
tm-set-pc,
tm-pc,
tm-set-oports,
tm-set-iports,
tm-set-clock,
tm-set-rwstate,
tm-set-svmode,
tm-set-slimit,
tm-set-limit,
tm-set-base,
tm-set-svcid,
tm-set-svcflag,
tm-set-error,
tm-set-cc,
tm-set-regs,
tm-set-memory,
tm-decr,
tm-incrn,
tm-incr,
tm-r0,
tm-r1,
tm-r2,
tm-r3,
tm-r4,
tm-r5,
tm-r6,
tm-r7,
tm-shells.\index{tm-definition}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-fetch-from-memory-in-supervisor-mode \\ \index{finite-numberp-tm-fetch-from-me!mory-in-supervisor-mode}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ ({\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode} $\wedge$ {\rm{finite-numberp}}\,({\it{n\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-fetch-from-memory}}\,({\it{n\/}}, {\it{tm\/}})\index{tm-fetch-from-memory}, {\tt{'}}{\tt{65536}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-fetch-from-memory-in-supervisor-mode.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-min-difference-memlength-base-limit \\ \index{finite-numberp-min-difference-me!mlength-base-limit}
\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{min}}\,({\tt{'}}{\tt{65536}} $-$ {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\index{min}, {\tt{'}}{\tt{65536}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-min-difference-memlength-base-limit.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-plus-base-addr-memlength \\ \index{lessp-plus-base-addr-memlength}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} $\not=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{real-addr-num}}\,({\it{addr\/}})\index{real-addr-num}) $<$ {\tt{'}}{\tt{65536}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-plus-base-addr-memlength.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-fetch \\ \index{finite-numberp-tm-fetch}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-fetch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch}, {\tt{'}}{\tt{65536}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-fetch.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 TM-STORE-PRESERVES-ALL-BUT-MEMORY-AND-REGS
 (REWRITE)
 (AND
  (EQUAL (TM-CC (TM-STORE VALUE ADDR TM))
         (TM-CC TM))
  (AND
   (EQUAL (TM-ERROR (TM-STORE VALUE ADDR TM))
          (TM-ERROR TM))
   (AND
    (EQUAL (TM-BASE (TM-STORE VALUE ADDR TM))
           (TM-BASE TM))
    (AND
     (EQUAL (TM-LIMIT (TM-STORE VALUE ADDR TM))
            (TM-LIMIT TM))
     (AND
      (EQUAL (TM-SLIMIT (TM-STORE VALUE ADDR TM))
             (TM-SLIMIT TM))
      (AND (EQUAL (TM-SVMODE (TM-STORE VALUE ADDR TM))
                  (TM-SVMODE TM))
           (AND (EQUAL (TM-SVCFLAG (TM-STORE VALUE ADDR TM))
                       (TM-SVCFLAG TM))
                (AND (EQUAL (TM-SVCID (TM-STORE VALUE ADDR TM))
                            (TM-SVCID TM))
                     (AND (EQUAL (TM-RWSTATE (TM-STORE VALUE ADDR TM))
                                 (TM-RWSTATE TM))
                          (AND (EQUAL (TM-CLOCK (TM-STORE VALUE ADDR TM))
                                      (TM-CLOCK TM))
                               (AND (EQUAL (TM-IPORTS (TM-STORE VALUE ADDR TM))
                                           (TM-IPORTS TM))
                                    (EQUAL (TM-OPORTS (TM-STORE VALUE ADDR TM))
                                           (TM-OPORTS TM)))))))))))))
 ((ENABLE TM-STORE-IN-MEMORY TM-STORE-IN-REGMEM TM-SET-REGS TM-SET-MEMORY
          TM-STORE)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable tm-store-preserves-all-but-memory-and-regs.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-good-memory-tm-store \\ \index{tm-good-memory-tm-store}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{value\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\rm{tm-memory}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store})\index{tm-memory})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store})\index{tm-memory})\index{length} $=$ {\tt{'}}{\tt{65536}}) \\ 
$\wedge$$\;\;\;\;${\rm{finite-number-listp}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store})\index{tm-memory}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-listp})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-good-memory-tm-store.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-good-regs-tm-store \\ \index{tm-good-regs-tm-store}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{value\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\rm{tm-regs}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store})\index{tm-regs})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\rm{tm-regs}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store})\index{tm-regs})\index{length} $=$ {\tt{'}}{\tt{8}}) \\ 
$\wedge$$\;\;\;\;${\rm{finite-number-listp}}\,(\=\+{\rm{tm-regs}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store})\index{tm-regs}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-listp})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-good-regs-tm-store.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-store \\ \index{good-tm-tm-store}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{value\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-store.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-set-regs \\ \index{good-tm-tm-set-regs}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-number-listp}}\,({\it{regs\/}}, {\tt{'}}{\tt{65536}})\index{finite-number-listp} \\ 
$\wedge$$\;\;\;\;$({\rm{plistp}}\,({\it{regs\/}})\index{plistp} $\wedge$ ({\rm{length}}\,({\it{regs\/}})\index{length} $=$ {\tt{'}}{\tt{8}})))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-set-regs}}\,({\it{regs\/}}, {\it{tm\/}})\index{tm-set-regs})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-set-regs.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 ACCESS-TM-SET-REGS
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-SET-REGS REGS TM))
         (TM-MEMORY TM))
  (AND
   (EQUAL (TM-REGS (TM-SET-REGS REGS TM))
          REGS)
   (AND
    (EQUAL (TM-CC (TM-SET-REGS REGS TM))
           (TM-CC TM))
    (AND
     (EQUAL (TM-ERROR (TM-SET-REGS REGS TM))
            (TM-ERROR TM))
     (AND
      (EQUAL (TM-BASE (TM-SET-REGS REGS TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-SET-REGS REGS TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-SET-REGS REGS TM))
               (TM-SLIMIT TM))
        (AND
         (EQUAL (TM-SVMODE (TM-SET-REGS REGS TM))
                (TM-SVMODE TM))
         (AND
          (EQUAL (TM-SVCFLAG (TM-SET-REGS REGS TM))
                 (TM-SVCFLAG TM))
          (AND
              (EQUAL (TM-SVCID (TM-SET-REGS REGS TM))
                     (TM-SVCID TM))
              (AND (EQUAL (TM-RWSTATE (TM-SET-REGS REGS TM))
                          (TM-RWSTATE TM))
                   (AND (EQUAL (TM-CLOCK (TM-SET-REGS REGS TM))
                               (TM-CLOCK TM))
                        (AND (EQUAL (TM-IPORTS (TM-SET-REGS REGS TM))
                                    (TM-IPORTS TM))
                             (AND (EQUAL (TM-OPORTS (TM-SET-REGS REGS TM))
                                         (TM-OPORTS TM))
                                  (AND (EQUAL (TM-PC (TM-SET-REGS REGS TM))
                                              (GETNTH '0 REGS))
                                       (EQUAL (TM-SP (TM-SET-REGS REGS TM))
                                              (GETNTH '1 REGS)))))))))))))))))
 ((ENABLE TM-SET-REGS TM-PC TM-SP)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable access-tm-set-regs.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-set-memory \\ \index{good-tm-tm-set-memory}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-number-listp}}\,({\it{memory\/}}, {\tt{'}}{\tt{65536}})\index{finite-number-listp} \\ 
$\wedge$$\;\;\;\;$({\rm{plistp}}\,({\it{memory\/}})\index{plistp} $\wedge$ ({\rm{length}}\,({\it{memory\/}})\index{length} $=$ {\tt{'}}{\tt{65536}})))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-set-memory}}\,({\it{memory\/}}, {\it{tm\/}})\index{tm-set-memory})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-set-memory.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 ACCESS-TM-SET-MEMORY
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-SET-MEMORY MEMORY TM))
         MEMORY)
  (AND
   (EQUAL (TM-REGS (TM-SET-MEMORY MEMORY TM))
          (TM-REGS TM))
   (AND
    (EQUAL (TM-CC (TM-SET-MEMORY MEMORY TM))
           (TM-CC TM))
    (AND
     (EQUAL (TM-ERROR (TM-SET-MEMORY MEMORY TM))
            (TM-ERROR TM))
     (AND
      (EQUAL (TM-BASE (TM-SET-MEMORY MEMORY TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-SET-MEMORY MEMORY TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-SET-MEMORY MEMORY TM))
               (TM-SLIMIT TM))
        (AND
         (EQUAL (TM-SVMODE (TM-SET-MEMORY MEMORY TM))
                (TM-SVMODE TM))
         (AND
          (EQUAL (TM-SVCFLAG (TM-SET-MEMORY MEMORY TM))
                 (TM-SVCFLAG TM))
          (AND
              (EQUAL (TM-SVCID (TM-SET-MEMORY MEMORY TM))
                     (TM-SVCID TM))
              (AND (EQUAL (TM-RWSTATE (TM-SET-MEMORY MEMORY TM))
                          (TM-RWSTATE TM))
                   (AND (EQUAL (TM-CLOCK (TM-SET-MEMORY MEMORY TM))
                               (TM-CLOCK TM))
                        (AND (EQUAL (TM-IPORTS (TM-SET-MEMORY MEMORY TM))
                                    (TM-IPORTS TM))
                             (AND (EQUAL (TM-OPORTS (TM-SET-MEMORY MEMORY TM))
                                         (TM-OPORTS TM))
                                  (AND (EQUAL (TM-PC (TM-SET-MEMORY MEMORY TM))
                                              (TM-PC TM))
                                       (EQUAL (TM-SP (TM-SET-MEMORY MEMORY TM))
                                              (TM-SP TM)))))))))))))))))
 ((ENABLE TM-SET-MEMORY TM-PC TM-SP)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable access-tm-set-memory.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-set-cc \\ \index{good-tm-tm-set-cc}
({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{cc\/}}, {\tt{'}}{\tt{4}})\index{finite-numberp}) $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-set-cc}}\,({\it{cc\/}}, {\it{tm\/}})\index{tm-set-cc})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-set-cc.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 ACCESS-TM-SET-CC
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-SET-CC CC TM))
         (TM-MEMORY TM))
  (AND
   (EQUAL (TM-REGS (TM-SET-CC CC TM))
          (TM-REGS TM))
   (AND
    (EQUAL (TM-CC (TM-SET-CC CC TM)) CC)
    (AND
     (EQUAL (TM-ERROR (TM-SET-CC CC TM))
            (TM-ERROR TM))
     (AND
      (EQUAL (TM-BASE (TM-SET-CC CC TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-SET-CC CC TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-SET-CC CC TM))
               (TM-SLIMIT TM))
        (AND
           (EQUAL (TM-SVMODE (TM-SET-CC CC TM))
                  (TM-SVMODE TM))
           (AND (EQUAL (TM-SVCFLAG (TM-SET-CC CC TM))
                       (TM-SVCFLAG TM))
                (AND (EQUAL (TM-SVCID (TM-SET-CC CC TM))
                            (TM-SVCID TM))
                     (AND (EQUAL (TM-RWSTATE (TM-SET-CC CC TM))
                                 (TM-RWSTATE TM))
                          (AND (EQUAL (TM-CLOCK (TM-SET-CC CC TM))
                                      (TM-CLOCK TM))
                               (AND (EQUAL (TM-IPORTS (TM-SET-CC CC TM))
                                           (TM-IPORTS TM))
                                    (AND (EQUAL (TM-OPORTS (TM-SET-CC CC TM))
                                                (TM-OPORTS TM))
                                         (AND (EQUAL (TM-PC (TM-SET-CC CC TM))
                                                     (TM-PC TM))
                                              (EQUAL (TM-SP (TM-SET-CC CC TM))
                                                     (TM-SP TM)))))))))))))))))
 ((ENABLE TM-SET-CC TM-PC TM-SP)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable access-tm-set-cc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-set-error \\ \index{good-tm-tm-set-error}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{error\/}}, {\tt{'}}{\tt{64}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-set-error}}\,({\it{error\/}}, {\it{tm\/}})\index{tm-set-error})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-set-error.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 ACCESS-TM-SET-ERROR
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-SET-ERROR ERROR TM))
         (TM-MEMORY TM))
  (AND
   (EQUAL (TM-REGS (TM-SET-ERROR ERROR TM))
          (TM-REGS TM))
   (AND
    (EQUAL (TM-CC (TM-SET-ERROR ERROR TM))
           (TM-CC TM))
    (AND
     (EQUAL (TM-ERROR (TM-SET-ERROR ERROR TM))
            ERROR)
     (AND
      (EQUAL (TM-BASE (TM-SET-ERROR ERROR TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-SET-ERROR ERROR TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-SET-ERROR ERROR TM))
               (TM-SLIMIT TM))
        (AND
         (EQUAL (TM-SVMODE (TM-SET-ERROR ERROR TM))
                (TM-SVMODE TM))
         (AND
           (EQUAL (TM-SVCFLAG (TM-SET-ERROR ERROR TM))
                  (TM-SVCFLAG TM))
           (AND (EQUAL (TM-SVCID (TM-SET-ERROR ERROR TM))
                       (TM-SVCID TM))
                (AND (EQUAL (TM-RWSTATE (TM-SET-ERROR ERROR TM))
                            (TM-RWSTATE TM))
                     (AND (EQUAL (TM-CLOCK (TM-SET-ERROR ERROR TM))
                                 (TM-CLOCK TM))
                          (AND (EQUAL (TM-IPORTS (TM-SET-ERROR ERROR TM))
                                      (TM-IPORTS TM))
                               (AND (EQUAL (TM-OPORTS (TM-SET-ERROR ERROR TM))
                                           (TM-OPORTS TM))
                                    (AND (EQUAL (TM-PC (TM-SET-ERROR ERROR TM))
                                                (TM-PC TM))
                                         (EQUAL (TM-SP (TM-SET-ERROR ERROR TM))
                                                (TM-SP TM)))))))))))))))))
 ((ENABLE TM-SET-ERROR TM-PC TM-SP)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable access-tm-set-error.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-set-base \\ \index{good-tm-tm-set-base}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{base\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-set-base}}\,({\it{base\/}}, {\it{tm\/}})\index{tm-set-base})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-set-base.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 ACCESS-TM-SET-BASE
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-SET-BASE BASE TM))
         (TM-MEMORY TM))
  (AND
   (EQUAL (TM-REGS (TM-SET-BASE BASE TM))
          (TM-REGS TM))
   (AND
    (EQUAL (TM-CC (TM-SET-BASE BASE TM))
           (TM-CC TM))
    (AND
     (EQUAL (TM-ERROR (TM-SET-BASE BASE TM))
            (TM-ERROR TM))
     (AND
      (EQUAL (TM-BASE (TM-SET-BASE BASE TM))
             BASE)
      (AND
       (EQUAL (TM-LIMIT (TM-SET-BASE BASE TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-SET-BASE BASE TM))
               (TM-SLIMIT TM))
        (AND
         (EQUAL (TM-SVMODE (TM-SET-BASE BASE TM))
                (TM-SVMODE TM))
         (AND
             (EQUAL (TM-SVCFLAG (TM-SET-BASE BASE TM))
                    (TM-SVCFLAG TM))
             (AND (EQUAL (TM-SVCID (TM-SET-BASE BASE TM))
                         (TM-SVCID TM))
                  (AND (EQUAL (TM-RWSTATE (TM-SET-BASE BASE TM))
                              (TM-RWSTATE TM))
                       (AND (EQUAL (TM-CLOCK (TM-SET-BASE BASE TM))
                                   (TM-CLOCK TM))
                            (AND (EQUAL (TM-IPORTS (TM-SET-BASE BASE TM))
                                        (TM-IPORTS TM))
                                 (AND (EQUAL (TM-OPORTS (TM-SET-BASE BASE TM))
                                             (TM-OPORTS TM))
                                      (AND (EQUAL (TM-PC (TM-SET-BASE BASE TM))
                                                  (TM-PC TM))
                                           (EQUAL (TM-SP (TM-SET-BASE BASE TM))
                                                  (TM-SP TM)))))))))))))))))
 ((ENABLE TM-SET-BASE TM-PC TM-SP)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable access-tm-set-base.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-set-limit \\ \index{good-tm-tm-set-limit}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{limit\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-set-limit}}\,({\it{limit\/}}, {\it{tm\/}})\index{tm-set-limit})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-set-limit.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 ACCESS-TM-SET-LIMIT
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-SET-LIMIT LIMIT TM))
         (TM-MEMORY TM))
  (AND
   (EQUAL (TM-REGS (TM-SET-LIMIT LIMIT TM))
          (TM-REGS TM))
   (AND
    (EQUAL (TM-CC (TM-SET-LIMIT LIMIT TM))
           (TM-CC TM))
    (AND
     (EQUAL (TM-ERROR (TM-SET-LIMIT LIMIT TM))
            (TM-ERROR TM))
     (AND
      (EQUAL (TM-BASE (TM-SET-LIMIT LIMIT TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-SET-LIMIT LIMIT TM))
              LIMIT)
       (AND
        (EQUAL (TM-SLIMIT (TM-SET-LIMIT LIMIT TM))
               (TM-SLIMIT TM))
        (AND
         (EQUAL (TM-SVMODE (TM-SET-LIMIT LIMIT TM))
                (TM-SVMODE TM))
         (AND
           (EQUAL (TM-SVCFLAG (TM-SET-LIMIT LIMIT TM))
                  (TM-SVCFLAG TM))
           (AND (EQUAL (TM-SVCID (TM-SET-LIMIT LIMIT TM))
                       (TM-SVCID TM))
                (AND (EQUAL (TM-RWSTATE (TM-SET-LIMIT LIMIT TM))
                            (TM-RWSTATE TM))
                     (AND (EQUAL (TM-CLOCK (TM-SET-LIMIT LIMIT TM))
                                 (TM-CLOCK TM))
                          (AND (EQUAL (TM-IPORTS (TM-SET-LIMIT LIMIT TM))
                                      (TM-IPORTS TM))
                               (AND (EQUAL (TM-OPORTS (TM-SET-LIMIT LIMIT TM))
                                           (TM-OPORTS TM))
                                    (AND (EQUAL (TM-PC (TM-SET-LIMIT LIMIT TM))
                                                (TM-PC TM))
                                         (EQUAL (TM-SP (TM-SET-LIMIT LIMIT TM))
                                                (TM-SP TM)))))))))))))))))
 ((ENABLE TM-SET-LIMIT TM-PC TM-SP)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable access-tm-set-limit.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-set-slimit \\ \index{good-tm-tm-set-slimit}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{slimit\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-set-slimit}}\,({\it{slimit\/}}, {\it{tm\/}})\index{tm-set-slimit})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-set-slimit.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 ACCESS-TM-SET-SLIMIT
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-SET-SLIMIT SLIMIT TM))
         (TM-MEMORY TM))
  (AND
   (EQUAL (TM-REGS (TM-SET-SLIMIT SLIMIT TM))
          (TM-REGS TM))
   (AND
    (EQUAL (TM-CC (TM-SET-SLIMIT SLIMIT TM))
           (TM-CC TM))
    (AND
     (EQUAL (TM-ERROR (TM-SET-SLIMIT SLIMIT TM))
            (TM-ERROR TM))
     (AND
      (EQUAL (TM-BASE (TM-SET-SLIMIT SLIMIT TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-SET-SLIMIT SLIMIT TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-SET-SLIMIT SLIMIT TM))
               SLIMIT)
        (AND
         (EQUAL (TM-SVMODE (TM-SET-SLIMIT SLIMIT TM))
                (TM-SVMODE TM))
         (AND
          (EQUAL (TM-SVCFLAG (TM-SET-SLIMIT SLIMIT TM))
                 (TM-SVCFLAG TM))
          (AND
              (EQUAL (TM-SVCID (TM-SET-SLIMIT SLIMIT TM))
                     (TM-SVCID TM))
              (AND (EQUAL (TM-RWSTATE (TM-SET-SLIMIT SLIMIT TM))
                          (TM-RWSTATE TM))
                   (AND (EQUAL (TM-CLOCK (TM-SET-SLIMIT SLIMIT TM))
                               (TM-CLOCK TM))
                        (AND (EQUAL (TM-IPORTS (TM-SET-SLIMIT SLIMIT TM))
                                    (TM-IPORTS TM))
                             (AND (EQUAL (TM-OPORTS (TM-SET-SLIMIT SLIMIT TM))
                                         (TM-OPORTS TM))
                                  (AND (EQUAL (TM-PC (TM-SET-SLIMIT SLIMIT TM))
                                              (TM-PC TM))
                                       (EQUAL (TM-SP (TM-SET-SLIMIT SLIMIT TM))
                                              (TM-SP TM)))))))))))))))))
 ((ENABLE TM-SET-SLIMIT TM-PC TM-SP)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable access-tm-set-slimit.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-set-svmode \\ \index{good-tm-tm-set-svmode}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{svmode\/}}, {\tt{'}}{\tt{2}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-set-svmode}}\,({\it{svmode\/}}, {\it{tm\/}})\index{tm-set-svmode})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-set-svmode.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 ACCESS-TM-SET-SVMODE
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-SET-SVMODE SVMODE TM))
         (TM-MEMORY TM))
  (AND
   (EQUAL (TM-REGS (TM-SET-SVMODE SVMODE TM))
          (TM-REGS TM))
   (AND
    (EQUAL (TM-CC (TM-SET-SVMODE SVMODE TM))
           (TM-CC TM))
    (AND
     (EQUAL (TM-ERROR (TM-SET-SVMODE SVMODE TM))
            (TM-ERROR TM))
     (AND
      (EQUAL (TM-BASE (TM-SET-SVMODE SVMODE TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-SET-SVMODE SVMODE TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-SET-SVMODE SVMODE TM))
               (TM-SLIMIT TM))
        (AND
         (EQUAL (TM-SVMODE (TM-SET-SVMODE SVMODE TM))
                SVMODE)
         (AND
          (EQUAL (TM-SVCFLAG (TM-SET-SVMODE SVMODE TM))
                 (TM-SVCFLAG TM))
          (AND
              (EQUAL (TM-SVCID (TM-SET-SVMODE SVMODE TM))
                     (TM-SVCID TM))
              (AND (EQUAL (TM-RWSTATE (TM-SET-SVMODE SVMODE TM))
                          (TM-RWSTATE TM))
                   (AND (EQUAL (TM-CLOCK (TM-SET-SVMODE SVMODE TM))
                               (TM-CLOCK TM))
                        (AND (EQUAL (TM-IPORTS (TM-SET-SVMODE SVMODE TM))
                                    (TM-IPORTS TM))
                             (AND (EQUAL (TM-OPORTS (TM-SET-SVMODE SVMODE TM))
                                         (TM-OPORTS TM))
                                  (AND (EQUAL (TM-PC (TM-SET-SVMODE SVMODE TM))
                                              (TM-PC TM))
                                       (EQUAL (TM-SP (TM-SET-SVMODE SVMODE TM))
                                              (TM-SP TM)))))))))))))))))
 ((ENABLE TM-SET-SVMODE TM-PC TM-SP)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable access-tm-set-svmode.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-set-svcflag \\ \index{good-tm-tm-set-svcflag}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{svcflag\/}}, {\tt{'}}{\tt{2}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-set-svcflag}}\,({\it{svcflag\/}}, {\it{tm\/}})\index{tm-set-svcflag})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-set-svcflag.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 ACCESS-TM-SET-SVCFLAG
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-SET-SVCFLAG SVCFLAG TM))
         (TM-MEMORY TM))
  (AND
   (EQUAL (TM-REGS (TM-SET-SVCFLAG SVCFLAG TM))
          (TM-REGS TM))
   (AND
    (EQUAL (TM-CC (TM-SET-SVCFLAG SVCFLAG TM))
           (TM-CC TM))
    (AND
     (EQUAL (TM-ERROR (TM-SET-SVCFLAG SVCFLAG TM))
            (TM-ERROR TM))
     (AND
      (EQUAL (TM-BASE (TM-SET-SVCFLAG SVCFLAG TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-SET-SVCFLAG SVCFLAG TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-SET-SVCFLAG SVCFLAG TM))
               (TM-SLIMIT TM))
        (AND
         (EQUAL (TM-SVMODE (TM-SET-SVCFLAG SVCFLAG TM))
                (TM-SVMODE TM))
         (AND
          (EQUAL (TM-SVCFLAG (TM-SET-SVCFLAG SVCFLAG TM))
                 SVCFLAG)
          (AND
            (EQUAL (TM-SVCID (TM-SET-SVCFLAG SVCFLAG TM))
                   (TM-SVCID TM))
            (AND (EQUAL (TM-RWSTATE (TM-SET-SVCFLAG SVCFLAG TM))
                        (TM-RWSTATE TM))
                 (AND (EQUAL (TM-CLOCK (TM-SET-SVCFLAG SVCFLAG TM))
                             (TM-CLOCK TM))
                      (AND (EQUAL (TM-IPORTS (TM-SET-SVCFLAG SVCFLAG TM))
                                  (TM-IPORTS TM))
                           (AND (EQUAL (TM-OPORTS (TM-SET-SVCFLAG SVCFLAG TM))
                                       (TM-OPORTS TM))
                                (AND (EQUAL (TM-PC (TM-SET-SVCFLAG SVCFLAG TM))
                                            (TM-PC TM))
                                     (EQUAL (TM-SP (TM-SET-SVCFLAG SVCFLAG TM))
                                            (TM-SP TM)))))))))))))))))
 ((ENABLE TM-SET-SVCFLAG TM-PC TM-SP)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable access-tm-set-svcflag.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-set-svcid \\ \index{good-tm-tm-set-svcid}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{svcid\/}}, {\tt{'}}{\tt{128}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-set-svcid}}\,({\it{svcid\/}}, {\it{tm\/}})\index{tm-set-svcid})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-set-svcid.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 ACCESS-TM-SET-SVCID
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-SET-SVCID SVCID TM))
         (TM-MEMORY TM))
  (AND
   (EQUAL (TM-REGS (TM-SET-SVCID SVCID TM))
          (TM-REGS TM))
   (AND
    (EQUAL (TM-CC (TM-SET-SVCID SVCID TM))
           (TM-CC TM))
    (AND
     (EQUAL (TM-ERROR (TM-SET-SVCID SVCID TM))
            (TM-ERROR TM))
     (AND
      (EQUAL (TM-BASE (TM-SET-SVCID SVCID TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-SET-SVCID SVCID TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-SET-SVCID SVCID TM))
               (TM-SLIMIT TM))
        (AND
         (EQUAL (TM-SVMODE (TM-SET-SVCID SVCID TM))
                (TM-SVMODE TM))
         (AND
           (EQUAL (TM-SVCFLAG (TM-SET-SVCID SVCID TM))
                  (TM-SVCFLAG TM))
           (AND (EQUAL (TM-SVCID (TM-SET-SVCID SVCID TM))
                       SVCID)
                (AND (EQUAL (TM-RWSTATE (TM-SET-SVCID SVCID TM))
                            (TM-RWSTATE TM))
                     (AND (EQUAL (TM-CLOCK (TM-SET-SVCID SVCID TM))
                                 (TM-CLOCK TM))
                          (AND (EQUAL (TM-IPORTS (TM-SET-SVCID SVCID TM))
                                      (TM-IPORTS TM))
                               (AND (EQUAL (TM-OPORTS (TM-SET-SVCID SVCID TM))
                                           (TM-OPORTS TM))
                                    (AND (EQUAL (TM-PC (TM-SET-SVCID SVCID TM))
                                                (TM-PC TM))
                                         (EQUAL (TM-SP (TM-SET-SVCID SVCID TM))
                                                (TM-SP TM)))))))))))))))))
 ((ENABLE TM-SET-SVCID TM-PC TM-SP)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable access-tm-set-svcid.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-set-rwstate \\ \index{good-tm-tm-set-rwstate}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{rwstate\/}}, {\tt{'}}{\tt{2}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-set-rwstate}}\,({\it{rwstate\/}}, {\it{tm\/}})\index{tm-set-rwstate})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-set-rwstate.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 ACCESS-TM-SET-RWSTATE
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-SET-RWSTATE RWSTATE TM))
         (TM-MEMORY TM))
  (AND
   (EQUAL (TM-REGS (TM-SET-RWSTATE RWSTATE TM))
          (TM-REGS TM))
   (AND
    (EQUAL (TM-CC (TM-SET-RWSTATE RWSTATE TM))
           (TM-CC TM))
    (AND
     (EQUAL (TM-ERROR (TM-SET-RWSTATE RWSTATE TM))
            (TM-ERROR TM))
     (AND
      (EQUAL (TM-BASE (TM-SET-RWSTATE RWSTATE TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-SET-RWSTATE RWSTATE TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-SET-RWSTATE RWSTATE TM))
               (TM-SLIMIT TM))
        (AND
         (EQUAL (TM-SVMODE (TM-SET-RWSTATE RWSTATE TM))
                (TM-SVMODE TM))
         (AND
          (EQUAL (TM-SVCFLAG (TM-SET-RWSTATE RWSTATE TM))
                 (TM-SVCFLAG TM))
          (AND
            (EQUAL (TM-SVCID (TM-SET-RWSTATE RWSTATE TM))
                   (TM-SVCID TM))
            (AND (EQUAL (TM-RWSTATE (TM-SET-RWSTATE RWSTATE TM))
                        RWSTATE)
                 (AND (EQUAL (TM-CLOCK (TM-SET-RWSTATE RWSTATE TM))
                             (TM-CLOCK TM))
                      (AND (EQUAL (TM-IPORTS (TM-SET-RWSTATE RWSTATE TM))
                                  (TM-IPORTS TM))
                           (AND (EQUAL (TM-OPORTS (TM-SET-RWSTATE RWSTATE TM))
                                       (TM-OPORTS TM))
                                (AND (EQUAL (TM-PC (TM-SET-RWSTATE RWSTATE TM))
                                            (TM-PC TM))
                                     (EQUAL (TM-SP (TM-SET-RWSTATE RWSTATE TM))
                                            (TM-SP TM)))))))))))))))))
 ((ENABLE TM-SET-RWSTATE TM-PC TM-SP)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable access-tm-set-rwstate.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-set-clock \\ \index{good-tm-tm-set-clock}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{clock\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-set-clock}}\,({\it{clock\/}}, {\it{tm\/}})\index{tm-set-clock})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-set-clock.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 ACCESS-TM-SET-CLOCK
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-SET-CLOCK CLOCK TM))
         (TM-MEMORY TM))
  (AND
   (EQUAL (TM-REGS (TM-SET-CLOCK CLOCK TM))
          (TM-REGS TM))
   (AND
    (EQUAL (TM-CC (TM-SET-CLOCK CLOCK TM))
           (TM-CC TM))
    (AND
     (EQUAL (TM-ERROR (TM-SET-CLOCK CLOCK TM))
            (TM-ERROR TM))
     (AND
      (EQUAL (TM-BASE (TM-SET-CLOCK CLOCK TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-SET-CLOCK CLOCK TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-SET-CLOCK CLOCK TM))
               (TM-SLIMIT TM))
        (AND
         (EQUAL (TM-SVMODE (TM-SET-CLOCK CLOCK TM))
                (TM-SVMODE TM))
         (AND
           (EQUAL (TM-SVCFLAG (TM-SET-CLOCK CLOCK TM))
                  (TM-SVCFLAG TM))
           (AND (EQUAL (TM-SVCID (TM-SET-CLOCK CLOCK TM))
                       (TM-SVCID TM))
                (AND (EQUAL (TM-RWSTATE (TM-SET-CLOCK CLOCK TM))
                            (TM-RWSTATE TM))
                     (AND (EQUAL (TM-CLOCK (TM-SET-CLOCK CLOCK TM))
                                 CLOCK)
                          (AND (EQUAL (TM-IPORTS (TM-SET-CLOCK CLOCK TM))
                                      (TM-IPORTS TM))
                               (AND (EQUAL (TM-OPORTS (TM-SET-CLOCK CLOCK TM))
                                           (TM-OPORTS TM))
                                    (AND (EQUAL (TM-PC (TM-SET-CLOCK CLOCK TM))
                                                (TM-PC TM))
                                         (EQUAL (TM-SP (TM-SET-CLOCK CLOCK TM))
                                                (TM-SP TM)))))))))))))))))
 ((ENABLE TM-SET-CLOCK TM-PC TM-SP)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable access-tm-set-clock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-set-iports \\ \index{good-tm-tm-set-iports}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\it{iports\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(({\rm{length}}\,({\it{iports\/}})\index{length} $=$ {\tt{'}}{\tt{16}}) $\wedge$ {\rm{good-tm-iport-array}}\,({\it{iports\/}})\index{good-tm-iport-array}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-set-iports}}\,({\it{iports\/}}, {\it{tm\/}})\index{tm-set-iports})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-set-iports.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 ACCESS-TM-SET-IPORTS
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-SET-IPORTS IPORTS TM))
         (TM-MEMORY TM))
  (AND
   (EQUAL (TM-REGS (TM-SET-IPORTS IPORTS TM))
          (TM-REGS TM))
   (AND
    (EQUAL (TM-CC (TM-SET-IPORTS IPORTS TM))
           (TM-CC TM))
    (AND
     (EQUAL (TM-ERROR (TM-SET-IPORTS IPORTS TM))
            (TM-ERROR TM))
     (AND
      (EQUAL (TM-BASE (TM-SET-IPORTS IPORTS TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-SET-IPORTS IPORTS TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-SET-IPORTS IPORTS TM))
               (TM-SLIMIT TM))
        (AND
         (EQUAL (TM-SVMODE (TM-SET-IPORTS IPORTS TM))
                (TM-SVMODE TM))
         (AND
          (EQUAL (TM-SVCFLAG (TM-SET-IPORTS IPORTS TM))
                 (TM-SVCFLAG TM))
          (AND
              (EQUAL (TM-SVCID (TM-SET-IPORTS IPORTS TM))
                     (TM-SVCID TM))
              (AND (EQUAL (TM-RWSTATE (TM-SET-IPORTS IPORTS TM))
                          (TM-RWSTATE TM))
                   (AND (EQUAL (TM-CLOCK (TM-SET-IPORTS IPORTS TM))
                               (TM-CLOCK TM))
                        (AND (EQUAL (TM-IPORTS (TM-SET-IPORTS IPORTS TM))
                                    IPORTS)
                             (AND (EQUAL (TM-OPORTS (TM-SET-IPORTS IPORTS TM))
                                         (TM-OPORTS TM))
                                  (AND (EQUAL (TM-PC (TM-SET-IPORTS IPORTS TM))
                                              (TM-PC TM))
                                       (EQUAL (TM-SP (TM-SET-IPORTS IPORTS TM))
                                              (TM-SP TM)))))))))))))))))
 ((ENABLE TM-SET-IPORTS TM-PC TM-SP)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable access-tm-set-iports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-set-oports \\ \index{good-tm-tm-set-oports}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\it{oports\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(({\rm{length}}\,({\it{oports\/}})\index{length} $=$ {\tt{'}}{\tt{16}}) $\wedge$ {\rm{good-tm-oport-array}}\,({\it{oports\/}})\index{good-tm-oport-array}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-set-oports}}\,({\it{oports\/}}, {\it{tm\/}})\index{tm-set-oports})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-set-oports.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 ACCESS-TM-SET-OPORTS
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-SET-OPORTS OPORTS TM))
         (TM-MEMORY TM))
  (AND
   (EQUAL (TM-REGS (TM-SET-OPORTS OPORTS TM))
          (TM-REGS TM))
   (AND
    (EQUAL (TM-CC (TM-SET-OPORTS OPORTS TM))
           (TM-CC TM))
    (AND
     (EQUAL (TM-ERROR (TM-SET-OPORTS OPORTS TM))
            (TM-ERROR TM))
     (AND
      (EQUAL (TM-BASE (TM-SET-OPORTS OPORTS TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-SET-OPORTS OPORTS TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-SET-OPORTS OPORTS TM))
               (TM-SLIMIT TM))
        (AND
         (EQUAL (TM-SVMODE (TM-SET-OPORTS OPORTS TM))
                (TM-SVMODE TM))
         (AND
          (EQUAL (TM-SVCFLAG (TM-SET-OPORTS OPORTS TM))
                 (TM-SVCFLAG TM))
          (AND
              (EQUAL (TM-SVCID (TM-SET-OPORTS OPORTS TM))
                     (TM-SVCID TM))
              (AND (EQUAL (TM-RWSTATE (TM-SET-OPORTS OPORTS TM))
                          (TM-RWSTATE TM))
                   (AND (EQUAL (TM-CLOCK (TM-SET-OPORTS OPORTS TM))
                               (TM-CLOCK TM))
                        (AND (EQUAL (TM-IPORTS (TM-SET-OPORTS OPORTS TM))
                                    (TM-IPORTS TM))
                             (AND (EQUAL (TM-OPORTS (TM-SET-OPORTS OPORTS TM))
                                         OPORTS)
                                  (AND (EQUAL (TM-PC (TM-SET-OPORTS OPORTS TM))
                                              (TM-PC TM))
                                       (EQUAL (TM-SP (TM-SET-OPORTS OPORTS TM))
                                              (TM-SP TM)))))))))))))))))
 ((ENABLE TM-SET-OPORTS TM-PC TM-SP)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable access-tm-set-oports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-set-pc \\ \index{good-tm-tm-set-pc}
({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{pc\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp}) $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-set-pc}}\,({\it{pc\/}}, {\it{tm\/}})\index{tm-set-pc})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-set-pc.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 ACCESS-TM-SET-PC
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-SET-PC PC TM))
         (TM-MEMORY TM))
  (AND
   (EQUAL (TM-CC (TM-SET-PC PC TM))
          (TM-CC TM))
   (AND
    (EQUAL (TM-ERROR (TM-SET-PC PC TM))
           (TM-ERROR TM))
    (AND
     (EQUAL (TM-BASE (TM-SET-PC PC TM))
            (TM-BASE TM))
     (AND
      (EQUAL (TM-LIMIT (TM-SET-PC PC TM))
             (TM-LIMIT TM))
      (AND
        (EQUAL (TM-SLIMIT (TM-SET-PC PC TM))
               (TM-SLIMIT TM))
        (AND (EQUAL (TM-SVMODE (TM-SET-PC PC TM))
                    (TM-SVMODE TM))
             (AND (EQUAL (TM-SVCFLAG (TM-SET-PC PC TM))
                         (TM-SVCFLAG TM))
                  (AND (EQUAL (TM-SVCID (TM-SET-PC PC TM))
                              (TM-SVCID TM))
                       (AND (EQUAL (TM-RWSTATE (TM-SET-PC PC TM))
                                   (TM-RWSTATE TM))
                            (AND (EQUAL (TM-CLOCK (TM-SET-PC PC TM))
                                        (TM-CLOCK TM))
                                 (AND (EQUAL (TM-IPORTS (TM-SET-PC PC TM))
                                             (TM-IPORTS TM))
                                      (AND (EQUAL (TM-OPORTS (TM-SET-PC PC TM))
                                                  (TM-OPORTS TM))
                                           (EQUAL (TM-SP (TM-SET-PC PC TM))
                                                  (TM-SP TM)))))))))))))))
 ((ENABLE TM-SET-PC TM-PC TM-SP TM-SET-REGS
          A-FINITE-NUMBER-IS-LESSP-THAN-ITS-LUB GETNTH-PUTNTH-NON-INTERFERENCE)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable access-tm-set-pc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-set-sp \\ \index{good-tm-tm-set-sp}
({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{finite-numberp}}\,({\it{sp\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp}) $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-set-sp}}\,({\it{sp\/}}, {\it{tm\/}})\index{tm-set-sp})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-set-sp.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 ACCESS-TM-SET-SP
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-SET-SP SP TM))
         (TM-MEMORY TM))
  (AND
   (EQUAL (TM-CC (TM-SET-SP SP TM))
          (TM-CC TM))
   (AND
    (EQUAL (TM-ERROR (TM-SET-SP SP TM))
           (TM-ERROR TM))
    (AND
     (EQUAL (TM-BASE (TM-SET-SP SP TM))
            (TM-BASE TM))
     (AND
      (EQUAL (TM-LIMIT (TM-SET-SP SP TM))
             (TM-LIMIT TM))
      (AND
        (EQUAL (TM-SLIMIT (TM-SET-SP SP TM))
               (TM-SLIMIT TM))
        (AND (EQUAL (TM-SVMODE (TM-SET-SP SP TM))
                    (TM-SVMODE TM))
             (AND (EQUAL (TM-SVCFLAG (TM-SET-SP SP TM))
                         (TM-SVCFLAG TM))
                  (AND (EQUAL (TM-SVCID (TM-SET-SP SP TM))
                              (TM-SVCID TM))
                       (AND (EQUAL (TM-RWSTATE (TM-SET-SP SP TM))
                                   (TM-RWSTATE TM))
                            (AND (EQUAL (TM-CLOCK (TM-SET-SP SP TM))
                                        (TM-CLOCK TM))
                                 (AND (EQUAL (TM-IPORTS (TM-SET-SP SP TM))
                                             (TM-IPORTS TM))
                                      (AND (EQUAL (TM-OPORTS (TM-SET-SP SP TM))
                                                  (TM-OPORTS TM))
                                           (EQUAL (TM-PC (TM-SET-SP SP TM))
                                                  (TM-PC TM)))))))))))))))
 ((ENABLE TM-SET-SP TM-PC TM-SP TM-SET-REGS
          A-FINITE-NUMBER-IS-LESSP-THAN-ITS-LUB GETNTH-PUTNTH-NON-INTERFERENCE)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable access-tm-set-sp.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-add \\ \index{good-tm-tm-execute-add}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-execute-add}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-add})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-add.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-branch \\ \index{good-tm-tm-execute-branch}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-execute-branch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-branch.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-branch-on-zero \\ \index{good-tm-tm-execute-branch-on-ze!ro}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-execute-branch-on-zero}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch-on-zero})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-branch-on-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-branch-not-zero \\ \index{good-tm-tm-execute-branch-not-ze!ro}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-execute-branch-not-zero}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch-not-zero})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-branch-not-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-call \\ \index{good-tm-tm-execute-call}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-call})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-call.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-compare \\ \index{good-tm-tm-execute-compare}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-execute-compare}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-compare})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-compare.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-decr \\ \index{good-tm-tm-execute-decr}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-decr})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-decr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-decr-mod \\ \index{good-tm-tm-execute-decr-mod}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ ({\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address} $\wedge$ {\rm{tm-good-address}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-good-address})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-execute-decr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-decr-mod})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-decr-mod.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-incr \\ \index{good-tm-tm-execute-incr}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-incr})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-incr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-incr-mod \\ \index{good-tm-tm-execute-incr-mod}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ ({\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address} $\wedge$ {\rm{tm-good-address}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-good-address})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-execute-incr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-incr-mod})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-incr-mod.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-load-base \\ \index{good-tm-tm-execute-load-base}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-execute-load-base}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-base})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-load-base.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-load-limit \\ \index{good-tm-tm-execute-load-limit}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-execute-load-limit}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-limit})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-load-limit.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tm-good-supervisor-address} \\  
\=\+{\rm{tm-good-supervisor-address}}\,({\it{addr\/}})\index{tm-good-supervisor-address} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} $\simeq {\tt{0}}$ \\ 
{\bf then }{\rm{finite-numberp}}\,({\rm{real-addr-num}}\,({\it{addr\/}})\index{real-addr-num}, {\tt{'}}{\tt{65536}})\index{finite-numberp} \\ 
{\bf elseif }{\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} $=$ {\tt{'}}{\tt{1}} \\ 
{\bf then }{\rm{finite-numberp}}\,({\rm{real-addr-num}}\,({\it{addr\/}})\index{real-addr-num}, {\tt{'}}{\tt{8}})\index{finite-numberp} \\ 
{\bf else }{\rm{finite-numberp}}\,({\rm{real-addr-num}}\,({\it{addr\/}})\index{real-addr-num}, {\tt{'}}{\tt{65536}})\index{finite-numberp}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-fetch-in-supervisor-mode \\ \index{finite-numberp-tm-fetch-in-supe!rvisor-mode}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode} $\wedge$ {\rm{tm-good-supervisor-address}}\,({\it{addr\/}})\index{tm-good-supervisor-address}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-fetch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch}, {\tt{'}}{\tt{65536}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-fetch-in-supervisor-mode.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-good-supervisor-address-tm-incr-address \\ \index{tm-good-supervisor-address-tm-i!ncr-address}
{\rm{tm-good-supervisor-address}}\,({\rm{tm-incr-address}}\,({\it{addr\/}})\index{tm-incr-address})\index{tm-good-supervisor-address}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-good-supervisor-address-tm-incr-address.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-good-supervisor-address-tm-incrn-address \\ \index{tm-good-supervisor-address-tm-i!ncrn-address}
\=\+{\rm{tm-good-supervisor-address}}\,({\it{addr\/}})\index{tm-good-supervisor-address} \\ 
$\rightarrow$$\;\;\;\;${\rm{tm-good-supervisor-address}}\,({\rm{tm-incrn-address}}\,({\it{n\/}}, {\it{addr\/}})\index{tm-incrn-address})\index{tm-good-supervisor-address}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-good-supervisor-address-tm-incrn-address.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-good-supervisor-address-tm-good-address \\ \index{tm-good-supervisor-address-tm-g!ood-address}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}) \\ 
$\rightarrow$$\;\;\;\;${\rm{tm-good-supervisor-address}}\,({\it{addr\/}})\index{tm-good-supervisor-address}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-good-supervisor-address-tm-good-address.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-load-psw \\ \index{good-tm-tm-execute-load-psw}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-execute-load-psw}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-psw})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-load-psw.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-mod \\ \index{good-tm-tm-execute-mod}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-execute-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-mod})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-mod.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-move \\ \index{good-tm-tm-execute-move}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{tm-good-address}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-good-address}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-execute-move}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-move})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-move.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-multiply \\ \index{good-tm-tm-execute-multiply}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-execute-multiply}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-multiply})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-multiply.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-add1-tm-sp \\ \index{finite-numberp-add1-tm-sp}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-stack-underflowp}}\,({\it{tm\/}})\index{tm-stack-underflowp})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,($1\;+$ {\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp}, {\tt{'}}{\tt{65536}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-add1-tm-sp.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-incr-sp-is-add1-sp \\ \index{tm-incr-sp-is-add1-sp}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-stack-underflowp}}\,({\it{tm\/}})\index{tm-stack-underflowp})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-incr}}\,({\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp})\index{tm-incr} $=$ ($1\;+$ {\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-incr-sp-is-add1-sp.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-return \\ \index{good-tm-tm-execute-return}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-return.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-test-iport \\ \index{good-tm-tm-execute-test-iport}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-execute-test-iport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-iport})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-test-iport.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-test-oport \\ \index{good-tm-tm-execute-test-oport}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-execute-test-oport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-oport})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-test-oport.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-set-clock \\ \index{good-tm-tm-execute-set-clock}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-execute-set-clock}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-set-clock})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-set-clock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-run \\ \index{good-tm-tm-execute-run}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-execute-run}}\,({\it{tm\/}})\index{tm-execute-run})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-run.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-wait \\ \index{good-tm-tm-execute-wait}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-execute-wait}}\,({\it{tm\/}})\index{tm-execute-wait})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-wait.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-oports-tm-post-output-interrupt \\ \index{good-tm-oports-tm-post-output-i!nterrupt}
\=\+({\rm{plistp}}\,({\it{l\/}})\index{plistp} $\wedge$ {\rm{good-tm-oport-array}}\,({\it{l\/}})\index{good-tm-oport-array}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\rm{tm-post-output-interrupt}}\,({\it{id\/}}, {\it{l\/}})\index{tm-post-output-interrupt})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\rm{tm-post-output-interrupt}}\,({\it{id\/}}, {\it{l\/}})\index{tm-post-output-interrupt})\index{length} $=$ {\rm{length}}\,({\it{l\/}})\index{length}) \\ 
$\wedge$$\;\;\;\;${\rm{good-tm-oport-array}}\,({\rm{tm-post-output-interrupt}}\,({\it{id\/}}, {\it{l\/}})\index{tm-post-output-interrupt})\index{good-tm-oport-array})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-oports-tm-post-output-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-post-output-interrupt \\ \index{good-tm-tm-execute-post-output-i!nterrupt}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-execute-post-output-interrupt}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-post-output-interrupt})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-post-output-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-oports-tm-start-output \\ \index{good-tm-oports-tm-start-output}
\=\+({\rm{plistp}}\,({\it{l\/}})\index{plistp} $\wedge$ {\rm{good-tm-oport-array}}\,({\it{l\/}})\index{good-tm-oport-array}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\rm{tm-start-output}}\,({\it{char\/}}, {\it{id\/}}, {\it{l\/}})\index{tm-start-output})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\rm{tm-start-output}}\,({\it{char\/}}, {\it{id\/}}, {\it{l\/}})\index{tm-start-output})\index{length} $=$ {\rm{length}}\,({\it{l\/}})\index{length}) \\ 
$\wedge$$\;\;\;\;${\rm{good-tm-oport-array}}\,({\rm{tm-start-output}}\,({\it{char\/}}, {\it{id\/}}, {\it{l\/}})\index{tm-start-output})\index{good-tm-oport-array})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-oports-tm-start-output.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-start-output \\ \index{good-tm-tm-execute-start-output}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-execute-start-output}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-start-output})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-start-output.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-svc \\ \index{good-tm-tm-execute-svc}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-execute-svc}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-svc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-svc-return \\ \index{good-tm-tm-execute-svc-return}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-execute-svc-return}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc-return})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-svc-return.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-nullary \\ \index{good-tm-tm-execute-nullary}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-execute-nullary}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-nullary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-unary \\ \index{good-tm-tm-execute-unary}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-execute-unary}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-unary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-binary \\ \index{good-tm-tm-execute-binary}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-execute-binary}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-binary})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-binary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-instruction \\ \index{good-tm-tm-execute-instruction}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-execute-instruction}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute-instruction})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-instruction.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plus-tm-base-tm-limit-tm-set-pc \\ \index{plus-tm-base-tm-limit-tm-set-pc}
\=\+({\rm{tm-base}}\,({\rm{tm-set-pc}}\,({\it{pc\/}}, {\it{tm\/}})\index{tm-set-pc})\index{tm-base} $+$ {\rm{tm-limit}}\,({\rm{tm-set-pc}}\,({\it{pc\/}}, {\it{tm\/}})\index{tm-set-pc})\index{tm-limit}) \\ 
$=$$\;\;\;\;$({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-
\end{tabbing}


\noindent{\sc Event}:   Disable plus-tm-base-tm-limit-tm-set-pc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-good-address \\ \index{finite-numberp-tm-good-address}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{tm-good-address}}\,({\rm{real-addr}}\,({\tt{'}}{\tt{2}}, {\it{n\/}})\index{real-addr}, {\it{tm\/}})\index{tm-good-address}) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\it{n\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-good-address.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute \\ \index{good-tm-tm-execute}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-execute}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-decrement-clock \\ \index{good-tm-tm-decrement-clock}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-decrement-clock}}\,({\it{tm\/}})\index{tm-decrement-clock})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-decrement-clock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plus-tm-base-tm-limit-tm-decrement-clock \\ \index{plus-tm-base-tm-limit-tm-decreme!nt-clock}
\=\+({\rm{tm-base}}\,({\rm{tm-decrement-clock}}\,({\it{tm\/}})\index{tm-decrement-clock})\index{tm-base} $+$ {\rm{tm-limit}}\,({\rm{tm-decrement-clock}}\,({\it{tm\/}})\index{tm-decrement-clock})\index{tm-limit}) \\ 
$=$$\;\;\;\;$({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-
\end{tabbing}


\noindent{\sc Event}:   Disable plus-tm-base-tm-limit-tm-decrement-clock.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 TM-DECREMENT-CLOCK-PRESERVES-ALL-BUT-CLOCK
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-DECREMENT-CLOCK TM))
         (TM-MEMORY TM))
  (AND
   (EQUAL (TM-REGS (TM-DECREMENT-CLOCK TM))
          (TM-REGS TM))
   (AND
    (EQUAL (TM-CC (TM-DECREMENT-CLOCK TM))
           (TM-CC TM))
    (AND
     (EQUAL (TM-ERROR (TM-DECREMENT-CLOCK TM))
            (TM-ERROR TM))
     (AND
      (EQUAL (TM-BASE (TM-DECREMENT-CLOCK TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-DECREMENT-CLOCK TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-DECREMENT-CLOCK TM))
               (TM-SLIMIT TM))
        (AND
           (EQUAL (TM-SVMODE (TM-DECREMENT-CLOCK TM))
                  (TM-SVMODE TM))
           (AND (EQUAL (TM-SVCFLAG (TM-DECREMENT-CLOCK TM))
                       (TM-SVCFLAG TM))
                (AND (EQUAL (TM-SVCID (TM-DECREMENT-CLOCK TM))
                            (TM-SVCID TM))
                     (AND (EQUAL (TM-RWSTATE (TM-DECREMENT-CLOCK TM))
                                 (TM-RWSTATE TM))
                          (AND (EQUAL (TM-IPORTS (TM-DECREMENT-CLOCK TM))
                                      (TM-IPORTS TM))
                               (AND (EQUAL (TM-OPORTS (TM-DECREMENT-CLOCK TM))
                                           (TM-OPORTS TM))
                                    (AND (EQUAL (TM-PC (TM-DECREMENT-CLOCK TM))
                                                (TM-PC TM))
                                         (EQUAL (TM-SP (TM-DECREMENT-CLOCK TM))
                                                (TM-SP TM))))))))))))))))
 ((ENABLE TM-DECREMENT-CLOCK ACCESS-TM-SET-CLOCK)
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable tm-decrement-clock-preserves-all-but-clock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-good-address-tm-decrement-clock \\ \index{tm-good-address-tm-decrement-cl!ock}
{\rm{tm-good-address}}\,({\it{addr\/}}, {\rm{tm-decrement-clock}}\,({\it{tm\/}})\index{tm-decrement-clock})\index{tm-good-address} $=$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-good-address-tm-decrement-clock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-fetch-execute \\ \index{good-tm-tm-fetch-execute}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-fetch-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-good-address-tm-store \\ \index{tm-good-address-tm-store}
{\rm{tm-good-address}}\,({\it{addr\/}}, {\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store})\index{tm-good-address} $=$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-good-address-tm-store.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-clock-interrupt \\ \index{good-tm-tm-execute-clock-interr!upt}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-execute-clock-interrupt}}\,({\it{tm\/}})\index{tm-execute-clock-interrupt})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-clock-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-error-interrupt \\ \index{good-tm-tm-execute-error-interr!upt}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-execute-error-interrupt}}\,({\it{tm\/}})\index{tm-execute-error-interrupt})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-error-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-svc-interrupt \\ \index{good-tm-tm-execute-svc-interrupt}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-execute-svc-interrupt}}\,({\it{tm\/}})\index{tm-execute-svc-interrupt})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-svc-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-input-interrupt \\ \index{good-tm-tm-execute-input-interr!upt}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-execute-input-interrupt}}\,({\it{tm\/}})\index{tm-execute-input-interrupt})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-input-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-execute-output-interrupt \\ \index{good-tm-tm-execute-output-inter!rupt}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{tm-execute-output-interrupt}}\,({\it{tm\/}})\index{tm-execute-output-interrupt})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-execute-output-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-step \\ \index{good-tm-tm-step}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-step}}\,({\it{tm\/}})\index{tm-step})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-step.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-iports-tm-post-input-interrupt \\ \index{good-tm-iports-tm-post-input-inte!rrupt}
\=\+(\=\+{\rm{plistp}}\,({\it{l\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{id\/}}, {\rm{length}}\,({\it{l\/}})\index{length})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$({\rm{finite-numberp}}\,({\it{char\/}}, {\tt{'}}{\tt{256}})\index{finite-numberp} $\wedge$ {\rm{good-tm-iport-array}}\,({\it{l\/}})\index{good-tm-iport-array}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\rm{tm-post-input-interrupt}}\,({\it{char\/}}, {\it{id\/}}, {\it{l\/}})\index{tm-post-input-interrupt})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\rm{tm-post-input-interrupt}}\,({\it{char\/}}, {\it{id\/}}, {\it{l\/}})\index{tm-post-input-interrupt})\index{length} $=$ {\rm{length}}\,({\it{l\/}})\index{length}) \\ 
$\wedge$$\;\;\;\;${\rm{good-tm-iport-array}}\,({\rm{tm-post-input-interrupt}}\,({\it{char\/}}, {\it{id\/}}, {\it{l\/}})\index{tm-post-input-interrupt})\index{good-tm-iport-array})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-iports-tm-post-input-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-post-interrupt \\ \index{good-tm-tm-post-interrupt}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-post-interrupt}}\,({\it{event\/}}, {\it{tm\/}})\index{tm-post-interrupt})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-post-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-tm-processor \\ \index{good-tm-tm-processor}
{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\rightarrow$ {\rm{good-tm}}\,({\rm{tm-processor}}\,({\it{tm\/}}, {\it{n\/}})\index{tm-processor})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-tm-processor.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  registers-untouched-by-tm-execute-add \\ \index{registers-untouched-by-tm-execute!-add}
\=\+({\rm{tm-error}}\,({\rm{tm-execute-add}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-add})\index{tm-error} $=$ {\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-base}}\,({\rm{tm-execute-add}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-add})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-limit}}\,({\rm{tm-execute-add}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-add})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-slimit}}\,({\rm{tm-execute-add}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-add})\index{tm-slimit} \\ 
$=$$\;\;\;\;${\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svmode}}\,({\rm{tm-execute-add}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-add})\index{tm-svmode} \\ 
$=$$\;\;\;\;${\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcflag}}\,({\rm{tm-execute-add}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-add})\index{tm-svcflag} \\ 
$=$$\;\;\;\;${\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcid}}\,({\rm{tm-execute-add}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-add})\index{tm-svcid} \\ 
$=$$\;\;\;\;${\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-rwstate}}\,({\rm{tm-execute-add}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-add})\index{tm-rwstate} \\ 
$=$$\;\;\;\;${\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-clock}}\,({\rm{tm-execute-add}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-add})\index{tm-clock} \\ 
$=$$\;\;\;\;${\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-iports}}\,({\rm{tm-execute-add}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-add})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-oports}}\,({\rm{tm-execute-add}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-add})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-)\-)\-)\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-add.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 REGISTERS-UNTOUCHED-BY-TM-EXECUTE-BRANCH
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-EXECUTE-BRANCH ADDR TM))
         (TM-MEMORY TM))
  (AND
   (EQUAL (TM-CC (TM-EXECUTE-BRANCH ADDR TM))
          (TM-CC TM))
   (AND
    (EQUAL (TM-ERROR (TM-EXECUTE-BRANCH ADDR TM))
           (TM-ERROR TM))
    (AND
     (EQUAL (TM-BASE (TM-EXECUTE-BRANCH ADDR TM))
            (TM-BASE TM))
     (AND
      (EQUAL (TM-LIMIT (TM-EXECUTE-BRANCH ADDR TM))
             (TM-LIMIT TM))
      (AND
       (EQUAL (TM-SLIMIT (TM-EXECUTE-BRANCH ADDR TM))
              (TM-SLIMIT TM))
       (AND
        (EQUAL (TM-SVMODE (TM-EXECUTE-BRANCH ADDR TM))
               (TM-SVMODE TM))
        (AND
         (EQUAL (TM-SVCFLAG (TM-EXECUTE-BRANCH ADDR TM))
                (TM-SVCFLAG TM))
         (AND
             (EQUAL (TM-SVCID (TM-EXECUTE-BRANCH ADDR TM))
                    (TM-SVCID TM))
             (AND (EQUAL (TM-RWSTATE (TM-EXECUTE-BRANCH ADDR TM))
                         (TM-RWSTATE TM))
                  (AND (EQUAL (TM-CLOCK (TM-EXECUTE-BRANCH ADDR TM))
                              (TM-CLOCK TM))
                       (AND (EQUAL (TM-IPORTS (TM-EXECUTE-BRANCH ADDR TM))
                                   (TM-IPORTS TM))
                            (AND (EQUAL (TM-OPORTS (TM-EXECUTE-BRANCH ADDR TM))
                                        (TM-OPORTS TM))
                                 (EQUAL (TM-SP (TM-EXECUTE-BRANCH ADDR TM))
                                        (TM-SP TM)))))))))))))))
 ((ENABLE TM-EXECUTE-BRANCH ACCESS-TM-SET-PC)
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-branch.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 REGISTERS-UNTOUCHED-BY-TM-EXECUTE-BRANCH-ON-ZERO
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-EXECUTE-BRANCH-ON-ZERO ADDR TM))
         (TM-MEMORY TM))
  (AND
   (EQUAL (TM-CC (TM-EXECUTE-BRANCH-ON-ZERO ADDR TM))
          (TM-CC TM))
   (AND
    (EQUAL (TM-ERROR (TM-EXECUTE-BRANCH-ON-ZERO ADDR TM))
           (TM-ERROR TM))
    (AND
     (EQUAL (TM-BASE (TM-EXECUTE-BRANCH-ON-ZERO ADDR TM))
            (TM-BASE TM))
     (AND
      (EQUAL (TM-LIMIT (TM-EXECUTE-BRANCH-ON-ZERO ADDR TM))
             (TM-LIMIT TM))
      (AND
       (EQUAL (TM-SLIMIT (TM-EXECUTE-BRANCH-ON-ZERO ADDR TM))
              (TM-SLIMIT TM))
       (AND
        (EQUAL (TM-SVMODE (TM-EXECUTE-BRANCH-ON-ZERO ADDR TM))
               (TM-SVMODE TM))
        (AND
         (EQUAL (TM-SVCFLAG (TM-EXECUTE-BRANCH-ON-ZERO ADDR TM))
                (TM-SVCFLAG TM))
         (AND
          (EQUAL (TM-SVCID (TM-EXECUTE-BRANCH-ON-ZERO ADDR TM))
                 (TM-SVCID TM))
          (AND
           (EQUAL (TM-RWSTATE (TM-EXECUTE-BRANCH-ON-ZERO ADDR TM))
                  (TM-RWSTATE TM))
           (AND
               (EQUAL (TM-CLOCK (TM-EXECUTE-BRANCH-ON-ZERO ADDR TM))
                      (TM-CLOCK TM))
               (AND (EQUAL (TM-IPORTS (TM-EXECUTE-BRANCH-ON-ZERO ADDR TM))
                           (TM-IPORTS TM))
                    (AND (EQUAL (TM-OPORTS (TM-EXECUTE-BRANCH-ON-ZERO ADDR TM))
                                (TM-OPORTS TM))
                         (EQUAL (TM-SP (TM-EXECUTE-BRANCH-ON-ZERO ADDR TM))
                                (TM-SP TM)))))))))))))))
 ((ENABLE TM-EXECUTE-BRANCH-ON-ZERO ACCESS-TM-SET-PC)
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-branch-on-zero.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 REGISTERS-UNTOUCHED-BY-TM-EXECUTE-BRANCH-NOT-ZERO
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-EXECUTE-BRANCH-NOT-ZERO ADDR TM))
         (TM-MEMORY TM))
  (AND
   (EQUAL (TM-CC (TM-EXECUTE-BRANCH-NOT-ZERO ADDR TM))
          (TM-CC TM))
   (AND
    (EQUAL (TM-ERROR (TM-EXECUTE-BRANCH-NOT-ZERO ADDR TM))
           (TM-ERROR TM))
    (AND
     (EQUAL (TM-BASE (TM-EXECUTE-BRANCH-NOT-ZERO ADDR TM))
            (TM-BASE TM))
     (AND
      (EQUAL (TM-LIMIT (TM-EXECUTE-BRANCH-NOT-ZERO ADDR TM))
             (TM-LIMIT TM))
      (AND
       (EQUAL (TM-SLIMIT (TM-EXECUTE-BRANCH-NOT-ZERO ADDR TM))
              (TM-SLIMIT TM))
       (AND
        (EQUAL (TM-SVMODE (TM-EXECUTE-BRANCH-NOT-ZERO ADDR TM))
               (TM-SVMODE TM))
        (AND
         (EQUAL (TM-SVCFLAG (TM-EXECUTE-BRANCH-NOT-ZERO ADDR TM))
                (TM-SVCFLAG TM))
         (AND
          (EQUAL (TM-SVCID (TM-EXECUTE-BRANCH-NOT-ZERO ADDR TM))
                 (TM-SVCID TM))
          (AND
           (EQUAL (TM-RWSTATE (TM-EXECUTE-BRANCH-NOT-ZERO ADDR TM))
                  (TM-RWSTATE TM))
           (AND
              (EQUAL (TM-CLOCK (TM-EXECUTE-BRANCH-NOT-ZERO ADDR TM))
                     (TM-CLOCK TM))
              (AND (EQUAL (TM-IPORTS (TM-EXECUTE-BRANCH-NOT-ZERO ADDR TM))
                          (TM-IPORTS TM))
                   (AND (EQUAL (TM-OPORTS (TM-EXECUTE-BRANCH-NOT-ZERO ADDR TM))
                               (TM-OPORTS TM))
                        (EQUAL (TM-SP (TM-EXECUTE-BRANCH-NOT-ZERO ADDR TM))
                               (TM-SP TM)))))))))))))))
 ((ENABLE TM-EXECUTE-BRANCH-NOT-ZERO ACCESS-TM-SET-PC)
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-branch-not-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  registers-untouched-by-tm-execute-call \\ \index{registers-untouched-by-tm-execute!-call}
\=\+({\rm{tm-cc}}\,({\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-call})\index{tm-cc} $=$ {\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-base}}\,({\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-call})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-limit}}\,({\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-call})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-slimit}}\,({\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-call})\index{tm-slimit} \\ 
$=$$\;\;\;\;${\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svmode}}\,({\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-call})\index{tm-svmode} \\ 
$=$$\;\;\;\;${\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcflag}}\,({\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-call})\index{tm-svcflag} \\ 
$=$$\;\;\;\;${\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcid}}\,({\rm{tm-execute-call}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-call})\index{tm-svcid} \\ 
$=$$\;\;\;\;${\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-rwstate}}\,({\rm{tm-execute-call}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-call})\index{tm-rwstate} \\ 
$=$$\;\;\;\;${\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-clock}}\,({\rm{tm-execute-call}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-call})\index{tm-clock} \\ 
$=$$\;\;\;\;${\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-iports}}\,({\rm{tm-execute-call}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-call})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-oports}}\,({\rm{tm-execute-call}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-call})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-)\-)\-)\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-call.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 REGISTERS-UNTOUCHED-BY-TM-EXECUTE-COMPARE
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-EXECUTE-COMPARE ADDR1 ADDR2 TM))
         (TM-MEMORY TM))
  (AND
   (EQUAL (TM-REGS (TM-EXECUTE-COMPARE ADDR1 ADDR2 TM))
          (TM-REGS TM))
   (AND
    (EQUAL (TM-ERROR (TM-EXECUTE-COMPARE ADDR1 ADDR2 TM))
           (TM-ERROR TM))
    (AND
     (EQUAL (TM-BASE (TM-EXECUTE-COMPARE ADDR1 ADDR2 TM))
            (TM-BASE TM))
     (AND
      (EQUAL (TM-LIMIT (TM-EXECUTE-COMPARE ADDR1 ADDR2 TM))
             (TM-LIMIT TM))
      (AND
       (EQUAL (TM-SLIMIT (TM-EXECUTE-COMPARE ADDR1 ADDR2 TM))
              (TM-SLIMIT TM))
       (AND
        (EQUAL (TM-SVMODE (TM-EXECUTE-COMPARE ADDR1 ADDR2 TM))
               (TM-SVMODE TM))
        (AND
         (EQUAL (TM-SVCFLAG (TM-EXECUTE-COMPARE ADDR1 ADDR2 TM))
                (TM-SVCFLAG TM))
         (AND
          (EQUAL (TM-SVCID (TM-EXECUTE-COMPARE ADDR1 ADDR2 TM))
                 (TM-SVCID TM))
          (AND
           (EQUAL (TM-RWSTATE (TM-EXECUTE-COMPARE ADDR1 ADDR2 TM))
                  (TM-RWSTATE TM))
           (AND
              (EQUAL (TM-CLOCK (TM-EXECUTE-COMPARE ADDR1 ADDR2 TM))
                     (TM-CLOCK TM))
              (AND (EQUAL (TM-IPORTS (TM-EXECUTE-COMPARE ADDR1 ADDR2 TM))
                          (TM-IPORTS TM))
                   (AND (EQUAL (TM-OPORTS (TM-EXECUTE-COMPARE ADDR1 ADDR2 TM))
                               (TM-OPORTS TM))
                        (AND (EQUAL (TM-PC (TM-EXECUTE-COMPARE ADDR1 ADDR2 TM))
                                    (TM-PC TM))
                             (EQUAL (TM-SP (TM-EXECUTE-COMPARE ADDR1 ADDR2 TM))
                                    (TM-SP TM))))))))))))))))
 ((ENABLE TM-EXECUTE-COMPARE ACCESS-TM-SET-CC)
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-compare.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  registers-untouched-by-tm-execute-decr \\ \index{registers-untouched-by-tm-execute!-decr}
\=\+({\rm{tm-error}}\,({\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-decr})\index{tm-error} $=$ {\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-base}}\,({\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-decr})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-limit}}\,({\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-decr})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-slimit}}\,({\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-decr})\index{tm-slimit} \\ 
$=$$\;\;\;\;${\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svmode}}\,({\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-decr})\index{tm-svmode} \\ 
$=$$\;\;\;\;${\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcflag}}\,({\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-decr})\index{tm-svcflag} \\ 
$=$$\;\;\;\;${\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcid}}\,({\rm{tm-execute-decr}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-decr})\index{tm-svcid} \\ 
$=$$\;\;\;\;${\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-rwstate}}\,({\rm{tm-execute-decr}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-decr})\index{tm-rwstate} \\ 
$=$$\;\;\;\;${\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-clock}}\,({\rm{tm-execute-decr}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-decr})\index{tm-clock} \\ 
$=$$\;\;\;\;${\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-iports}}\,({\rm{tm-execute-decr}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-decr})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-oports}}\,({\rm{tm-execute-decr}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-decr})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-)\-)\-)\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-decr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  registers-untouched-by-tm-execute-decr-mod \\ \index{registers-untouched-by-tm-execute!-decr-mod}
\=\+({\rm{tm-error}}\,({\rm{tm-execute-decr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-decr-mod})\index{tm-error} $=$ {\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-base}}\,({\rm{tm-execute-decr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-decr-mod})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-limit}}\,({\rm{tm-execute-decr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-decr-mod})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-slimit}}\,({\rm{tm-execute-decr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-decr-mod})\index{tm-slimit} \\ 
$=$$\;\;\;\;${\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svmode}}\,({\rm{tm-execute-decr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-decr-mod})\index{tm-svmode} \\ 
$=$$\;\;\;\;${\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcflag}}\,({\rm{tm-execute-decr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-decr-mod})\index{tm-svcflag} \\ 
$=$$\;\;\;\;${\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcid}}\,({\rm{tm-execute-decr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-decr-mod})\index{tm-svcid} \\ 
$=$$\;\;\;\;${\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-rwstate}}\,({\rm{tm-execute-decr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-decr-mod})\index{tm-rwstate} \\ 
$=$$\;\;\;\;${\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-clock}}\,({\rm{tm-execute-decr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-decr-mod})\index{tm-clock} \\ 
$=$$\;\;\;\;${\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-iports}}\,({\rm{tm-execute-decr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-decr-mod})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-oports}}\,({\rm{tm-execute-decr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-decr-mod})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-)\-)\-)\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-decr-mod.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  registers-untouched-by-tm-execute-incr \\ \index{registers-untouched-by-tm-execute!-incr}
\=\+({\rm{tm-error}}\,({\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-incr})\index{tm-error} $=$ {\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-base}}\,({\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-incr})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-limit}}\,({\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-incr})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-slimit}}\,({\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-incr})\index{tm-slimit} \\ 
$=$$\;\;\;\;${\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svmode}}\,({\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-incr})\index{tm-svmode} \\ 
$=$$\;\;\;\;${\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcflag}}\,({\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-incr})\index{tm-svcflag} \\ 
$=$$\;\;\;\;${\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcid}}\,({\rm{tm-execute-incr}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-incr})\index{tm-svcid} \\ 
$=$$\;\;\;\;${\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-rwstate}}\,({\rm{tm-execute-incr}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-incr})\index{tm-rwstate} \\ 
$=$$\;\;\;\;${\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-clock}}\,({\rm{tm-execute-incr}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-incr})\index{tm-clock} \\ 
$=$$\;\;\;\;${\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-iports}}\,({\rm{tm-execute-incr}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-incr})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-oports}}\,({\rm{tm-execute-incr}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-incr})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-)\-)\-)\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-incr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  registers-untouched-by-tm-execute-incr-mod \\ \index{registers-untouched-by-tm-execute!-incr-mod}
\=\+({\rm{tm-error}}\,({\rm{tm-execute-incr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-incr-mod})\index{tm-error} $=$ {\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-base}}\,({\rm{tm-execute-incr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-incr-mod})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-limit}}\,({\rm{tm-execute-incr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-incr-mod})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-slimit}}\,({\rm{tm-execute-incr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-incr-mod})\index{tm-slimit} \\ 
$=$$\;\;\;\;${\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svmode}}\,({\rm{tm-execute-incr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-incr-mod})\index{tm-svmode} \\ 
$=$$\;\;\;\;${\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcflag}}\,({\rm{tm-execute-incr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-incr-mod})\index{tm-svcflag} \\ 
$=$$\;\;\;\;${\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcid}}\,({\rm{tm-execute-incr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-incr-mod})\index{tm-svcid} \\ 
$=$$\;\;\;\;${\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-rwstate}}\,({\rm{tm-execute-incr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-incr-mod})\index{tm-rwstate} \\ 
$=$$\;\;\;\;${\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-clock}}\,({\rm{tm-execute-incr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-incr-mod})\index{tm-clock} \\ 
$=$$\;\;\;\;${\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-iports}}\,({\rm{tm-execute-incr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-incr-mod})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-oports}}\,({\rm{tm-execute-incr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-incr-mod})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-)\-)\-)\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-incr-mod.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 REGISTERS-UNTOUCHED-BY-TM-EXECUTE-LOAD-BASE
 (REWRITE)
 (IMPLIES
  (NOT (TM-IN-SUPERVISOR-MODE TM))
  (AND
   (EQUAL (TM-MEMORY (TM-EXECUTE-LOAD-BASE ADDR TM))
          (TM-MEMORY TM))
   (AND
    (EQUAL (TM-REGS (TM-EXECUTE-LOAD-BASE ADDR TM))
           (TM-REGS TM))
    (AND
     (EQUAL (TM-CC (TM-EXECUTE-LOAD-BASE ADDR TM))
            (TM-CC TM))
     (AND
      (EQUAL (TM-BASE (TM-EXECUTE-LOAD-BASE ADDR TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-EXECUTE-LOAD-BASE ADDR TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-EXECUTE-LOAD-BASE ADDR TM))
               (TM-SLIMIT TM))
        (AND
         (EQUAL (TM-SVMODE (TM-EXECUTE-LOAD-BASE ADDR TM))
                (TM-SVMODE TM))
         (AND
          (EQUAL (TM-SVCFLAG (TM-EXECUTE-LOAD-BASE ADDR TM))
                 (TM-SVCFLAG TM))
          (AND
           (EQUAL (TM-SVCID (TM-EXECUTE-LOAD-BASE ADDR TM))
                  (TM-SVCID TM))
           (AND
              (EQUAL (TM-RWSTATE (TM-EXECUTE-LOAD-BASE ADDR TM))
                     (TM-RWSTATE TM))
              (AND (EQUAL (TM-CLOCK (TM-EXECUTE-LOAD-BASE ADDR TM))
                          (TM-CLOCK TM))
                   (AND (EQUAL (TM-IPORTS (TM-EXECUTE-LOAD-BASE ADDR TM))
                               (TM-IPORTS TM))
                        (AND (EQUAL (TM-OPORTS (TM-EXECUTE-LOAD-BASE ADDR TM))
                                    (TM-OPORTS TM))
                             (AND (EQUAL (TM-PC (TM-EXECUTE-LOAD-BASE ADDR TM))
                                         (TM-PC TM))
                                  (EQUAL (TM-SP (TM-EXECUTE-LOAD-BASE ADDR TM))
                                         (TM-SP TM)))))))))))))))))
 ((ENABLE TM-EXECUTE-LOAD-BASE ACCESS-TM-SET-ERROR)
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-load-base.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 REGISTERS-UNTOUCHED-BY-TM-EXECUTE-LOAD-LIMIT
 (REWRITE)
 (IMPLIES
  (NOT (TM-IN-SUPERVISOR-MODE TM))
  (AND
   (EQUAL (TM-MEMORY (TM-EXECUTE-LOAD-LIMIT ADDR TM))
          (TM-MEMORY TM))
   (AND
    (EQUAL (TM-REGS (TM-EXECUTE-LOAD-LIMIT ADDR TM))
           (TM-REGS TM))
    (AND
     (EQUAL (TM-CC (TM-EXECUTE-LOAD-LIMIT ADDR TM))
            (TM-CC TM))
     (AND
      (EQUAL (TM-BASE (TM-EXECUTE-LOAD-LIMIT ADDR TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-EXECUTE-LOAD-LIMIT ADDR TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-EXECUTE-LOAD-LIMIT ADDR TM))
               (TM-SLIMIT TM))
        (AND
         (EQUAL (TM-SVMODE (TM-EXECUTE-LOAD-LIMIT ADDR TM))
                (TM-SVMODE TM))
         (AND
          (EQUAL (TM-SVCFLAG (TM-EXECUTE-LOAD-LIMIT ADDR TM))
                 (TM-SVCFLAG TM))
          (AND
           (EQUAL (TM-SVCID (TM-EXECUTE-LOAD-LIMIT ADDR TM))
                  (TM-SVCID TM))
           (AND
             (EQUAL (TM-RWSTATE (TM-EXECUTE-LOAD-LIMIT ADDR TM))
                    (TM-RWSTATE TM))
             (AND (EQUAL (TM-CLOCK (TM-EXECUTE-LOAD-LIMIT ADDR TM))
                         (TM-CLOCK TM))
                  (AND (EQUAL (TM-IPORTS (TM-EXECUTE-LOAD-LIMIT ADDR TM))
                              (TM-IPORTS TM))
                       (AND (EQUAL (TM-OPORTS (TM-EXECUTE-LOAD-LIMIT ADDR TM))
                                   (TM-OPORTS TM))
                            (AND (EQUAL (TM-PC (TM-EXECUTE-LOAD-LIMIT ADDR TM))
                                        (TM-PC TM))
                                 (EQUAL (TM-SP (TM-EXECUTE-LOAD-LIMIT ADDR TM))
                                        (TM-SP TM)))))))))))))))))
 ((ENABLE TM-EXECUTE-LOAD-LIMIT ACCESS-TM-SET-ERROR)
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-load-limit.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 REGISTERS-UNTOUCHED-BY-TM-EXECUTE-LOAD-PSW
 (REWRITE)
 (IMPLIES
  (NOT (TM-IN-SUPERVISOR-MODE TM))
  (AND
   (EQUAL (TM-MEMORY (TM-EXECUTE-LOAD-PSW ADDR TM))
          (TM-MEMORY TM))
   (AND
    (EQUAL (TM-REGS (TM-EXECUTE-LOAD-PSW ADDR TM))
           (TM-REGS TM))
    (AND
     (EQUAL (TM-CC (TM-EXECUTE-LOAD-PSW ADDR TM))
            (TM-CC TM))
     (AND
      (EQUAL (TM-BASE (TM-EXECUTE-LOAD-PSW ADDR TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-EXECUTE-LOAD-PSW ADDR TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-EXECUTE-LOAD-PSW ADDR TM))
               (TM-SLIMIT TM))
        (AND
         (EQUAL (TM-SVMODE (TM-EXECUTE-LOAD-PSW ADDR TM))
                (TM-SVMODE TM))
         (AND
          (EQUAL (TM-SVCFLAG (TM-EXECUTE-LOAD-PSW ADDR TM))
                 (TM-SVCFLAG TM))
          (AND
           (EQUAL (TM-SVCID (TM-EXECUTE-LOAD-PSW ADDR TM))
                  (TM-SVCID TM))
           (AND
               (EQUAL (TM-RWSTATE (TM-EXECUTE-LOAD-PSW ADDR TM))
                      (TM-RWSTATE TM))
               (AND (EQUAL (TM-CLOCK (TM-EXECUTE-LOAD-PSW ADDR TM))
                           (TM-CLOCK TM))
                    (AND (EQUAL (TM-IPORTS (TM-EXECUTE-LOAD-PSW ADDR TM))
                                (TM-IPORTS TM))
                         (AND (EQUAL (TM-OPORTS (TM-EXECUTE-LOAD-PSW ADDR TM))
                                     (TM-OPORTS TM))
                              (AND (EQUAL (TM-PC (TM-EXECUTE-LOAD-PSW ADDR TM))
                                          (TM-PC TM))
                                   (EQUAL (TM-SP (TM-EXECUTE-LOAD-PSW ADDR TM))
                                          (TM-SP TM)))))))))))))))))
 ((ENABLE TM-EXECUTE-LOAD-PSW ACCESS-TM-SET-ERROR)
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-load-psw.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  registers-untouched-by-tm-execute-mod \\ \index{registers-untouched-by-tm-execute!-mod}
\=\+({\rm{tm-error}}\,({\rm{tm-execute-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-mod})\index{tm-error} $=$ {\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-base}}\,({\rm{tm-execute-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-mod})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-limit}}\,({\rm{tm-execute-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-mod})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-slimit}}\,({\rm{tm-execute-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-mod})\index{tm-slimit} \\ 
$=$$\;\;\;\;${\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svmode}}\,({\rm{tm-execute-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-mod})\index{tm-svmode} \\ 
$=$$\;\;\;\;${\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcflag}}\,({\rm{tm-execute-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-mod})\index{tm-svcflag} \\ 
$=$$\;\;\;\;${\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcid}}\,({\rm{tm-execute-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-mod})\index{tm-svcid} \\ 
$=$$\;\;\;\;${\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-rwstate}}\,({\rm{tm-execute-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-mod})\index{tm-rwstate} \\ 
$=$$\;\;\;\;${\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-clock}}\,({\rm{tm-execute-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-mod})\index{tm-clock} \\ 
$=$$\;\;\;\;${\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-iports}}\,({\rm{tm-execute-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-mod})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-oports}}\,({\rm{tm-execute-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-mod})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-)\-)\-)\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-mod.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 REGISTERS-UNTOUCHED-BY-TM-EXECUTE-MOVE
 (REWRITE)
 (AND
  (EQUAL (TM-CC (TM-EXECUTE-MOVE ADDR1 ADDR2 TM))
         (TM-CC TM))
  (AND
   (EQUAL (TM-ERROR (TM-EXECUTE-MOVE ADDR1 ADDR2 TM))
          (TM-ERROR TM))
   (AND
    (EQUAL (TM-BASE (TM-EXECUTE-MOVE ADDR1 ADDR2 TM))
           (TM-BASE TM))
    (AND
     (EQUAL (TM-LIMIT (TM-EXECUTE-MOVE ADDR1 ADDR2 TM))
            (TM-LIMIT TM))
     (AND
      (EQUAL (TM-SLIMIT (TM-EXECUTE-MOVE ADDR1 ADDR2 TM))
             (TM-SLIMIT TM))
      (AND
       (EQUAL (TM-SVMODE (TM-EXECUTE-MOVE ADDR1 ADDR2 TM))
              (TM-SVMODE TM))
       (AND
        (EQUAL (TM-SVCFLAG (TM-EXECUTE-MOVE ADDR1 ADDR2 TM))
               (TM-SVCFLAG TM))
        (AND (EQUAL (TM-SVCID (TM-EXECUTE-MOVE ADDR1 ADDR2 TM))
                    (TM-SVCID TM))
             (AND (EQUAL (TM-RWSTATE (TM-EXECUTE-MOVE ADDR1 ADDR2 TM))
                         (TM-RWSTATE TM))
                  (AND (EQUAL (TM-CLOCK (TM-EXECUTE-MOVE ADDR1 ADDR2 TM))
                              (TM-CLOCK TM))
                       (AND (EQUAL (TM-IPORTS (TM-EXECUTE-MOVE ADDR1 ADDR2 TM))
                                   (TM-IPORTS TM))
                            (EQUAL (TM-OPORTS (TM-EXECUTE-MOVE ADDR1 ADDR2 TM))
                                   (TM-OPORTS TM)))))))))))))
 ((ENABLE TM-EXECUTE-MOVE TM-STORE-PRESERVES-ALL-BUT-MEMORY-AND-REGS)
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-move.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  registers-untouched-by-tm-execute-multiply \\ \index{registers-untouched-by-tm-execute!-multiply}
\=\+({\rm{tm-error}}\,({\rm{tm-execute-multiply}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-multiply})\index{tm-error} $=$ {\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-base}}\,({\rm{tm-execute-multiply}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-multiply})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-limit}}\,({\rm{tm-execute-multiply}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-multiply})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-slimit}}\,({\rm{tm-execute-multiply}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-multiply})\index{tm-slimit} \\ 
$=$$\;\;\;\;${\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svmode}}\,({\rm{tm-execute-multiply}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-multiply})\index{tm-svmode} \\ 
$=$$\;\;\;\;${\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcflag}}\,({\rm{tm-execute-multiply}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-multiply})\index{tm-svcflag} \\ 
$=$$\;\;\;\;${\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcid}}\,({\rm{tm-execute-multiply}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-multiply})\index{tm-svcid} \\ 
$=$$\;\;\;\;${\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-rwstate}}\,({\rm{tm-execute-multiply}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-multiply})\index{tm-rwstate} \\ 
$=$$\;\;\;\;${\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-clock}}\,({\rm{tm-execute-multiply}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-multiply})\index{tm-clock} \\ 
$=$$\;\;\;\;${\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-iports}}\,({\rm{tm-execute-multiply}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-multiply})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-oports}}\,({\rm{tm-execute-multiply}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-multiply})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-)\-)\-)\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-multiply.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  registers-untouched-by-tm-execute-return \\ \index{registers-untouched-by-tm-execute!-return}
\=\+({\rm{tm-memory}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-memory} $=$ {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-cc}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-cc} $=$ {\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-base}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-limit}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-slimit}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-slimit} \\ 
$=$$\;\;\;\;${\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svmode}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-svmode} \\ 
$=$$\;\;\;\;${\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcflag}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-svcflag} \\ 
$=$$\;\;\;\;${\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcid}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-svcid} \\ 
$=$$\;\;\;\;${\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-rwstate}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-rwstate} \\ 
$=$$\;\;\;\;${\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-clock}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-clock} \\ 
$=$$\;\;\;\;${\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-iports}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-oports}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-)\-)\-)\-)\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-return.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 REGISTERS-UNTOUCHED-BY-TM-EXECUTE-SET-CLOCK
 (REWRITE)
 (IMPLIES
  (NOT (TM-IN-SUPERVISOR-MODE TM))
  (AND
   (EQUAL (TM-MEMORY (TM-EXECUTE-SET-CLOCK ADDR TM))
          (TM-MEMORY TM))
   (AND
    (EQUAL (TM-REGS (TM-EXECUTE-SET-CLOCK ADDR TM))
           (TM-REGS TM))
    (AND
     (EQUAL (TM-CC (TM-EXECUTE-SET-CLOCK ADDR TM))
            (TM-CC TM))
     (AND
      (EQUAL (TM-BASE (TM-EXECUTE-SET-CLOCK ADDR TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-EXECUTE-SET-CLOCK ADDR TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-EXECUTE-SET-CLOCK ADDR TM))
               (TM-SLIMIT TM))
        (AND
         (EQUAL (TM-SVMODE (TM-EXECUTE-SET-CLOCK ADDR TM))
                (TM-SVMODE TM))
         (AND
          (EQUAL (TM-SVCFLAG (TM-EXECUTE-SET-CLOCK ADDR TM))
                 (TM-SVCFLAG TM))
          (AND
           (EQUAL (TM-SVCID (TM-EXECUTE-SET-CLOCK ADDR TM))
                  (TM-SVCID TM))
           (AND
              (EQUAL (TM-RWSTATE (TM-EXECUTE-SET-CLOCK ADDR TM))
                     (TM-RWSTATE TM))
              (AND (EQUAL (TM-CLOCK (TM-EXECUTE-SET-CLOCK ADDR TM))
                          (TM-CLOCK TM))
                   (AND (EQUAL (TM-IPORTS (TM-EXECUTE-SET-CLOCK ADDR TM))
                               (TM-IPORTS TM))
                        (AND (EQUAL (TM-OPORTS (TM-EXECUTE-SET-CLOCK ADDR TM))
                                    (TM-OPORTS TM))
                             (AND (EQUAL (TM-PC (TM-EXECUTE-SET-CLOCK ADDR TM))
                                         (TM-PC TM))
                                  (EQUAL (TM-SP (TM-EXECUTE-SET-CLOCK ADDR TM))
                                         (TM-SP TM)))))))))))))))))
 ((ENABLE TM-EXECUTE-SET-CLOCK ACCESS-TM-SET-ERROR)
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-set-clock.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 REGISTERS-UNTOUCHED-BY-TM-EXECUTE-RUN
 (REWRITE)
 (IMPLIES
  (NOT (TM-IN-SUPERVISOR-MODE TM))
  (AND
   (EQUAL (TM-MEMORY (TM-EXECUTE-RUN TM))
          (TM-MEMORY TM))
   (AND
    (EQUAL (TM-CC (TM-EXECUTE-RUN TM))
           (TM-CC TM))
    (AND
     (EQUAL (TM-BASE (TM-EXECUTE-RUN TM))
            (TM-BASE TM))
     (AND
      (EQUAL (TM-LIMIT (TM-EXECUTE-RUN TM))
             (TM-LIMIT TM))
      (AND
       (EQUAL (TM-SLIMIT (TM-EXECUTE-RUN TM))
              (TM-SLIMIT TM))
       (AND
          (EQUAL (TM-SVMODE (TM-EXECUTE-RUN TM))
                 (TM-SVMODE TM))
          (AND (EQUAL (TM-SVCFLAG (TM-EXECUTE-RUN TM))
                      (TM-SVCFLAG TM))
               (AND (EQUAL (TM-SVCID (TM-EXECUTE-RUN TM))
                           (TM-SVCID TM))
                    (AND (EQUAL (TM-RWSTATE (TM-EXECUTE-RUN TM))
                                (TM-RWSTATE TM))
                         (AND (EQUAL (TM-CLOCK (TM-EXECUTE-RUN TM))
                                     (TM-CLOCK TM))
                              (AND (EQUAL (TM-IPORTS (TM-EXECUTE-RUN TM))
                                          (TM-IPORTS TM))
                                   (AND (EQUAL (TM-OPORTS (TM-EXECUTE-RUN TM))
                                               (TM-OPORTS TM))
                                        (AND (EQUAL (TM-PC (TM-EXECUTE-RUN TM))
                                                    (TM-PC TM))
                                             (EQUAL (TM-SP (TM-EXECUTE-RUN TM))
                                                    (TM-SP TM))))))))))))))))
 ((ENABLE TM-EXECUTE-RUN ACCESS-TM-SET-ERROR)
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-run.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 REGISTERS-UNTOUCHED-BY-TM-EXECUTE-WAIT
 (REWRITE)
 (IMPLIES
  (NOT (TM-IN-SUPERVISOR-MODE TM))
  (AND
   (EQUAL (TM-MEMORY (TM-EXECUTE-WAIT TM))
          (TM-MEMORY TM))
   (AND
    (EQUAL (TM-CC (TM-EXECUTE-WAIT TM))
           (TM-CC TM))
    (AND
     (EQUAL (TM-BASE (TM-EXECUTE-WAIT TM))
            (TM-BASE TM))
     (AND
      (EQUAL (TM-LIMIT (TM-EXECUTE-WAIT TM))
             (TM-LIMIT TM))
      (AND
       (EQUAL (TM-SLIMIT (TM-EXECUTE-WAIT TM))
              (TM-SLIMIT TM))
       (AND
         (EQUAL (TM-SVMODE (TM-EXECUTE-WAIT TM))
                (TM-SVMODE TM))
         (AND (EQUAL (TM-SVCFLAG (TM-EXECUTE-WAIT TM))
                     (TM-SVCFLAG TM))
              (AND (EQUAL (TM-SVCID (TM-EXECUTE-WAIT TM))
                          (TM-SVCID TM))
                   (AND (EQUAL (TM-RWSTATE (TM-EXECUTE-WAIT TM))
                               (TM-RWSTATE TM))
                        (AND (EQUAL (TM-CLOCK (TM-EXECUTE-WAIT TM))
                                    (TM-CLOCK TM))
                             (AND (EQUAL (TM-IPORTS (TM-EXECUTE-WAIT TM))
                                         (TM-IPORTS TM))
                                  (AND (EQUAL (TM-OPORTS (TM-EXECUTE-WAIT TM))
                                              (TM-OPORTS TM))
                                       (AND (EQUAL (TM-PC (TM-EXECUTE-WAIT TM))
                                                   (TM-PC TM))
                                            (EQUAL (TM-SP (TM-EXECUTE-WAIT TM))
                                                   (TM-SP TM))))))))))))))))
 ((ENABLE TM-EXECUTE-WAIT ACCESS-TM-SET-ERROR)
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-wait.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 REGISTERS-UNTOUCHED-BY-TM-EXECUTE-TEST-IPORT
 (REWRITE)
 (IMPLIES
  (NOT (TM-IN-SUPERVISOR-MODE TM))
  (AND
   (EQUAL (TM-MEMORY (TM-EXECUTE-TEST-IPORT ADDR TM))
          (TM-MEMORY TM))
   (AND
    (EQUAL (TM-REGS (TM-EXECUTE-TEST-IPORT ADDR TM))
           (TM-REGS TM))
    (AND
     (EQUAL (TM-CC (TM-EXECUTE-TEST-IPORT ADDR TM))
            (TM-CC TM))
     (AND
      (EQUAL (TM-BASE (TM-EXECUTE-TEST-IPORT ADDR TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-EXECUTE-TEST-IPORT ADDR TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-EXECUTE-TEST-IPORT ADDR TM))
               (TM-SLIMIT TM))
        (AND
         (EQUAL (TM-SVMODE (TM-EXECUTE-TEST-IPORT ADDR TM))
                (TM-SVMODE TM))
         (AND
          (EQUAL (TM-SVCFLAG (TM-EXECUTE-TEST-IPORT ADDR TM))
                 (TM-SVCFLAG TM))
          (AND
           (EQUAL (TM-SVCID (TM-EXECUTE-TEST-IPORT ADDR TM))
                  (TM-SVCID TM))
           (AND
             (EQUAL (TM-RWSTATE (TM-EXECUTE-TEST-IPORT ADDR TM))
                    (TM-RWSTATE TM))
             (AND (EQUAL (TM-CLOCK (TM-EXECUTE-TEST-IPORT ADDR TM))
                         (TM-CLOCK TM))
                  (AND (EQUAL (TM-IPORTS (TM-EXECUTE-TEST-IPORT ADDR TM))
                              (TM-IPORTS TM))
                       (AND (EQUAL (TM-OPORTS (TM-EXECUTE-TEST-IPORT ADDR TM))
                                   (TM-OPORTS TM))
                            (AND (EQUAL (TM-PC (TM-EXECUTE-TEST-IPORT ADDR TM))
                                        (TM-PC TM))
                                 (EQUAL (TM-SP (TM-EXECUTE-TEST-IPORT ADDR TM))
                                        (TM-SP TM)))))))))))))))))
 ((ENABLE TM-EXECUTE-TEST-IPORT ACCESS-TM-SET-ERROR)
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-test-iport.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 REGISTERS-UNTOUCHED-BY-TM-EXECUTE-TEST-OPORT
 (REWRITE)
 (IMPLIES
  (NOT (TM-IN-SUPERVISOR-MODE TM))
  (AND
   (EQUAL (TM-MEMORY (TM-EXECUTE-TEST-OPORT ADDR TM))
          (TM-MEMORY TM))
   (AND
    (EQUAL (TM-REGS (TM-EXECUTE-TEST-OPORT ADDR TM))
           (TM-REGS TM))
    (AND
     (EQUAL (TM-CC (TM-EXECUTE-TEST-OPORT ADDR TM))
            (TM-CC TM))
     (AND
      (EQUAL (TM-BASE (TM-EXECUTE-TEST-OPORT ADDR TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-EXECUTE-TEST-OPORT ADDR TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-EXECUTE-TEST-OPORT ADDR TM))
               (TM-SLIMIT TM))
        (AND
         (EQUAL (TM-SVMODE (TM-EXECUTE-TEST-OPORT ADDR TM))
                (TM-SVMODE TM))
         (AND
          (EQUAL (TM-SVCFLAG (TM-EXECUTE-TEST-OPORT ADDR TM))
                 (TM-SVCFLAG TM))
          (AND
           (EQUAL (TM-SVCID (TM-EXECUTE-TEST-OPORT ADDR TM))
                  (TM-SVCID TM))
           (AND
             (EQUAL (TM-RWSTATE (TM-EXECUTE-TEST-OPORT ADDR TM))
                    (TM-RWSTATE TM))
             (AND (EQUAL (TM-CLOCK (TM-EXECUTE-TEST-OPORT ADDR TM))
                         (TM-CLOCK TM))
                  (AND (EQUAL (TM-IPORTS (TM-EXECUTE-TEST-OPORT ADDR TM))
                              (TM-IPORTS TM))
                       (AND (EQUAL (TM-OPORTS (TM-EXECUTE-TEST-OPORT ADDR TM))
                                   (TM-OPORTS TM))
                            (AND (EQUAL (TM-PC (TM-EXECUTE-TEST-OPORT ADDR TM))
                                        (TM-PC TM))
                                 (EQUAL (TM-SP (TM-EXECUTE-TEST-OPORT ADDR TM))
                                        (TM-SP TM)))))))))))))))))
 ((ENABLE TM-EXECUTE-TEST-OPORT ACCESS-TM-SET-ERROR)
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-test-oport.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 REGISTERS-UNTOUCHED-BY-TM-EXECUTE-START-OUTPUT
 (REWRITE)
 (IMPLIES
  (NOT (TM-IN-SUPERVISOR-MODE TM))
  (AND
   (EQUAL (TM-MEMORY (TM-EXECUTE-START-OUTPUT ADDR1 ADDR2 TM))
          (TM-MEMORY TM))
   (AND
    (EQUAL (TM-REGS (TM-EXECUTE-START-OUTPUT ADDR1 ADDR2 TM))
           (TM-REGS TM))
    (AND
     (EQUAL (TM-CC (TM-EXECUTE-START-OUTPUT ADDR1 ADDR2 TM))
            (TM-CC TM))
     (AND
      (EQUAL (TM-BASE (TM-EXECUTE-START-OUTPUT ADDR1 ADDR2 TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-EXECUTE-START-OUTPUT ADDR1 ADDR2 TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-EXECUTE-START-OUTPUT ADDR1 ADDR2 TM))
               (TM-SLIMIT TM))
        (AND
         (EQUAL (TM-SVMODE (TM-EXECUTE-START-OUTPUT ADDR1 ADDR2 TM))
                (TM-SVMODE TM))
         (AND
          (EQUAL (TM-SVCFLAG (TM-EXECUTE-START-OUTPUT ADDR1 ADDR2 TM))
                 (TM-SVCFLAG TM))
          (AND
           (EQUAL (TM-SVCID (TM-EXECUTE-START-OUTPUT ADDR1 ADDR2 TM))
                  (TM-SVCID TM))
           (AND
               (EQUAL (TM-RWSTATE (TM-EXECUTE-START-OUTPUT ADDR1 ADDR2 TM))
                      (TM-RWSTATE TM))
               (AND (EQUAL (TM-CLOCK (TM-EXECUTE-START-OUTPUT ADDR1 ADDR2 TM))
                           (TM-CLOCK TM))
                    (AND (EQUAL (TM-IPORTS (TM-EXECUTE-START-OUTPUT ADDR1
                                                                    ADDR2 TM))
                                (TM-IPORTS TM))
                         (AND (EQUAL (TM-OPORTS (TM-EXECUTE-START-OUTPUT ADDR1
                                                                         ADDR2
                                                                         TM))
                                     (TM-OPORTS TM))
                              (AND (EQUAL (TM-PC (TM-EXECUTE-START-OUTPUT ADDR1
                                                                          ADDR2
                                                                          TM))
                                          (TM-PC TM))
                                   (EQUAL (TM-SP (TM-EXECUTE-START-OUTPUT ADDR1
                                                                          ADDR2
                                                                          TM))
                                          (TM-SP TM)))))))))))))))))
 ((ENABLE TM-EXECUTE-START-OUTPUT ACCESS-TM-SET-ERROR)
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-start-output.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 REGISTERS-UNTOUCHED-BY-TM-EXECUTE-POST-OUTPUT-INTERRUPT
 (REWRITE)
 (IMPLIES
  (NOT (TM-IN-SUPERVISOR-MODE TM))
  (AND
   (EQUAL (TM-MEMORY (TM-EXECUTE-POST-OUTPUT-INTERRUPT ADDR TM))
          (TM-MEMORY TM))
   (AND
    (EQUAL (TM-REGS (TM-EXECUTE-POST-OUTPUT-INTERRUPT ADDR TM))
           (TM-REGS TM))
    (AND
     (EQUAL (TM-CC (TM-EXECUTE-POST-OUTPUT-INTERRUPT ADDR TM))
            (TM-CC TM))
     (AND
      (EQUAL (TM-BASE (TM-EXECUTE-POST-OUTPUT-INTERRUPT ADDR TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-EXECUTE-POST-OUTPUT-INTERRUPT ADDR TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-EXECUTE-POST-OUTPUT-INTERRUPT ADDR TM))
               (TM-SLIMIT TM))
        (AND
         (EQUAL (TM-SVMODE (TM-EXECUTE-POST-OUTPUT-INTERRUPT ADDR TM))
                (TM-SVMODE TM))
         (AND
          (EQUAL (TM-SVCFLAG (TM-EXECUTE-POST-OUTPUT-INTERRUPT ADDR TM))
                 (TM-SVCFLAG TM))
          (AND
           (EQUAL (TM-SVCID (TM-EXECUTE-POST-OUTPUT-INTERRUPT ADDR TM))
                  (TM-SVCID TM))
           (AND
            (EQUAL (TM-RWSTATE (TM-EXECUTE-POST-OUTPUT-INTERRUPT ADDR TM))
                   (TM-RWSTATE TM))
            (AND
             (EQUAL (TM-CLOCK (TM-EXECUTE-POST-OUTPUT-INTERRUPT ADDR TM))
                    (TM-CLOCK TM))
             (AND
                 (EQUAL (TM-IPORTS (TM-EXECUTE-POST-OUTPUT-INTERRUPT ADDR TM))
                        (TM-IPORTS TM))
                 (AND (EQUAL (TM-OPORTS (TM-EXECUTE-POST-OUTPUT-INTERRUPT ADDR
                                                                          TM))
                             (TM-OPORTS TM))
                      (AND (EQUAL (TM-PC (TM-EXECUTE-POST-OUTPUT-INTERRUPT ADDR
                                                                           TM))
                                  (TM-PC TM))
                           (EQUAL (TM-SP (TM-EXECUTE-POST-OUTPUT-INTERRUPT ADDR
                                                                           TM))
                                  (TM-SP TM)))))))))))))))))
 ((ENABLE TM-EXECUTE-POST-OUTPUT-INTERRUPT ACCESS-TM-SET-ERROR)
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-post-output-interrupt.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 REGISTERS-UNTOUCHED-BY-TM-EXECUTE-SVC
 (REWRITE)
 (AND
  (EQUAL (TM-MEMORY (TM-EXECUTE-SVC ADDR TM))
         (TM-MEMORY TM))
  (AND
   (EQUAL (TM-REGS (TM-EXECUTE-SVC ADDR TM))
          (TM-REGS TM))
   (AND
    (EQUAL (TM-CC (TM-EXECUTE-SVC ADDR TM))
           (TM-CC TM))
    (AND
     (EQUAL (TM-ERROR (TM-EXECUTE-SVC ADDR TM))
            (TM-ERROR TM))
     (AND
      (EQUAL (TM-BASE (TM-EXECUTE-SVC ADDR TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-EXECUTE-SVC ADDR TM))
              (TM-LIMIT TM))
       (AND
          (EQUAL (TM-SLIMIT (TM-EXECUTE-SVC ADDR TM))
                 (TM-SLIMIT TM))
          (AND (EQUAL (TM-SVMODE (TM-EXECUTE-SVC ADDR TM))
                      (TM-SVMODE TM))
               (AND (EQUAL (TM-RWSTATE (TM-EXECUTE-SVC ADDR TM))
                           (TM-RWSTATE TM))
                    (AND (EQUAL (TM-CLOCK (TM-EXECUTE-SVC ADDR TM))
                                (TM-CLOCK TM))
                         (AND (EQUAL (TM-IPORTS (TM-EXECUTE-SVC ADDR TM))
                                     (TM-IPORTS TM))
                              (AND (EQUAL (TM-OPORTS (TM-EXECUTE-SVC ADDR TM))
                                          (TM-OPORTS TM))
                                   (AND (EQUAL (TM-PC (TM-EXECUTE-SVC ADDR TM))
                                               (TM-PC TM))
                                        (EQUAL (TM-SP (TM-EXECUTE-SVC ADDR TM))
                                               (TM-SP TM)))))))))))))))
 ((ENABLE TM-EXECUTE-SVC ACCESS-TM-SET-SVCID ACCESS-TM-SET-SVCFLAG)
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-svc.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 REGISTERS-UNTOUCHED-BY-TM-EXECUTE-SVC-RETURN
 (REWRITE)
 (IMPLIES
  (NOT (TM-IN-SUPERVISOR-MODE TM))
  (AND
   (EQUAL (TM-MEMORY (TM-EXECUTE-SVC-RETURN ADDR TM))
          (TM-MEMORY TM))
   (AND
    (EQUAL (TM-REGS (TM-EXECUTE-SVC-RETURN ADDR TM))
           (TM-REGS TM))
    (AND
     (EQUAL (TM-CC (TM-EXECUTE-SVC-RETURN ADDR TM))
            (TM-CC TM))
     (AND
      (EQUAL (TM-BASE (TM-EXECUTE-SVC-RETURN ADDR TM))
             (TM-BASE TM))
      (AND
       (EQUAL (TM-LIMIT (TM-EXECUTE-SVC-RETURN ADDR TM))
              (TM-LIMIT TM))
       (AND
        (EQUAL (TM-SLIMIT (TM-EXECUTE-SVC-RETURN ADDR TM))
               (TM-SLIMIT TM))
        (AND
         (EQUAL (TM-SVMODE (TM-EXECUTE-SVC-RETURN ADDR TM))
                (TM-SVMODE TM))
         (AND
          (EQUAL (TM-SVCFLAG (TM-EXECUTE-SVC-RETURN ADDR TM))
                 (TM-SVCFLAG TM))
          (AND
           (EQUAL (TM-SVCID (TM-EXECUTE-SVC-RETURN ADDR TM))
                  (TM-SVCID TM))
           (AND
             (EQUAL (TM-RWSTATE (TM-EXECUTE-SVC-RETURN ADDR TM))
                    (TM-RWSTATE TM))
             (AND (EQUAL (TM-CLOCK (TM-EXECUTE-SVC-RETURN ADDR TM))
                         (TM-CLOCK TM))
                  (AND (EQUAL (TM-IPORTS (TM-EXECUTE-SVC-RETURN ADDR TM))
                              (TM-IPORTS TM))
                       (AND (EQUAL (TM-OPORTS (TM-EXECUTE-SVC-RETURN ADDR TM))
                                   (TM-OPORTS TM))
                            (AND (EQUAL (TM-PC (TM-EXECUTE-SVC-RETURN ADDR TM))
                                        (TM-PC TM))
                                 (EQUAL (TM-SP (TM-EXECUTE-SVC-RETURN ADDR TM))
                                        (TM-SP TM)))))))))))))))))
 ((ENABLE TM-EXECUTE-SVC-RETURN ACCESS-TM-SET-ERROR)
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-svc-return.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  registers-untouched-by-tm-execute-nullary \\ \index{registers-untouched-by-tm-execute!-nullary}
\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{tm-base}}\,({\rm{tm-execute-nullary}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-limit}}\,({\rm{tm-execute-nullary}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-slimit}}\,({\rm{tm-execute-nullary}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary})\index{tm-slimit} \\ 
$=$$\;\;\;\;${\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svmode}}\,({\rm{tm-execute-nullary}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary})\index{tm-svmode} \\ 
$=$$\;\;\;\;${\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcflag}}\,({\rm{tm-execute-nullary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-nullary})\index{tm-svcflag} \\ 
$=$$\;\;\;\;${\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcid}}\,({\rm{tm-execute-nullary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-nullary})\index{tm-svcid} \\ 
$=$$\;\;\;\;${\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-rwstate}}\,({\rm{tm-execute-nullary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-nullary})\index{tm-rwstate} \\ 
$=$$\;\;\;\;${\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-clock}}\,({\rm{tm-execute-nullary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-nullary})\index{tm-clock} \\ 
$=$$\;\;\;\;${\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-iports}}\,({\rm{tm-execute-nullary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-nullary})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-oports}}\,({\rm{tm-execute-nullary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-nullary})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-)\-)\-)\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-nullary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  registers-untouched-by-tm-execute-unary \\ \index{registers-untouched-by-tm-execute!-unary}
\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{tm-base}}\,({\rm{tm-execute-unary}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-limit}}\,({\rm{tm-execute-unary}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-slimit}}\,({\rm{tm-execute-unary}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary})\index{tm-slimit} \\ 
$=$$\;\;\;\;${\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svmode}}\,({\rm{tm-execute-unary}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary})\index{tm-svmode} \\ 
$=$$\;\;\;\;${\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-rwstate}}\,({\rm{tm-execute-unary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary})\index{tm-rwstate} \\ 
$=$$\;\;\;\;${\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-clock}}\,({\rm{tm-execute-unary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary})\index{tm-clock} \\ 
$=$$\;\;\;\;${\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-iports}}\,({\rm{tm-execute-unary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-oports}}\,({\rm{tm-execute-unary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-)\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-unary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  registers-untouched-by-tm-execute-binary \\ \index{registers-untouched-by-tm-execute!-binary}
\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{tm-base}}\,({\rm{tm-execute-binary}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-binary})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-limit}}\,({\rm{tm-execute-binary}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-binary})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-slimit}}\,({\rm{tm-execute-binary}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-binary})\index{tm-slimit} \\ 
$=$$\;\;\;\;${\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svmode}}\,({\rm{tm-execute-binary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary})\index{tm-svmode} \\ 
$=$$\;\;\;\;${\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcflag}}\,({\rm{tm-execute-binary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary})\index{tm-svcflag} \\ 
$=$$\;\;\;\;${\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svcid}}\,({\rm{tm-execute-binary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary})\index{tm-svcid} \\ 
$=$$\;\;\;\;${\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-rwstate}}\,({\rm{tm-execute-binary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary})\index{tm-rwstate} \\ 
$=$$\;\;\;\;${\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-clock}}\,({\rm{tm-execute-binary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary})\index{tm-clock} \\ 
$=$$\;\;\;\;${\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-iports}}\,({\rm{tm-execute-binary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-oports}}\,({\rm{tm-execute-binary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-)\-)\-)\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-binary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  registers-untouched-by-tm-execute-instruction \\ \index{registers-untouched-by-tm-execute!-instruction}
\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{tm-base}}\,({\rm{tm-execute-instruction}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute-instruction})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-limit}}\,({\rm{tm-execute-instruction}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute-instruction})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-slimit}}\,({\rm{tm-execute-instruction}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute-instruction})\index{tm-slimit} \\ 
$=$$\;\;\;\;${\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svmode}}\,({\rm{tm-execute-instruction}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction})\index{tm-svmode} \\ 
$=$$\;\;\;\;${\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-rwstate}}\,({\rm{tm-execute-instruction}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction})\index{tm-rwstate} \\ 
$=$$\;\;\;\;${\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-clock}}\,({\rm{tm-execute-instruction}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction})\index{tm-clock} \\ 
$=$$\;\;\;\;${\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-iports}}\,({\rm{tm-execute-instruction}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-oports}}\,({\rm{tm-execute-instruction}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-)\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute-instruction.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  registers-untouched-by-tm-execute \\ \index{registers-untouched-by-tm-execute}
\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{tm-base}}\,({\rm{tm-execute}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-limit}}\,({\rm{tm-execute}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-slimit}}\,({\rm{tm-execute}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svmode}}\,({\rm{tm-execute}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute})\index{tm-svmode} \\ 
$=$$\;\;\;\;${\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-rwstate}}\,({\rm{tm-execute}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute})\index{tm-rwstate} \\ 
$=$$\;\;\;\;${\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-clock}}\,({\rm{tm-execute}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute})\index{tm-clock} \\ 
$=$$\;\;\;\;${\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-iports}}\,({\rm{tm-execute}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-oports}}\,({\rm{tm-execute}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-)\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable registers-untouched-by-tm-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  registers-untouched-by-tm-fetch-execute \\ \index{registers-untouched-by-tm-fetch!-execute}
\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{tm-base}}\,({\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-limit}}\,({\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{tm-slimit}}\,({\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{tm\/}})\index{tm-slimit}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-svmode}}\,({\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute})\index{tm-svmode} \\ 
$=$$\;\;\;\;${\rm{tm-svmode}}\,({\it{tm\/}})\index{tm-svmode})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-rwstate}}\,({\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute})\index{tm-rwstate} \\ 
$=$$\;\;\;\;${\rm{tm-rwstate}}\,({\it{tm\/}})\index{tm-rwstate})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-iports}}\,({\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-iports}}\,({\it{tm\/}})\index{tm-iports})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-oports}}\,({\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable registers-untouched-by-tm-fetch-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-tm-fetch-execute \\ \index{tm-clock-tm-fetch-execute}
\=\+(($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) $\wedge$ ($\neg$ {\rm{tm-clock-interruptp}}\,({\it{tm\/}})\index{tm-clock-interruptp})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-clock}}\,({\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute})\index{tm-clock} $=$ ({\rm{tm-clock}}\,({\it{tm\/}})\index{tm-clock} $-\;1$))\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-tm-fetch-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{base-limit} \\  
{\rm{base-limit}}\,({\it{base\/}}, {\it{limit\/}})\index{base-limit} $=$ {\rm{cons}}\,({\it{base\/}}, {\rm{cons}}\,({\it{limit\/}}, {\tt{'}}{\tt{nil}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{base}$\;\;$
{\rm{base}}\,({\it{base-limit\/}})\index{base} $=$ {\rm{car}}\,({\it{base-limit\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{limit}$\;\;$
{\rm{limit}}\,({\it{base-limit\/}})\index{limit} $=$ {\rm{car}}\,({\rm{cdr}}\,({\it{base-limit\/}}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{disjoint} \\  
\=\+{\rm{disjoint}}\,({\it{b1\/}}, {\it{l1\/}}, {\it{b2\/}}, {\it{l2\/}})\index{disjoint} \\ 
$=$$\;\;\;\;$(\=\+\=\+{\bf if }{\it{b2\/}} $<$ ({\it{b1\/}} $+$ {\it{l1\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\vee$$\;\;\;\;$\=\+{\bf if }{\it{b1\/}} $<$ ({\it{b2\/}} $+$ {\it{l2\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  symmetry-of-disjoint \\ \index{symmetry-of-disjoint}
{\rm{disjoint}}\,({\it{b2\/}}, {\it{l2\/}}, {\it{b1\/}}, {\it{l1\/}})\index{disjoint} $=$ {\rm{disjoint}}\,({\it{b1\/}}, {\it{l1\/}}, {\it{b2\/}}, {\it{l2\/}})\index{disjoint}
\end{tabbing}


\noindent{\sc Event}:   Disable symmetry-of-disjoint.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{disjoint-everywhere} \\  
\=\+{\rm{disjoint-everywhere}}\,({\it{b\/}}, {\it{l\/}}, {\it{table\/}})\index{disjoint-everywhere} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{table\/}}) \\ 
{\bf then }\=\+{\rm{disjoint}}\,({\it{b\/}}, {\it{l\/}}, {\rm{base}}\,({\rm{car}}\,({\it{table\/}}))\index{base}, {\rm{limit}}\,({\rm{car}}\,({\it{table\/}}))\index{limit})\index{disjoint} \\ 
$\wedge$$\;\;\;\;${\rm{disjoint-everywhere}}\,({\it{b\/}}, {\it{l\/}}, {\rm{cdr}}\,({\it{table\/}}))\index{disjoint-everywhere}\- \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{mutually-disjoint} \\  
\=\+{\rm{mutually-disjoint}}\,({\it{table\/}})\index{mutually-disjoint} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{table\/}}) \\ 
{\bf then }\=\+{\rm{disjoint-everywhere}}\,(\=\+{\rm{base}}\,({\rm{car}}\,({\it{table\/}}))\index{base}, \\ 
{\rm{limit}}\,({\rm{car}}\,({\it{table\/}}))\index{limit}, \\ 
{\rm{cdr}}\,({\it{table\/}}))\-\index{disjoint-everywhere} \\ 
$\wedge$$\;\;\;\;${\rm{mutually-disjoint}}\,({\rm{cdr}}\,({\it{table\/}}))\index{mutually-disjoint}\- \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{finite-segment-tablep} \\  
\=\+{\rm{finite-segment-tablep}}\,({\it{table\/}}, {\it{max\/}})\index{finite-segment-tablep} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{table\/}}) \\ 
{\bf then }\=\+\=\+{\bf if }{\it{max\/}} $<$ ({\rm{base}}\,({\rm{car}}\,({\it{table\/}}))\index{base} $+$ {\rm{limit}}\,({\rm{car}}\,({\it{table\/}}))\index{limit}) \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;${\rm{finite-segment-tablep}}\,({\rm{cdr}}\,({\it{table\/}}), {\it{max\/}})\index{finite-segment-tablep}\- \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  disjoint-getnth \\ \index{disjoint-getnth}
\=\+({\rm{disjoint-everywhere}}\,({\it{b\/}}, {\it{l\/}}, {\it{table\/}})\index{disjoint-everywhere} $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{table\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;${\rm{disjoint}}\,({\it{b\/}}, {\it{l\/}}, {\rm{base}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{table\/}})\index{getnth})\index{base}, {\rm{limit}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{table\/}})\index{getnth})\index{limit})\index{disjoint}\-
\end{tabbing}


\noindent{\sc Event}:   Disable disjoint-getnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-good-address-tm-set-cc \\ \index{tm-good-address-tm-set-cc}
{\rm{tm-good-address}}\,({\it{addr\/}}, {\rm{tm-set-cc}}\,({\it{cc\/}}, {\it{tm\/}})\index{tm-set-cc})\index{tm-good-address} $=$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-good-address-tm-set-cc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-good-address-tm-set-pc \\ \index{tm-good-address-tm-set-pc}
{\rm{tm-good-address}}\,({\it{addr\/}}, {\rm{tm-set-pc}}\,({\it{pc\/}}, {\it{tm\/}})\index{tm-set-pc})\index{tm-good-address} $=$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-good-address-tm-set-pc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-good-address-tm-set-sp \\ \index{tm-good-address-tm-set-sp}
{\rm{tm-good-address}}\,({\it{addr\/}}, {\rm{tm-set-sp}}\,({\it{sp\/}}, {\it{tm\/}})\index{tm-set-sp})\index{tm-good-address} $=$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-good-address-tm-set-sp.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-store-in-memory-protection-theorem \\ \index{tm-store-in-memory-protection-t!heorem}
\=\+(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{disjoint}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\index{disjoint} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,(\=\+{\it{addr\/}}, \\ 
{\rm{min}}\,({\tt{'}}{\tt{65536}} $-$ {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\index{min})\-\index{finite-numberp})\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\rm{tm-store-in-memory}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store-in-memory})\index{tm-memory})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-store-in-memory-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-store-protection-theorem \\ \index{tm-store-protection-theorem}
\=\+(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$({\rm{disjoint}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\index{disjoint} $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store})\index{tm-memory})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-store-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-add-protection-theorem \\ \index{tm-execute-add-protection-theore!m}
\=\+(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{disjoint}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\index{disjoint} \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address})\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\rm{tm-execute-add}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-add})\index{tm-memory})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-add-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-branch-protection-theorem \\ \index{tm-execute-branch-protection-the!orem}
{\rm{tm-memory}}\,({\rm{tm-execute-branch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch})\index{tm-memory} $=$ {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-branch-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-branch-on-zero-protection-theorem \\ \index{tm-execute-branch-on-zero-prote!ction-theorem}
{\rm{tm-memory}}\,({\rm{tm-execute-branch-on-zero}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch-on-zero})\index{tm-memory} $=$ {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-branch-on-zero-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-branch-not-zero-protection-theorem \\ \index{tm-execute-branch-not-zero-prote!ction-theorem}
{\rm{tm-memory}}\,({\rm{tm-execute-branch-not-zero}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch-not-zero})\index{tm-memory} $=$ {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-branch-not-zero-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-call-protection-theorem \\ \index{tm-execute-call-protection-theo!rem}
\=\+(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$({\rm{disjoint}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\index{disjoint} $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-call})\index{tm-memory})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-call-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-compare-protection-theorem \\ \index{tm-execute-compare-protection-t!heorem}
{\rm{tm-memory}}\,({\rm{tm-execute-compare}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-compare})\index{tm-memory} $=$ {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-compare-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-decr-protection-theorem \\ \index{tm-execute-decr-protection-theo!rem}
\=\+(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$({\rm{disjoint}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\index{disjoint} $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-decr})\index{tm-memory})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-decr-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-decr-mod-protection-theorem \\ \index{tm-execute-decr-mod-protection-t!heorem}
\=\+(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{disjoint}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\index{disjoint} \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address})\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\rm{tm-execute-decr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-decr-mod})\index{tm-memory})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-decr-mod-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-incr-protection-theorem \\ \index{tm-execute-incr-protection-theo!rem}
\=\+(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$({\rm{disjoint}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\index{disjoint} $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-incr})\index{tm-memory})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-incr-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-incr-mod-protection-theorem \\ \index{tm-execute-incr-mod-protection-t!heorem}
\=\+(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{disjoint}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\index{disjoint} \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address})\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\rm{tm-execute-incr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-incr-mod})\index{tm-memory})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-incr-mod-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-load-base-protection-theorem \\ \index{tm-execute-load-base-protection!-theorem}
{\rm{tm-memory}}\,({\rm{tm-execute-load-base}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-base})\index{tm-memory} $=$ {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-load-base-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-load-limit-protection-theorem \\ \index{tm-execute-load-limit-protectio!n-theorem}
{\rm{tm-memory}}\,({\rm{tm-execute-load-limit}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-limit})\index{tm-memory} $=$ {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-load-limit-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-load-psw-protection-theorem \\ \index{tm-execute-load-psw-protection-t!heorem}
{\rm{tm-memory}}\,({\rm{tm-execute-load-psw}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-psw})\index{tm-memory} $=$ {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-load-psw-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-mod-protection-theorem \\ \index{tm-execute-mod-protection-theore!m}
\=\+(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{disjoint}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\index{disjoint} \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address})\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\rm{tm-execute-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-mod})\index{tm-memory})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-mod-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-move-protection-theorem \\ \index{tm-execute-move-protection-theo!rem}
\=\+(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{disjoint}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\index{disjoint} \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address})\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\rm{tm-execute-move}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-move})\index{tm-memory})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-move-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-multiply-protection-theorem \\ \index{tm-execute-multiply-protection-t!heorem}
\=\+(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{disjoint}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\index{disjoint} \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address})\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\rm{tm-execute-multiply}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-multiply})\index{tm-memory})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-multiply-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-return-protection-theorem \\ \index{tm-execute-return-protection-the!orem}
{\rm{tm-memory}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-memory} $=$ {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-return-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-test-iport-protection-theorem \\ \index{tm-execute-test-iport-protectio!n-theorem}
{\rm{tm-memory}}\,({\rm{tm-execute-test-iport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-iport})\index{tm-memory} $=$ {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-test-iport-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-test-oport-protection-theorem \\ \index{tm-execute-test-oport-protectio!n-theorem}
{\rm{tm-memory}}\,({\rm{tm-execute-test-oport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-oport})\index{tm-memory} $=$ {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-test-oport-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-set-clock-protection-theorem \\ \index{tm-execute-set-clock-protection!-theorem}
{\rm{tm-memory}}\,({\rm{tm-execute-set-clock}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-set-clock})\index{tm-memory} $=$ {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-set-clock-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-run-protection-theorem \\ \index{tm-execute-run-protection-theore!m}
{\rm{tm-memory}}\,({\rm{tm-execute-run}}\,({\it{tm\/}})\index{tm-execute-run})\index{tm-memory} $=$ {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-run-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-wait-protection-theorem \\ \index{tm-execute-wait-protection-theo!rem}
{\rm{tm-memory}}\,({\rm{tm-execute-wait}}\,({\it{tm\/}})\index{tm-execute-wait})\index{tm-memory} $=$ {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-wait-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-start-output-protection-theorem \\ \index{tm-execute-start-output-protecti!on-theorem}
{\rm{tm-memory}}\,({\rm{tm-execute-start-output}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-start-output})\index{tm-memory} $=$ {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-start-output-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-post-output-interrupt-protection-theorem \\ \index{tm-execute-post-output-interrupt!-protection-theorem}
{\rm{tm-memory}}\,({\rm{tm-execute-post-output-interrupt}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-post-output-interrupt})\index{tm-memory} $=$ {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-post-output-interrupt-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-svc-protection-theorem \\ \index{tm-execute-svc-protection-theore!m}
{\rm{tm-memory}}\,({\rm{tm-execute-svc}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc})\index{tm-memory} $=$ {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-svc-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-svc-return-protection-theorem \\ \index{tm-execute-svc-return-protectio!n-theorem}
{\rm{tm-memory}}\,({\rm{tm-execute-svc-return}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc-return})\index{tm-memory} $=$ {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-svc-return-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-nullary-protection-theorem \\ \index{tm-execute-nullary-protection-t!heorem}
{\rm{tm-memory}}\,({\rm{tm-execute-nullary}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary})\index{tm-memory} $=$ {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-nullary-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-unary-protection-theorem \\ \index{tm-execute-unary-protection-the!orem}
\=\+(($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) $\wedge$ {\rm{disjoint}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\index{disjoint}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\rm{tm-execute-unary}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary})\index{tm-memory})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-unary-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-binary-protection-theorem \\ \index{tm-execute-binary-protection-the!orem}
\=\+(($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) $\wedge$ {\rm{disjoint}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\index{disjoint}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\rm{tm-execute-binary}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-binary})\index{tm-memory})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-binary-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-instruction-protection-theorem \\ \index{tm-execute-instruction-protecti!on-theorem}
\=\+(($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) $\wedge$ {\rm{disjoint}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\index{disjoint}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\rm{tm-execute-instruction}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute-instruction})\index{tm-memory})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-instruction-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-protection-theorem \\ \index{tm-execute-protection-theorem}
\=\+(($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) $\wedge$ {\rm{disjoint}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\index{disjoint}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\rm{tm-execute}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute})\index{tm-memory})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-fetch-execute-protection-theorem \\ \index{tm-fetch-execute-protection-the!orem}
\=\+(($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) $\wedge$ {\rm{disjoint}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\index{disjoint}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute})\index{tm-memory})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\it{b\/}}, {\it{l\/}}, {\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-fetch-execute-protection-theorem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-store \\ \index{length-tm-memory-tm-store}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-store.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-add \\ \index{length-tm-memory-tm-execute-add}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-add}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-add})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-add.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-branch \\ \index{length-tm-memory-tm-execute-bra!nch}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-branch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-branch.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-branch-on-zero \\ \index{length-tm-memory-tm-execute-bra!nch-on-zero}
\=\+{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-branch-on-zero}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch-on-zero})\index{tm-memory})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-branch-on-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-branch-not-zero \\ \index{length-tm-memory-tm-execute-bra!nch-not-zero}
\=\+{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-branch-not-zero}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch-not-zero})\index{tm-memory})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-branch-not-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-call \\ \index{length-tm-memory-tm-execute-cal!l}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-call})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-call.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-compare \\ \index{length-tm-memory-tm-execute-comp!are}
\=\+{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-compare}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-compare})\index{tm-memory})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-compare.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-decr \\ \index{length-tm-memory-tm-execute-dec!r}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-decr})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-decr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-decr-mod \\ \index{length-tm-memory-tm-execute-dec!r-mod}
\=\+{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-decr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-decr-mod})\index{tm-memory})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-decr-mod.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-incr \\ \index{length-tm-memory-tm-execute-inc!r}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-incr})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-incr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-incr-mod \\ \index{length-tm-memory-tm-execute-inc!r-mod}
\=\+{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-incr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-incr-mod})\index{tm-memory})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-incr-mod.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-load-base \\ \index{length-tm-memory-tm-execute-loa!d-base}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-load-base}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-base})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-load-base.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-load-limit \\ \index{length-tm-memory-tm-execute-loa!d-limit}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-load-limit}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-limit})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-load-limit.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-load-psw \\ \index{length-tm-memory-tm-execute-loa!d-psw}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-load-psw}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-psw})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-load-psw.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-mod \\ \index{length-tm-memory-tm-execute-mod}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-mod})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-mod.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-move \\ \index{length-tm-memory-tm-execute-move}
\=\+{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-move}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-move})\index{tm-memory})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-move.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-multiply \\ \index{length-tm-memory-tm-execute-multip!ly}
\=\+{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-multiply}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-multiply})\index{tm-memory})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-multiply.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-return \\ \index{length-tm-memory-tm-execute-ret!urn}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-return.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-test-iport \\ \index{length-tm-memory-tm-execute-test!-iport}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-test-iport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-iport})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-test-iport.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-test-oport \\ \index{length-tm-memory-tm-execute-test!-oport}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-test-oport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-oport})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-test-oport.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-set-clock \\ \index{length-tm-memory-tm-execute-set!-clock}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-set-clock}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-set-clock})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-set-clock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-run \\ \index{length-tm-memory-tm-execute-run}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-run}}\,({\it{tm\/}})\index{tm-execute-run})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-run.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-wait \\ \index{length-tm-memory-tm-execute-wait}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-wait}}\,({\it{tm\/}})\index{tm-execute-wait})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-wait.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-post-output-interrupt \\ \index{length-tm-memory-tm-execute-post!-output-interrupt}
\=\+{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-post-output-interrupt}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-post-output-interrupt})\index{tm-memory})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-post-output-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-start-output \\ \index{length-tm-memory-tm-execute-sta!rt-output}
\=\+{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-start-output}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-start-output})\index{tm-memory})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-start-output.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-svc \\ \index{length-tm-memory-tm-execute-svc}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-svc}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-svc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-svc-return \\ \index{length-tm-memory-tm-execute-svc!-return}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-svc-return}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc-return})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-svc-return.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-nullary \\ \index{length-tm-memory-tm-execute-nul!lary}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-nullary}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-nullary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-unary \\ \index{length-tm-memory-tm-execute-una!ry}
\=\+{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-unary}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary})\index{tm-memory})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-unary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-binary \\ \index{length-tm-memory-tm-execute-bin!ary}
\=\+{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-binary}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-binary})\index{tm-memory})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-binary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute-instruction \\ \index{length-tm-memory-tm-execute-inst!ruction}
\=\+{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute-instruction}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute-instruction})\index{tm-memory})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute-instruction.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-execute \\ \index{length-tm-memory-tm-execute}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-execute}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-tm-fetch-execute \\ \index{length-tm-memory-tm-fetch-execute}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-tm-fetch-execute.

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN
 GOOD-ADDRESS-SPACE
 (X MEMLENGTH)
 (AND
  (TM-SHELLP X)
  (AND
   (NUMBERP MEMLENGTH)
   (AND
    (IF (LESSP '65536 MEMLENGTH)
        '*1*FALSE
        '*1*TRUE)
    (AND
     (PLISTP (TM-MEMORY X))
     (AND
      (FINITE-NUMBER-LISTP (TM-MEMORY X)
                           '65536)
      (AND
       (EQUAL (LENGTH (TM-MEMORY X))
              MEMLENGTH)
       (AND
         (PLISTP (TM-REGS X))
         (AND (FINITE-NUMBER-LISTP (TM-REGS X)
                                   '65536)
              (AND (EQUAL (LENGTH (TM-REGS X)) '8)
                   (AND (FINITE-NUMBERP (TM-CC X) '4)
                        (AND (FINITE-NUMBERP (TM-ERROR X) '64)
                             (AND (FINITE-NUMBERP (TM-SVCFLAG X) '2)
                                  (AND (FINITE-NUMBERP (TM-SVCID X) '128)
                                       (AND (EQUAL (TM-BASE X) '0)
                                            (AND (EQUAL (TM-LIMIT X) MEMLENGTH)
                                                 (EQUAL (TM-SVMODE X)
                                                        '0))))))))))))))))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  tm-shellp-address-space \\ \index{tm-shellp-address-space}
{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} $\rightarrow$ {\rm{tm-shellp}}\,({\it{address-space\/}})\index{tm-shellp}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-shellp-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  non-number-memlength-gives-bad-address-space \\ \index{non-number-memlength-gives-bad-!address-space}
({\it{memlength\/}} $\not\in\;${\bf{N}}${}$) $\rightarrow$ ($\neg$ {\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space})
\end{tabbing}


\noindent{\sc Event}:   Disable non-number-memlength-gives-bad-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  address-space-memlength \\ \index{address-space-memlength}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;$\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ {\it{memlength\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plistp-address-space-memory \\ \index{plistp-address-space-memory}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{plistp}}\,({\rm{tm-memory}}\,({\it{address-space\/}})\index{tm-memory})\index{plistp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-address-space-memory.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-address-space-memory \\ \index{finite-number-listp-address-spa!ce-memory}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-listp}}\,({\rm{tm-memory}}\,({\it{address-space\/}})\index{tm-memory}, {\tt{'}}{\tt{65536}})\index{finite-number-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-address-space-memory.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-address-space-memory \\ \index{length-address-space-memory}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;$({\rm{length}}\,({\rm{tm-memory}}\,({\it{address-space\/}})\index{tm-memory})\index{length} $=$ {\it{memlength\/}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-address-space-memory.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-address-space-regs \\ \index{plistp-address-space-regs}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{plistp}}\,({\rm{tm-regs}}\,({\it{address-space\/}})\index{tm-regs})\index{plistp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-address-space-regs.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-address-space-regs \\ \index{finite-number-listp-address-spa!ce-regs}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-listp}}\,({\rm{tm-regs}}\,({\it{address-space\/}})\index{tm-regs}, {\tt{'}}{\tt{65536}})\index{finite-number-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-address-space-regs.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-address-space-regs \\ \index{length-address-space-regs}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;$({\rm{length}}\,({\rm{tm-regs}}\,({\it{address-space\/}})\index{tm-regs})\index{length} $=$ {\tt{'}}{\tt{8}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-address-space-regs.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-address-space-cc \\ \index{finite-numberp-address-space-cc}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-cc}}\,({\it{address-space\/}})\index{tm-cc}, {\tt{'}}{\tt{4}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-address-space-cc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-address-space-error \\ \index{finite-numberp-address-space-er!ror}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-error}}\,({\it{address-space\/}})\index{tm-error}, {\tt{'}}{\tt{64}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-address-space-error.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-address-space-svcflag \\ \index{finite-numberp-address-space-sv!cflag}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-svcflag}}\,({\it{address-space\/}})\index{tm-svcflag}, {\tt{'}}{\tt{2}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-address-space-svcflag.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-address-space-svcid \\ \index{finite-numberp-address-space-sv!cid}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-svcid}}\,({\it{address-space\/}})\index{tm-svcid}, {\tt{'}}{\tt{128}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-address-space-svcid.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-address-space-pc \\ \index{finite-numberp-address-space-pc}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-pc}}\,({\it{address-space\/}})\index{tm-pc}, {\tt{'}}{\tt{65536}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-address-space-pc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-address-space-sp \\ \index{finite-numberp-address-space-sp}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-sp}}\,({\it{address-space\/}})\index{tm-sp}, {\tt{'}}{\tt{65536}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-address-space-sp.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-address-space \\ \index{tm-base-address-space}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-base}}\,({\it{address-space\/}})\index{tm-base} $=$ {\tt{'}}{\tt{0}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-address-space \\ \index{tm-limit-address-space}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-limit}}\,({\it{address-space\/}})\index{tm-limit} $=$ {\it{memlength\/}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-svmode-address-space \\ \index{tm-svmode-address-space}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-svmode}}\,({\it{address-space\/}})\index{tm-svmode} $=$ {\tt{'}}{\tt{0}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-svmode-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-in-supervisor-mode-good-address-space \\ \index{tm-in-supervisor-mode-good-addre!ss-space}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-in-supervisor-mode}}\,({\it{address-space\/}})\index{tm-in-supervisor-mode} $=$ {\tt{'}}{\tt{*1*false}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-in-supervisor-mode-good-address-space.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{good-address-space-properties}} to consist of the following events: tm-in-supervisor-mode-good-address-space,
non-number-memlength-gives-bad-address-space,
tm-svmode-address-space,
tm-limit-address-space,
tm-base-address-space,
finite-numberp-address-space-svcid,
finite-numberp-address-space-svcflag,
finite-numberp-address-space-error,
finite-numberp-address-space-cc,
length-address-space-regs,
finite-number-listp-address-space-regs,
plistp-address-space-regs,
length-address-space-memory,
finite-number-listp-address-space-memory,
plistp-address-space-memory,
address-space-memlength,
tm-shellp-address-space,
finite-numberp-address-space-pc,
finite-numberp-address-space-sp.\index{good-address-space-properties}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-base-limit-property \\ \index{good-address-space-base-limit-p!roperty}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{min}}\,({\tt{'}}{\tt{65536}} $-$ {\rm{tm-base}}\,({\it{address-space\/}})\index{tm-base}, {\rm{tm-limit}}\,({\it{address-space\/}})\index{tm-limit})\index{min} \\ 
$=$$\;\;\;\;${\rm{tm-limit}}\,({\it{address-space\/}})\index{tm-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-base-limit-property.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  min-tm-memlength-memlength-in-good-address-space \\ \index{min-tm-memlength-memlength-in-g!ood-address-space}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;$({\rm{min}}\,({\tt{'}}{\tt{65536}}, {\it{memlength\/}})\index{min} $=$ {\it{memlength\/}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable min-tm-memlength-memlength-in-good-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-memory-address-implies-non-zero-limit-for-address-space \\ \index{good-memory-address-implies-non!-zero-limit-for-address-space}
\=\+(\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\rm{real-addr}}\,({\tt{'}}{\tt{2}}, {\it{pc\/}})\index{real-addr}, {\it{address-space\/}})\index{tm-good-address})\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-limit}}\,({\it{address-space\/}})\index{tm-limit} $\not\simeq {\tt{0}}$)\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-good-address-for-address-space \\ \index{finite-numberp-tm-good-address-!for-address-space}
\=\+(\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\rm{real-addr}}\,({\tt{'}}{\tt{2}}, {\it{n\/}})\index{real-addr}, {\it{address-space\/}})\index{tm-good-address})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\it{n\/}}, {\it{memlength\/}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-good-address-for-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-fetch-from-address-space \\ \index{finite-numberp-tm-fetch-from-ad!dress-space}
\=\+(\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr\/}}, {\it{address-space\/}})\index{tm-good-address})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-fetch}}\,({\it{addr\/}}, {\it{address-space\/}})\index{tm-fetch}, {\tt{'}}{\tt{65536}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-fetch-from-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  address-space-good-memory-tm-store \\ \index{address-space-good-memory-tm-st!ore}
\=\+(\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\it{value\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\rm{tm-memory}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{address-space\/}})\index{tm-store})\index{tm-memory})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{length}}\,({\rm{tm-memory}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{address-space\/}})\index{tm-store})\index{tm-memory})\index{length} \\ 
$=$$\;\;\;\;${\rm{fix}}\,({\it{memlength\/}}))\- \\ 
$\wedge$$\;\;\;\;${\rm{finite-number-listp}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-store}}\,(\=\+{\it{value\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{address-space\/}})\-\index{tm-store})\index{tm-memory}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-listp})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable address-space-good-memory-tm-store.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  address-space-good-regs-tm-store \\ \index{address-space-good-regs-tm-store}
\=\+(\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\it{value\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\rm{tm-regs}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{address-space\/}})\index{tm-store})\index{tm-regs})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\rm{tm-regs}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{address-space\/}})\index{tm-store})\index{tm-regs})\index{length} $=$ {\tt{'}}{\tt{8}}) \\ 
$\wedge$$\;\;\;\;${\rm{finite-number-listp}}\,(\=\+{\rm{tm-regs}}\,({\rm{tm-store}}\,(\=\+{\it{value\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{address-space\/}})\-\index{tm-store})\index{tm-regs}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-listp})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable address-space-good-regs-tm-store.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-store \\ \index{good-address-space-tm-store}
\=\+(\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\it{value\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{address-space\/}})\index{tm-store}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-store.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-set-cc \\ \index{good-address-space-tm-set-cc}
\=\+({\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} $\wedge$ {\rm{finite-numberp}}\,({\it{cc\/}}, {\tt{'}}{\tt{4}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-set-cc}}\,({\it{cc\/}}, {\it{address-space\/}})\index{tm-set-cc}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-set-cc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-set-error \\ \index{good-address-space-tm-set-error}
\=\+({\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} $\wedge$ {\rm{finite-numberp}}\,({\it{error\/}}, {\tt{'}}{\tt{64}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-set-error}}\,({\it{error\/}}, {\it{address-space\/}})\index{tm-set-error}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-set-error.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-set-svcflag \\ \index{good-address-space-tm-set-svcfl!ag}
\=\+({\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} $\wedge$ {\rm{finite-numberp}}\,({\it{svcflag\/}}, {\tt{'}}{\tt{2}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-set-svcflag}}\,({\it{svcflag\/}}, {\it{address-space\/}})\index{tm-set-svcflag}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-set-svcflag.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-set-svcid \\ \index{good-address-space-tm-set-svcid}
\=\+(\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\it{svcid\/}}, {\tt{'}}{\tt{128}})\index{finite-numberp})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-set-svcid}}\,({\it{svcid\/}}, {\it{address-space\/}})\index{tm-set-svcid}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-set-svcid.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-set-pc \\ \index{good-address-space-tm-set-pc}
\=\+({\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} $\wedge$ {\rm{finite-numberp}}\,({\it{pc\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-set-pc}}\,({\it{pc\/}}, {\it{address-space\/}})\index{tm-set-pc}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-set-pc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-set-sp \\ \index{good-address-space-tm-set-sp}
\=\+({\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} $\wedge$ {\rm{finite-numberp}}\,({\it{sp\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-set-sp}}\,({\it{sp\/}}, {\it{address-space\/}})\index{tm-set-sp}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-set-sp.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-add \\ \index{good-address-space-tm-execute-a!dd}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,(\=\+{\rm{tm-execute-add}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{address-space\/}})\index{tm-execute-add}, \\ 
{\it{memlength\/}})\-\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-add.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-branch \\ \index{good-address-space-tm-execute-b!ranch}
\=\+(\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr\/}}, {\it{address-space\/}})\index{tm-good-address})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-execute-branch}}\,({\it{addr\/}}, {\it{address-space\/}})\index{tm-execute-branch}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-branch.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-branch-on-zero \\ \index{good-address-space-tm-execute-b!ranch-on-zero}
\=\+(\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr\/}}, {\it{address-space\/}})\index{tm-good-address})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,(\=\+{\rm{tm-execute-branch-on-zero}}\,({\it{addr\/}}, {\it{address-space\/}})\index{tm-execute-branch-on-zero}, \\ 
{\it{memlength\/}})\-\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-branch-on-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-branch-not-zero \\ \index{good-address-space-tm-execute-b!ranch-not-zero}
\=\+(\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr\/}}, {\it{address-space\/}})\index{tm-good-address})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,(\=\+{\rm{tm-execute-branch-not-zero}}\,({\it{addr\/}}, {\it{address-space\/}})\index{tm-execute-branch-not-zero}, \\ 
{\it{memlength\/}})\-\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-branch-not-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-call \\ \index{good-address-space-tm-execute-c!all}
\=\+(\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr\/}}, {\it{address-space\/}})\index{tm-good-address})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{address-space\/}})\index{tm-execute-call}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-call.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-compare \\ \index{good-address-space-tm-execute-c!ompare}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,(\=\+{\rm{tm-execute-compare}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{address-space\/}})\index{tm-execute-compare}, \\ 
{\it{memlength\/}})\-\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-compare.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-decr \\ \index{good-address-space-tm-execute-de!cr}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{address-space\/}})\index{tm-execute-decr}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-decr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-decr-mod \\ \index{good-address-space-tm-execute-de!cr-mod}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,(\=\+{\rm{tm-execute-decr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{address-space\/}})\index{tm-execute-decr-mod}, \\ 
{\it{memlength\/}})\-\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-decr-mod.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-incr \\ \index{good-address-space-tm-execute-i!ncr}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{address-space\/}})\index{tm-execute-incr}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-incr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-incr-mod \\ \index{good-address-space-tm-execute-i!ncr-mod}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,(\=\+{\rm{tm-execute-incr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{address-space\/}})\index{tm-execute-incr-mod}, \\ 
{\it{memlength\/}})\-\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-incr-mod.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-load-base \\ \index{good-address-space-tm-execute-l!oad-base}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-execute-load-base}}\,({\it{addr\/}}, {\it{address-space\/}})\index{tm-execute-load-base}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-load-base.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-load-limit \\ \index{good-address-space-tm-execute-l!oad-limit}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,(\=\+{\rm{tm-execute-load-limit}}\,({\it{addr\/}}, {\it{address-space\/}})\index{tm-execute-load-limit}, \\ 
{\it{memlength\/}})\-\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-load-limit.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-load-psw \\ \index{good-address-space-tm-execute-l!oad-psw}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-execute-load-psw}}\,({\it{addr\/}}, {\it{address-space\/}})\index{tm-execute-load-psw}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-load-psw.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-mod \\ \index{good-address-space-tm-execute-m!od}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,(\=\+{\rm{tm-execute-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{address-space\/}})\index{tm-execute-mod}, \\ 
{\it{memlength\/}})\-\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-mod.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-move \\ \index{good-address-space-tm-execute-m!ove}
\=\+(\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr2\/}}, {\it{address-space\/}})\index{tm-good-address})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,(\=\+{\rm{tm-execute-move}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{address-space\/}})\index{tm-execute-move}, \\ 
{\it{memlength\/}})\-\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-move.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-multiply \\ \index{good-address-space-tm-execute-m!ultiply}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,(\=\+{\rm{tm-execute-multiply}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{address-space\/}})\index{tm-execute-multiply}, \\ 
{\it{memlength\/}})\-\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-multiply.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-add1-address-space-sp \\ \index{finite-numberp-add1-address-spa!ce-sp}
\=\+(\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-stack-underflowp}}\,({\it{address-space\/}})\index{tm-stack-underflowp}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,($1\;+$ {\rm{tm-sp}}\,({\it{address-space\/}})\index{tm-sp}, {\tt{'}}{\tt{65536}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-add1-address-space-sp.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  min-memlength-tm-memlength-in-good-address-space \\ \index{min-memlength-tm-memlength-in-g!ood-address-space}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;$({\rm{min}}\,({\tt{'}}{\tt{65536}}, {\it{memlength\/}})\index{min} $=$ {\it{memlength\/}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-numberp-tm-incr-memlength \\ \index{finite-numberp-tm-incr-memlengt!h}
\=\+(\=\+({\it{memlength\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(({\rm{min}}\,({\tt{'}}{\tt{65536}}, {\it{memlength\/}})\index{min} $=$ {\it{memlength\/}}) $\wedge$ ({\it{b\/}} $<$ ({\it{memlength\/}} $-\;1$))))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-incr}}\,({\it{b\/}})\index{tm-incr}, {\it{memlength\/}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-tm-incr-memlength.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-good-address-tm-incr-tm-sp-for-address-space \\ \index{tm-good-address-tm-incr-tm-sp-f!or-address-space}
\=\+(\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-stack-underflowp}}\,({\it{address-space\/}})\index{tm-stack-underflowp}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{tm-good-address}}\,(\=\+{\rm{real-addr}}\,({\tt{'}}{\tt{2}}, {\rm{tm-incr}}\,({\rm{tm-sp}}\,({\it{address-space\/}})\index{tm-sp})\index{tm-incr})\index{real-addr}, \\ 
{\it{address-space\/}})\-\index{tm-good-address}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-good-address-tm-incr-tm-sp-for-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-return \\ \index{good-address-space-tm-execute-ret!urn}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-execute-return}}\,({\it{address-space\/}})\index{tm-execute-return}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-return.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-set-clock \\ \index{good-address-space-tm-execute-set!-clock}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-execute-set-clock}}\,({\it{addr\/}}, {\it{address-space\/}})\index{tm-execute-set-clock}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-set-clock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-run \\ \index{good-address-space-tm-execute-r!un}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-execute-run}}\,({\it{address-space\/}})\index{tm-execute-run}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-run.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-wait \\ \index{good-address-space-tm-execute-w!ait}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-execute-wait}}\,({\it{address-space\/}})\index{tm-execute-wait}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-wait.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-test-iport \\ \index{good-address-space-tm-execute-te!st-iport}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,(\=\+{\rm{tm-execute-test-iport}}\,({\it{addr\/}}, {\it{address-space\/}})\index{tm-execute-test-iport}, \\ 
{\it{memlength\/}})\-\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-test-iport.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-test-oport \\ \index{good-address-space-tm-execute-te!st-oport}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,(\=\+{\rm{tm-execute-test-oport}}\,({\it{addr\/}}, {\it{address-space\/}})\index{tm-execute-test-oport}, \\ 
{\it{memlength\/}})\-\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-test-oport.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-start-output \\ \index{good-address-space-tm-execute-st!art-output}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,(\=\+{\rm{tm-execute-start-output}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{address-space\/}})\index{tm-execute-start-output}, \\ 
{\it{memlength\/}})\-\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-start-output.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-post-output-interrupt \\ \index{good-address-space-tm-execute-p!ost-output-interrupt}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,(\=\+{\rm{tm-execute-post-output-interrupt}}\,(\=\+{\it{addr\/}}, \\ 
{\it{address-space\/}})\-\index{tm-execute-post-output-interrupt}, \\ 
{\it{memlength\/}})\-\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-post-output-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-svc \\ \index{good-address-space-tm-execute-sv!c}
\=\+(\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr\/}}, {\it{address-space\/}})\index{tm-good-address})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-execute-svc}}\,({\it{addr\/}}, {\it{address-space\/}})\index{tm-execute-svc}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-svc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-svc-return \\ \index{good-address-space-tm-execute-sv!c-return}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,(\=\+{\rm{tm-execute-svc-return}}\,({\it{addr\/}}, {\it{address-space\/}})\index{tm-execute-svc-return}, \\ 
{\it{memlength\/}})\-\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-svc-return.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-nullary \\ \index{good-address-space-tm-execute-n!ullary}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-execute-nullary}}\,({\it{opcode\/}}, {\it{address-space\/}})\index{tm-execute-nullary}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-nullary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-unary \\ \index{good-address-space-tm-execute-u!nary}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,(\=\+{\rm{tm-execute-unary}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{address-space\/}})\index{tm-execute-unary}, \\ 
{\it{memlength\/}})\-\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-unary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-binary \\ \index{good-address-space-tm-execute-bi!nary}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,(\=\+{\rm{tm-execute-binary}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{address-space\/}})\index{tm-execute-binary}, \\ 
{\it{memlength\/}})\-\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-binary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute-instruction \\ \index{good-address-space-tm-execute-i!nstruction}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,(\=\+{\rm{tm-execute-instruction}}\,({\it{instruction\/}}, {\it{address-space\/}})\index{tm-execute-instruction}, \\ 
{\it{memlength\/}})\-\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute-instruction.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-execute \\ \index{good-address-space-tm-execute}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-execute}}\,({\it{instruction\/}}, {\it{address-space\/}})\index{tm-execute}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-decrement-clock \\ \index{good-address-space-tm-decrement!-clock}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-decrement-clock}}\,({\it{address-space\/}})\index{tm-decrement-clock}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-decrement-clock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-tm-fetch-execute \\ \index{good-address-space-tm-fetch-exe!cute}
\=\+{\rm{good-address-space}}\,({\it{address-space\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{tm-fetch-execute}}\,({\it{address-space\/}})\index{tm-fetch-execute}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-tm-fetch-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{mapup-address-space} \\  
\=\+{\rm{mapup-address-space}}\,({\it{memory\/}}, {\it{regs\/}}, {\it{cc\/}}, {\it{error\/}}, {\it{svcflag\/}}, {\it{svcid\/}}, {\it{base\/}}, {\it{limit\/}})\index{mapup-address-space} \\ 
$=$$\;\;\;\;${\rm{tm}}\,(\=\+{\rm{getseg}}\,({\it{base\/}}, {\it{limit\/}}, {\it{memory\/}})\index{getseg}, \\ 
{\it{regs\/}}, \\ 
{\it{cc\/}}, \\ 
{\it{error\/}}, \\ 
{\it{svcflag\/}}, \\ 
{\it{svcid\/}}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{fix}}\,({\it{limit\/}}), \\ 
{\tt{'}}{\tt{0}}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\tt{'}}{\tt{0}})\-\index{tm}\-
\end{tabbing}

%\item 
\begin{verbatim}


(PROVE-LEMMA GOOD-ADDRESS-SPACE-MAPUP-ADDRESS-SPACE
 (REWRITE)
 (IMPLIES
  (AND
     (FINITE-NUMBER-LISTP MEMORY '65536)
     (AND (NUMBERP LIMIT)
          (AND (IF (LESSP '65536 (LENGTH MEMORY))
                   '*1*FALSE
                   '*1*TRUE)
               (AND (PLISTP REGS)
                    (AND (FINITE-NUMBER-LISTP REGS '65536)
                         (AND (EQUAL (LENGTH REGS) '8)
                              (AND (FINITE-NUMBERP CC '4)
                                   (AND (FINITE-NUMBERP ERROR '64)
                                        (AND (FINITE-NUMBERP SVCFLAG '2)
                                             (AND (FINITE-NUMBERP SVCID '128)
                                                  (IF (LESSP (LENGTH MEMORY)
                                                             (PLUS BASE LIMIT))
                                                      '*1*FALSE
                                                      '*1*TRUE)))))))))))
  (GOOD-ADDRESS-SPACE (MAPUP-ADDRESS-SPACE MEMORY REGS CC ERROR SVCFLAG SVCID
                                           BASE LIMIT)
                      LIMIT))
 ((ENABLE GOOD-ADDRESS-SPACE MAPUP-ADDRESS-SPACE PLISTP-GETSEG LENGTH-GETSEG
          FINITE-NUMBER-LISTP-GETSEG)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable good-address-space-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-fetch-from-memory-mapup-address-space \\ \index{tm-fetch-from-memory-mapup-addre!ss-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) $\wedge$ ({\it{addr\/}} $<$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-fetch-from-memory}}\,(\=\+{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-fetch-from-memory} \\ 
$=$$\;\;\;\;${\rm{tm-fetch-from-memory}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch-from-memory})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-fetch-from-memory-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-fetch-from-regmem-mapup-address-space \\ \index{tm-fetch-from-regmem-mapup-addre!ss-space}
\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-fetch-from-regmem}}\,(\=\+{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-fetch-from-regmem} \\ 
$=$$\;\;\;\;${\rm{tm-fetch-from-regmem}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch-from-regmem})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-fetch-from-regmem-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-good-memory-address-limit \\ \index{lessp-good-memory-address-limit}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} $\not=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{real-addr-num}}\,({\it{addr\/}})\index{real-addr-num} $<$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tm-fetch-mapup-address-space \\ \index{tm-fetch-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-fetch}}\,(\=\+{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-fetch} \\ 
$=$$\;\;\;\;${\rm{tm-fetch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-fetch})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-fetch-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-store-in-memory-commutes-with-mapup-address-space \\ \index{tm-store-in-memory-commutes-wit!h-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$({\it{addr\/}} $<$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-store-in-memory}}\,(\=\+{\it{value\/}}, \\ 
{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-store-in-memory} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-store-in-memory}}\,(\=\+{\it{value\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-store-in-memory})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-store-in-memory}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store-in-memory})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-store-in-memory}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store-in-memory})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-store-in-memory}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store-in-memory})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-store-in-memory}}\,(\=\+{\it{value\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-store-in-memory})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-store-in-memory}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store-in-memory})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-store-in-memory}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store-in-memory})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-store-in-memory}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store-in-memory})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-store-in-memory-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-store-in-regmem-commutes-with-mapup-address-space \\ \index{tm-store-in-regmem-commutes-wit!h-mapup-address-space}
\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-store-in-regmem}}\,(\=\+{\it{value\/}}, \\ 
{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-store-in-regmem} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-store-in-regmem}}\,(\=\+{\it{value\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-store-in-regmem})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-store-in-regmem}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store-in-regmem})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-store-in-regmem}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store-in-regmem})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-store-in-regmem}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store-in-regmem})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-store-in-regmem}}\,(\=\+{\it{value\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-store-in-regmem})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-store-in-regmem}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store-in-regmem})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-store-in-regmem}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store-in-regmem})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-store-in-regmem}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store-in-regmem})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-store-in-regmem-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-store-commutes-with-mapup-address-space \\ \index{tm-store-commutes-with-mapup-ad!dress-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-store}}\,(\=\+{\it{value\/}}, \\ 
{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-store} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-store})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-store-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-set-pc-commutes-with-mapup-address-space \\ \index{tm-set-pc-commutes-with-mapup-a!ddress-space}
\=\+{\rm{tm-set-pc}}\,(\=\+{\it{pc\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-set-pc} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-set-pc}}\,({\it{pc\/}}, {\it{tm\/}})\index{tm-set-pc})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-set-pc}}\,({\it{pc\/}}, {\it{tm\/}})\index{tm-set-pc})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-set-pc}}\,({\it{pc\/}}, {\it{tm\/}})\index{tm-set-pc})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-set-pc}}\,({\it{pc\/}}, {\it{tm\/}})\index{tm-set-pc})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-set-pc}}\,({\it{pc\/}}, {\it{tm\/}})\index{tm-set-pc})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-set-pc}}\,({\it{pc\/}}, {\it{tm\/}})\index{tm-set-pc})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-set-pc}}\,({\it{pc\/}}, {\it{tm\/}})\index{tm-set-pc})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-set-pc}}\,({\it{pc\/}}, {\it{tm\/}})\index{tm-set-pc})\index{tm-limit})\-\index{mapup-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-set-pc-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-set-sp-commutes-with-mapup-address-space \\ \index{tm-set-sp-commutes-with-mapup-a!ddress-space}
\=\+{\rm{tm-set-sp}}\,(\=\+{\it{sp\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-set-sp} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-set-sp}}\,({\it{sp\/}}, {\it{tm\/}})\index{tm-set-sp})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-set-sp}}\,({\it{sp\/}}, {\it{tm\/}})\index{tm-set-sp})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-set-sp}}\,({\it{sp\/}}, {\it{tm\/}})\index{tm-set-sp})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-set-sp}}\,({\it{sp\/}}, {\it{tm\/}})\index{tm-set-sp})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-set-sp}}\,({\it{sp\/}}, {\it{tm\/}})\index{tm-set-sp})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-set-sp}}\,({\it{sp\/}}, {\it{tm\/}})\index{tm-set-sp})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-set-sp}}\,({\it{sp\/}}, {\it{tm\/}})\index{tm-set-sp})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-set-sp}}\,({\it{sp\/}}, {\it{tm\/}})\index{tm-set-sp})\index{tm-limit})\-\index{mapup-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-set-sp-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-set-cc-commutes-with-mapup-address-space \\ \index{tm-set-cc-commutes-with-mapup-a!ddress-space}
\=\+{\rm{tm-set-cc}}\,(\=\+{\it{cc\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-set-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-set-cc}}\,({\it{cc\/}}, {\it{tm\/}})\index{tm-set-cc})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-set-cc}}\,({\it{cc\/}}, {\it{tm\/}})\index{tm-set-cc})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-set-cc}}\,({\it{cc\/}}, {\it{tm\/}})\index{tm-set-cc})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-set-cc}}\,({\it{cc\/}}, {\it{tm\/}})\index{tm-set-cc})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-set-cc}}\,({\it{cc\/}}, {\it{tm\/}})\index{tm-set-cc})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-set-cc}}\,({\it{cc\/}}, {\it{tm\/}})\index{tm-set-cc})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-set-cc}}\,({\it{cc\/}}, {\it{tm\/}})\index{tm-set-cc})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-set-cc}}\,({\it{cc\/}}, {\it{tm\/}})\index{tm-set-cc})\index{tm-limit})\-\index{mapup-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-set-cc-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-set-error-commutes-with-mapup-address-space \\ \index{tm-set-error-commutes-with-mapup!-address-space}
\=\+{\rm{tm-set-error}}\,(\=\+{\it{error\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-set-error} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-set-error}}\,({\it{error\/}}, {\it{tm\/}})\index{tm-set-error})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-set-error}}\,({\it{error\/}}, {\it{tm\/}})\index{tm-set-error})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-set-error}}\,({\it{error\/}}, {\it{tm\/}})\index{tm-set-error})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-set-error}}\,({\it{error\/}}, {\it{tm\/}})\index{tm-set-error})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-set-error}}\,({\it{error\/}}, {\it{tm\/}})\index{tm-set-error})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-set-error}}\,({\it{error\/}}, {\it{tm\/}})\index{tm-set-error})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-set-error}}\,({\it{error\/}}, {\it{tm\/}})\index{tm-set-error})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-set-error}}\,({\it{error\/}}, {\it{tm\/}})\index{tm-set-error})\index{tm-limit})\-\index{mapup-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-set-error-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-set-svcflag-commutes-with-mapup-address-space \\ \index{tm-set-svcflag-commutes-with-map!up-address-space}
\=\+{\rm{tm-set-svcflag}}\,(\=\+{\it{svcflag\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-set-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-set-svcflag}}\,({\it{svcflag\/}}, {\it{tm\/}})\index{tm-set-svcflag})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-set-svcflag}}\,({\it{svcflag\/}}, {\it{tm\/}})\index{tm-set-svcflag})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-set-svcflag}}\,({\it{svcflag\/}}, {\it{tm\/}})\index{tm-set-svcflag})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-set-svcflag}}\,({\it{svcflag\/}}, {\it{tm\/}})\index{tm-set-svcflag})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-set-svcflag}}\,({\it{svcflag\/}}, {\it{tm\/}})\index{tm-set-svcflag})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-set-svcflag}}\,({\it{svcflag\/}}, {\it{tm\/}})\index{tm-set-svcflag})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-set-svcflag}}\,({\it{svcflag\/}}, {\it{tm\/}})\index{tm-set-svcflag})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-set-svcflag}}\,({\it{svcflag\/}}, {\it{tm\/}})\index{tm-set-svcflag})\index{tm-limit})\-\index{mapup-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-set-svcflag-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-set-svcid-commutes-with-mapup-address-space \\ \index{tm-set-svcid-commutes-with-mapup!-address-space}
\=\+{\rm{tm-set-svcid}}\,(\=\+{\it{svcid\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-set-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-set-svcid}}\,({\it{svcid\/}}, {\it{tm\/}})\index{tm-set-svcid})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-set-svcid}}\,({\it{svcid\/}}, {\it{tm\/}})\index{tm-set-svcid})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-set-svcid}}\,({\it{svcid\/}}, {\it{tm\/}})\index{tm-set-svcid})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-set-svcid}}\,({\it{svcid\/}}, {\it{tm\/}})\index{tm-set-svcid})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-set-svcid}}\,({\it{svcid\/}}, {\it{tm\/}})\index{tm-set-svcid})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-set-svcid}}\,({\it{svcid\/}}, {\it{tm\/}})\index{tm-set-svcid})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-set-svcid}}\,({\it{svcid\/}}, {\it{tm\/}})\index{tm-set-svcid})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-set-svcid}}\,({\it{svcid\/}}, {\it{tm\/}})\index{tm-set-svcid})\index{tm-limit})\-\index{mapup-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-set-svcid-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-in-supervisor-mode-tm-set-cc \\ \index{tm-in-supervisor-mode-tm-set-cc}
{\rm{tm-in-supervisor-mode}}\,({\rm{tm-set-cc}}\,({\it{cc\/}}, {\it{tm\/}})\index{tm-set-cc})\index{tm-in-supervisor-mode} $=$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-in-supervisor-mode-tm-set-cc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-in-supervisor-mode-tm-set-svcflag \\ \index{tm-in-supervisor-mode-tm-set-sv!cflag}
\=\+{\rm{tm-in-supervisor-mode}}\,({\rm{tm-set-svcflag}}\,({\it{svcflag\/}}, {\it{tm\/}})\index{tm-set-svcflag})\index{tm-in-supervisor-mode} \\ 
$=$$\;\;\;\;${\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-in-supervisor-mode-tm-set-svcflag.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-in-supervisor-mode-tm-set-svcid \\ \index{tm-in-supervisor-mode-tm-set-sv!cid}
{\rm{tm-in-supervisor-mode}}\,({\rm{tm-set-svcid}}\,({\it{svcid\/}}, {\it{tm\/}})\index{tm-set-svcid})\index{tm-in-supervisor-mode} $=$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-in-supervisor-mode-tm-set-svcid.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-in-supervisor-mode-tm-set-sp \\ \index{tm-in-supervisor-mode-tm-set-sp}
{\rm{tm-in-supervisor-mode}}\,({\rm{tm-set-sp}}\,({\it{sp\/}}, {\it{tm\/}})\index{tm-set-sp})\index{tm-in-supervisor-mode} $=$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-in-supervisor-mode-tm-set-sp.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-in-supervisor-mode-tm-set-pc \\ \index{tm-in-supervisor-mode-tm-set-pc}
{\rm{tm-in-supervisor-mode}}\,({\rm{tm-set-pc}}\,({\it{pc\/}}, {\it{tm\/}})\index{tm-set-pc})\index{tm-in-supervisor-mode} $=$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-in-supervisor-mode-tm-set-pc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-mapup-address-space \\ \index{tm-limit-mapup-address-space}
\=\+{\rm{tm-limit}}\,({\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{fix}}\,({\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-mapup-address-space \\ \index{tm-base-mapup-address-space}
\=\+{\rm{tm-base}}\,({\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\index{tm-base} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{0}}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plus-tm-base-tm-limit-tm-set-cc \\ \index{plus-tm-base-tm-limit-tm-set-cc}
\=\+({\rm{tm-base}}\,({\rm{tm-set-cc}}\,({\it{cc\/}}, {\it{tm\/}})\index{tm-set-cc})\index{tm-base} $+$ {\rm{tm-limit}}\,({\rm{tm-set-cc}}\,({\it{cc\/}}, {\it{tm\/}})\index{tm-set-cc})\index{tm-limit}) \\ 
$=$$\;\;\;\;$({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-
\end{tabbing}


\noindent{\sc Event}:   Disable plus-tm-base-tm-limit-tm-set-cc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plus-tm-base-tm-limit-tm-set-sp \\ \index{plus-tm-base-tm-limit-tm-set-sp}
\=\+({\rm{tm-base}}\,({\rm{tm-set-sp}}\,({\it{sp\/}}, {\it{tm\/}})\index{tm-set-sp})\index{tm-base} $+$ {\rm{tm-limit}}\,({\rm{tm-set-sp}}\,({\it{sp\/}}, {\it{tm\/}})\index{tm-set-sp})\index{tm-limit}) \\ 
$=$$\;\;\;\;$({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-
\end{tabbing}


\noindent{\sc Event}:   Disable plus-tm-base-tm-limit-tm-set-sp.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-add-commutes-with-mapup-address-space \\ \index{tm-execute-add-commutes-with-map!up-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-good-address})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-add}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-add} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-add}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-add})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-add}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-add})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-add}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-add})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-add}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-add})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-add}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-add})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-add}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-add})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-add}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-add})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-add}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-add})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-add-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-branch-commutes-with-mapup-address-space \\ \index{tm-execute-branch-commutes-with!-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-branch}}\,(\=\+{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-branch} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-branch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-branch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-branch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-branch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-branch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-branch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-branch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-branch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-branch-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cc-mapup-address-space \\ \index{tm-cc-mapup-address-space}
\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cc}}\,({\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\index{tm-cc} \\ 
$=$$\;\;\;\;${\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cc-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-error-mapup-address-space \\ \index{tm-error-mapup-address-space}
\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-error}}\,({\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\index{tm-error} \\ 
$=$$\;\;\;\;${\rm{tm-error}}\,({\it{tm\/}})\index{tm-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-error-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-svcflag-mapup-address-space \\ \index{tm-svcflag-mapup-address-space}
\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-svcflag}}\,({\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\index{tm-svcflag} \\ 
$=$$\;\;\;\;${\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-svcflag-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-svcid-mapup-address-space \\ \index{tm-svcid-mapup-address-space}
\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-svcid}}\,({\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\index{tm-svcid} \\ 
$=$$\;\;\;\;${\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-svcid-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-pc-mapup-address-space \\ \index{tm-pc-mapup-address-space}
\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-pc}}\,({\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\index{tm-pc} \\ 
$=$$\;\;\;\;${\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-pc-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-sp-mapup-address-space \\ \index{tm-sp-mapup-address-space}
\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-sp}}\,({\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\index{tm-sp} \\ 
$=$$\;\;\;\;${\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-sp-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-branch-on-zero-commutes-with-mapup-address-space \\ \index{tm-execute-branch-on-zero-commute!s-with-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-branch-on-zero}}\,(\=\+{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-branch-on-zero} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-branch-on-zero}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-branch-on-zero})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-branch-on-zero}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch-on-zero})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-branch-on-zero}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch-on-zero})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-branch-on-zero}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-branch-on-zero})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-branch-on-zero}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-branch-on-zero})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-branch-on-zero}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-branch-on-zero})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-branch-on-zero}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch-on-zero})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-branch-on-zero}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-branch-on-zero})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-branch-on-zero-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-branch-not-zero-commutes-with-mapup-address-space \\ \index{tm-execute-branch-not-zero-comm!utes-with-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-branch-not-zero}}\,(\=\+{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-branch-not-zero} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-branch-not-zero}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-branch-not-zero})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-branch-not-zero}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-branch-not-zero})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-branch-not-zero}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch-not-zero})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-branch-not-zero}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-branch-not-zero})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-branch-not-zero}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-branch-not-zero})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-branch-not-zero}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-branch-not-zero})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-branch-not-zero}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-branch-not-zero})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-branch-not-zero}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-branch-not-zero})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-branch-not-zero-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-stack-overflowp-mapup-address-space \\ \index{tm-stack-overflowp-mapup-addres!s-space}
\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-stack-overflowp}}\,({\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\index{tm-stack-overflowp} \\ 
$=$$\;\;\;\;${\rm{tm-stack-overflowp}}\,({\it{tm\/}})\index{tm-stack-overflowp})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-stack-overflowp-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-good-address-mapup-address-space \\ \index{tm-good-address-mapup-address-sp!ace}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,(\=\+{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-good-address} \\ 
$=$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-good-address-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-call-commutes-with-mapup-address-space \\ \index{tm-execute-call-commutes-with-m!apup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-call}}\,(\=\+{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-call} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-call})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-call})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-call})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-call})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-call})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-call})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-call})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-call})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-call-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-compare-commutes-with-mapup-address-space \\ \index{tm-execute-compare-commutes-wit!h-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$({\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address} $\wedge$ {\rm{tm-good-address}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-good-address}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-compare}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-compare} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-compare}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-compare})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-compare}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-compare})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-compare}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-compare})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-compare}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-compare})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-compare}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-compare})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-compare}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-compare})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-compare}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-compare})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-compare}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-compare})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-compare-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-decr-commutes-with-mapup-address-space \\ \index{tm-execute-decr-commutes-with-m!apup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-decr}}\,(\=\+{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-decr} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-decr})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-decr})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-decr})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-decr})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-decr})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-decr})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-decr})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-decr})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-decr-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-decr-mod-commutes-with-mapup-address-space \\ \index{tm-execute-decr-mod-commutes-wit!h-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-good-address})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-decr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-decr-mod} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-decr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-decr-mod})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-decr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-decr-mod})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-decr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-decr-mod})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-decr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-decr-mod})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-decr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-decr-mod})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-decr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-decr-mod})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-decr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-decr-mod})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-decr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-decr-mod})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-decr-mod-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-incr-commutes-with-mapup-address-space \\ \index{tm-execute-incr-commutes-with-m!apup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-incr}}\,(\=\+{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-incr} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-incr})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-incr})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-incr})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-incr})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-incr})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-incr})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-incr})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-incr})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-incr-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-incr-mod-commutes-with-mapup-address-space \\ \index{tm-execute-incr-mod-commutes-wit!h-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-good-address})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-incr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-incr-mod} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-incr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-incr-mod})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-incr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-incr-mod})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-incr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-incr-mod})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-incr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-incr-mod})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-incr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-incr-mod})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-incr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-incr-mod})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-incr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-incr-mod})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-incr-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-incr-mod})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-incr-mod-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-in-supervisor-mode-mapup-address-space \\ \index{tm-in-supervisor-mode-mapup-add!ress-space}
\=\+{\rm{tm-in-supervisor-mode}}\,({\rm{mapup-address-space}}\,(\=\+{\it{memory\/}}, \\ 
{\it{regs\/}}, \\ 
{\it{cc\/}}, \\ 
{\it{error\/}}, \\ 
{\it{svcflag\/}}, \\ 
{\it{svcid\/}}, \\ 
{\it{base\/}}, \\ 
{\it{limit\/}})\-\index{mapup-address-space})\index{tm-in-supervisor-mode} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*false}}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-in-supervisor-mode-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-load-base-commutes-with-mapup-address-space \\ \index{tm-execute-load-base-commutes-wit!h-mapup-address-space}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-load-base}}\,(\=\+{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-load-base} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-load-base}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-base})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-load-base}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-base})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-load-base}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-base})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-load-base}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-base})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-load-base}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-base})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-load-base}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-base})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-load-base}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-base})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-load-base}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-base})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-load-base-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-load-limit-commutes-with-mapup-address-space \\ \index{tm-execute-load-limit-commutes-!with-mapup-address-space}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-load-limit}}\,(\=\+{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-load-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-load-limit}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-limit})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-load-limit}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-limit})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-load-limit}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-limit})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-load-limit}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-limit})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-load-limit}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-limit})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-load-limit}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-limit})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-load-limit}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-limit})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-load-limit}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-limit})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-load-limit-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-load-psw-commutes-with-mapup-address-space \\ \index{tm-execute-load-psw-commutes-wit!h-mapup-address-space}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-load-psw}}\,(\=\+{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-load-psw} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-load-psw}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-psw})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-load-psw}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-psw})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-load-psw}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-psw})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-load-psw}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-psw})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-load-psw}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-psw})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-load-psw}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-psw})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-load-psw}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-psw})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-load-psw}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-psw})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-load-psw-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-mod-commutes-with-mapup-address-space \\ \index{tm-execute-mod-commutes-with-map!up-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-good-address})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-mod}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-mod} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-mod})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-mod})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-mod})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-mod})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-mod})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-mod})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-mod})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-mod})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-mod-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-move-commutes-with-mapup-address-space \\ \index{tm-execute-move-commutes-with-m!apup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-good-address})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-move}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-move} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-move}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-move})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-move}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-move})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-move}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-move})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-move}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-move})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-move}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-move})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-move}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-move})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-move}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-move})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-move}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-move})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-move-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-multiply-commutes-with-mapup-address-space \\ \index{tm-execute-multiply-commutes-wit!h-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-good-address})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-multiply}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-multiply} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-multiply}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-multiply})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-multiply}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-multiply})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-multiply}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-multiply})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-multiply}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-multiply})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-multiply}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-multiply})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-multiply}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-multiply})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-multiply}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-multiply})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-multiply}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-multiply})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-multiply-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-stack-underflowp-mapup-address-space \\ \index{tm-stack-underflowp-mapup-addre!ss-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-stack-underflowp}}\,({\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\index{tm-stack-underflowp} \\ 
$=$$\;\;\;\;${\rm{tm-stack-underflowp}}\,({\it{tm\/}})\index{tm-stack-underflowp})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-stack-underflowp-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-return-commutes-with-mapup-address-space \\ \index{tm-execute-return-commutes-with!-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-return}}\,({\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\index{tm-execute-return} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-return-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-set-clock-commutes-with-mapup-address-space \\ \index{tm-execute-set-clock-commutes-wit!h-mapup-address-space}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-set-clock}}\,(\=\+{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-set-clock} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-set-clock}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-set-clock})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-set-clock}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-set-clock})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-set-clock}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-set-clock})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-set-clock}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-set-clock})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-set-clock}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-set-clock})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-set-clock}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-set-clock})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-set-clock}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-set-clock})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-set-clock}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-set-clock})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-set-clock-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-run-commutes-with-mapup-address-space \\ \index{tm-execute-run-commutes-with-map!up-address-space}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-run}}\,({\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\index{tm-execute-run} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-run}}\,({\it{tm\/}})\index{tm-execute-run})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-run}}\,({\it{tm\/}})\index{tm-execute-run})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-run}}\,({\it{tm\/}})\index{tm-execute-run})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-run}}\,({\it{tm\/}})\index{tm-execute-run})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-run}}\,({\it{tm\/}})\index{tm-execute-run})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-run}}\,({\it{tm\/}})\index{tm-execute-run})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-run}}\,({\it{tm\/}})\index{tm-execute-run})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-run}}\,({\it{tm\/}})\index{tm-execute-run})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-run-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-wait-commutes-with-mapup-address-space \\ \index{tm-execute-wait-commutes-with-m!apup-address-space}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-wait}}\,({\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\index{tm-execute-wait} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-wait}}\,({\it{tm\/}})\index{tm-execute-wait})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-wait}}\,({\it{tm\/}})\index{tm-execute-wait})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-wait}}\,({\it{tm\/}})\index{tm-execute-wait})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-wait}}\,({\it{tm\/}})\index{tm-execute-wait})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-wait}}\,({\it{tm\/}})\index{tm-execute-wait})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-wait}}\,({\it{tm\/}})\index{tm-execute-wait})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-wait}}\,({\it{tm\/}})\index{tm-execute-wait})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-wait}}\,({\it{tm\/}})\index{tm-execute-wait})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-wait-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-test-iport-commutes-with-mapup-address-space \\ \index{tm-execute-test-iport-commutes-!with-mapup-address-space}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-test-iport}}\,(\=\+{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-test-iport} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-test-iport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-iport})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-test-iport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-iport})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-test-iport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-iport})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-test-iport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-iport})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-test-iport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-iport})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-test-iport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-iport})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-test-iport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-iport})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-test-iport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-iport})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-test-iport-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-test-oport-commutes-with-mapup-address-space \\ \index{tm-execute-test-oport-commutes-!with-mapup-address-space}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-test-oport}}\,(\=\+{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-test-oport} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-test-oport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-oport})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-test-oport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-oport})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-test-oport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-oport})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-test-oport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-oport})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-test-oport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-oport})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-test-oport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-oport})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-test-oport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-oport})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-test-oport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-oport})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-test-oport-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-start-output-commutes-with-mapup-address-space \\ \index{tm-execute-start-output-commute!s-with-mapup-address-space}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-start-output}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-start-output} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-start-output}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-start-output})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-start-output}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-start-output})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-start-output}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-start-output})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-start-output}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-start-output})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-start-output}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-start-output})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-start-output}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-start-output})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-start-output}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-start-output})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-start-output}}\,(\=\+{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-start-output})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-start-output-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-post-output-interrupt-commutes-with-mapup-address-space \\ \index{tm-execute-post-output-interrupt!-commutes-with-mapup-address-space}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-post-output-interrupt}}\,(\=\+{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-post-output-interrupt} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-post-output-interrupt}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-post-output-interrupt})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-post-output-interrupt}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-post-output-interrupt})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-post-output-interrupt}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-post-output-interrupt})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-post-output-interrupt}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-post-output-interrupt})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-post-output-interrupt}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-post-output-interrupt})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-post-output-interrupt}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-post-output-interrupt})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-post-output-interrupt}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-post-output-interrupt})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-post-output-interrupt}}\,(\=\+{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-post-output-interrupt})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-post-output-interrupt-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-svc-commutes-with-mapup-address-space \\ \index{tm-execute-svc-commutes-with-map!up-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-svc}}\,(\=\+{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-svc} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-svc}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-svc}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-svc}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-svc}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-svc}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-svc}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-svc}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-svc}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-svc-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-svc-return-commutes-with-mapup-address-space \\ \index{tm-execute-svc-return-commutes-!with-mapup-address-space}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-svc-return}}\,(\=\+{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-svc-return} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-svc-return}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc-return})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-svc-return}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc-return})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-svc-return}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc-return})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-svc-return}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc-return})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-svc-return}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc-return})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-svc-return}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc-return})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-svc-return}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc-return})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-svc-return}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc-return})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-svc-return-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tm-execute-nullary2} \\  
\=\+{\rm{tm-execute-nullary2}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary2} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{opcode\/}} $=$ {\tt{'}}{\tt{8}}$\;\;${\bf then }{\rm{tm-execute-run}}\,({\it{tm\/}})\index{tm-execute-run} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{4}}$\;\;${\bf then }{\rm{tm-execute-wait}}\,({\it{tm\/}})\index{tm-execute-wait} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{2}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-nullary1} \\  
\=\+{\rm{tm-execute-nullary1}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary1} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{opcode\/}} $=$ {\tt{'}}{\tt{0}}$\;\;${\bf then }{\rm{tm-execute-return}}\,({\it{tm\/}})\index{tm-execute-return} \\ 
{\bf else }{\rm{tm-execute-nullary2}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary2}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tm-execute-nullary1-equals-tm-execute-nullary \\ \index{tm-execute-nullary1-equals-tm-e!xecute-nullary}
{\rm{tm-execute-nullary1}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary1} $=$ {\rm{tm-execute-nullary}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-nullary1-equals-tm-execute-nullary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-nullary2-commutes-with-mapup-address-space \\ \index{tm-execute-nullary2-commutes-wit!h-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-nullary2}}\,(\=\+{\it{opcode\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-nullary2} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-nullary2}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary2})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-nullary2}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary2})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-nullary2}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary2})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-nullary2}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary2})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-nullary2}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary2})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-nullary2}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary2})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-nullary2}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary2})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-nullary2}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary2})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-nullary2-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-nullary1-commutes-with-mapup-address-space \\ \index{tm-execute-nullary1-commutes-wit!h-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-nullary1}}\,(\=\+{\it{opcode\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-nullary1} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-nullary1}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary1})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-nullary1}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary1})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-nullary1}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary1})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-nullary1}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary1})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-nullary1}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary1})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-nullary1}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary1})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-nullary1}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary1})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-nullary1}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary1})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-nullary1-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-nullary-commutes-with-mapup-address-space \\ \index{tm-execute-nullary-commutes-wit!h-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-nullary}}\,(\=\+{\it{opcode\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-nullary} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-nullary}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-nullary}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-nullary}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-nullary}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-nullary}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-nullary}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-nullary}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-nullary}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute-nullary})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-nullary-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tm-execute-unary8} \\  
\=\+{\rm{tm-execute-unary8}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary8} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{opcode\/}} $=$ {\tt{'}}{\tt{50}}$\;\;${\bf then }{\rm{tm-execute-test-iport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-iport} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{54}}$\;\;${\bf then }{\rm{tm-execute-test-oport}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-test-oport} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{2}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-unary7} \\  
\=\+{\rm{tm-execute-unary7}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary7} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{opcode\/}} $=$ {\tt{'}}{\tt{46}}$\;\;${\bf then }{\rm{tm-execute-svc-return}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc-return} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{38}}$\;\;${\bf then }{\rm{tm-execute-post-output-interrupt}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-post-output-interrupt} \\ 
{\bf else }{\rm{tm-execute-unary8}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary8}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-unary6} \\  
\=\+{\rm{tm-execute-unary6}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary6} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{opcode\/}} $=$ {\tt{'}}{\tt{58}}$\;\;${\bf then }{\rm{tm-execute-set-clock}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-set-clock} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{42}}$\;\;${\bf then }{\rm{tm-execute-svc}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-svc} \\ 
{\bf else }{\rm{tm-execute-unary7}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary7}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-unary5} \\  
\=\+{\rm{tm-execute-unary5}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary5} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{opcode\/}} $=$ {\tt{'}}{\tt{30}}$\;\;${\bf then }{\rm{tm-execute-load-limit}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-limit} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{34}}$\;\;${\bf then }{\rm{tm-execute-load-psw}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-psw} \\ 
{\bf else }{\rm{tm-execute-unary6}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary6}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-unary4} \\  
\=\+{\rm{tm-execute-unary4}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary4} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{opcode\/}} $=$ {\tt{'}}{\tt{22}}$\;\;${\bf then }{\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-incr} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{26}}$\;\;${\bf then }{\rm{tm-execute-load-base}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-load-base} \\ 
{\bf else }{\rm{tm-execute-unary5}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary5}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-unary3} \\  
\=\+{\rm{tm-execute-unary3}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary3} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{opcode\/}} $=$ {\tt{'}}{\tt{6}}$\;\;${\bf then }{\rm{tm-execute-branch-not-zero}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch-not-zero} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{18}}$\;\;${\bf then }{\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-decr} \\ 
{\bf else }{\rm{tm-execute-unary4}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary4}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-unary2} \\  
\=\+{\rm{tm-execute-unary2}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary2} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{opcode\/}} $=$ {\tt{'}}{\tt{10}}$\;\;${\bf then }{\rm{tm-execute-branch-on-zero}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch-on-zero} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{14}}$\;\;${\bf then }{\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-call} \\ 
{\bf else }{\rm{tm-execute-unary3}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary3}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-unary1} \\  
\=\+{\rm{tm-execute-unary1}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary1} \\ 
$=$$\;\;\;\;$\=\+{\bf if }$\neg$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address}$\;\;${\bf then }{\rm{tm-set-error}}\,({\tt{'}}{\tt{6}}, {\it{tm\/}})\index{tm-set-error} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{2}}$\;\;${\bf then }{\rm{tm-execute-branch}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-execute-branch} \\ 
{\bf else }{\rm{tm-execute-unary2}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary2}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tm-execute-unary1-equals-tm-execute-unary \\ \index{tm-execute-unary1-equals-tm-exe!cute-unary}
{\rm{tm-execute-unary1}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary1} $=$ {\rm{tm-execute-unary}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-unary1-equals-tm-execute-unary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-unary8-commutes-with-mapup-address-space \\ \index{tm-execute-unary8-commutes-with!-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-unary8}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-unary8} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-unary8}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary8})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-unary8}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary8})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-unary8}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary8})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-unary8}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary8})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-unary8}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary8})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-unary8}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary8})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-unary8}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary8})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-unary8}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary8})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-unary8-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-unary7-commutes-with-mapup-address-space \\ \index{tm-execute-unary7-commutes-with!-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-unary7}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-unary7} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-unary7}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary7})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-unary7}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary7})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-unary7}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary7})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-unary7}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary7})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-unary7}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary7})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-unary7}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary7})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-unary7}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary7})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-unary7}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary7})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-unary7-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-unary6-commutes-with-mapup-address-space \\ \index{tm-execute-unary6-commutes-with!-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-unary6}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-unary6} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-unary6}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary6})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-unary6}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary6})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-unary6}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary6})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-unary6}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary6})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-unary6}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary6})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-unary6}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary6})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-unary6}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary6})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-unary6}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary6})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-unary6-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-unary5-commutes-with-mapup-address-space \\ \index{tm-execute-unary5-commutes-with!-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-unary5}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-unary5} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-unary5}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary5})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-unary5}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary5})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-unary5}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary5})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-unary5}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary5})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-unary5}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary5})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-unary5}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary5})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-unary5}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary5})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-unary5}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary5})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-unary5-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-unary4-commutes-with-mapup-address-space \\ \index{tm-execute-unary4-commutes-with!-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-unary4}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-unary4} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-unary4}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary4})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-unary4}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary4})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-unary4}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary4})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-unary4}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary4})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-unary4}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary4})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-unary4}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary4})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-unary4}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary4})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-unary4}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary4})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-unary4-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-unary3-commutes-with-mapup-address-space \\ \index{tm-execute-unary3-commutes-with!-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-unary3}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-unary3} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-unary3}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary3})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-unary3}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary3})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-unary3}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary3})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-unary3}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary3})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-unary3}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary3})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-unary3}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary3})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-unary3}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary3})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-unary3}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary3})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-unary3-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-unary2-commutes-with-mapup-address-space \\ \index{tm-execute-unary2-commutes-with!-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-unary2}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-unary2} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-unary2}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary2})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-unary2}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary2})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-unary2}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary2})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-unary2}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary2})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-unary2}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary2})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-unary2}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary2})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-unary2}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary2})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-unary2}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary2})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-unary2-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-unary1-commutes-with-mapup-address-space \\ \index{tm-execute-unary1-commutes-with!-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-unary1}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-unary1} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-unary1}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary1})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-unary1}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary1})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-unary1}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary1})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-unary1}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary1})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-unary1}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary1})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-unary1}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary1})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-unary1}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary1})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-unary1}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary1})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-unary1-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-unary-commutes-with-mapup-address-space \\ \index{tm-execute-unary-commutes-with-!mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-unary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-unary} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-unary}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-unary}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-unary}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-unary}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-unary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-unary}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-unary}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-unary}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{tm\/}})\index{tm-execute-unary})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-unary-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tm-execute-binary6} \\  
\=\+{\rm{tm-execute-binary6}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-binary6} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{opcode\/}} $=$ {\tt{'}}{\tt{7}}$\;\;${\bf then }{\rm{tm-execute-incr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-incr-mod} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{2}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-binary5} \\  
\=\+{\rm{tm-execute-binary5}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-binary5} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{opcode\/}} $=$ {\tt{'}}{\tt{15}}$\;\;${\bf then }{\rm{tm-execute-start-output}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-start-output} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{5}}$\;\;${\bf then }{\rm{tm-execute-decr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-decr-mod} \\ 
{\bf else }{\rm{tm-execute-binary6}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-binary6}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-binary4} \\  
\=\+{\rm{tm-execute-binary4}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-binary4} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{opcode\/}} $=$ {\tt{'}}{\tt{11}}$\;\;${\bf then }{\rm{tm-execute-move}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-move} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{13}}$\;\;${\bf then }{\rm{tm-execute-multiply}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-multiply} \\ 
{\bf else }{\rm{tm-execute-binary5}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-binary5}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-binary3} \\  
\=\+{\rm{tm-execute-binary3}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-binary3} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{opcode\/}} $=$ {\tt{'}}{\tt{3}}$\;\;${\bf then }{\rm{tm-execute-compare}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-compare} \\ 
{\bf elseif }{\it{opcode\/}} $=$ {\tt{'}}{\tt{9}}$\;\;${\bf then }{\rm{tm-execute-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-mod} \\ 
{\bf else }{\rm{tm-execute-binary4}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-binary4}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-binary2} \\  
\=\+{\rm{tm-execute-binary2}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-binary2} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{opcode\/}} $=$ {\tt{'}}{\tt{1}}$\;\;${\bf then }{\rm{tm-execute-add}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-add} \\ 
{\bf else }{\rm{tm-execute-binary3}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-binary3}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-binary1} \\  
\=\+{\rm{tm-execute-binary1}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-binary1} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+($\neg$ {\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address}) \\ 
$\vee$$\;\;\;\;$($\neg$ {\rm{tm-good-address}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-good-address})\-$\;\;${\bf then }{\rm{tm-set-error}}\,({\tt{'}}{\tt{6}}, {\it{tm\/}})\index{tm-set-error} \\ 
{\bf else }{\rm{tm-execute-binary2}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-binary2}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tm-execute-binary1-equals-tm-execute-binary \\ \index{tm-execute-binary1-equals-tm-exe!cute-binary}
\=\+{\rm{tm-execute-binary1}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-binary1} \\ 
$=$$\;\;\;\;${\rm{tm-execute-binary}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{tm\/}})\index{tm-execute-binary}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-binary1-equals-tm-execute-binary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-binary6-commutes-with-mapup-address-space \\ \index{tm-execute-binary6-commutes-wit!h-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-binary6}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-binary6} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-binary6}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary6})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-binary6}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary6})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-binary6}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary6})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-binary6}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary6})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-binary6}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary6})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-binary6}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary6})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-binary6}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary6})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-binary6}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary6})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-binary6-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-binary5-commutes-with-mapup-address-space \\ \index{tm-execute-binary5-commutes-wit!h-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-binary5}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-binary5} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-binary5}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary5})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-binary5}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary5})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-binary5}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary5})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-binary5}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary5})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-binary5}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary5})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-binary5}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary5})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-binary5}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary5})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-binary5}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary5})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-binary5-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-binary4-commutes-with-mapup-address-space \\ \index{tm-execute-binary4-commutes-wit!h-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-binary4}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-binary4} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-binary4}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary4})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-binary4}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary4})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-binary4}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary4})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-binary4}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary4})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-binary4}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary4})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-binary4}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary4})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-binary4}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary4})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-binary4}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary4})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-binary4-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-binary3-commutes-with-mapup-address-space \\ \index{tm-execute-binary3-commutes-wit!h-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-binary3}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-binary3} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-binary3}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary3})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-binary3}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary3})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-binary3}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary3})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-binary3}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary3})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-binary3}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary3})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-binary3}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary3})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-binary3}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary3})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-binary3}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary3})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-binary3-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-binary2-commutes-with-mapup-address-space \\ \index{tm-execute-binary2-commutes-wit!h-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr2\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-binary2}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-binary2} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-binary2}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary2})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-binary2}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary2})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-binary2}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary2})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-binary2}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary2})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-binary2}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary2})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-binary2}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary2})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-binary2}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary2})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-binary2}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary2})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-binary2-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-binary1-commutes-with-mapup-address-space \\ \index{tm-execute-binary1-commutes-wit!h-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-binary1}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-binary1} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-binary1}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary1})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-binary1}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary1})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-binary1}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary1})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-binary1}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary1})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-binary1}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary1})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-binary1}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary1})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-binary1}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary1})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-binary1}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary1})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-binary1-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-binary-commutes-with-mapup-address-space \\ \index{tm-execute-binary-commutes-with!-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-binary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-binary} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-binary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-binary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-binary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-binary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-binary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-binary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-binary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-binary}}\,(\=\+{\it{opcode\/}}, \\ 
{\it{addr1\/}}, \\ 
{\it{addr2\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-binary-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-compute-address-mapup-address-space \\ \index{tm-compute-address-mapup-addres!s-space}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-compute-address}}\,(\=\+{\it{arg\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-compute-address} \\ 
$=$$\;\;\;\;${\rm{tm-compute-address}}\,({\it{arg\/}}, {\it{tm\/}})\index{tm-compute-address})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-compute-address-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tm-execute-instruction2} \\  
\=\+{\rm{tm-execute-instruction2}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute-instruction2} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{instruction\/}})\index{length} $=$ {\tt{'}}{\tt{3}} \\ 
{\bf then }{\rm{tm-execute-binary}}\,(\=\+{\rm{tm-opcode}}\,({\rm{car}}\,({\it{instruction\/}}))\index{tm-opcode}, \\ 
{\rm{tm-compute-address}}\,({\rm{tm-arg1}}\,({\it{instruction\/}})\index{tm-arg1}, {\it{tm\/}})\index{tm-compute-address}, \\ 
{\rm{tm-compute-address}}\,({\rm{tm-arg2}}\,({\it{instruction\/}})\index{tm-arg2}, {\it{tm\/}})\index{tm-compute-address}, \\ 
{\it{tm\/}})\-\index{tm-execute-binary} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{2}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute-instruction1} \\  
\=\+{\rm{tm-execute-instruction1}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute-instruction1} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{instruction\/}})\index{length} $=$ {\tt{'}}{\tt{1}} \\ 
{\bf then }{\rm{tm-execute-nullary}}\,({\rm{tm-opcode}}\,({\rm{car}}\,({\it{instruction\/}}))\index{tm-opcode}, {\it{tm\/}})\index{tm-execute-nullary} \\ 
{\bf elseif }{\rm{length}}\,({\it{instruction\/}})\index{length} $=$ {\tt{'}}{\tt{2}} \\ 
{\bf then }{\rm{tm-execute-unary}}\,(\=\+{\rm{tm-opcode}}\,({\rm{car}}\,({\it{instruction\/}}))\index{tm-opcode}, \\ 
{\rm{tm-compute-address}}\,({\rm{tm-arg1}}\,({\it{instruction\/}})\index{tm-arg1}, {\it{tm\/}})\index{tm-compute-address}, \\ 
{\it{tm\/}})\-\index{tm-execute-unary} \\ 
{\bf else }{\rm{tm-execute-instruction2}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute-instruction2}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tm-execute-instruction1-equals-tm-execute-instruction \\ \index{tm-execute-instruction1-equals-t!m-execute-instruction}
\=\+{\rm{tm-execute-instruction1}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute-instruction1} \\ 
$=$$\;\;\;\;${\rm{tm-execute-instruction}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute-instruction}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-instruction1-equals-tm-execute-instruction.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-instruction2-commutes-with-mapup-address-space \\ \index{tm-execute-instruction2-commute!s-with-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-instruction2}}\,(\=\+{\it{instruction\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-instruction2} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-instruction2}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction2})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-instruction2}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction2})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-instruction2}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction2})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-instruction2}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction2})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-instruction2}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction2})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-instruction2}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction2})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-instruction2}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction2})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-instruction2}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction2})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-instruction2-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-instruction1-commutes-with-mapup-address-space \\ \index{tm-execute-instruction1-commute!s-with-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-instruction1}}\,(\=\+{\it{instruction\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-instruction1} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-instruction1}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction1})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-instruction1}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction1})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-instruction1}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction1})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-instruction1}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction1})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-instruction1}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction1})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-instruction1}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction1})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-instruction1}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction1})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-instruction1}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction1})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-instruction1-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-instruction-commutes-with-mapup-address-space \\ \index{tm-execute-instruction-commutes!-with-mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-instruction}}\,(\=\+{\it{instruction\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute-instruction} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute-instruction}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute-instruction}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute-instruction}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute-instruction}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute-instruction}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute-instruction}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute-instruction}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute-instruction}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{tm\/}})\-\index{tm-execute-instruction})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-instruction-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-decrement-clock-commutes-with-mapup-address-space \\ \index{tm-decrement-clock-commutes-wit!h-mapup-address-space}
\=\+({\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-decrement-clock}}\,({\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\index{tm-decrement-clock} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-decrement-clock}}\,({\it{tm\/}})\index{tm-decrement-clock})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-decrement-clock}}\,({\it{tm\/}})\index{tm-decrement-clock})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-decrement-clock}}\,({\it{tm\/}})\index{tm-decrement-clock})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-decrement-clock}}\,({\it{tm\/}})\index{tm-decrement-clock})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-decrement-clock}}\,({\it{tm\/}})\index{tm-decrement-clock})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-decrement-clock}}\,({\it{tm\/}})\index{tm-decrement-clock})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-decrement-clock}}\,({\it{tm\/}})\index{tm-decrement-clock})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-decrement-clock}}\,({\it{tm\/}})\index{tm-decrement-clock})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-decrement-clock-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-in-supervisor-mode-tm-decrement-clock \\ \index{tm-in-supervisor-mode-tm-decreme!nt-clock}
{\rm{tm-in-supervisor-mode}}\,({\rm{tm-decrement-clock}}\,({\it{tm\/}})\index{tm-decrement-clock})\index{tm-in-supervisor-mode} $=$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-in-supervisor-mode-tm-decrement-clock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-fetch-arg1-mapup-address-space \\ \index{tm-fetch-arg1-mapup-address-spa!ce}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\rm{real-addr}}\,({\tt{'}}{\tt{2}}, {\rm{tm-incrn}}\,({\tt{'}}{\tt{1}}, {\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc})\index{tm-incrn})\index{real-addr}, {\it{tm\/}})\index{tm-good-address})\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-fetch-arg1}}\,({\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\index{tm-fetch-arg1} \\ 
$=$$\;\;\;\;${\rm{tm-fetch-arg1}}\,({\it{tm\/}})\index{tm-fetch-arg1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-fetch-arg1-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-fetch-arg2-mapup-address-space \\ \index{tm-fetch-arg2-mapup-address-spa!ce}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\rm{real-addr}}\,({\tt{'}}{\tt{2}}, {\rm{tm-incrn}}\,({\tt{'}}{\tt{2}}, {\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc})\index{tm-incrn})\index{real-addr}, {\it{tm\/}})\index{tm-good-address})\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-fetch-arg2}}\,({\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\index{tm-fetch-arg2} \\ 
$=$$\;\;\;\;${\rm{tm-fetch-arg2}}\,({\it{tm\/}})\index{tm-fetch-arg2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-fetch-arg2-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tm-execute2} \\  
\=\+{\rm{tm-execute2}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute2} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-unary-instructionp}}\,({\it{opcode\/}})\index{tm-unary-instructionp} \\ 
{\bf then }{\rm{tm-execute-instruction}}\,(\=\+{\rm{cons}}\,(\=\+{\it{opcode\/}}, \\ 
{\rm{cons}}\,({\rm{tm-fetch-arg1}}\,({\it{tm\/}})\index{tm-fetch-arg1}, {\tt{'}}{\tt{nil}}))\-, \\ 
{\rm{tm-set-pc}}\,({\rm{tm-incrn}}\,({\tt{'}}{\tt{2}}, {\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc})\index{tm-incrn}, {\it{tm\/}})\index{tm-set-pc})\-\index{tm-execute-instruction} \\ 
{\bf elseif }{\rm{tm-good-address}}\,({\rm{real-addr}}\,({\tt{'}}{\tt{2}}, {\rm{tm-incrn}}\,({\tt{'}}{\tt{2}}, {\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc})\index{tm-incrn})\index{real-addr}, {\it{tm\/}})\index{tm-good-address} \\ 
{\bf then }{\rm{tm-execute-instruction}}\,(\=\+{\rm{cons}}\,(\=\+{\it{opcode\/}}, \\ 
{\rm{cons}}\,(\=\+{\rm{tm-fetch-arg1}}\,({\it{tm\/}})\index{tm-fetch-arg1}, \\ 
{\rm{cons}}\,({\rm{tm-fetch-arg2}}\,({\it{tm\/}})\index{tm-fetch-arg2}, {\tt{'}}{\tt{nil}}))\-)\-, \\ 
{\rm{tm-set-pc}}\,({\rm{tm-incrn}}\,({\tt{'}}{\tt{3}}, {\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc})\index{tm-incrn}, {\it{tm\/}})\index{tm-set-pc})\-\index{tm-execute-instruction} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{7}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{tm-execute1} \\  
\=\+{\rm{tm-execute1}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute1} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-nullary-instructionp}}\,({\it{opcode\/}})\index{tm-nullary-instructionp} \\ 
{\bf then }{\rm{tm-execute-instruction}}\,(\=\+{\rm{cons}}\,({\it{opcode\/}}, {\tt{'}}{\tt{nil}}), \\ 
{\rm{tm-set-pc}}\,({\rm{tm-incrn}}\,({\tt{'}}{\tt{1}}, {\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc})\index{tm-incrn}, {\it{tm\/}})\index{tm-set-pc})\-\index{tm-execute-instruction} \\ 
{\bf elseif }{\rm{tm-good-address}}\,({\rm{real-addr}}\,({\tt{'}}{\tt{2}}, {\rm{tm-incrn}}\,({\tt{'}}{\tt{1}}, {\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc})\index{tm-incrn})\index{real-addr}, {\it{tm\/}})\index{tm-good-address} \\ 
{\bf then }{\rm{tm-execute2}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute2} \\ 
{\bf else }{\rm{tm-set-error}}\,({\tt{'}}{\tt{7}}, {\it{tm\/}})\index{tm-set-error}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tm-execute1-equals-tm-execute \\ \index{tm-execute1-equals-tm-execute}
{\rm{tm-execute1}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute1} $=$ {\rm{tm-execute}}\,({\it{opcode\/}}, {\it{tm\/}})\index{tm-execute}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute1-equals-tm-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute2-commutes-with-mapup-address-space \\ \index{tm-execute2-commutes-with-mapup!-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,(\=\+{\rm{real-addr}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{tm-incrn}}\,({\tt{'}}{\tt{1}}, {\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc})\index{tm-incrn})\-\index{real-addr}, \\ 
{\it{tm\/}})\-\index{tm-good-address})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute2}}\,(\=\+{\it{instruction\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute2} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute2}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute2})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute2}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute2})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute2}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute2})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute2}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute2})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute2}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute2})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute2}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute2})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute2}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute2})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute2}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute2})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute2-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute1-commutes-with-mapup-address-space \\ \index{tm-execute1-commutes-with-mapup!-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute1}}\,(\=\+{\it{instruction\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute1} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute1}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute1})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute1}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute1})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute1}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute1})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute1}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute1})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute1}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute1})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute1}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute1})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute1}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute1})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute1}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute1})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute1-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-execute-commutes-with-mapup-address-space \\ \index{tm-execute-commutes-with-mapup-!address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute}}\,(\=\+{\it{instruction\/}}, \\ 
{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\-\index{tm-execute} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-execute}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-execute}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-execute}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-execute}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-execute}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-execute}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-execute}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-execute}}\,({\it{instruction\/}}, {\it{tm\/}})\index{tm-execute})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-execute-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-fetch-opcode-mapup-address-space \\ \index{tm-fetch-opcode-mapup-address-sp!ace}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-good-address}}\,({\rm{real-addr}}\,({\tt{'}}{\tt{2}}, {\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc})\index{real-addr}, {\it{tm\/}})\index{tm-good-address})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-fetch-opcode}}\,({\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\index{tm-fetch-opcode} \\ 
$=$$\;\;\;\;${\rm{tm-fetch-opcode}}\,({\it{tm\/}})\index{tm-fetch-opcode})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-fetch-opcode-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-fetch-execute-commutes-with-mapup-address-space \\ \index{tm-fetch-execute-commutes-with-!mapup-address-space}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\tt{'}}{\tt{65536}} $<$ ({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-fetch-execute}}\,({\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\it{tm\/}})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\it{tm\/}})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit})\-\index{mapup-address-space})\index{tm-fetch-execute} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute})\index{tm-memory}, \\ 
{\rm{tm-regs}}\,({\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute})\index{tm-regs}, \\ 
{\rm{tm-cc}}\,({\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute})\index{tm-svcid}, \\ 
{\rm{tm-base}}\,({\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute})\index{tm-base}, \\ 
{\rm{tm-limit}}\,({\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute})\index{tm-limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-fetch-execute-commutes-with-mapup-address-space.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{deq-ith-buffer} \\  
{\rm{deq-ith-buffer}}\,({\it{id\/}}, {\it{buffers\/}})\index{deq-ith-buffer} $=$ {\rm{putnth}}\,({\rm{deq}}\,({\rm{getnth}}\,({\it{id\/}}, {\it{buffers\/}})\index{getnth})\index{deq}, {\it{id\/}}, {\it{buffers\/}})\index{putnth}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{enq-ith-buffer} \\  
\=\+{\rm{enq-ith-buffer}}\,({\it{item\/}}, {\it{id\/}}, {\it{buffers\/}})\index{enq-ith-buffer} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,({\rm{enq}}\,({\it{item\/}}, {\rm{getnth}}\,({\it{id\/}}, {\it{buffers\/}})\index{getnth})\index{enq}, {\it{id\/}}, {\it{buffers\/}})\index{putnth}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{qreplace-ith-buffer} \\  
\=\+{\rm{qreplace-ith-buffer}}\,({\it{item\/}}, {\it{id\/}}, {\it{buffers\/}})\index{qreplace-ith-buffer} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,({\rm{qreplace}}\,({\it{item\/}}, {\rm{getnth}}\,({\it{id\/}}, {\it{buffers\/}})\index{getnth})\index{qreplace}, {\it{id\/}}, {\it{buffers\/}})\index{putnth}\-
\end{tabbing}


\noindent{\sc Event}:   Add the shell {\it{task\/}}\index{task}, with recognizer function symbol {\it{task-shellp\/}} and 2 accessors: {\it{task-pstate\/}}, with type restriction (none-of) and default value zero; {\it{task-channels\/}}, with type restriction (none-of) and default value zero.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{task-shell}} to consist of the following events: task.\index{task-shell}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{task-ibuffers}$\;\;$
{\rm{task-ibuffers}}\,({\it{task\/}})\index{task-ibuffers} $=$ {\rm{car}}\,({\rm{task-channels}}\,({\it{task\/}})\index{task-channels})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-obuffers}$\;\;$
{\rm{task-obuffers}}\,({\it{task\/}})\index{task-obuffers} $=$ {\rm{car}}\,({\rm{cdr}}\,({\rm{task-channels}}\,({\it{task\/}})\index{task-channels}))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-mbuffers} \\  
{\rm{task-mbuffers}}\,({\it{task\/}})\index{task-mbuffers} $=$ {\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\rm{task-channels}}\,({\it{task\/}})\index{task-channels})))
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-ibuffer-capacity}$\;\;$
{\sc{task-ibuffer-capacity}}\index{task-ibuffer-capacity} $=$ {\tt{'}}{\tt{4}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-obuffer-capacity}$\;\;$
{\sc{task-obuffer-capacity}}\index{task-obuffer-capacity} $=$ {\tt{'}}{\tt{4}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-mbuffer-capacity}$\;\;$
{\sc{task-mbuffer-capacity}}\index{task-mbuffer-capacity} $=$ {\tt{'}}{\tt{4}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-send-id}$\;\;$
{\sc{os-svc-send-id}}\index{os-svc-send-id} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-receive-id}$\;\;$
{\sc{os-svc-receive-id}}\index{os-svc-receive-id} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-tyo-id}$\;\;$
{\sc{os-svc-tyo-id}}\index{os-svc-tyo-id} $=$ {\tt{'}}{\tt{2}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-tyi-id}$\;\;$
{\sc{os-svc-tyi-id}}\index{os-svc-tyi-id} $=$ {\tt{'}}{\tt{3}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-send-instructionp} \\  
\=\+{\rm{task-send-instructionp}}\,({\it{task\/}})\index{task-send-instructionp} \\ 
$=$$\;\;\;\;$(({\rm{tm-svcid}}\,({\rm{task-pstate}}\,({\it{task\/}})\index{task-pstate})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-receive-instructionp} \\  
\=\+{\rm{task-receive-instructionp}}\,({\it{task\/}})\index{task-receive-instructionp} \\ 
$=$$\;\;\;\;$(({\rm{tm-svcid}}\,({\rm{task-pstate}}\,({\it{task\/}})\index{task-pstate})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-tyo-instructionp} \\  
\=\+{\rm{task-tyo-instructionp}}\,({\it{task\/}})\index{task-tyo-instructionp} \\ 
$=$$\;\;\;\;$(({\rm{tm-svcid}}\,({\rm{task-pstate}}\,({\it{task\/}})\index{task-pstate})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-tyi-instructionp} \\  
\=\+{\rm{task-tyi-instructionp}}\,({\it{task\/}})\index{task-tyi-instructionp} \\ 
$=$$\;\;\;\;$(({\rm{tm-svcid}}\,({\rm{task-pstate}}\,({\it{task\/}})\index{task-pstate})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{3}})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-update-control} \\  
{\rm{task-update-control}}\,({\it{pstate\/}})\index{task-update-control} $=$ {\rm{tm-set-svcflag}}\,({\tt{'}}{\tt{0}}, {\it{pstate\/}})\index{tm-set-svcflag}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-communicationp} \\  
{\rm{task-communicationp}}\,({\it{task\/}})\index{task-communicationp} $=$ {\rm{tm-svc-interruptp}}\,({\rm{task-pstate}}\,({\it{task\/}})\index{task-pstate})\index{tm-svc-interruptp}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-srcid}$\;\;$
{\rm{os-srcid}}\,({\it{task\/}}, {\it{max\/}})\index{os-srcid} $=$ ({\rm{tm-r2}}\,({\it{task\/}})\index{tm-r2} ${}${\bf{mod}}${}$ {\it{max\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-destid}$\;\;$
{\rm{os-destid}}\,({\it{task\/}}, {\it{max\/}})\index{os-destid} $=$ ({\rm{tm-r2}}\,({\it{task\/}})\index{tm-r2} ${}${\bf{mod}}${}$ {\it{max\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-idevid}$\;\;$
{\rm{os-idevid}}\,({\it{task\/}}, {\it{max\/}})\index{os-idevid} $=$ ({\rm{tm-r2}}\,({\it{task\/}})\index{tm-r2} ${}${\bf{mod}}${}$ {\it{max\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-odevid}$\;\;$
{\rm{os-odevid}}\,({\it{task\/}}, {\it{max\/}})\index{os-odevid} $=$ ({\rm{tm-r2}}\,({\it{task\/}})\index{tm-r2} ${}${\bf{mod}}${}$ {\it{max\/}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-message}$\;\;$
{\rm{os-message}}\,({\it{task\/}})\index{os-message} $=$ {\rm{tm-r3}}\,({\it{task\/}})\index{tm-r3}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-store-message} \\  
{\rm{os-store-message}}\,({\it{msg\/}}, {\it{task\/}})\index{os-store-message} $=$ {\rm{tm-store}}\,({\it{msg\/}}, {\tt{'}}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{3}}{\tt{)}}, {\it{task\/}})\index{tm-store}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-srcid} \\  
\=\+{\rm{task-srcid}}\,({\it{task\/}})\index{task-srcid} \\ 
$=$$\;\;\;\;${\rm{os-srcid}}\,({\rm{task-pstate}}\,({\it{task\/}})\index{task-pstate}, {\rm{length}}\,({\rm{task-mbuffers}}\,({\it{task\/}})\index{task-mbuffers})\index{length})\index{os-srcid}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-destid} \\  
\=\+{\rm{task-destid}}\,({\it{task\/}})\index{task-destid} \\ 
$=$$\;\;\;\;${\rm{os-destid}}\,({\rm{task-pstate}}\,({\it{task\/}})\index{task-pstate}, {\rm{length}}\,({\rm{task-mbuffers}}\,({\it{task\/}})\index{task-mbuffers})\index{length})\index{os-destid}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-idevid} \\  
\=\+{\rm{task-idevid}}\,({\it{task\/}})\index{task-idevid} \\ 
$=$$\;\;\;\;${\rm{os-idevid}}\,({\rm{task-pstate}}\,({\it{task\/}})\index{task-pstate}, {\rm{length}}\,({\rm{task-ibuffers}}\,({\it{task\/}})\index{task-ibuffers})\index{length})\index{os-idevid}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-odevid} \\  
\=\+{\rm{task-odevid}}\,({\it{task\/}})\index{task-odevid} \\ 
$=$$\;\;\;\;${\rm{os-odevid}}\,({\rm{task-pstate}}\,({\it{task\/}})\index{task-pstate}, {\rm{length}}\,({\rm{task-ibuffers}}\,({\it{task\/}})\index{task-ibuffers})\index{length})\index{os-odevid}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-message}$\;\;$
{\rm{task-message}}\,({\it{task\/}})\index{task-message} $=$ {\rm{os-message}}\,({\rm{task-pstate}}\,({\it{task\/}})\index{task-pstate})\index{os-message}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-store-message} \\  
{\rm{task-store-message}}\,({\it{msg\/}}, {\it{pstate\/}})\index{task-store-message} $=$ {\rm{os-store-message}}\,({\it{msg\/}}, {\it{pstate\/}})\index{os-store-message}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-fetch-execute} \\  
{\rm{task-fetch-execute}}\,({\it{pstate\/}})\index{task-fetch-execute} $=$ {\rm{tm-fetch-execute}}\,({\it{pstate\/}})\index{tm-fetch-execute}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-execute-send} \\  
\=\+{\rm{task-execute-send}}\,({\it{msg\/}}, {\it{srcid\/}}, {\it{destid\/}}, {\it{task\/}})\index{task-execute-send} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{qfullp2}}\,({\it{srcid\/}}, {\it{destid\/}}, {\rm{task-mbuffers}}\,({\it{task\/}})\index{task-mbuffers}, {\tt{'}}{\tt{4}})\index{qfullp2}$\;\;${\bf then }{\it{task\/}} \\ 
{\bf else }{\rm{task}}\,(\=\+{\rm{task-update-control}}\,({\rm{task-pstate}}\,({\it{task\/}})\index{task-pstate})\index{task-update-control}, \\ 
{\rm{cons}}\,(\=\+{\rm{task-ibuffers}}\,({\it{task\/}})\index{task-ibuffers}, \\ 
{\rm{cons}}\,(\=\+{\rm{task-obuffers}}\,({\it{task\/}})\index{task-obuffers}, \\ 
{\rm{cons}}\,(\=\+{\rm{enq2}}\,(\=\+{\it{msg\/}}, \\ 
{\it{srcid\/}}, \\ 
{\it{destid\/}}, \\ 
{\rm{task-mbuffers}}\,({\it{task\/}})\index{task-mbuffers})\-\index{enq2}, \\ 
{\tt{'}}{\tt{nil}})\-)\-)\-)\-\index{task}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-execute-receive} \\  
\=\+{\rm{task-execute-receive}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{task\/}})\index{task-execute-receive} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{qemptyp2}}\,({\it{srcid\/}}, {\it{destid\/}}, {\rm{task-mbuffers}}\,({\it{task\/}})\index{task-mbuffers})\index{qemptyp2}$\;\;${\bf then }{\it{task\/}} \\ 
{\bf else }{\rm{task}}\,(\=\+{\rm{task-update-control}}\,({\rm{task-store-message}}\,(\=\+{\rm{qfirst2}}\,(\=\+{\it{srcid\/}}, \\ 
{\it{destid\/}}, \\ 
{\rm{task-mbuffers}}\,({\it{task\/}})\index{task-mbuffers})\-\index{qfirst2}, \\ 
{\rm{task-pstate}}\,({\it{task\/}})\index{task-pstate})\-\index{task-store-message})\index{task-update-control}, \\ 
{\rm{cons}}\,(\=\+{\rm{task-ibuffers}}\,({\it{task\/}})\index{task-ibuffers}, \\ 
{\rm{cons}}\,(\=\+{\rm{task-obuffers}}\,({\it{task\/}})\index{task-obuffers}, \\ 
{\rm{cons}}\,(\=\+{\rm{deq2}}\,({\it{srcid\/}}, {\it{destid\/}}, {\rm{task-mbuffers}}\,({\it{task\/}})\index{task-mbuffers})\index{deq2}, \\ 
{\tt{'}}{\tt{nil}})\-)\-)\-)\-\index{task}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-execute-output} \\  
\=\+{\rm{task-execute-output}}\,({\it{char\/}}, {\it{id\/}}, {\it{task\/}})\index{task-execute-output} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{qfullp}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{task-obuffers}}\,({\it{task\/}})\index{task-obuffers})\index{getnth}, {\tt{'}}{\tt{4}})\index{qfullp}$\;\;${\bf then }{\it{task\/}} \\ 
{\bf else }{\rm{task}}\,(\=\+{\rm{task-update-control}}\,({\rm{task-pstate}}\,({\it{task\/}})\index{task-pstate})\index{task-update-control}, \\ 
{\rm{cons}}\,(\=\+{\rm{task-ibuffers}}\,({\it{task\/}})\index{task-ibuffers}, \\ 
{\rm{cons}}\,(\=\+{\rm{enq-ith-buffer}}\,({\it{char\/}}, {\it{id\/}}, {\rm{task-obuffers}}\,({\it{task\/}})\index{task-obuffers})\index{enq-ith-buffer}, \\ 
{\rm{cons}}\,({\rm{task-mbuffers}}\,({\it{task\/}})\index{task-mbuffers}, {\tt{'}}{\tt{nil}}))\-)\-)\-\index{task}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-execute-input} \\  
\=\+{\rm{task-execute-input}}\,({\it{id\/}}, {\it{task\/}})\index{task-execute-input} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{qemptyp}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{task-ibuffers}}\,({\it{task\/}})\index{task-ibuffers})\index{getnth})\index{qemptyp}$\;\;${\bf then }{\it{task\/}} \\ 
{\bf else }{\rm{task}}\,(\=\+{\rm{task-update-control}}\,({\rm{task-store-message}}\,(\=\+{\rm{qfirst}}\,({\rm{getnth}}\,(\=\+{\it{id\/}}, \\ 
{\rm{task-ibuffers}}\,({\it{task\/}})\index{task-ibuffers})\-\index{getnth})\index{qfirst}, \\ 
{\rm{task-pstate}}\,({\it{task\/}})\index{task-pstate})\-\index{task-store-message})\index{task-update-control}, \\ 
{\rm{cons}}\,(\=\+{\rm{deq-ith-buffer}}\,({\it{id\/}}, {\rm{task-ibuffers}}\,({\it{task\/}})\index{task-ibuffers})\index{deq-ith-buffer}, \\ 
{\rm{cons}}\,(\=\+{\rm{task-obuffers}}\,({\it{task\/}})\index{task-obuffers}, \\ 
{\rm{cons}}\,({\rm{task-mbuffers}}\,({\it{task\/}})\index{task-mbuffers}, {\tt{'}}{\tt{nil}}))\-)\-)\-\index{task}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-communication-step} \\  
\=\+{\rm{task-communication-step}}\,({\it{task\/}}, {\it{i\/}})\index{task-communication-step} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{task-send-instructionp}}\,({\it{task\/}})\index{task-send-instructionp} \\ 
{\bf then }{\rm{task-execute-send}}\,({\rm{task-message}}\,({\it{task\/}})\index{task-message}, {\it{i\/}}, {\rm{task-destid}}\,({\it{task\/}})\index{task-destid}, {\it{task\/}})\index{task-execute-send} \\ 
{\bf elseif }{\rm{task-receive-instructionp}}\,({\it{task\/}})\index{task-receive-instructionp} \\ 
{\bf then }{\rm{task-execute-receive}}\,({\rm{task-srcid}}\,({\it{task\/}})\index{task-srcid}, {\it{i\/}}, {\it{task\/}})\index{task-execute-receive} \\ 
{\bf elseif }{\rm{task-tyo-instructionp}}\,({\it{task\/}})\index{task-tyo-instructionp} \\ 
{\bf then }{\rm{task-execute-output}}\,({\rm{task-message}}\,({\it{task\/}})\index{task-message}, {\it{i\/}}, {\it{task\/}})\index{task-execute-output} \\ 
{\bf else }{\rm{task-execute-input}}\,({\it{i\/}}, {\it{task\/}})\index{task-execute-input}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-private-step} \\  
\=\+{\rm{task-private-step}}\,({\it{task\/}})\index{task-private-step} \\ 
$=$$\;\;\;\;${\rm{task}}\,({\rm{task-fetch-execute}}\,({\rm{task-pstate}}\,({\it{task\/}})\index{task-pstate})\index{task-fetch-execute}, {\rm{task-channels}}\,({\it{task\/}})\index{task-channels})\index{task}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-step} \\  
\=\+{\rm{task-step}}\,({\it{task\/}}, {\it{i\/}})\index{task-step} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{task-communicationp}}\,({\it{task\/}})\index{task-communicationp}$\;\;${\bf then }{\rm{task-communication-step}}\,({\it{task\/}}, {\it{i\/}})\index{task-communication-step} \\ 
{\bf else }{\rm{task-private-step}}\,({\it{task\/}})\index{task-private-step}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-update-channels} \\  
{\rm{task-update-channels}}\,({\it{task\/}}, {\it{channels\/}})\index{task-update-channels} $=$ {\rm{task}}\,({\rm{task-pstate}}\,({\it{task\/}})\index{task-pstate}, {\it{channels\/}})\index{task}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-activep}$\;\;$
{\rm{task-activep}}\,({\it{x\/}})\index{task-activep} $=$ ({\it{x\/}} $=$ {\tt{'}}{\tt{*1*true}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{task-processor} \\  
\=\+{\rm{task-processor}}\,({\it{task\/}}, {\it{i\/}}, {\it{oracle\/}})\index{task-processor} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{oracle\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{task-activep}}\,({\rm{car}}\,({\it{oracle\/}}))\index{task-activep} \\ 
{\bf then }{\rm{task-processor}}\,({\rm{task-step}}\,({\it{task\/}}, {\it{i\/}})\index{task-step}, {\it{i\/}}, {\rm{cdr}}\,({\it{oracle\/}}))\index{task-processor} \\ 
{\bf else }{\rm{task-processor}}\,(\=\+{\rm{task-update-channels}}\,({\it{task\/}}, {\rm{car}}\,({\it{oracle\/}}))\index{task-update-channels}, \\ 
{\it{i\/}}, \\ 
{\rm{cdr}}\,({\it{oracle\/}}))\-\index{task-processor}$\;${\bf  endif}\- \\ 
{\bf else }{\it{task\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-numberp-os-message \\ \index{finite-numberp-os-message}
\=\+{\rm{good-address-space}}\,({\it{machine\/}}, {\it{memlength\/}})\index{good-address-space} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{os-message}}\,({\it{machine\/}})\index{os-message}, {\tt{'}}{\tt{65536}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-os-message.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-os-store-message \\ \index{good-address-space-os-store-mes!sage}
\=\+({\rm{good-address-space}}\,({\it{tm\/}}, {\it{memlength\/}})\index{good-address-space} $\wedge$ {\rm{finite-numberp}}\,({\it{msg\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{os-store-message}}\,({\it{msg\/}}, {\it{tm\/}})\index{os-store-message}, {\it{memlength\/}})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-os-store-message.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-os-store-message1 \\ \index{good-address-space-os-store-mes!sage1}
\=\+(\=\+{\rm{good-address-space}}\,({\it{task\/}}, {\rm{length}}\,({\rm{tm-memory}}\,({\it{task\/}})\index{tm-memory})\index{length})\index{good-address-space} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\it{msg\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{os-store-message}}\,({\it{msg\/}}, {\it{task\/}})\index{os-store-message}, {\rm{length}}\,({\rm{tm-memory}}\,({\it{task\/}})\index{tm-memory})\index{length})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-os-store-message1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-os-store-message \\ \index{length-tm-memory-os-store-messa!ge}
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{os-store-message}}\,({\it{msg\/}}, {\it{task\/}})\index{os-store-message})\index{tm-memory})\index{length} $=$ {\rm{length}}\,({\rm{tm-memory}}\,({\it{task\/}})\index{tm-memory})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-os-store-message.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{good-task-buffer} \\  
\=\+{\rm{good-task-buffer}}\,({\it{buffer\/}}, {\it{capacity\/}})\index{good-task-buffer} \\ 
$=$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\it{buffer\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\it{buffer\/}})\index{length} $<$ ($1\;+$ {\it{capacity\/}})) \\ 
$\wedge$$\;\;\;\;${\rm{finite-number-listp}}\,({\it{buffer\/}}, {\tt{'}}{\tt{65536}})\index{finite-number-listp})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{good-task-buffer-list} \\  
\=\+{\rm{good-task-buffer-list}}\,({\it{l\/}}, {\it{capacity\/}})\index{good-task-buffer-list} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}}) \\ 
{\bf then }\=\+{\rm{good-task-buffer}}\,({\rm{car}}\,({\it{l\/}}), {\it{capacity\/}})\index{good-task-buffer} \\ 
$\wedge$$\;\;\;\;${\rm{good-task-buffer-list}}\,({\rm{cdr}}\,({\it{l\/}}), {\it{capacity\/}})\index{good-task-buffer-list}\- \\ 
{\bf else }{\it{l\/}} $=$ {\tt{'}}{\tt{nil}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{good-task-buffer-table} \\  
\=\+{\rm{good-task-buffer-table}}\,({\it{l\/}}, {\it{length\/}}, {\it{capacity\/}})\index{good-task-buffer-table} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}}) \\ 
{\bf then }\=\+{\rm{plistp}}\,({\rm{car}}\,({\it{l\/}}))\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\rm{car}}\,({\it{l\/}}))\index{length} $=$ {\it{length\/}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{good-task-buffer-list}}\,({\rm{car}}\,({\it{l\/}}), {\it{capacity\/}})\index{good-task-buffer-list} \\ 
$\wedge$$\;\;\;\;${\rm{good-task-buffer-table}}\,(\=\+{\rm{cdr}}\,({\it{l\/}}), \\ 
{\it{length\/}}, \\ 
{\it{capacity\/}})\-\index{good-task-buffer-table})\-)\-\- \\ 
{\bf else }{\it{l\/}} $=$ {\tt{'}}{\tt{nil}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{good-task} \\  
\=\+{\rm{good-task}}\,({\it{task\/}}, {\it{ilength\/}}, {\it{olength\/}}, {\it{mlength\/}})\index{good-task} \\ 
$=$$\;\;\;\;$(\=\+{\rm{task-shellp}}\,({\it{task\/}})\index{task-shellp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{good-address-space}}\,(\=\+{\rm{task-pstate}}\,({\it{task\/}})\index{task-pstate}, \\ 
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{task-pstate}}\,({\it{task\/}})\index{task-pstate})\index{tm-memory})\index{length})\-\index{good-address-space} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\rm{task-ibuffers}}\,({\it{task\/}})\index{task-ibuffers})\index{length} $=$ {\it{ilength\/}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{good-task-buffer-list}}\,(\=\+{\rm{task-ibuffers}}\,({\it{task\/}})\index{task-ibuffers}, \\ 
{\tt{'}}{\tt{4}})\-\index{good-task-buffer-list} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{length}}\,({\rm{task-obuffers}}\,({\it{task\/}})\index{task-obuffers})\index{length} \\ 
$=$$\;\;\;\;${\it{olength\/}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{good-task-buffer-list}}\,(\=\+{\rm{task-obuffers}}\,({\it{task\/}})\index{task-obuffers}, \\ 
{\tt{'}}{\tt{4}})\-\index{good-task-buffer-list} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{length}}\,({\rm{task-mbuffers}}\,({\it{task\/}})\index{task-mbuffers})\index{length} \\ 
$=$$\;\;\;\;${\it{mlength\/}})\- \\ 
$\wedge$$\;\;\;\;${\rm{good-task-buffer-table}}\,(\=\+{\rm{task-mbuffers}}\,({\it{task\/}})\index{task-mbuffers}, \\ 
{\it{mlength\/}}, \\ 
{\tt{'}}{\tt{4}})\-\index{good-task-buffer-table})\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-properties \\ \index{good-task-buffer-properties}
\=\+{\rm{good-task-buffer}}\,({\it{buffer\/}}, {\it{capacity\/}})\index{good-task-buffer} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\it{buffer\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\it{buffer\/}})\index{length} $<$ ($1\;+$ {\it{capacity\/}})) \\ 
$\wedge$$\;\;\;\;${\rm{finite-number-listp}}\,({\it{buffer\/}}, {\tt{'}}{\tt{65536}})\index{finite-number-listp})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-properties.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-getnth \\ \index{good-task-buffer-getnth}
\=\+({\rm{good-task-buffer-list}}\,({\it{l\/}}, {\it{capacity\/}})\index{good-task-buffer-list} $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-task-buffer}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth}, {\it{capacity\/}})\index{good-task-buffer}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-getnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-good-task-buffer-list \\ \index{plistp-good-task-buffer-list}
{\rm{good-task-buffer-list}}\,({\it{l\/}}, {\it{capacity\/}})\index{good-task-buffer-list} $\rightarrow$ {\rm{plistp}}\,({\it{l\/}})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-good-task-buffer-list.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-list-putnth \\ \index{good-task-buffer-list-putnth}
\=\+(\=\+{\rm{good-task-buffer-list}}\,({\it{l\/}}, {\it{capacity\/}})\index{good-task-buffer-list} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\it{buffer\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\it{buffer\/}})\index{length} $<$ ($1\;+$ {\it{capacity\/}})) \\ 
$\wedge$$\;\;\;\;${\rm{finite-number-listp}}\,({\it{buffer\/}}, {\tt{'}}{\tt{65536}})\index{finite-number-listp})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-task-buffer-list}}\,({\rm{putnth}}\,({\it{buffer\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth}, {\it{capacity\/}})\index{good-task-buffer-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-list-putnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-list-getnth \\ \index{good-task-buffer-list-getnth}
\=\+({\rm{good-task-buffer-table}}\,({\it{l\/}}, {\it{length\/}}, {\it{capacity\/}})\index{good-task-buffer-table} $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{length} $=$ {\it{length\/}}) \\ 
$\wedge$$\;\;\;\;${\rm{good-task-buffer-list}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth}, {\it{capacity\/}})\index{good-task-buffer-list})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-list-getnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-getnth2 \\ \index{good-task-buffer-getnth2}
\=\+(\=\+{\rm{good-task-buffer-table}}\,({\it{l\/}}, {\it{length\/}}, {\it{capacity\/}})\index{good-task-buffer-table} \\ 
$\wedge$$\;\;\;\;$(({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) $\wedge$ ({\it{j\/}} $<$ {\it{length\/}})))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-task-buffer}}\,({\rm{getnth2}}\,({\it{i\/}}, {\it{j\/}}, {\it{l\/}})\index{getnth2}, {\it{capacity\/}})\index{good-task-buffer}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-getnth2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-table-putnth \\ \index{good-task-buffer-table-putnth}
\=\+(\=\+{\rm{good-task-buffer-table}}\,({\it{l\/}}, {\it{length\/}}, {\it{capacity\/}})\index{good-task-buffer-table} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\it{x\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\it{x\/}})\index{length} $=$ {\it{length\/}}) \\ 
$\wedge$$\;\;\;\;${\rm{good-task-buffer-list}}\,({\it{x\/}}, {\it{capacity\/}})\index{good-task-buffer-list})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-task-buffer-table}}\,({\rm{putnth}}\,({\it{x\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth}, {\it{length\/}}, {\it{capacity\/}})\index{good-task-buffer-table}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-table-putnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-table-putnth2 \\ \index{good-task-buffer-table-putnth2}
\=\+(\=\+{\rm{good-task-buffer-table}}\,({\it{l\/}}, {\it{length\/}}, {\it{capacity\/}})\index{good-task-buffer-table} \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\it{buffer\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\it{buffer\/}})\index{length} $<$ ($1\;+$ {\it{capacity\/}})) \\ 
$\wedge$$\;\;\;\;${\rm{finite-number-listp}}\,({\it{buffer\/}}, {\tt{'}}{\tt{65536}})\index{finite-number-listp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-task-buffer-table}}\,({\rm{putnth2}}\,({\it{buffer\/}}, {\it{i\/}}, {\it{j\/}}, {\it{l\/}})\index{putnth2}, {\it{length\/}}, {\it{capacity\/}})\index{good-task-buffer-table}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-table-putnth2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-good-task-buffer-table \\ \index{plistp-good-task-buffer-table}
{\rm{good-task-buffer-table}}\,({\it{l\/}}, {\it{length\/}}, {\it{capacity\/}})\index{good-task-buffer-table} $\rightarrow$ {\rm{plistp}}\,({\it{l\/}})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-good-task-buffer-table.

\addvspace{18pt}


\noindent{\sc Event}:   Add the shell {\it{ak\/}}\index{ak}, with recognizer function symbol {\it{ak-shellp\/}} and 10 accessors: {\it{ak-pstates\/}}, with type restriction (none-of) and default value zero; {\it{ak-ibuffers\/}}, with type restriction (none-of) and default value zero; {\it{ak-obuffers\/}}, with type restriction (none-of) and default value zero; {\it{ak-mbuffers\/}}, with type restriction (none-of) and default value zero; {\it{ak-readyq\/}}, with type restriction (none-of) and default value zero; {\it{ak-status\/}}, with type restriction (none-of) and default value zero; {\it{ak-rwstate\/}}, with type restriction (none-of) and default value zero; {\it{ak-clock\/}}, with type restriction (none-of) and default value zero; {\it{ak-iports\/}}, with type restriction (none-of) and default value zero; {\it{ak-oports\/}}, with type restriction (none-of) and default value zero.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{ak-shell}} to consist of the following events: ak.\index{ak-shell}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ak-taskidlub}$\;\;$
{\sc{ak-taskidlub}}\index{ak-taskidlub} $=$ {\tt{'}}{\tt{16}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-time-slice}$\;\;$
{\sc{ak-time-slice}}\index{ak-time-slice} $=$ {\tt{'}}{\tt{1000}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-taskid}$\;\;$
{\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid} $=$ {\rm{qfirst}}\,({\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq})\index{qfirst}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-send-instructionp} \\  
\=\+{\rm{ak-send-instructionp}}\,({\it{ak\/}})\index{ak-send-instructionp} \\ 
$=$$\;\;\;\;$(({\rm{tm-svcid}}\,({\rm{getnth}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-receive-instructionp} \\  
\=\+{\rm{ak-receive-instructionp}}\,({\it{ak\/}})\index{ak-receive-instructionp} \\ 
$=$$\;\;\;\;$(({\rm{tm-svcid}}\,({\rm{getnth}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-tyo-instructionp} \\  
\=\+{\rm{ak-tyo-instructionp}}\,({\it{ak\/}})\index{ak-tyo-instructionp} \\ 
$=$$\;\;\;\;$(({\rm{tm-svcid}}\,({\rm{getnth}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-tyi-instructionp} \\  
\=\+{\rm{ak-tyi-instructionp}}\,({\it{ak\/}})\index{ak-tyi-instructionp} \\ 
$=$$\;\;\;\;$(({\rm{tm-svcid}}\,({\rm{getnth}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{3}})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-update-control} \\  
\=\+{\rm{ak-update-control}}\,({\it{id\/}}, {\it{pstates\/}})\index{ak-update-control} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,({\rm{tm-set-svcflag}}\,({\tt{'}}{\tt{0}}, {\rm{getnth}}\,({\it{id\/}}, {\it{pstates\/}})\index{getnth})\index{tm-set-svcflag}, {\it{id\/}}, {\it{pstates\/}})\index{putnth}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-communicationp} \\  
\=\+{\rm{ak-communicationp}}\,({\it{ak\/}})\index{ak-communicationp} \\ 
$=$$\;\;\;\;${\rm{tm-svc-interruptp}}\,({\rm{getnth}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth})\index{tm-svc-interruptp}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-errorp} \\  
{\rm{ak-errorp}}\,({\it{ak\/}})\index{ak-errorp} $=$ {\rm{tm-errorp}}\,({\rm{getnth}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth})\index{tm-errorp}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-svc-interruptp} \\  
\=\+{\rm{ak-svc-interruptp}}\,({\it{ak\/}})\index{ak-svc-interruptp} \\ 
$=$$\;\;\;\;${\rm{tm-svc-interruptp}}\,({\rm{getnth}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth})\index{tm-svc-interruptp}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-destid} \\  
{\rm{ak-destid}}\,({\it{ak\/}})\index{ak-destid} $=$ {\rm{os-destid}}\,({\rm{getnth}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth}, {\tt{'}}{\tt{16}})\index{os-destid}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-srcid} \\  
{\rm{ak-srcid}}\,({\it{ak\/}})\index{ak-srcid} $=$ {\rm{os-srcid}}\,({\rm{getnth}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth}, {\tt{'}}{\tt{16}})\index{os-srcid}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-idevid} \\  
{\rm{ak-idevid}}\,({\it{ak\/}})\index{ak-idevid} $=$ {\rm{os-idevid}}\,({\rm{getnth}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth}, {\tt{'}}{\tt{16}})\index{os-idevid}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-odevid} \\  
{\rm{ak-odevid}}\,({\it{ak\/}})\index{ak-odevid} $=$ {\rm{os-odevid}}\,({\rm{getnth}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth}, {\tt{'}}{\tt{16}})\index{os-odevid}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-message} \\  
{\rm{ak-message}}\,({\it{ak\/}})\index{ak-message} $=$ {\rm{os-message}}\,({\rm{getnth}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth})\index{os-message}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-store-message} \\  
\=\+{\rm{ak-store-message}}\,({\it{msg\/}}, {\it{taskid\/}}, {\it{pstates\/}})\index{ak-store-message} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,({\rm{os-store-message}}\,({\it{msg\/}}, {\rm{getnth}}\,({\it{taskid\/}}, {\it{pstates\/}})\index{getnth})\index{os-store-message}, {\it{taskid\/}}, {\it{pstates\/}})\index{putnth}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-fetch-execute} \\  
\=\+{\rm{ak-fetch-execute}}\,({\it{id\/}}, {\it{pstates\/}})\index{ak-fetch-execute} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,({\rm{tm-fetch-execute}}\,({\rm{getnth}}\,({\it{id\/}}, {\it{pstates\/}})\index{getnth})\index{tm-fetch-execute}, {\it{id\/}}, {\it{pstates\/}})\index{putnth}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-oport-idlep} \\  
{\rm{ak-oport-idlep}}\,({\it{id\/}}, {\it{oports\/}})\index{ak-oport-idlep} $=$ {\rm{tm-oport-idlep}}\,({\it{id\/}}, {\it{oports\/}})\index{tm-oport-idlep}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-post-output-interrupt} \\  
{\rm{ak-post-output-interrupt}}\,({\it{id\/}}, {\it{oports\/}})\index{ak-post-output-interrupt} $=$ {\rm{tm-post-output-interrupt}}\,({\it{id\/}}, {\it{oports\/}})\index{tm-post-output-interrupt}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-clear-input-interrupt} \\  
{\rm{ak-clear-input-interrupt}}\,({\it{id\/}}, {\it{iports\/}})\index{ak-clear-input-interrupt} $=$ {\rm{tm-clear-input-interrupt}}\,({\it{id\/}}, {\it{iports\/}})\index{tm-clear-input-interrupt}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-clear-output-interrupt} \\  
\=\+{\rm{ak-clear-output-interrupt}}\,({\it{id\/}}, {\it{oports\/}})\index{ak-clear-output-interrupt} \\ 
$=$$\;\;\;\;${\rm{tm-clear-output-interrupt}}\,({\it{id\/}}, {\it{oports\/}})\index{tm-clear-output-interrupt}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-start-output} \\  
{\rm{ak-start-output}}\,({\it{char\/}}, {\it{id\/}}, {\it{oports\/}})\index{ak-start-output} $=$ {\rm{tm-start-output}}\,({\it{char\/}}, {\it{id\/}}, {\it{oports\/}})\index{tm-start-output}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-input-interruptp} \\  
{\rm{ak-input-interruptp}}\,({\it{ak\/}})\index{ak-input-interruptp} $=$ {\rm{tm-some-input-interruptp}}\,({\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports})\index{tm-some-input-interruptp}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-output-interruptp} \\  
{\rm{ak-output-interruptp}}\,({\it{ak\/}})\index{ak-output-interruptp} $=$ {\rm{tm-some-output-interruptp}}\,({\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\index{tm-some-output-interruptp}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-interrupting-input-port} \\  
{\rm{ak-interrupting-input-port}}\,({\it{iports\/}})\index{ak-interrupting-input-port} $=$ {\rm{tm-interrupting-input-port}}\,({\it{iports\/}})\index{tm-interrupting-input-port}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-interrupting-output-port} \\  
{\rm{ak-interrupting-output-port}}\,({\it{oports\/}})\index{ak-interrupting-output-port} $=$ {\rm{tm-interrupting-output-port}}\,({\it{oports\/}})\index{tm-interrupting-output-port}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-status-flag-field}$\;\;$
{\sc{ak-status-flag-field}}\index{ak-status-flag-field} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-status-taskid-field}$\;\;$
{\sc{ak-status-taskid-field}}\index{ak-status-taskid-field} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-ready-status}$\;\;$
{\sc{ak-ready-status}}\index{ak-ready-status} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-error-status}$\;\;$
{\sc{ak-error-status}}\index{ak-error-status} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-send-status}$\;\;$
{\sc{ak-send-status}}\index{ak-send-status} $=$ {\tt{'}}{\tt{2}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-receive-status}$\;\;$
{\sc{ak-receive-status}}\index{ak-receive-status} $=$ {\tt{'}}{\tt{3}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-output-status}$\;\;$
{\sc{ak-output-status}}\index{ak-output-status} $=$ {\tt{'}}{\tt{4}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-input-status}$\;\;$
{\sc{ak-input-status}}\index{ak-input-status} $=$ {\tt{'}}{\tt{5}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-status-lub}$\;\;$
{\sc{ak-status-lub}}\index{ak-status-lub} $=$ {\tt{'}}{\tt{6}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-status-length}$\;\;$
{\sc{ak-status-length}}\index{ak-status-length} $=$ {\tt{'}}{\tt{2}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-ready-statusp} \\  
\=\+{\rm{ak-ready-statusp}}\,({\it{taskid\/}}, {\it{ak\/}})\index{ak-ready-statusp} \\ 
$=$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{getnth}}\,({\it{taskid\/}}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{getnth})\index{getnth} $=$ {\tt{'}}{\tt{0}})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-waiting-to-sendp} \\  
\=\+{\rm{ak-waiting-to-sendp}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-waiting-to-sendp} \\ 
$=$$\;\;\;\;$(\=\+({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{getnth}}\,({\it{srcid\/}}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{getnth})\index{getnth} $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\rm{getnth}}\,({\it{srcid\/}}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{getnth})\index{getnth} $=$ {\it{destid\/}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-waiting-to-receivep} \\  
\=\+{\rm{ak-waiting-to-receivep}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-waiting-to-receivep} \\ 
$=$$\;\;\;\;$(\=\+({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{getnth}}\,({\it{destid\/}}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{getnth})\index{getnth} $=$ {\tt{'}}{\tt{3}}) \\ 
$\wedge$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\rm{getnth}}\,({\it{destid\/}}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{getnth})\index{getnth} $=$ {\it{srcid\/}}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-waiting-to-outputp} \\  
\=\+{\rm{ak-waiting-to-outputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-outputp} \\ 
$=$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{getnth}}\,({\it{id\/}}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{getnth})\index{getnth} $=$ {\tt{'}}{\tt{4}})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-waiting-to-inputp} \\  
\=\+{\rm{ak-waiting-to-inputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-inputp} \\ 
$=$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{getnth}}\,({\it{id\/}}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{getnth})\index{getnth} $=$ {\tt{'}}{\tt{5}})\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-wait-state}$\;\;$
{\sc{ak-wait-state}}\index{ak-wait-state} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-run-state}$\;\;$
{\sc{ak-run-state}}\index{ak-run-state} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-waiting}$\;\;$
{\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting} $=$ ({\rm{ak-rwstate}}\,({\it{ak\/}})\index{ak-rwstate} $=$ {\tt{'}}{\tt{1}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-dispatcher} \\  
\=\+{\rm{ak-dispatcher}}\,({\it{ak\/}})\index{ak-dispatcher} \\ 
$=$$\;\;\;\;${\rm{ak}}\,(\=\+{\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}, \\ 
{\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers}, \\ 
{\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers}, \\ 
{\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers}, \\ 
{\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq}, \\ 
{\rm{ak-status}}\,({\it{ak\/}})\index{ak-status}, \\ 
\=\+{\bf if }{\rm{qemptyp}}\,({\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq})\index{qemptyp}$\;\;${\bf then }{\tt{'}}{\tt{1}} \\ 
{\bf else }{\tt{'}}{\tt{0}}$\;${\bf  endif}\-, \\ 
\=\+{\bf if }{\rm{qemptyp}}\,({\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq})\index{qemptyp}$\;\;${\bf then }{\rm{ak-clock}}\,({\it{ak\/}})\index{ak-clock} \\ 
{\bf else }{\tt{'}}{\tt{1000}}$\;${\bf  endif}\-, \\ 
{\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports}, \\ 
{\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\-\index{ak}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-clock-interrupt-handler} \\  
\=\+{\rm{ak-clock-interrupt-handler}}\,({\it{ak\/}})\index{ak-clock-interrupt-handler} \\ 
$=$$\;\;\;\;${\rm{ak-dispatcher}}\,({\rm{ak}}\,(\=\+{\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}, \\ 
{\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers}, \\ 
{\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers}, \\ 
{\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers}, \\ 
{\rm{enq}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\rm{deq}}\,({\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq})\index{deq})\index{enq}, \\ 
{\rm{ak-status}}\,({\it{ak\/}})\index{ak-status}, \\ 
{\rm{ak-rwstate}}\,({\it{ak\/}})\index{ak-rwstate}, \\ 
{\rm{ak-clock}}\,({\it{ak\/}})\index{ak-clock}, \\ 
{\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports}, \\ 
{\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\-\index{ak})\index{ak-dispatcher}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-error-handler} \\  
\=\+{\rm{ak-error-handler}}\,({\it{ak\/}})\index{ak-error-handler} \\ 
$=$$\;\;\;\;${\rm{ak-dispatcher}}\,({\rm{ak}}\,(\=\+{\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}, \\ 
{\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers}, \\ 
{\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers}, \\ 
{\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers}, \\ 
{\rm{deq}}\,({\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq})\index{deq}, \\ 
{\rm{putnth}}\,({\tt{'}}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{0}}{\tt{)}}, {\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{putnth}, \\ 
{\rm{ak-rwstate}}\,({\it{ak\/}})\index{ak-rwstate}, \\ 
{\rm{ak-clock}}\,({\it{ak\/}})\index{ak-clock}, \\ 
{\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports}, \\ 
{\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\-\index{ak})\index{ak-dispatcher}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-block-send} \\  
\=\+{\rm{ak-block-send}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-block-send} \\ 
$=$$\;\;\;\;${\rm{ak-dispatcher}}\,({\rm{ak}}\,(\=\+{\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}, \\ 
{\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers}, \\ 
{\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers}, \\ 
{\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers}, \\ 
{\rm{deq}}\,({\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq})\index{deq}, \\ 
{\rm{putnth}}\,(\=\+{\rm{cons}}\,({\tt{'}}{\tt{2}}, {\rm{cons}}\,({\it{destid\/}}, {\tt{'}}{\tt{nil}})), \\ 
{\it{srcid\/}}, \\ 
{\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\-\index{putnth}, \\ 
{\rm{ak-rwstate}}\,({\it{ak\/}})\index{ak-rwstate}, \\ 
{\rm{ak-clock}}\,({\it{ak\/}})\index{ak-clock}, \\ 
{\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports}, \\ 
{\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\-\index{ak})\index{ak-dispatcher}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-execute-send-to-buffer} \\  
\=\+{\rm{ak-execute-send-to-buffer}}\,({\it{msg\/}}, {\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-execute-send-to-buffer} \\ 
$=$$\;\;\;\;${\rm{ak}}\,(\=\+{\rm{ak-update-control}}\,({\it{srcid\/}}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{ak-update-control}, \\ 
{\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers}, \\ 
{\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers}, \\ 
{\rm{enq2}}\,({\it{msg\/}}, {\it{srcid\/}}, {\it{destid\/}}, {\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers})\index{enq2}, \\ 
\=\+{\bf if }{\rm{ak-waiting-to-receivep}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-waiting-to-receivep} \\ 
{\bf then }{\rm{enq}}\,({\it{destid\/}}, {\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq})\index{enq} \\ 
{\bf else }{\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq}$\;${\bf  endif}\-, \\ 
\=\+{\bf if }{\rm{ak-waiting-to-receivep}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-waiting-to-receivep} \\ 
{\bf then }{\rm{putnth}}\,({\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, {\it{destid\/}}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{putnth} \\ 
{\bf else }{\rm{ak-status}}\,({\it{ak\/}})\index{ak-status}$\;${\bf  endif}\-, \\ 
{\rm{ak-rwstate}}\,({\it{ak\/}})\index{ak-rwstate}, \\ 
{\rm{ak-clock}}\,({\it{ak\/}})\index{ak-clock}, \\ 
{\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports}, \\ 
{\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\-\index{ak}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-execute-send} \\  
\=\+{\rm{ak-execute-send}}\,({\it{msg\/}}, {\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-execute-send} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{qfullp2}}\,({\it{srcid\/}}, {\it{destid\/}}, {\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers}, {\tt{'}}{\tt{4}})\index{qfullp2} \\ 
{\bf then }{\rm{ak-block-send}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-block-send} \\ 
{\bf else }{\rm{ak-execute-send-to-buffer}}\,({\it{msg\/}}, {\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-execute-send-to-buffer}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-block-receive} \\  
\=\+{\rm{ak-block-receive}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-block-receive} \\ 
$=$$\;\;\;\;${\rm{ak-dispatcher}}\,({\rm{ak}}\,(\=\+{\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}, \\ 
{\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers}, \\ 
{\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers}, \\ 
{\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers}, \\ 
{\rm{deq}}\,({\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq})\index{deq}, \\ 
{\rm{putnth}}\,(\=\+{\rm{cons}}\,({\tt{'}}{\tt{3}}, {\rm{cons}}\,({\it{srcid\/}}, {\tt{'}}{\tt{nil}})), \\ 
{\it{destid\/}}, \\ 
{\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\-\index{putnth}, \\ 
{\rm{ak-rwstate}}\,({\it{ak\/}})\index{ak-rwstate}, \\ 
{\rm{ak-clock}}\,({\it{ak\/}})\index{ak-clock}, \\ 
{\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports}, \\ 
{\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\-\index{ak})\index{ak-dispatcher}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-execute-receive-from-buffer} \\  
\=\+{\rm{ak-execute-receive-from-buffer}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-execute-receive-from-buffer} \\ 
$=$$\;\;\;\;${\rm{ak}}\,(\=\+{\rm{ak-update-control}}\,(\=\+{\it{destid\/}}, \\ 
{\rm{ak-store-message}}\,(\=\+{\rm{qfirst2}}\,(\=\+{\it{srcid\/}}, \\ 
{\it{destid\/}}, \\ 
{\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers})\-\index{qfirst2}, \\ 
{\it{destid\/}}, \\ 
{\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\-\index{ak-store-message})\-\index{ak-update-control}, \\ 
{\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers}, \\ 
{\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers}, \\ 
{\rm{deq2}}\,({\it{srcid\/}}, {\it{destid\/}}, {\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers})\index{deq2}, \\ 
\=\+{\bf if }{\rm{ak-waiting-to-sendp}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-waiting-to-sendp} \\ 
{\bf then }{\rm{enq}}\,({\it{srcid\/}}, {\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq})\index{enq} \\ 
{\bf else }{\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq}$\;${\bf  endif}\-, \\ 
\=\+{\bf if }{\rm{ak-waiting-to-sendp}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-waiting-to-sendp} \\ 
{\bf then }{\rm{putnth}}\,({\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, {\it{srcid\/}}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{putnth} \\ 
{\bf else }{\rm{ak-status}}\,({\it{ak\/}})\index{ak-status}$\;${\bf  endif}\-, \\ 
{\rm{ak-rwstate}}\,({\it{ak\/}})\index{ak-rwstate}, \\ 
{\rm{ak-clock}}\,({\it{ak\/}})\index{ak-clock}, \\ 
{\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports}, \\ 
{\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\-\index{ak}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-execute-receive} \\  
\=\+{\rm{ak-execute-receive}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-execute-receive} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{qemptyp2}}\,({\it{srcid\/}}, {\it{destid\/}}, {\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers})\index{qemptyp2} \\ 
{\bf then }{\rm{ak-block-receive}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-block-receive} \\ 
{\bf else }{\rm{ak-execute-receive-from-buffer}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-execute-receive-from-buffer}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-block-output} \\  
\=\+{\rm{ak-block-output}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-block-output} \\ 
$=$$\;\;\;\;${\rm{ak-dispatcher}}\,({\rm{ak}}\,(\=\+{\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}, \\ 
{\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers}, \\ 
{\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers}, \\ 
{\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers}, \\ 
{\rm{deq}}\,({\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq})\index{deq}, \\ 
{\rm{putnth}}\,({\tt{'}}{\tt{(}}{\tt{4}}{\tt{ }}{\tt{0}}{\tt{)}}, {\it{id\/}}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{putnth}, \\ 
{\rm{ak-rwstate}}\,({\it{ak\/}})\index{ak-rwstate}, \\ 
{\rm{ak-clock}}\,({\it{ak\/}})\index{ak-clock}, \\ 
{\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports}, \\ 
{\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\-\index{ak})\index{ak-dispatcher}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-execute-output-to-buffer} \\  
\=\+{\rm{ak-execute-output-to-buffer}}\,({\it{char\/}}, {\it{id\/}}, {\it{ak\/}})\index{ak-execute-output-to-buffer} \\ 
$=$$\;\;\;\;${\rm{ak}}\,(\=\+{\rm{ak-update-control}}\,({\it{id\/}}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{ak-update-control}, \\ 
{\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers}, \\ 
{\rm{enq-ith-buffer}}\,({\it{char\/}}, {\it{id\/}}, {\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers})\index{enq-ith-buffer}, \\ 
{\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers}, \\ 
{\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq}, \\ 
{\rm{ak-status}}\,({\it{ak\/}})\index{ak-status}, \\ 
{\rm{ak-rwstate}}\,({\it{ak\/}})\index{ak-rwstate}, \\ 
{\rm{ak-clock}}\,({\it{ak\/}})\index{ak-clock}, \\ 
{\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports}, \\ 
\=\+{\bf if }{\rm{ak-oport-idlep}}\,({\it{id\/}}, {\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\index{ak-oport-idlep} \\ 
{\bf then }{\rm{ak-post-output-interrupt}}\,({\it{id\/}}, {\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\index{ak-post-output-interrupt} \\ 
{\bf else }{\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports}$\;${\bf  endif}\-)\-\index{ak}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-execute-output} \\  
\=\+{\rm{ak-execute-output}}\,({\it{char\/}}, {\it{id\/}}, {\it{ak\/}})\index{ak-execute-output} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{qfullp}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers})\index{getnth}, {\tt{'}}{\tt{4}})\index{qfullp}$\;\;${\bf then }{\rm{ak-block-output}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-block-output} \\ 
{\bf else }{\rm{ak-execute-output-to-buffer}}\,({\it{char\/}}, {\it{id\/}}, {\it{ak\/}})\index{ak-execute-output-to-buffer}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-block-input} \\  
\=\+{\rm{ak-block-input}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-block-input} \\ 
$=$$\;\;\;\;${\rm{ak-dispatcher}}\,({\rm{ak}}\,(\=\+{\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}, \\ 
{\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers}, \\ 
{\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers}, \\ 
{\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers}, \\ 
{\rm{deq}}\,({\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq})\index{deq}, \\ 
{\rm{putnth}}\,({\tt{'}}{\tt{(}}{\tt{5}}{\tt{ }}{\tt{0}}{\tt{)}}, {\it{id\/}}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{putnth}, \\ 
{\rm{ak-rwstate}}\,({\it{ak\/}})\index{ak-rwstate}, \\ 
{\rm{ak-clock}}\,({\it{ak\/}})\index{ak-clock}, \\ 
{\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports}, \\ 
{\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\-\index{ak})\index{ak-dispatcher}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-execute-input-from-buffer} \\  
\=\+{\rm{ak-execute-input-from-buffer}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-execute-input-from-buffer} \\ 
$=$$\;\;\;\;${\rm{ak}}\,(\=\+{\rm{ak-update-control}}\,(\=\+{\it{id\/}}, \\ 
{\rm{ak-store-message}}\,(\=\+{\rm{qfirst}}\,({\rm{getnth}}\,(\=\+{\it{id\/}}, \\ 
{\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers})\-\index{getnth})\index{qfirst}, \\ 
{\it{id\/}}, \\ 
{\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\-\index{ak-store-message})\-\index{ak-update-control}, \\ 
{\rm{putnth}}\,({\rm{deq}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers})\index{getnth})\index{deq}, {\it{id\/}}, {\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers})\index{putnth}, \\ 
{\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers}, \\ 
{\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers}, \\ 
{\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq}, \\ 
{\rm{ak-status}}\,({\it{ak\/}})\index{ak-status}, \\ 
{\rm{ak-rwstate}}\,({\it{ak\/}})\index{ak-rwstate}, \\ 
{\rm{ak-clock}}\,({\it{ak\/}})\index{ak-clock}, \\ 
{\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports}, \\ 
{\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\-\index{ak}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-execute-input} \\  
\=\+{\rm{ak-execute-input}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-execute-input} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{qemptyp}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers})\index{getnth})\index{qemptyp}$\;\;${\bf then }{\rm{ak-block-input}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-block-input} \\ 
{\bf else }{\rm{ak-execute-input-from-buffer}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-execute-input-from-buffer}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-svc-handler} \\  
\=\+{\rm{ak-svc-handler}}\,({\it{ak\/}})\index{ak-svc-handler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{ak-send-instructionp}}\,({\it{ak\/}})\index{ak-send-instructionp} \\ 
{\bf then }{\rm{ak-execute-send}}\,({\rm{ak-message}}\,({\it{ak\/}})\index{ak-message}, {\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\rm{ak-destid}}\,({\it{ak\/}})\index{ak-destid}, {\it{ak\/}})\index{ak-execute-send} \\ 
{\bf elseif }{\rm{ak-receive-instructionp}}\,({\it{ak\/}})\index{ak-receive-instructionp} \\ 
{\bf then }{\rm{ak-execute-receive}}\,({\rm{ak-srcid}}\,({\it{ak\/}})\index{ak-srcid}, {\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\it{ak\/}})\index{ak-execute-receive} \\ 
{\bf elseif }{\rm{ak-tyo-instructionp}}\,({\it{ak\/}})\index{ak-tyo-instructionp} \\ 
{\bf then }{\rm{ak-execute-output}}\,({\rm{ak-message}}\,({\it{ak\/}})\index{ak-message}, {\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\it{ak\/}})\index{ak-execute-output} \\ 
{\bf else }{\rm{ak-execute-input}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\it{ak\/}})\index{ak-execute-input}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-private-step} \\  
\=\+{\rm{ak-private-step}}\,({\it{ak\/}})\index{ak-private-step} \\ 
$=$$\;\;\;\;${\rm{ak}}\,(\=\+{\rm{ak-fetch-execute}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{ak-fetch-execute}, \\ 
{\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers}, \\ 
{\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers}, \\ 
{\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers}, \\ 
{\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq}, \\ 
{\rm{ak-status}}\,({\it{ak\/}})\index{ak-status}, \\ 
{\rm{ak-rwstate}}\,({\it{ak\/}})\index{ak-rwstate}, \\ 
{\rm{ak-clock}}\,({\it{ak\/}})\index{ak-clock} $-\;1$, \\ 
{\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports}, \\ 
{\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\-\index{ak}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-update-ibuffer} \\  
\=\+{\rm{ak-update-ibuffer}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-update-ibuffer} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{qfullp}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers})\index{getnth}, {\tt{'}}{\tt{4}})\index{qfullp} \\ 
{\bf then }{\rm{qreplace-ith-buffer}}\,(\=\+{\rm{tm-overflow-char}}\,({\rm{tm-ichar}}\,({\rm{getnth}}\,(\=\+{\it{id\/}}, \\ 
{\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports})\-\index{getnth})\index{tm-ichar})\index{tm-overflow-char}, \\ 
{\it{id\/}}, \\ 
{\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers})\-\index{qreplace-ith-buffer} \\ 
{\bf elseif }{\rm{tm-iport-errorp}}\,({\it{id\/}}, {\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports})\index{tm-iport-errorp} \\ 
{\bf then }{\rm{enq-ith-buffer}}\,(\=\+{\rm{tm-overflow-char}}\,({\rm{tm-ichar}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports})\index{getnth})\index{tm-ichar})\index{tm-overflow-char}, \\ 
{\it{id\/}}, \\ 
{\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers})\-\index{enq-ith-buffer} \\ 
{\bf else }{\rm{enq-ith-buffer}}\,(\=\+{\rm{tm-ichar}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports})\index{getnth})\index{tm-ichar}, \\ 
{\it{id\/}}, \\ 
{\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers})\-\index{enq-ith-buffer}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-waiting-input-interrupt-hand!ler} \\  
\=\+{\rm{ak-waiting-input-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-input-interrupt-hand!ler} \\ 
$=$$\;\;\;\;${\rm{ak-dispatcher}}\,({\rm{ak}}\,(\=\+{\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}, \\ 
{\rm{ak-update-ibuffer}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-update-ibuffer}, \\ 
{\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers}, \\ 
{\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers}, \\ 
\=\+{\bf if }{\rm{ak-waiting-to-inputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-inputp} \\ 
{\bf then }{\rm{enq}}\,({\it{id\/}}, {\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq})\index{enq} \\ 
{\bf else }{\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq}$\;${\bf  endif}\-, \\ 
\=\+{\bf if }{\rm{ak-waiting-to-inputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-inputp} \\ 
{\bf then }{\rm{putnth}}\,({\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, {\it{id\/}}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{putnth} \\ 
{\bf else }{\rm{ak-status}}\,({\it{ak\/}})\index{ak-status}$\;${\bf  endif}\-, \\ 
{\rm{ak-rwstate}}\,({\it{ak\/}})\index{ak-rwstate}, \\ 
{\rm{ak-clock}}\,({\it{ak\/}})\index{ak-clock}, \\ 
{\rm{ak-clear-input-interrupt}}\,({\it{id\/}}, {\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports})\index{ak-clear-input-interrupt}, \\ 
{\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\-\index{ak})\index{ak-dispatcher}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-running-input-interrupt-hand!ler} \\  
\=\+{\rm{ak-running-input-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-running-input-interrupt-hand!ler} \\ 
$=$$\;\;\;\;${\rm{ak}}\,(\=\+{\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}, \\ 
{\rm{ak-update-ibuffer}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-update-ibuffer}, \\ 
{\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers}, \\ 
{\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers}, \\ 
\=\+{\bf if }{\rm{ak-waiting-to-inputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-inputp}$\;\;${\bf then }{\rm{enq}}\,({\it{id\/}}, {\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq})\index{enq} \\ 
{\bf else }{\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq}$\;${\bf  endif}\-, \\ 
\=\+{\bf if }{\rm{ak-waiting-to-inputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-inputp} \\ 
{\bf then }{\rm{putnth}}\,({\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, {\it{id\/}}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{putnth} \\ 
{\bf else }{\rm{ak-status}}\,({\it{ak\/}})\index{ak-status}$\;${\bf  endif}\-, \\ 
{\rm{ak-rwstate}}\,({\it{ak\/}})\index{ak-rwstate}, \\ 
{\rm{ak-clock}}\,({\it{ak\/}})\index{ak-clock}, \\ 
{\rm{ak-clear-input-interrupt}}\,({\it{id\/}}, {\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports})\index{ak-clear-input-interrupt}, \\ 
{\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\-\index{ak}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-input-interrupt-handler} \\  
\=\+{\rm{ak-input-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-input-interrupt-handler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}$\;\;${\bf then }{\rm{ak-waiting-input-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-input-interrupt-hand!ler} \\ 
{\bf else }{\rm{ak-running-input-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-running-input-interrupt-hand!ler}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-waiting-output-interrupt-han!dler} \\  
\=\+{\rm{ak-waiting-output-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-output-interrupt-han!dler} \\ 
$=$$\;\;\;\;${\rm{ak-dispatcher}}\,({\rm{ak}}\,(\=\+{\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}, \\ 
{\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers}, \\ 
\=\+{\bf if }{\rm{qemptyp}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers})\index{getnth})\index{qemptyp} \\ 
{\bf then }{\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers} \\ 
{\bf else }{\rm{deq-ith-buffer}}\,({\it{id\/}}, {\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers})\index{deq-ith-buffer}$\;${\bf  endif}\-, \\ 
{\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers}, \\ 
\=\+{\bf if }{\rm{ak-waiting-to-outputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-outputp} \\ 
{\bf then }{\rm{enq}}\,({\it{id\/}}, {\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq})\index{enq} \\ 
{\bf else }{\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq}$\;${\bf  endif}\-, \\ 
\=\+{\bf if }{\rm{ak-waiting-to-outputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-outputp} \\ 
{\bf then }{\rm{putnth}}\,({\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, {\it{id\/}}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{putnth} \\ 
{\bf else }{\rm{ak-status}}\,({\it{ak\/}})\index{ak-status}$\;${\bf  endif}\-, \\ 
{\rm{ak-rwstate}}\,({\it{ak\/}})\index{ak-rwstate}, \\ 
{\rm{ak-clock}}\,({\it{ak\/}})\index{ak-clock}, \\ 
{\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports}, \\ 
\=\+{\bf if }{\rm{qemptyp}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers})\index{getnth})\index{qemptyp} \\ 
{\bf then }{\rm{ak-clear-output-interrupt}}\,({\it{id\/}}, {\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\index{ak-clear-output-interrupt} \\ 
{\bf else }{\rm{ak-start-output}}\,(\=\+{\rm{qfirst}}\,({\rm{getnth}}\,(\=\+{\it{id\/}}, \\ 
{\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers})\-\index{getnth})\index{qfirst}, \\ 
{\it{id\/}}, \\ 
{\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\-\index{ak-start-output}$\;${\bf  endif}\-)\-\index{ak})\index{ak-dispatcher}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-running-output-interrupt-han!dler} \\  
\=\+{\rm{ak-running-output-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-running-output-interrupt-han!dler} \\ 
$=$$\;\;\;\;${\rm{ak}}\,(\=\+{\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}, \\ 
{\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers}, \\ 
\=\+{\bf if }{\rm{qemptyp}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers})\index{getnth})\index{qemptyp}$\;\;${\bf then }{\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers} \\ 
{\bf else }{\rm{deq-ith-buffer}}\,({\it{id\/}}, {\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers})\index{deq-ith-buffer}$\;${\bf  endif}\-, \\ 
{\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers}, \\ 
\=\+{\bf if }{\rm{ak-waiting-to-outputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-outputp}$\;\;${\bf then }{\rm{enq}}\,({\it{id\/}}, {\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq})\index{enq} \\ 
{\bf else }{\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq}$\;${\bf  endif}\-, \\ 
\=\+{\bf if }{\rm{ak-waiting-to-outputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-outputp} \\ 
{\bf then }{\rm{putnth}}\,({\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, {\it{id\/}}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{putnth} \\ 
{\bf else }{\rm{ak-status}}\,({\it{ak\/}})\index{ak-status}$\;${\bf  endif}\-, \\ 
{\rm{ak-rwstate}}\,({\it{ak\/}})\index{ak-rwstate}, \\ 
{\rm{ak-clock}}\,({\it{ak\/}})\index{ak-clock}, \\ 
{\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports}, \\ 
\=\+{\bf if }{\rm{qemptyp}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers})\index{getnth})\index{qemptyp} \\ 
{\bf then }{\rm{ak-clear-output-interrupt}}\,({\it{id\/}}, {\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\index{ak-clear-output-interrupt} \\ 
{\bf else }{\rm{ak-start-output}}\,(\=\+{\rm{qfirst}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers})\index{getnth})\index{qfirst}, \\ 
{\it{id\/}}, \\ 
{\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\-\index{ak-start-output}$\;${\bf  endif}\-)\-\index{ak}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-output-interrupt-handler} \\  
\=\+{\rm{ak-output-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-output-interrupt-handler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}$\;\;${\bf then }{\rm{ak-waiting-output-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-output-interrupt-han!dler} \\ 
{\bf else }{\rm{ak-running-output-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-running-output-interrupt-han!dler}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-clock-interruptp}$\;\;$
{\rm{ak-clock-interruptp}}\,({\it{ak\/}})\index{ak-clock-interruptp} $=$ ({\rm{ak-clock}}\,({\it{ak\/}})\index{ak-clock} $\simeq {\tt{0}}$)
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-step} \\  
\=\+{\rm{ak-step}}\,({\it{ak\/}})\index{ak-step} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{ak-input-interruptp}}\,({\it{ak\/}})\index{ak-input-interruptp} \\ 
{\bf then }{\rm{ak-input-interrupt-handler}}\,(\=\+{\rm{ak-interrupting-input-port}}\,({\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports})\index{ak-interrupting-input-port}, \\ 
{\it{ak\/}})\-\index{ak-input-interrupt-handler} \\ 
{\bf elseif }{\rm{ak-output-interruptp}}\,({\it{ak\/}})\index{ak-output-interruptp} \\ 
{\bf then }{\rm{ak-output-interrupt-handler}}\,(\=\+{\rm{ak-interrupting-output-port}}\,({\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\index{ak-interrupting-output-port}, \\ 
{\it{ak\/}})\-\index{ak-output-interrupt-handler} \\ 
{\bf elseif }{\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}$\;\;${\bf then }{\it{ak\/}} \\ 
{\bf elseif }{\rm{ak-errorp}}\,({\it{ak\/}})\index{ak-errorp}$\;\;${\bf then }{\rm{ak-error-handler}}\,({\it{ak\/}})\index{ak-error-handler} \\ 
{\bf elseif }{\rm{ak-clock-interruptp}}\,({\it{ak\/}})\index{ak-clock-interruptp}$\;\;${\bf then }{\rm{ak-clock-interrupt-handler}}\,({\it{ak\/}})\index{ak-clock-interrupt-handler} \\ 
{\bf elseif }{\rm{ak-svc-interruptp}}\,({\it{ak\/}})\index{ak-svc-interruptp}$\;\;${\bf then }{\rm{ak-svc-handler}}\,({\it{ak\/}})\index{ak-svc-handler} \\ 
{\bf else }{\rm{ak-private-step}}\,({\it{ak\/}})\index{ak-private-step}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-post-interrupt} \\  
\=\+{\rm{ak-post-interrupt}}\,({\it{interrupt\/}}, {\it{ak\/}})\index{ak-post-interrupt} \\ 
$=$$\;\;\;\;${\rm{ak}}\,(\=\+{\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}, \\ 
{\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers}, \\ 
{\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers}, \\ 
{\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers}, \\ 
{\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq}, \\ 
{\rm{ak-status}}\,({\it{ak\/}})\index{ak-status}, \\ 
{\rm{ak-rwstate}}\,({\it{ak\/}})\index{ak-rwstate}, \\ 
{\rm{ak-clock}}\,({\it{ak\/}})\index{ak-clock}, \\ 
\=\+{\bf if }{\rm{tm-device-input-eventp}}\,({\it{interrupt\/}})\index{tm-device-input-eventp} \\ 
{\bf then }{\rm{tm-post-input-interrupt}}\,(\=\+{\rm{tm-idatum}}\,({\it{interrupt\/}})\index{tm-idatum} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{256}}, \\ 
{\rm{tm-idevid}}\,({\it{interrupt\/}})\index{tm-idevid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{16}}, \\ 
{\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports})\-\index{tm-post-input-interrupt} \\ 
{\bf else }{\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports}$\;${\bf  endif}\-, \\ 
\=\+{\bf if }{\rm{tm-device-output-eventp}}\,({\it{interrupt\/}})\index{tm-device-output-eventp} \\ 
{\bf then }{\rm{tm-post-output-interrupt}}\,(\=\+{\rm{tm-odevid}}\,({\it{interrupt\/}})\index{tm-odevid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{16}}, \\ 
{\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\-\index{tm-post-output-interrupt} \\ 
{\bf else }{\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports}$\;${\bf  endif}\-)\-\index{ak}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-processor} \\  
\=\+{\rm{ak-processor}}\,({\it{ak\/}}, {\it{oracle\/}})\index{ak-processor} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{oracle\/}}) \\ 
{\bf then }{\rm{ak-processor}}\,(\=\+{\rm{ak-step}}\,({\rm{ak-post-interrupt}}\,({\rm{car}}\,({\it{oracle\/}}), {\it{ak\/}})\index{ak-post-interrupt})\index{ak-step}, \\ 
{\rm{cdr}}\,({\it{oracle\/}}))\-\index{ak-processor} \\ 
{\bf else }{\it{ak\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-tm-iport-array-putnth1 \\ \index{good-tm-iport-array-putnth1}
\=\+(\=\+{\rm{good-tm-iport-array}}\,({\it{l\/}})\index{good-tm-iport-array} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-iportp}}\,({\it{iport\/}})\index{tm-iportp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\rm{tm-iinterrupt-flag}}\,({\it{iport\/}})\index{tm-iinterrupt-flag}, {\tt{'}}{\tt{2}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\rm{tm-ierror-flag}}\,({\it{iport\/}})\index{tm-ierror-flag}, {\tt{'}}{\tt{2}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-ichar}}\,({\it{iport\/}})\index{tm-ichar}, {\tt{'}}{\tt{256}})\index{finite-numberp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm-iport-array}}\,({\rm{putnth}}\,({\it{iport\/}}, {\it{n\/}}, {\it{l\/}})\index{putnth})\index{good-tm-iport-array}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-iport-array-putnth1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-oport-array-putnth1 \\ \index{good-tm-oport-array-putnth1}
\=\+(\=\+{\rm{good-tm-oport-array}}\,({\it{l\/}})\index{good-tm-oport-array} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-oportp}}\,({\it{oport\/}})\index{tm-oportp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\rm{tm-ointerrupt-flag}}\,({\it{oport\/}})\index{tm-ointerrupt-flag}, {\tt{'}}{\tt{2}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\rm{tm-obusy-flag}}\,({\it{oport\/}})\index{tm-obusy-flag}, {\tt{'}}{\tt{2}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-ochar}}\,({\it{oport\/}})\index{tm-ochar}, {\tt{'}}{\tt{256}})\index{finite-numberp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm-oport-array}}\,({\rm{putnth}}\,({\it{oport\/}}, {\it{n\/}}, {\it{l\/}})\index{putnth})\index{good-tm-oport-array}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-oport-array-putnth1.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{good-address-space-list} \\  
\=\+{\rm{good-address-space-list}}\,({\it{l\/}})\index{good-address-space-list} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}}) \\ 
{\bf then }\=\+{\rm{good-address-space}}\,({\rm{car}}\,({\it{l\/}}), {\rm{length}}\,({\rm{tm-memory}}\,({\rm{car}}\,({\it{l\/}}))\index{tm-memory})\index{length})\index{good-address-space} \\ 
$\wedge$$\;\;\;\;${\rm{good-address-space-list}}\,({\rm{cdr}}\,({\it{l\/}}))\index{good-address-space-list}\- \\ 
{\bf else }{\it{l\/}} $=$ {\tt{'}}{\tt{nil}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plistp-good-address-space-list \\ \index{plistp-good-address-space-list}
{\rm{good-address-space-list}}\,({\it{l\/}})\index{good-address-space-list} $\rightarrow$ {\rm{plistp}}\,({\it{l\/}})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-good-address-space-list.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-getnth \\ \index{good-address-space-getnth}
\=\+({\rm{good-address-space-list}}\,({\it{l\/}})\index{good-address-space-list} $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth}, {\rm{length}}\,({\rm{tm-memory}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{tm-memory})\index{length})\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-getnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-list-putnth \\ \index{good-address-space-list-putnth}
\=\+(\=\+{\rm{good-address-space-list}}\,({\it{l\/}})\index{good-address-space-list} \\ 
$\wedge$$\;\;\;\;${\rm{good-address-space}}\,({\it{task\/}}, {\rm{length}}\,({\rm{tm-memory}}\,({\it{task\/}})\index{tm-memory})\index{length})\index{good-address-space})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space-list}}\,({\rm{putnth}}\,({\it{task\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth})\index{good-address-space-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-list-putnth.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{good-status} \\  
\=\+{\rm{good-status}}\,({\it{task-status\/}})\index{good-status} \\ 
$=$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\it{task-status\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\it{task-status\/}})\index{length} $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{task-status\/}})\index{getnth}, {\tt{'}}{\tt{6}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{task-status\/}})\index{getnth}, {\tt{'}}{\tt{16}})\index{finite-numberp})\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{good-status-list} \\  
\=\+{\rm{good-status-list}}\,({\it{status\/}})\index{good-status-list} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{status\/}}) \\ 
{\bf then }{\rm{good-status}}\,({\rm{car}}\,({\it{status\/}}))\index{good-status} $\wedge$ {\rm{good-status-list}}\,({\rm{cdr}}\,({\it{status\/}}))\index{good-status-list} \\ 
{\bf else }{\it{status\/}} $=$ {\tt{'}}{\tt{nil}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plistp-good-status-list \\ \index{plistp-good-status-list}
{\rm{good-status-list}}\,({\it{l\/}})\index{good-status-list} $\rightarrow$ {\rm{plistp}}\,({\it{l\/}})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-good-status-list.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-status-getnth \\ \index{good-status-getnth}
({\rm{good-status-list}}\,({\it{l\/}})\index{good-status-list} $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) $\rightarrow$ {\rm{good-status}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{good-status}
\end{tabbing}


\noindent{\sc Event}:   Disable good-status-getnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-status-list-putnth \\ \index{good-status-list-putnth}
\=\+(\=\+{\rm{good-status-list}}\,({\it{l\/}})\index{good-status-list} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\it{status\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\it{status\/}})\index{length} $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{status\/}})\index{getnth}, {\tt{'}}{\tt{6}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{status\/}})\index{getnth}, {\tt{'}}{\tt{16}})\index{finite-numberp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-status-list}}\,({\rm{putnth}}\,({\it{status\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth})\index{good-status-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-status-list-putnth.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{good-ak-construction}} to consist of the following events: good-task-buffer-table-putnth2,
good-task-buffer-table-putnth,
good-task-buffer-getnth2,
good-task-buffer-list-getnth,
good-task-buffer-list-putnth,
plistp-good-task-buffer-list,
good-task-buffer-getnth,
good-status-list-putnth,
good-status-getnth,
plistp-good-status-list,
good-tm-iport-getnth,
good-tm-oport-getnth,
good-tm-iport-array-putnth1,
good-tm-oport-array-putnth1,
good-address-space-getnth,
good-address-space-list-putnth,
plistp-good-address-space-list,
a-finite-number-is-lessp-than-its-lub,
length-putnth,
length-putnth2,
plistp-putnth,
plistp-putnth2.\index{good-ak-construction}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{status-flag-readyp} \\  
{\rm{status-flag-readyp}}\,({\it{task-status\/}})\index{status-flag-readyp} $=$ ({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{task-status\/}})\index{getnth} $=$ {\tt{'}}{\tt{0}})
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{index-ready-set} \\  
\=\+{\rm{index-ready-set}}\,({\it{n\/}}, {\it{status\/}})\index{index-ready-set} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{status\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{status-flag-readyp}}\,({\rm{car}}\,({\it{status\/}}))\index{status-flag-readyp} \\ 
{\bf then }{\rm{cons}}\,({\rm{fix}}\,({\it{n\/}}), {\rm{index-ready-set}}\,($1\;+$ {\it{n\/}}, {\rm{cdr}}\,({\it{status\/}}))\index{index-ready-set}) \\ 
{\bf else }{\rm{index-ready-set}}\,($1\;+$ {\it{n\/}}, {\rm{cdr}}\,({\it{status\/}}))\index{index-ready-set}$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{nil}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{ak-ready-set} \\  
{\rm{ak-ready-set}}\,({\it{ak\/}})\index{ak-ready-set} $=$ {\rm{index-ready-set}}\,({\tt{'}}{\tt{0}}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{index-ready-set}
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN GOOD-AK
 (AK)
 (AND
  (AK-SHELLP AK)
  (AND
   (EQUAL (LENGTH (AK-PSTATES AK)) '16)
   (AND
    (GOOD-ADDRESS-SPACE-LIST (AK-PSTATES AK))
    (AND
     (EQUAL (LENGTH (AK-IBUFFERS AK)) '16)
     (AND
      (GOOD-TASK-BUFFER-LIST (AK-IBUFFERS AK)
                             '4)
      (AND
       (EQUAL (LENGTH (AK-OBUFFERS AK)) '16)
       (AND
        (GOOD-TASK-BUFFER-LIST (AK-OBUFFERS AK)
                               '4)
        (AND
         (EQUAL (LENGTH (AK-MBUFFERS AK)) '16)
         (AND
          (GOOD-TASK-BUFFER-TABLE (AK-MBUFFERS AK)
                                  '16
                                  '4)
          (AND
           (PLISTP (AK-READYQ AK))
           (AND
            (LESSP (LENGTH (AK-READYQ AK)) '17)
            (AND
             (FINITE-NUMBER-LISTP (AK-READYQ AK)
                                  '16)
             (AND
              (EQUAL (LENGTH (AK-STATUS AK)) '16)
              (AND
               (GOOD-STATUS-LIST (AK-STATUS AK))
               (AND
                (FINITE-NUMBERP (AK-RWSTATE AK) '2)
                (AND
                 (FINITE-NUMBERP (AK-CLOCK AK) '65536)
                 (AND
                  (PLISTP (AK-IPORTS AK))
                  (AND
                   (EQUAL (LENGTH (AK-IPORTS AK)) '16)
                   (AND
                    (GOOD-TM-IPORT-ARRAY (AK-IPORTS AK))
                    (AND
                     (PLISTP (AK-OPORTS AK))
                     (AND
                      (EQUAL (LENGTH (AK-OPORTS AK)) '16)
                      (AND
                       (GOOD-TM-OPORT-ARRAY (AK-OPORTS AK))
                       (AND
                          (PERMUTATION (AK-READYQ AK)
                                       (AK-READY-SET AK))
                          (IFF (AK-WAITING AK)
                               (QEMPTYP (AK-READYQ AK))))))))))))))))))))))))))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  ak-shellp-ak \\ \index{ak-shellp-ak}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{ak-shellp}}\,({\it{ak\/}})\index{ak-shellp}
\end{tabbing}


\noindent{\sc Event}:   Disable ak-shellp-ak.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-ak-pstates \\ \index{length-ak-pstates}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ ({\rm{length}}\,({\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{length} $=$ {\tt{'}}{\tt{16}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-ak-pstates.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-list-ak-pstates \\ \index{good-address-space-list-ak-pstate!s}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{good-address-space-list}}\,({\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{good-address-space-list}
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-list-ak-pstates.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-getnth-from-ak \\ \index{good-address-space-getnth-from-!ak}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ({\it{i\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,(\=\+{\rm{getnth}}\,({\it{i\/}}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth}, \\ 
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{getnth}}\,({\it{i\/}}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth})\index{tm-memory})\index{length})\-\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-getnth-from-ak.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-ak-ibuffers \\ \index{length-ak-ibuffers}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ ({\rm{length}}\,({\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers})\index{length} $=$ {\tt{'}}{\tt{16}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-ak-ibuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-list-ak-ibuffers \\ \index{good-task-buffer-list-ak-ibuffe!rs}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{good-task-buffer-list}}\,({\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers}, {\tt{'}}{\tt{4}})\index{good-task-buffer-list}
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-list-ak-ibuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-ak-ibuffers \\ \index{plistp-ak-ibuffers}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{plistp}}\,({\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-ak-ibuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-getnth-from-ak-ibuffers \\ \index{good-task-buffer-getnth-from-ak!-ibuffers}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ {\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-task-buffer}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers})\index{getnth}, {\tt{'}}{\tt{4}})\index{good-task-buffer}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-getnth-from-ak-ibuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-ak-obuffers \\ \index{length-ak-obuffers}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ ({\rm{length}}\,({\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers})\index{length} $=$ {\tt{'}}{\tt{16}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-ak-obuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-list-ak-obuffers \\ \index{good-task-buffer-list-ak-obuffe!rs}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{good-task-buffer-list}}\,({\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers}, {\tt{'}}{\tt{4}})\index{good-task-buffer-list}
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-list-ak-obuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-ak-obuffers \\ \index{plistp-ak-obuffers}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{plistp}}\,({\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-ak-obuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-getnth-from-ak-obuffers \\ \index{good-task-buffer-getnth-from-ak!-obuffers}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ {\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-task-buffer}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers})\index{getnth}, {\tt{'}}{\tt{4}})\index{good-task-buffer}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-getnth-from-ak-obuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-ak-mbuffers \\ \index{length-ak-mbuffers}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ ({\rm{length}}\,({\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers})\index{length} $=$ {\tt{'}}{\tt{16}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-ak-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-table-ak-mbuffers \\ \index{good-task-buffer-table-ak-mbuffe!rs}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{good-task-buffer-table}}\,({\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers}, {\tt{'}}{\tt{16}}, {\tt{'}}{\tt{4}})\index{good-task-buffer-table}
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-table-ak-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-ak-mbuffers \\ \index{plistp-ak-mbuffers}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{plistp}}\,({\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-ak-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-getnth2-from-ak-mbuffers \\ \index{good-task-buffer-getnth2-from-a!k-mbuffers}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ (({\it{i\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{j\/}} $<$ {\tt{'}}{\tt{16}}))) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-task-buffer}}\,({\rm{getnth2}}\,({\it{i\/}}, {\it{j\/}}, {\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers})\index{getnth2}, {\tt{'}}{\tt{4}})\index{good-task-buffer}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-getnth2-from-ak-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-ak-taskid \\ \index{finite-numberp-ak-taskid}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\tt{'}}{\tt{16}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-ak-taskid.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-ak-readyq \\ \index{plistp-ak-readyq}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{plistp}}\,({\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-ak-readyq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-ak-readyq \\ \index{length-ak-readyq}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ ({\rm{length}}\,({\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq})\index{length} $<$ {\tt{'}}{\tt{17}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-ak-readyq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-ak-readyq \\ \index{finite-number-listp-ak-readyq}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{finite-number-listp}}\,({\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq}, {\tt{'}}{\tt{16}})\index{finite-number-listp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-ak-readyq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-ak-status \\ \index{length-ak-status}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ ({\rm{length}}\,({\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{length} $=$ {\tt{'}}{\tt{16}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-ak-status.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-status-list-ak-status \\ \index{good-status-list-ak-status}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{good-status-list}}\,({\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{good-status-list}
\end{tabbing}


\noindent{\sc Event}:   Disable good-status-list-ak-status.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-ak-status \\ \index{plistp-ak-status}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{plistp}}\,({\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-ak-status.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-status-getnth-from-ak-status \\ \index{good-status-getnth-from-ak-stat!us}
({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ({\it{i\/}} $<$ {\tt{'}}{\tt{16}})) $\rightarrow$ {\rm{good-status}}\,({\rm{getnth}}\,({\it{i\/}}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{getnth})\index{good-status}
\end{tabbing}


\noindent{\sc Event}:   Disable good-status-getnth-from-ak-status.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-ak-rwstate \\ \index{finite-numberp-ak-rwstate}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{finite-numberp}}\,({\rm{ak-rwstate}}\,({\it{ak\/}})\index{ak-rwstate}, {\tt{'}}{\tt{2}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-ak-rwstate.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-ak-clock \\ \index{finite-numberp-ak-clock}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{finite-numberp}}\,({\rm{ak-clock}}\,({\it{ak\/}})\index{ak-clock}, {\tt{'}}{\tt{65536}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-ak-clock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-ak-iports \\ \index{plistp-ak-iports}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{plistp}}\,({\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-ak-iports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-ak-iports \\ \index{length-ak-iports}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ ({\rm{length}}\,({\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports})\index{length} $=$ {\tt{'}}{\tt{16}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-ak-iports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-iport-array-ak-iports \\ \index{good-tm-iport-array-ak-iports}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{good-tm-iport-array}}\,({\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports})\index{good-tm-iport-array}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-iport-array-ak-iports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-iport-getnth-from-ak-iports \\ \index{good-tm-iport-getnth-from-ak-ip!orts}
({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ({\it{i\/}} $<$ {\tt{'}}{\tt{16}})) $\rightarrow$ {\rm{good-tm-iport}}\,({\rm{getnth}}\,({\it{i\/}}, {\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports})\index{getnth})\index{good-tm-iport}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-iport-getnth-from-ak-iports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-ak-oports \\ \index{plistp-ak-oports}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{plistp}}\,({\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-ak-oports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-ak-oports \\ \index{length-ak-oports}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ ({\rm{length}}\,({\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\index{length} $=$ {\tt{'}}{\tt{16}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-ak-oports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-oport-array-ak-oports \\ \index{good-tm-oport-array-ak-oports}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{good-tm-oport-array}}\,({\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\index{good-tm-oport-array}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-oport-array-ak-oports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-oport-getnth-from-ak-oports \\ \index{good-tm-oport-getnth-from-ak-op!orts}
({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ({\it{i\/}} $<$ {\tt{'}}{\tt{16}})) $\rightarrow$ {\rm{good-tm-oport}}\,({\rm{getnth}}\,({\it{i\/}}, {\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\index{getnth})\index{good-tm-oport}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-oport-getnth-from-ak-oports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-ak-readyq-ak-ready-set \\ \index{permutation-ak-readyq-ak-ready-!set}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{permutation}}\,({\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq}, {\rm{ak-ready-set}}\,({\it{ak\/}})\index{ak-ready-set})\index{permutation}
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-ak-readyq-ak-ready-set.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-waiting-iff-qemptyp-ak-readyq \\ \index{ak-waiting-iff-qemptyp-ak-readyq}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ ({\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting} $\leftrightarrow$ {\rm{qemptyp}}\,({\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq})\index{qemptyp})
\end{tabbing}


\noindent{\sc Event}:   Disable ak-waiting-iff-qemptyp-ak-readyq.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{good-ak-properties}} to consist of the following events: ak-waiting-iff-qemptyp-ak-readyq,
permutation-ak-readyq-ak-ready-set,
good-tm-oport-getnth-from-ak-oports,
good-tm-oport-array-ak-oports,
length-ak-oports,
plistp-ak-oports,
good-tm-iport-getnth-from-ak-iports,
good-tm-iport-array-ak-iports,
length-ak-iports,
plistp-ak-iports,
finite-numberp-ak-clock,
finite-numberp-ak-rwstate,
good-status-getnth-from-ak-status,
plistp-ak-status,
good-status-list-ak-status,
length-ak-status,
finite-number-listp-ak-readyq,
length-ak-readyq,
plistp-ak-readyq,
finite-numberp-ak-taskid,
good-task-buffer-getnth2-from-ak-mbuffers,
plistp-ak-mbuffers,
plistp-good-task-buffer-table,
good-task-buffer-table-ak-mbuffers,
length-ak-mbuffers,
good-task-buffer-getnth-from-ak-obuffers,
plistp-ak-obuffers,
good-task-buffer-list-ak-obuffers,
length-ak-obuffers,
good-task-buffer-getnth-from-ak-ibuffers,
plistp-ak-ibuffers,
good-task-buffer-list-ak-ibuffers,
length-ak-ibuffers,
good-address-space-getnth-from-ak,
good-address-space-list-ak-pstates,
length-ak-pstates,
ak-shellp-ak.\index{good-ak-properties}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{queue-facts}} to consist of the following events: not-qemptyp-enq,
not-qfullp-deq,
length-enq,
length-deq,
length-qreplace,
qfirst-enq,
plistp-enq,
plistp-deq,
plistp-qreplace,
finite-numberp-qfirst,
finite-number-listp-enq,
finite-number-listp-deq,
finite-number-listp-qreplace.\index{queue-facts}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-member-index-ready-set \\ \index{not-member-index-ready-set}
({\it{i\/}} $<$ {\it{n\/}}) $\rightarrow$ ({\it{i\/}} $\not\in$ {\rm{index-ready-set}}\,({\it{n\/}}, {\it{status\/}})\index{index-ready-set})
\end{tabbing}


\noindent{\sc Event}:   Disable not-member-index-ready-set.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  setp-index-ready-set \\ \index{setp-index-ready-set}
{\rm{setp}}\,({\rm{index-ready-set}}\,({\it{n\/}}, {\it{status\/}})\index{index-ready-set})\index{setp}
\end{tabbing}


\noindent{\sc Event}:   Disable setp-index-ready-set.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{set-status-induction} \\  
\=\+{\rm{set-status-induction}}\,({\it{i\/}}, {\it{n\/}}, {\it{l\/}})\index{set-status-induction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{i\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf elseif }{\rm{listp}}\,({\it{l\/}})$\;\;${\bf then }{\rm{set-status-induction}}\,({\it{i\/}} $-\;1$, $1\;+$ {\it{n\/}}, {\rm{cdr}}\,({\it{l\/}}))\index{set-status-induction} \\ 
{\bf else }{\tt{'}}{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  index-ready-set-putnth-unready-status \\ \index{index-ready-set-putnth-unready-!status}
\=\+(\=\+({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) \\ 
$\wedge$$\;\;\;\;$({\rm{status-flag-readyp}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{status-flag-readyp} $\wedge$ ($\neg$ {\rm{status-flag-readyp}}\,({\it{v\/}})\index{status-flag-readyp})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{index-ready-set}}\,({\it{n\/}}, {\rm{putnth}}\,({\it{v\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth})\index{index-ready-set} \\ 
$=$$\;\;\;\;${\rm{remove}}\,({\it{n\/}} $+$ {\it{i\/}}, {\rm{index-ready-set}}\,({\it{n\/}}, {\it{l\/}})\index{index-ready-set})\index{remove})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable index-ready-set-putnth-unready-status.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-status-flag-readyp-list \\ \index{not-status-flag-readyp-list}
({\it{flag\/}} $\not=$ {\tt{'}}{\tt{0}}) $\rightarrow$ ($\neg$ {\rm{status-flag-readyp}}\,({\rm{cons}}\,({\it{flag\/}}, {\rm{cons}}\,({\it{taskid\/}}, {\tt{'}}{\tt{nil}})))\index{status-flag-readyp})
\end{tabbing}


\noindent{\sc Event}:   Disable not-status-flag-readyp-list.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  status-flag-readyp-iff-member-index-ready-set1 \\ \index{status-flag-readyp-iff-member-i!ndex-ready-set1}
\=\+({\it{i\/}} $<$ {\rm{length}}\,({\it{status\/}})\index{length}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{status-flag-readyp}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{status\/}})\index{getnth})\index{status-flag-readyp} \\ 
$=$$\;\;\;\;$(({\it{n\/}} $+$ {\it{i\/}}) $\in$ {\rm{index-ready-set}}\,({\it{n\/}}, {\it{status\/}})\index{index-ready-set}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  status-flag-readyp-iff-member-index-ready-set \\ \index{status-flag-readyp-iff-member-i!ndex-ready-set}
\=\+(({\it{i\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{status\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{status-flag-readyp}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{status\/}})\index{getnth})\index{status-flag-readyp} \\ 
$=$$\;\;\;\;$({\it{i\/}} $\in$ {\rm{index-ready-set}}\,({\tt{'}}{\tt{0}}, {\it{status\/}})\index{index-ready-set}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable status-flag-readyp-iff-member-index-ready-set.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  status-flag-readyp-getnth \\ \index{status-flag-readyp-getnth}
\=\+(\=\+{\rm{permutation}}\,({\it{queue\/}}, {\rm{index-ready-set}}\,({\tt{'}}{\tt{0}}, {\it{status\/}})\index{index-ready-set})\index{permutation} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{qemptyp}}\,({\it{queue\/}})\index{qemptyp}) \\ 
$\wedge$$\;\;\;\;$({\rm{number-listp}}\,({\it{queue\/}})\index{number-listp} $\wedge$ ({\rm{qfirst}}\,({\it{queue\/}})\index{qfirst} $<$ {\rm{length}}\,({\it{status\/}})\index{length})))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{status-flag-readyp}}\,({\rm{getnth}}\,({\rm{qfirst}}\,({\it{queue\/}})\index{qfirst}, {\it{status\/}})\index{getnth})\index{status-flag-readyp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable status-flag-readyp-getnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-deq-index-ready-set-putnth \\ \index{permutation-deq-index-ready-set!-putnth}
\=\+(\=\+{\rm{permutation}}\,({\it{queue\/}}, {\rm{index-ready-set}}\,({\tt{'}}{\tt{0}}, {\it{status\/}})\index{index-ready-set})\index{permutation} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{number-listp}}\,({\it{queue\/}})\index{number-listp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\it{queue\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{qemptyp}}\,({\it{queue\/}})\index{qemptyp}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $=$ {\rm{qfirst}}\,({\it{queue\/}})\index{qfirst}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{flag\/}} $\not=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\it{taskid\/}} $<$ {\rm{length}}\,({\it{status\/}})\index{length}))\-)\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{deq}}\,({\it{queue\/}})\index{deq}, \\ 
{\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{cons}}\,({\it{flag\/}}, {\rm{cons}}\,({\it{x\/}}, {\tt{'}}{\tt{nil}})), \\ 
{\it{taskid\/}}, \\ 
{\it{status\/}})\-\index{putnth})\-\index{index-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-deq-index-ready-set-putnth.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{number-of-ready-tasks} \\  
\=\+{\rm{number-of-ready-tasks}}\,({\it{status\/}})\index{number-of-ready-tasks} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{status\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{status-flag-readyp}}\,({\rm{car}}\,({\it{status\/}}))\index{status-flag-readyp} \\ 
{\bf then }$1\;+$ {\rm{number-of-ready-tasks}}\,({\rm{cdr}}\,({\it{status\/}}))\index{number-of-ready-tasks} \\ 
{\bf else }{\rm{number-of-ready-tasks}}\,({\rm{cdr}}\,({\it{status\/}}))\index{number-of-ready-tasks}$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{number-of-unready-tasks} \\  
\=\+{\rm{number-of-unready-tasks}}\,({\it{status\/}})\index{number-of-unready-tasks} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{status\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{status-flag-readyp}}\,({\rm{car}}\,({\it{status\/}}))\index{status-flag-readyp} \\ 
{\bf then }{\rm{number-of-unready-tasks}}\,({\rm{cdr}}\,({\it{status\/}}))\index{number-of-unready-tasks} \\ 
{\bf else }$1\;+$ {\rm{number-of-unready-tasks}}\,({\rm{cdr}}\,({\it{status\/}}))\index{number-of-unready-tasks}$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equal-length-status-sum-of-ready-and-unready-tasks \\ \index{equal-length-status-sum-of-read!y-and-unready-tasks}
\=\+{\rm{length}}\,({\it{status\/}})\index{length} \\ 
$=$$\;\;\;\;$({\rm{number-of-ready-tasks}}\,({\it{status\/}})\index{number-of-ready-tasks} $+$ {\rm{number-of-unready-tasks}}\,({\it{status\/}})\index{number-of-unready-tasks})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  leq-number-of-ready-tasks-length-status \\ \index{leq-number-of-ready-tasks-lengt!h-status}
\=\+{\bf if }{\rm{length}}\,({\it{status\/}})\index{length} $<$ {\rm{number-of-ready-tasks}}\,({\it{status\/}})\index{number-of-ready-tasks}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  number-of-unready-tasks-non-zero \\ \index{number-of-unready-tasks-non-zer!o}
\=\+(({\it{i\/}} $<$ {\rm{length}}\,({\it{status\/}})\index{length}) $\wedge$ ($\neg$ {\rm{status-flag-readyp}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{status\/}})\index{getnth})\index{status-flag-readyp})) \\ 
$\rightarrow$$\;\;\;\;$({\tt{'}}{\tt{0}} $<$ {\rm{number-of-unready-tasks}}\,({\it{status\/}})\index{number-of-unready-tasks})\-
\end{tabbing}


\noindent{\sc Event}:   Disable number-of-unready-tasks-non-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-equal-number-of-ready-tasks-length-status \\ \index{not-equal-number-of-ready-tasks!-length-status}
\=\+(({\it{i\/}} $<$ {\rm{length}}\,({\it{status\/}})\index{length}) $\wedge$ ($\neg$ {\rm{status-flag-readyp}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{status\/}})\index{getnth})\index{status-flag-readyp})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{number-of-ready-tasks}}\,({\it{status\/}})\index{number-of-ready-tasks} $\not=$ {\rm{length}}\,({\it{status\/}})\index{length})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-number-of-ready-tasks-length-status \\ \index{lessp-number-of-ready-tasks-len!gth-status}
\=\+(({\it{i\/}} $<$ {\rm{length}}\,({\it{status\/}})\index{length}) $\wedge$ ($\neg$ {\rm{status-flag-readyp}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{status\/}})\index{getnth})\index{status-flag-readyp})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{number-of-ready-tasks}}\,({\it{status\/}})\index{number-of-ready-tasks} $<$ {\rm{length}}\,({\it{status\/}})\index{length})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  number-of-ready-tasks-equals-length-index-ready-set \\ \index{number-of-ready-tasks-equals-le!ngth-index-ready-set}
{\rm{number-of-ready-tasks}}\,({\it{status\/}})\index{number-of-ready-tasks} $=$ {\rm{length}}\,({\rm{index-ready-set}}\,({\it{n\/}}, {\it{status\/}})\index{index-ready-set})\index{length}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  status-flag-readyp-list \\ \index{status-flag-readyp-list}
{\rm{status-flag-readyp}}\,({\rm{cons}}\,({\tt{'}}{\tt{0}}, {\rm{cons}}\,({\it{x\/}}, {\tt{'}}{\tt{nil}})))\index{status-flag-readyp}
\end{tabbing}


\noindent{\sc Event}:   Disable status-flag-readyp-list.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-car-index-ready-set \\ \index{lessp-car-index-ready-set}
\=\+(({\it{i\/}} $<$ {\it{n\/}}) $\wedge$ {\rm{listp}}\,({\rm{index-ready-set}}\,({\it{n\/}}, {\it{l\/}})\index{index-ready-set})) \\ 
$\rightarrow$$\;\;\;\;$({\it{i\/}} $<$ {\rm{car}}\,({\rm{index-ready-set}}\,({\it{n\/}}, {\it{l\/}})\index{index-ready-set}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  lessp-car-index-ready-set-instance \\ \index{lessp-car-index-ready-set-insta!nce}
{\rm{listp}}\,({\rm{index-ready-set}}\,($1\;+$ {\it{n\/}}, {\it{l\/}})\index{index-ready-set}) $\rightarrow$ ({\it{n\/}} $<$ {\rm{car}}\,({\rm{index-ready-set}}\,($1\;+$ {\it{n\/}}, {\it{l\/}})\index{index-ready-set}))
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-car-index-ready-set-instance.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-insert-to-cons-crock1 \\ \index{rewrite-insert-to-cons-crock1}
\=\+{\rm{listp}}\,({\rm{index-ready-set}}\,($1\;+$ {\it{n\/}}, {\it{z\/}})\index{index-ready-set}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{insert}}\,({\it{n\/}}, {\rm{index-ready-set}}\,($1\;+$ {\it{n\/}}, {\it{z\/}})\index{index-ready-set})\index{insert} \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\it{n\/}}, {\rm{index-ready-set}}\,($1\;+$ {\it{n\/}}, {\it{z\/}})\index{index-ready-set}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-insert-to-cons-crock2 \\ \index{rewrite-insert-to-cons-crock2}
\=\+($\neg$ {\rm{listp}}\,({\rm{index-ready-set}}\,($1\;+$ {\it{n\/}}, {\it{z\/}})\index{index-ready-set})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{insert}}\,({\it{n\/}}, {\rm{index-ready-set}}\,($1\;+$ {\it{n\/}}, {\it{z\/}})\index{index-ready-set})\index{insert} \\ 
$=$$\;\;\;\;${\rm{cons}}\,({\it{n\/}}, {\rm{index-ready-set}}\,($1\;+$ {\it{n\/}}, {\it{z\/}})\index{index-ready-set}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-insert-to-cons-crock \\ \index{rewrite-insert-to-cons-crock}
{\rm{insert}}\,({\it{n\/}}, {\rm{index-ready-set}}\,($1\;+$ {\it{n\/}}, {\it{z\/}})\index{index-ready-set})\index{insert} $=$ {\rm{cons}}\,({\it{n\/}}, {\rm{index-ready-set}}\,($1\;+$ {\it{n\/}}, {\it{z\/}})\index{index-ready-set})
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-insert-to-cons-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  index-ready-set-putnth-ready-status \\ \index{index-ready-set-putnth-ready-st!atus}
\=\+(\=\+({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{status-flag-readyp}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{status-flag-readyp}) $\wedge$ {\rm{status-flag-readyp}}\,({\it{v\/}})\index{status-flag-readyp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{index-ready-set}}\,({\it{n\/}}, {\rm{putnth}}\,({\it{v\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth})\index{index-ready-set} \\ 
$=$$\;\;\;\;${\rm{insert}}\,({\it{n\/}} $+$ {\it{i\/}}, {\rm{index-ready-set}}\,({\it{n\/}}, {\it{l\/}})\index{index-ready-set})\index{insert})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable index-ready-set-putnth-ready-status.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  sorted-index-ready-set \\ \index{sorted-index-ready-set}
{\rm{sorted}}\,({\rm{index-ready-set}}\,({\it{n\/}}, {\it{l\/}})\index{index-ready-set})\index{sorted}
\end{tabbing}


\noindent{\sc Event}:   Disable sorted-index-ready-set.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-enq-index-ready-set-putnth \\ \index{permutation-enq-index-ready-set!-putnth}
\=\+(\=\+{\rm{permutation}}\,({\it{queue\/}}, {\rm{index-ready-set}}\,({\tt{'}}{\tt{0}}, {\it{status\/}})\index{index-ready-set})\index{permutation} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{status-flag-readyp}}\,({\rm{getnth}}\,({\it{taskid\/}}, {\it{status\/}})\index{getnth})\index{status-flag-readyp}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\it{queue\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\rm{length}}\,({\it{status\/}})\index{length})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{enq}}\,({\it{taskid\/}}, {\it{queue\/}})\index{enq}, \\ 
{\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{cons}}\,({\tt{'}}{\tt{0}}, {\rm{cons}}\,({\it{x\/}}, {\tt{'}}{\tt{nil}})), \\ 
{\it{taskid\/}}, \\ 
{\it{status\/}})\-\index{putnth})\-\index{index-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-enq-index-ready-set-putnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  number-of-ready-tasks-equals-length-ak-readyq \\ \index{number-of-ready-tasks-equals-le!ngth-ak-readyq}
\=\+{\rm{permutation}}\,({\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq}, {\rm{ak-ready-set}}\,({\it{ak\/}})\index{ak-ready-set})\index{permutation} \\ 
$\rightarrow$$\;\;\;\;$({\rm{number-of-ready-tasks}}\,({\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{number-of-ready-tasks} $=$ {\rm{length}}\,({\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq})\index{length})\-
\end{tabbing}


\noindent{\sc Event}:   Disable number-of-ready-tasks-equals-length-ak-readyq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-waiting-to-sendp-implies-readyq-not-full \\ \index{ak-waiting-to-sendp-implies-rea!dyq-not-full}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$({\rm{ak-waiting-to-sendp}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-waiting-to-sendp} $\wedge$ {\rm{finite-numberp}}\,({\it{srcid\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp}))\- \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{qfullp}}\,({\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq}, {\tt{'}}{\tt{16}})\index{qfullp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ak-waiting-to-receivep-implies-readyq-not-full \\ \index{ak-waiting-to-receivep-implies-!readyq-not-full}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{ak-waiting-to-receivep}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-waiting-to-receivep} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\it{destid\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp})\-)\- \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{qfullp}}\,({\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq}, {\tt{'}}{\tt{16}})\index{qfullp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ak-waiting-to-outputp-implies-readyq-not-full \\ \index{ak-waiting-to-outputp-implies-re!adyq-not-full}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ({\rm{ak-waiting-to-outputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-outputp} $\wedge$ {\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp})) \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{qfullp}}\,({\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq}, {\tt{'}}{\tt{16}})\index{qfullp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ak-waiting-to-inputp-implies-readyq-not-full \\ \index{ak-waiting-to-inputp-implies-re!adyq-not-full}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ({\rm{ak-waiting-to-inputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-inputp} $\wedge$ {\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp})) \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{qfullp}}\,({\rm{ak-readyq}}\,({\it{ak\/}})\index{ak-readyq}, {\tt{'}}{\tt{16}})\index{qfullp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-error-handler \\ \index{good-ak-ak-error-handler}
({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting})) $\rightarrow$ {\rm{good-ak}}\,({\rm{ak-error-handler}}\,({\it{ak\/}})\index{ak-error-handler})\index{good-ak}
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-error-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-clock-interrupt-handler \\ \index{good-ak-ak-clock-interrupt-hand!ler}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-clock-interrupt-handler}}\,({\it{ak\/}})\index{ak-clock-interrupt-handler})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-block-send \\ \index{good-ak-ak-block-send}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}) \\ 
$\wedge$$\;\;\;\;$(({\it{srcid\/}} $=$ {\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}) $\wedge$ {\rm{finite-numberp}}\,({\it{destid\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-block-send}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-block-send})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-block-send.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-waiting-to-receivep-implies-not-status-flag-readyp \\ \index{ak-waiting-to-receivep-implies-!not-status-flag-readyp}
\=\+{\rm{ak-waiting-to-receivep}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-waiting-to-receivep} \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{status-flag-readyp}}\,({\rm{getnth}}\,({\it{destid\/}}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{getnth})\index{status-flag-readyp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-execute-send-to-buffer \\ \index{good-ak-ak-execute-send-to-buffe!r}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{qfullp2}}\,({\it{srcid\/}}, {\it{destid\/}}, {\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers}, {\tt{'}}{\tt{4}})\index{qfullp2}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{srcid\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{destid\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\it{msg\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-execute-send-to-buffer}}\,({\it{msg\/}}, {\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-execute-send-to-buffer})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-execute-send-to-buffer.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-execute-send \\ \index{good-ak-ak-execute-send}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{destid\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\it{msg\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-execute-send}}\,({\it{msg\/}}, {\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\it{destid\/}}, {\it{ak\/}})\index{ak-execute-send})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-execute-send.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-block-receive \\ \index{good-ak-ak-block-receive}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}) \\ 
$\wedge$$\;\;\;\;$(({\it{destid\/}} $=$ {\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}) $\wedge$ {\rm{finite-numberp}}\,({\it{srcid\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-block-receive}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-block-receive})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-block-receive.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-waiting-to-sendp-implies-not-status-flag-readyp \\ \index{ak-waiting-to-sendp-implies-not!-status-flag-readyp}
\=\+{\rm{ak-waiting-to-sendp}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-waiting-to-sendp} \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{status-flag-readyp}}\,({\rm{getnth}}\,({\it{srcid\/}}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{getnth})\index{status-flag-readyp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-status-properties \\ \index{good-status-properties}
\=\+{\rm{good-status}}\,({\it{status\/}})\index{good-status} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\it{status\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\it{status\/}})\index{length} $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{status\/}})\index{getnth}, {\tt{'}}{\tt{6}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{status\/}})\index{getnth}, {\tt{'}}{\tt{16}})\index{finite-numberp})\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-status-properties.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-execute-receive-from-buffer \\ \index{good-ak-ak-execute-receive-from!-buffer}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{qemptyp2}}\,({\it{srcid\/}}, {\it{destid\/}}, {\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers})\index{qemptyp2}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{srcid\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\it{destid\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-execute-receive-from-buffer}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-execute-receive-from-buffer})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-execute-receive-from-buffer.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-execute-receive \\ \index{good-ak-ak-execute-receive}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ (($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}) $\wedge$ {\rm{finite-numberp}}\,({\it{srcid\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-execute-receive}}\,({\it{srcid\/}}, {\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\it{ak\/}})\index{ak-execute-receive})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-execute-receive.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-block-output \\ \index{good-ak-ak-block-output}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ (($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}) $\wedge$ ({\it{id\/}} $=$ {\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}))) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-block-output}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-block-output})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-block-output.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-obuffers-properties \\ \index{good-ak-obuffers-properties}
\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\rightarrow$$\;\;\;\;$({\rm{plistp}}\,({\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers})\index{plistp} $\wedge$ ({\rm{length}}\,({\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers})\index{length} $=$ {\tt{'}}{\tt{16}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-obuffers-properties.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-execute-output-to-buffer \\ \index{good-ak-ak-execute-output-to-bu!ffer}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{qfullp}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers})\index{getnth}, {\tt{'}}{\tt{4}})\index{qfullp}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\it{char\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-execute-output-to-buffer}}\,({\it{char\/}}, {\it{id\/}}, {\it{ak\/}})\index{ak-execute-output-to-buffer})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-execute-output-to-buffer.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-execute-output \\ \index{good-ak-ak-execute-output}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ (($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}) $\wedge$ {\rm{finite-numberp}}\,({\it{char\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-execute-output}}\,({\it{char\/}}, {\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\it{ak\/}})\index{ak-execute-output})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-execute-output.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-block-input \\ \index{good-ak-ak-block-input}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ (($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}) $\wedge$ ({\it{id\/}} $=$ {\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}))) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-block-input}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-block-input})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-block-input.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ibuffers-properties \\ \index{good-ak-ibuffers-properties}
\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\rightarrow$$\;\;\;\;$({\rm{plistp}}\,({\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers})\index{plistp} $\wedge$ ({\rm{length}}\,({\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers})\index{length} $=$ {\tt{'}}{\tt{16}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ibuffers-properties.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-execute-input-from-buffer \\ \index{good-ak-ak-execute-input-from-b!uffer}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{qemptyp}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers})\index{getnth})\index{qemptyp}))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-execute-input-from-buffer}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-execute-input-from-buffer})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-execute-input-from-buffer.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-execute-input \\ \index{good-ak-ak-execute-input}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-execute-input}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\it{ak\/}})\index{ak-execute-input})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-execute-input.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-ak-srcid \\ \index{finite-numberp-ak-srcid}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{finite-numberp}}\,({\rm{ak-srcid}}\,({\it{ak\/}})\index{ak-srcid}, {\tt{'}}{\tt{16}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-ak-srcid.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-ak-destid \\ \index{finite-numberp-ak-destid}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{finite-numberp}}\,({\rm{ak-destid}}\,({\it{ak\/}})\index{ak-destid}, {\tt{'}}{\tt{16}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-ak-destid.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-ak-message \\ \index{finite-numberp-ak-message}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{ak-message}}\,({\it{ak\/}})\index{ak-message}, {\tt{'}}{\tt{65536}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-ak-message.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-svc-handler \\ \index{good-ak-ak-svc-handler}
({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting})) $\rightarrow$ {\rm{good-ak}}\,({\rm{ak-svc-handler}}\,({\it{ak\/}})\index{ak-svc-handler})\index{good-ak}
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-svc-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-private-step \\ \index{good-ak-ak-private-step}
({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting})) $\rightarrow$ {\rm{good-ak}}\,({\rm{ak-private-step}}\,({\it{ak\/}})\index{ak-private-step})\index{good-ak}
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-private-step.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-waiting-to-inputp-implies-not-status-flag-readyp \\ \index{ak-waiting-to-inputp-implies-not!-status-flag-readyp}
\=\+{\rm{ak-waiting-to-inputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-inputp} \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{status-flag-readyp}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{getnth})\index{status-flag-readyp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  ak-waiting-to-outputp-implies-not-status-flag-readyp \\ \index{ak-waiting-to-outputp-implies-n!ot-status-flag-readyp}
\=\+{\rm{ak-waiting-to-outputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-outputp} \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{status-flag-readyp}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{ak-status}}\,({\it{ak\/}})\index{ak-status})\index{getnth})\index{status-flag-readyp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-tm-iport-properties \\ \index{good-tm-iport-properties}
\=\+{\rm{good-tm-iport}}\,({\it{port\/}})\index{good-tm-iport} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-iportp}}\,({\it{port\/}})\index{tm-iportp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\rm{tm-iinterrupt-flag}}\,({\it{port\/}})\index{tm-iinterrupt-flag}, {\tt{'}}{\tt{2}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\rm{tm-ierror-flag}}\,({\it{port\/}})\index{tm-ierror-flag}, {\tt{'}}{\tt{2}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-ichar}}\,({\it{port\/}})\index{tm-ichar}, {\tt{'}}{\tt{256}})\index{finite-numberp})\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-iport-properties.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-waiting-input-interrupt-handler-case1 \\ \index{good-ak-ak-waiting-input-interr!upt-handler-case1}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$({\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting} $\wedge$ {\rm{ak-waiting-to-inputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-inputp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-waiting-input-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-input-interrupt-hand!ler})\index{good-ak}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-waiting-input-interrupt-handler-case2 \\ \index{good-ak-ak-waiting-input-interr!upt-handler-case2}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$({\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting} $\wedge$ ($\neg$ {\rm{ak-waiting-to-inputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-inputp})))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-waiting-input-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-input-interrupt-hand!ler})\index{good-ak}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-waiting-input-interrupt-handler \\ \index{good-ak-ak-waiting-input-interr!upt-handler}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ({\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp} $\wedge$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-waiting-input-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-input-interrupt-hand!ler})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-waiting-input-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-running-input-interrupt-handler-case1 \\ \index{good-ak-ak-running-input-interr!upt-handler-case1}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}) $\wedge$ {\rm{ak-waiting-to-inputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-inputp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-running-input-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-running-input-interrupt-hand!ler})\index{good-ak}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-running-input-interrupt-handler-case2 \\ \index{good-ak-ak-running-input-interr!upt-handler-case2}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}) $\wedge$ ($\neg$ {\rm{ak-waiting-to-inputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-inputp})))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-running-input-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-running-input-interrupt-hand!ler})\index{good-ak}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-running-input-interrupt-handler \\ \index{good-ak-ak-running-input-interr!upt-handler}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ({\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp} $\wedge$ ($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}))) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-running-input-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-running-input-interrupt-hand!ler})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-running-input-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-interrupting-ak-input-port \\ \index{finite-numberp-interrupting-ak-i!nput-port}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-interrupting-input-port}}\,({\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports})\index{tm-interrupting-input-port}, {\tt{'}}{\tt{16}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-interrupting-ak-input-port.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-input-interrupt-handler \\ \index{good-ak-ak-input-interrupt-hand!ler}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ {\rm{ak-input-interruptp}}\,({\it{ak\/}})\index{ak-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-input-interrupt-handler}}\,(\=\+{\rm{ak-interrupting-input-port}}\,({\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports})\index{ak-interrupting-input-port}, \\ 
{\it{ak\/}})\-\index{ak-input-interrupt-handler})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-input-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-oport-properties \\ \index{good-tm-oport-properties}
\=\+{\rm{good-tm-oport}}\,({\it{port\/}})\index{good-tm-oport} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-oportp}}\,({\it{port\/}})\index{tm-oportp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\rm{tm-ointerrupt-flag}}\,({\it{port\/}})\index{tm-ointerrupt-flag}, {\tt{'}}{\tt{2}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\rm{tm-obusy-flag}}\,({\it{port\/}})\index{tm-obusy-flag}, {\tt{'}}{\tt{2}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-ochar}}\,({\it{port\/}})\index{tm-ochar}, {\tt{'}}{\tt{256}})\index{finite-numberp})\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-oport-properties.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-waiting-output-interrupt-handler-case1 \\ \index{good-ak-ak-waiting-output-inter!rupt-handler-case1}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$({\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting} $\wedge$ {\rm{ak-waiting-to-outputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-outputp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-waiting-output-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-output-interrupt-han!dler})\index{good-ak}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-waiting-output-interrupt-handler-case2 \\ \index{good-ak-ak-waiting-output-inter!rupt-handler-case2}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$({\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting} $\wedge$ ($\neg$ {\rm{ak-waiting-to-outputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-outputp})))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-waiting-output-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-output-interrupt-han!dler})\index{good-ak}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-waiting-output-interrupt-handler \\ \index{good-ak-ak-waiting-output-inter!rupt-handler}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ({\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp} $\wedge$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-waiting-output-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-output-interrupt-han!dler})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-waiting-output-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-running-output-interrupt-handler-case1 \\ \index{good-ak-ak-running-output-inter!rupt-handler-case1}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}) $\wedge$ {\rm{ak-waiting-to-outputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-outputp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-running-output-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-running-output-interrupt-han!dler})\index{good-ak}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-running-output-interrupt-handler-case2 \\ \index{good-ak-ak-running-output-inter!rupt-handler-case2}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}) $\wedge$ ($\neg$ {\rm{ak-waiting-to-outputp}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-waiting-to-outputp})))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-running-output-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-running-output-interrupt-han!dler})\index{good-ak}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-running-output-interrupt-handler \\ \index{good-ak-ak-running-output-inter!rupt-handler}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ({\rm{finite-numberp}}\,({\it{id\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp} $\wedge$ ($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}))) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-running-output-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-running-output-interrupt-han!dler})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-running-output-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-interrupting-ak-output-port \\ \index{finite-numberp-interrupting-ak-!output-port}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{tm-interrupting-output-port}}\,({\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\index{tm-interrupting-output-port}, {\tt{'}}{\tt{16}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-interrupting-ak-output-port.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-output-interrupt-handler \\ \index{good-ak-ak-output-interrupt-han!dler}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ {\rm{ak-output-interruptp}}\,({\it{ak\/}})\index{ak-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-output-interrupt-handler}}\,(\=\+{\rm{ak-interrupting-output-port}}\,({\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\index{ak-interrupting-output-port}, \\ 
{\it{ak\/}})\-\index{ak-output-interrupt-handler})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-output-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-step \\ \index{good-ak-ak-step}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{good-ak}}\,({\rm{ak-step}}\,({\it{ak\/}})\index{ak-step})\index{good-ak}
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-step.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-post-input-interrupt \\ \index{good-ak-ak-post-input-interrupt}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ {\rm{tm-device-input-eventp}}\,({\it{interrupt\/}})\index{tm-device-input-eventp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-post-interrupt}}\,({\it{interrupt\/}}, {\it{ak\/}})\index{ak-post-interrupt})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-post-input-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-post-output-interrupt \\ \index{good-ak-ak-post-output-interrupt}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ {\rm{tm-device-output-eventp}}\,({\it{interrupt\/}})\index{tm-device-output-eventp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-post-interrupt}}\,({\it{interrupt\/}}, {\it{ak\/}})\index{ak-post-interrupt})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-post-output-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-post-interrupt-noop \\ \index{good-ak-ak-post-interrupt-noop}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-device-input-eventp}}\,({\it{interrupt\/}})\index{tm-device-input-eventp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-device-output-eventp}}\,({\it{interrupt\/}})\index{tm-device-output-eventp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-ak}}\,({\rm{ak-post-interrupt}}\,({\it{interrupt\/}}, {\it{ak\/}})\index{ak-post-interrupt})\index{good-ak}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-post-interrupt-noop.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-post-interrupt \\ \index{good-ak-ak-post-interrupt}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{good-ak}}\,({\rm{ak-post-interrupt}}\,({\it{interrupt\/}}, {\it{ak\/}})\index{ak-post-interrupt})\index{good-ak}
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-post-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-ak-processor \\ \index{good-ak-ak-processor}
{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\rightarrow$ {\rm{good-ak}}\,({\rm{ak-processor}}\,({\it{ak\/}}, {\it{oracle\/}})\index{ak-processor})\index{good-ak}
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-ak-processor.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-pstates-ak-clock-interrupt-handler \\ \index{ak-pstates-ak-clock-interrupt-h!andler}
{\rm{ak-pstates}}\,({\rm{ak-clock-interrupt-handler}}\,({\it{ak\/}})\index{ak-clock-interrupt-handler})\index{ak-pstates} $=$ {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}
\end{tabbing}


\noindent{\sc Event}:   Disable ak-pstates-ak-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-pstates-ak-error-handler \\ \index{ak-pstates-ak-error-handler}
{\rm{ak-pstates}}\,({\rm{ak-error-handler}}\,({\it{ak\/}})\index{ak-error-handler})\index{ak-pstates} $=$ {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}
\end{tabbing}


\noindent{\sc Event}:   Disable ak-pstates-ak-error-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-pstates-ak-block-send \\ \index{ak-pstates-ak-block-send}
{\rm{ak-pstates}}\,({\rm{ak-block-send}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-block-send})\index{ak-pstates} $=$ {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}
\end{tabbing}


\noindent{\sc Event}:   Disable ak-pstates-ak-block-send.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-ak-pstates-ak-execute-send-to-buffer \\ \index{length-ak-pstates-ak-execute-se!nd-to-buffer}
\=\+{\rm{length}}\,({\rm{ak-pstates}}\,({\rm{ak-execute-send-to-buffer}}\,({\it{msg\/}}, {\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-execute-send-to-buffer})\index{ak-pstates})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{length}\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-ak-pstates-ak-execute-send-to-buffer.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-ak-pstates-ak-execute-send \\ \index{length-ak-pstates-ak-execute-se!nd}
\=\+{\rm{length}}\,({\rm{ak-pstates}}\,({\rm{ak-execute-send}}\,({\it{msg\/}}, {\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-execute-send})\index{ak-pstates})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{length}\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-ak-pstates-ak-execute-send.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-pstates-ak-block-receive \\ \index{ak-pstates-ak-block-receive}
{\rm{ak-pstates}}\,({\rm{ak-block-receive}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-block-receive})\index{ak-pstates} $=$ {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}
\end{tabbing}


\noindent{\sc Event}:   Disable ak-pstates-ak-block-receive.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-ak-pstates-ak-execute-receive-from-buffer \\ \index{length-ak-pstates-ak-execute-re!ceive-from-buffer}
\=\+{\rm{length}}\,({\rm{ak-pstates}}\,({\rm{ak-execute-receive-from-buffer}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-execute-receive-from-buffer})\index{ak-pstates})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{length}\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-ak-pstates-ak-execute-receive-from-buffer.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-ak-pstates-ak-execute-receive \\ \index{length-ak-pstates-ak-execute-re!ceive}
\=\+{\rm{length}}\,({\rm{ak-pstates}}\,({\rm{ak-execute-receive}}\,({\it{srcid\/}}, {\it{destid\/}}, {\it{ak\/}})\index{ak-execute-receive})\index{ak-pstates})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{length}\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-ak-pstates-ak-execute-receive.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-pstates-ak-block-output \\ \index{ak-pstates-ak-block-output}
{\rm{ak-pstates}}\,({\rm{ak-block-output}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-block-output})\index{ak-pstates} $=$ {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}
\end{tabbing}


\noindent{\sc Event}:   Disable ak-pstates-ak-block-output.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-ak-pstates-ak-execute-output-to-buffer \\ \index{length-ak-pstates-ak-execute-outp!ut-to-buffer}
\=\+{\rm{length}}\,({\rm{ak-pstates}}\,({\rm{ak-execute-output-to-buffer}}\,({\it{char\/}}, {\it{id\/}}, {\it{ak\/}})\index{ak-execute-output-to-buffer})\index{ak-pstates})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{length}\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-ak-pstates-ak-execute-output-to-buffer.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-ak-pstates-ak-execute-output \\ \index{length-ak-pstates-ak-execute-outp!ut}
\=\+{\rm{length}}\,({\rm{ak-pstates}}\,({\rm{ak-execute-output}}\,({\it{char\/}}, {\it{id\/}}, {\it{ak\/}})\index{ak-execute-output})\index{ak-pstates})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{length}\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-ak-pstates-ak-execute-output.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-pstates-ak-block-input \\ \index{ak-pstates-ak-block-input}
{\rm{ak-pstates}}\,({\rm{ak-block-input}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-block-input})\index{ak-pstates} $=$ {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}
\end{tabbing}


\noindent{\sc Event}:   Disable ak-pstates-ak-block-input.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-ak-pstates-ak-execute-input-from-buffer \\ \index{length-ak-pstates-ak-execute-inp!ut-from-buffer}
\=\+{\rm{length}}\,({\rm{ak-pstates}}\,({\rm{ak-execute-input-from-buffer}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-execute-input-from-buffer})\index{ak-pstates})\index{length} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{length}\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-ak-pstates-ak-execute-input-from-buffer.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-ak-pstates-ak-execute-input \\ \index{length-ak-pstates-ak-execute-inp!ut}
{\rm{length}}\,({\rm{ak-pstates}}\,({\rm{ak-execute-input}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-execute-input})\index{ak-pstates})\index{length} $=$ {\rm{length}}\,({\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-ak-pstates-ak-execute-input.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-ak-pstates-ak-svc-handler \\ \index{length-ak-pstates-ak-svc-handle!r}
{\rm{length}}\,({\rm{ak-pstates}}\,({\rm{ak-svc-handler}}\,({\it{ak\/}})\index{ak-svc-handler})\index{ak-pstates})\index{length} $=$ {\rm{length}}\,({\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-ak-pstates-ak-svc-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-pstates-ak-input-interrupt-handler \\ \index{ak-pstates-ak-input-interrupt-h!andler}
{\rm{ak-pstates}}\,({\rm{ak-input-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-input-interrupt-handler})\index{ak-pstates} $=$ {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}
\end{tabbing}


\noindent{\sc Event}:   Disable ak-pstates-ak-input-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-pstates-ak-output-interrupt-handler \\ \index{ak-pstates-ak-output-interrupt-!handler}
{\rm{ak-pstates}}\,({\rm{ak-output-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-output-interrupt-handler})\index{ak-pstates} $=$ {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}
\end{tabbing}


\noindent{\sc Event}:   Disable ak-pstates-ak-output-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-ak-pstates-ak-private-step \\ \index{length-ak-pstates-ak-private-step}
{\rm{length}}\,({\rm{ak-pstates}}\,({\rm{ak-private-step}}\,({\it{ak\/}})\index{ak-private-step})\index{ak-pstates})\index{length} $=$ {\rm{length}}\,({\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-ak-pstates-ak-private-step.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-ak-pstates-ak-step \\ \index{length-ak-pstates-ak-step}
{\rm{length}}\,({\rm{ak-pstates}}\,({\rm{ak-step}}\,({\it{ak\/}})\index{ak-step})\index{ak-pstates})\index{length} $=$ {\rm{length}}\,({\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-ak-pstates-ak-step.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{ak-channels} \\  
\=\+{\rm{ak-channels}}\,({\it{ak\/}})\index{ak-channels} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers}, \\ 
{\rm{cons}}\,({\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers}, {\rm{cons}}\,({\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers}, {\tt{'}}{\tt{nil}})))\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{project} \\  
{\rm{project}}\,({\it{i\/}}, {\it{ak\/}})\index{project} $=$ {\rm{task}}\,({\rm{getnth}}\,({\it{i\/}}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth}, {\rm{ak-channels}}\,({\it{ak\/}})\index{ak-channels})\index{task}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{control-oracle-step} \\  
\=\+{\rm{control-oracle-step}}\,({\it{i\/}}, {\it{ak\/}})\index{control-oracle-step} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{ak-input-interruptp}}\,({\it{ak\/}})\index{ak-input-interruptp} \\ 
{\bf then }{\rm{ak-channels}}\,({\rm{ak-input-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{ak-iports}}\,({\it{ak\/}})\index{ak-iports})\index{tm-interrupting-input-port}, \\ 
{\it{ak\/}})\-\index{ak-input-interrupt-handler})\index{ak-channels} \\ 
{\bf elseif }{\rm{ak-output-interruptp}}\,({\it{ak\/}})\index{ak-output-interruptp} \\ 
{\bf then }{\rm{ak-channels}}\,({\rm{ak-output-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{ak-oports}}\,({\it{ak\/}})\index{ak-oports})\index{tm-interrupting-output-port}, \\ 
{\it{ak\/}})\-\index{ak-output-interrupt-handler})\index{ak-channels} \\ 
{\bf elseif }{\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}$\;\;${\bf then }{\rm{ak-channels}}\,({\it{ak\/}})\index{ak-channels} \\ 
{\bf elseif }{\rm{ak-errorp}}\,({\it{ak\/}})\index{ak-errorp}$\;\;${\bf then }{\rm{ak-channels}}\,({\rm{ak-error-handler}}\,({\it{ak\/}})\index{ak-error-handler})\index{ak-channels} \\ 
{\bf elseif }{\rm{ak-clock-interruptp}}\,({\it{ak\/}})\index{ak-clock-interruptp} \\ 
{\bf then }{\rm{ak-channels}}\,({\rm{ak-clock-interrupt-handler}}\,({\it{ak\/}})\index{ak-clock-interrupt-handler})\index{ak-channels} \\ 
{\bf elseif }{\rm{ak-svc-interruptp}}\,({\it{ak\/}})\index{ak-svc-interruptp} \\ 
{\bf then }\=\+{\bf if }{\it{i\/}} $=$ {\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}$\;\;${\bf then }{\tt{'}}{\tt{*1*true}} \\ 
{\bf else }{\rm{ak-channels}}\,({\rm{ak-svc-handler}}\,({\it{ak\/}})\index{ak-svc-handler})\index{ak-channels}$\;${\bf  endif}\- \\ 
{\bf elseif }{\it{i\/}} $=$ {\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}$\;\;${\bf then }{\tt{'}}{\tt{*1*true}} \\ 
{\bf else }{\rm{ak-channels}}\,({\rm{ak-private-step}}\,({\it{ak\/}})\index{ak-private-step})\index{ak-channels}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{control-oracle} \\  
\=\+{\rm{control-oracle}}\,({\it{i\/}}, {\it{ak\/}}, {\it{oracle\/}})\index{control-oracle} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{oracle\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{control-oracle-step}}\,({\it{i\/}}, {\rm{ak-post-interrupt}}\,({\rm{car}}\,({\it{oracle\/}}), {\it{ak\/}})\index{ak-post-interrupt})\index{control-oracle-step}, \\ 
{\rm{control-oracle}}\,(\=\+{\it{i\/}}, \\ 
{\rm{ak-step}}\,({\rm{ak-post-interrupt}}\,({\rm{car}}\,({\it{oracle\/}}), {\it{ak\/}})\index{ak-post-interrupt})\index{ak-step}, \\ 
{\rm{cdr}}\,({\it{oracle\/}}))\-\index{control-oracle})\- \\ 
{\bf else }{\tt{'}}{\tt{nil}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  access-ak-post-interrupt \\ \index{access-ak-post-interrupt}
\=\+({\rm{ak-pstates}}\,({\rm{ak-post-interrupt}}\,({\it{interrupt\/}}, {\it{ak\/}})\index{ak-post-interrupt})\index{ak-pstates} $=$ {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{ak-ibuffers}}\,({\rm{ak-post-interrupt}}\,({\it{interrupt\/}}, {\it{ak\/}})\index{ak-post-interrupt})\index{ak-ibuffers} $=$ {\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{ak-obuffers}}\,({\rm{ak-post-interrupt}}\,({\it{interrupt\/}}, {\it{ak\/}})\index{ak-post-interrupt})\index{ak-obuffers} \\ 
$=$$\;\;\;\;${\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{ak-mbuffers}}\,({\rm{ak-post-interrupt}}\,({\it{interrupt\/}}, {\it{ak\/}})\index{ak-post-interrupt})\index{ak-mbuffers} \\ 
$=$$\;\;\;\;${\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{ak-taskid}}\,({\rm{ak-post-interrupt}}\,({\it{interrupt\/}}, {\it{ak\/}})\index{ak-post-interrupt})\index{ak-taskid} \\ 
$=$$\;\;\;\;${\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid})\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable access-ak-post-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  access-ak-input-interrupt-handler \\ \index{access-ak-input-interrupt-handle!r}
\=\+({\rm{ak-pstates}}\,({\rm{ak-input-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-input-interrupt-handler})\index{ak-pstates} $=$ {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{ak-obuffers}}\,({\rm{ak-input-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-input-interrupt-handler})\index{ak-obuffers} $=$ {\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{ak-mbuffers}}\,({\rm{ak-input-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-input-interrupt-handler})\index{ak-mbuffers} \\ 
$=$$\;\;\;\;${\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable access-ak-input-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  access-ak-output-interrupt-handler \\ \index{access-ak-output-interrupt-hand!ler}
\=\+({\rm{ak-pstates}}\,({\rm{ak-output-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-output-interrupt-handler})\index{ak-pstates} $=$ {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{ak-ibuffers}}\,({\rm{ak-output-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-output-interrupt-handler})\index{ak-ibuffers} $=$ {\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{ak-mbuffers}}\,({\rm{ak-output-interrupt-handler}}\,({\it{id\/}}, {\it{ak\/}})\index{ak-output-interrupt-handler})\index{ak-mbuffers} \\ 
$=$$\;\;\;\;${\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable access-ak-output-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  access-ak-error-handler \\ \index{access-ak-error-handler}
\=\+({\rm{ak-pstates}}\,({\rm{ak-error-handler}}\,({\it{ak\/}})\index{ak-error-handler})\index{ak-pstates} $=$ {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{ak-ibuffers}}\,({\rm{ak-error-handler}}\,({\it{ak\/}})\index{ak-error-handler})\index{ak-ibuffers} $=$ {\rm{ak-ibuffers}}\,({\it{ak\/}})\index{ak-ibuffers}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{ak-obuffers}}\,({\rm{ak-error-handler}}\,({\it{ak\/}})\index{ak-error-handler})\index{ak-obuffers} $=$ {\rm{ak-obuffers}}\,({\it{ak\/}})\index{ak-obuffers}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{ak-mbuffers}}\,({\rm{ak-error-handler}}\,({\it{ak\/}})\index{ak-error-handler})\index{ak-mbuffers} \\ 
$=$$\;\;\;\;${\rm{ak-mbuffers}}\,({\it{ak\/}})\index{ak-mbuffers})\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable access-ak-error-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-private-step-non-interference \\ \index{ak-private-step-non-interference}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{i\/}}, {\rm{length}}\,({\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{length})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$(({\it{i\/}} $\not=$ {\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}) $\wedge$ ($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting})))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\it{i\/}}, {\rm{ak-pstates}}\,({\rm{ak-private-step}}\,({\it{ak\/}})\index{ak-private-step})\index{ak-pstates})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\it{i\/}}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable ak-private-step-non-interference.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-svc-handler-non-interference \\ \index{ak-svc-handler-non-interference}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{i\/}}, {\rm{length}}\,({\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{length})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$(({\it{i\/}} $\not=$ {\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}) $\wedge$ ($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting})))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\it{i\/}}, {\rm{ak-pstates}}\,({\rm{ak-svc-handler}}\,({\it{ak\/}})\index{ak-svc-handler})\index{ak-pstates})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\it{i\/}}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable ak-svc-handler-non-interference.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-implements-non-active-task-step \\ \index{ak-implements-non-active-task-step}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{i\/}}, {\rm{length}}\,({\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{length})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{task-activep}}\,({\rm{control-oracle-step}}\,(\=\+{\it{i\/}}, \\ 
{\rm{ak-post-interrupt}}\,(\=\+{\rm{car}}\,({\it{oracle\/}}), \\ 
{\it{ak\/}})\-\index{ak-post-interrupt})\-\index{control-oracle-step})\index{task-activep}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{project}}\,({\it{i\/}}, {\rm{ak-step}}\,({\rm{ak-post-interrupt}}\,({\rm{car}}\,({\it{oracle\/}}), {\it{ak\/}})\index{ak-post-interrupt})\index{ak-step})\index{project} \\ 
$=$$\;\;\;\;${\rm{task-update-channels}}\,(\=\+{\rm{project}}\,({\it{i\/}}, {\it{ak\/}})\index{project}, \\ 
{\rm{control-oracle-step}}\,(\=\+{\it{i\/}}, \\ 
{\rm{ak-post-interrupt}}\,(\=\+{\rm{car}}\,({\it{oracle\/}}), \\ 
{\it{ak\/}})\-\index{ak-post-interrupt})\-\index{control-oracle-step})\-\index{task-update-channels})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable ak-implements-non-active-task-step.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-execute-receive-implements-task-execute-receive \\ \index{ak-execute-receive-implements-t!ask-execute-receive}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{task}}\,(\=\+{\rm{getnth}}\,(\=\+{\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, \\ 
{\rm{ak-pstates}}\,({\rm{ak-execute-receive}}\,(\=\+{\rm{ak-srcid}}\,({\it{ak\/}})\index{ak-srcid}, \\ 
{\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, \\ 
{\it{ak\/}})\-\index{ak-execute-receive})\index{ak-pstates})\-\index{getnth}, \\ 
{\rm{ak-channels}}\,({\rm{ak-execute-receive}}\,({\rm{ak-srcid}}\,({\it{ak\/}})\index{ak-srcid}, {\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\it{ak\/}})\index{ak-execute-receive})\index{ak-channels})\-\index{task} \\ 
$=$$\;\;\;\;${\rm{task-execute-receive}}\,(\=\+{\rm{task-srcid}}\,({\rm{task}}\,(\=\+{\rm{getnth}}\,(\=\+{\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, \\ 
{\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\-\index{getnth}, \\ 
{\rm{ak-channels}}\,({\it{ak\/}})\index{ak-channels})\-\index{task})\index{task-srcid}, \\ 
{\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, \\ 
{\rm{task}}\,(\=\+{\rm{getnth}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth}, \\ 
{\rm{ak-channels}}\,({\it{ak\/}})\index{ak-channels})\-\index{task})\-\index{task-execute-receive})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable ak-execute-receive-implements-task-execute-receive.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-execute-send-implements-task-execute-send \\ \index{ak-execute-send-implements-task!-execute-send}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{task}}\,(\=\+{\rm{getnth}}\,(\=\+{\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, \\ 
{\rm{ak-pstates}}\,({\rm{ak-execute-send}}\,(\=\+{\rm{ak-message}}\,({\it{ak\/}})\index{ak-message}, \\ 
{\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, \\ 
{\rm{ak-destid}}\,({\it{ak\/}})\index{ak-destid}, \\ 
{\it{ak\/}})\-\index{ak-execute-send})\index{ak-pstates})\-\index{getnth}, \\ 
{\rm{ak-channels}}\,({\rm{ak-execute-send}}\,(\=\+{\rm{ak-message}}\,({\it{ak\/}})\index{ak-message}, \\ 
{\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, \\ 
{\rm{ak-destid}}\,({\it{ak\/}})\index{ak-destid}, \\ 
{\it{ak\/}})\-\index{ak-execute-send})\index{ak-channels})\-\index{task} \\ 
$=$$\;\;\;\;${\rm{task-execute-send}}\,(\=\+{\rm{task-message}}\,({\rm{task}}\,(\=\+{\rm{getnth}}\,(\=\+{\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, \\ 
{\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\-\index{getnth}, \\ 
{\rm{ak-channels}}\,({\it{ak\/}})\index{ak-channels})\-\index{task})\index{task-message}, \\ 
{\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, \\ 
{\rm{task-destid}}\,({\rm{task}}\,(\=\+{\rm{getnth}}\,(\=\+{\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, \\ 
{\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\-\index{getnth}, \\ 
{\rm{ak-channels}}\,({\it{ak\/}})\index{ak-channels})\-\index{task})\index{task-destid}, \\ 
{\rm{task}}\,(\=\+{\rm{getnth}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth}, \\ 
{\rm{ak-channels}}\,({\it{ak\/}})\index{ak-channels})\-\index{task})\-\index{task-execute-send})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable ak-execute-send-implements-task-execute-send.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-execute-input-implements-task-execute-input \\ \index{ak-execute-input-implements-tas!k-execute-input}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{task}}\,(\=\+{\rm{getnth}}\,(\=\+{\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, \\ 
{\rm{ak-pstates}}\,({\rm{ak-execute-input}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\it{ak\/}})\index{ak-execute-input})\index{ak-pstates})\-\index{getnth}, \\ 
{\rm{ak-channels}}\,({\rm{ak-execute-input}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\it{ak\/}})\index{ak-execute-input})\index{ak-channels})\-\index{task} \\ 
$=$$\;\;\;\;${\rm{task-execute-input}}\,(\=\+{\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, \\ 
{\rm{task}}\,(\=\+{\rm{getnth}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth}, \\ 
{\rm{ak-channels}}\,({\it{ak\/}})\index{ak-channels})\-\index{task})\-\index{task-execute-input})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable ak-execute-input-implements-task-execute-input.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-execute-output-implements-task-execute-output \\ \index{ak-execute-output-implements-ta!sk-execute-output}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{task}}\,(\=\+{\rm{getnth}}\,(\=\+{\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, \\ 
{\rm{ak-pstates}}\,({\rm{ak-execute-output}}\,(\=\+{\rm{ak-message}}\,({\it{ak\/}})\index{ak-message}, \\ 
{\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, \\ 
{\it{ak\/}})\-\index{ak-execute-output})\index{ak-pstates})\-\index{getnth}, \\ 
{\rm{ak-channels}}\,({\rm{ak-execute-output}}\,({\rm{ak-message}}\,({\it{ak\/}})\index{ak-message}, {\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\it{ak\/}})\index{ak-execute-output})\index{ak-channels})\-\index{task} \\ 
$=$$\;\;\;\;${\rm{task-execute-output}}\,(\=\+{\rm{task-message}}\,({\rm{task}}\,(\=\+{\rm{getnth}}\,(\=\+{\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, \\ 
{\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\-\index{getnth}, \\ 
{\rm{ak-channels}}\,({\it{ak\/}})\index{ak-channels})\-\index{task})\index{task-message}, \\ 
{\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, \\ 
{\rm{task}}\,(\=\+{\rm{getnth}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth}, \\ 
{\rm{ak-channels}}\,({\it{ak\/}})\index{ak-channels})\-\index{task})\-\index{task-execute-output})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable ak-execute-output-implements-task-execute-output.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-svc-handler-implements-task-communication-step \\ \index{ak-svc-handler-implements-task-!communication-step}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ ($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{task}}\,(\=\+{\rm{getnth}}\,({\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, {\rm{ak-pstates}}\,({\rm{ak-svc-handler}}\,({\it{ak\/}})\index{ak-svc-handler})\index{ak-pstates})\index{getnth}, \\ 
{\rm{ak-channels}}\,({\rm{ak-svc-handler}}\,({\it{ak\/}})\index{ak-svc-handler})\index{ak-channels})\-\index{task} \\ 
$=$$\;\;\;\;${\rm{task-communication-step}}\,(\=\+{\rm{task}}\,(\=\+{\rm{getnth}}\,(\=\+{\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}, \\ 
{\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\-\index{getnth}, \\ 
{\rm{ak-channels}}\,({\it{ak\/}})\index{ak-channels})\-\index{task}, \\ 
{\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid})\-\index{task-communication-step})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable ak-svc-handler-implements-task-communication-step.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-private-step-implements-task-fetch-execute \\ \index{ak-private-step-implements-task!-fetch-execute}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{ak-waiting}}\,({\it{ak\/}})\index{ak-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{i\/}}, {\rm{length}}\,({\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{length})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$({\it{i\/}} $=$ {\rm{ak-taskid}}\,({\it{ak\/}})\index{ak-taskid}))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{task}}\,(\=\+{\rm{getnth}}\,({\it{i\/}}, {\rm{ak-pstates}}\,({\rm{ak-private-step}}\,({\it{ak\/}})\index{ak-private-step})\index{ak-pstates})\index{getnth}, \\ 
{\rm{ak-channels}}\,({\rm{ak-private-step}}\,({\it{ak\/}})\index{ak-private-step})\index{ak-channels})\-\index{task} \\ 
$=$$\;\;\;\;${\rm{task}}\,(\=\+{\rm{tm-fetch-execute}}\,({\rm{getnth}}\,({\it{i\/}}, {\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{getnth})\index{tm-fetch-execute}, \\ 
{\rm{ak-channels}}\,({\it{ak\/}})\index{ak-channels})\-\index{task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable ak-private-step-implements-task-fetch-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-implements-active-task-step \\ \index{ak-implements-active-task-step}
\=\+(\=\+{\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{i\/}}, {\rm{length}}\,({\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{length})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;${\rm{task-activep}}\,({\rm{control-oracle-step}}\,(\=\+{\it{i\/}}, \\ 
{\rm{ak-post-interrupt}}\,(\=\+{\rm{car}}\,({\it{oracle\/}}), \\ 
{\it{ak\/}})\-\index{ak-post-interrupt})\-\index{control-oracle-step})\index{task-activep})\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{project}}\,({\it{i\/}}, {\rm{ak-step}}\,({\rm{ak-post-interrupt}}\,({\rm{car}}\,({\it{oracle\/}}), {\it{ak\/}})\index{ak-post-interrupt})\index{ak-step})\index{project} \\ 
$=$$\;\;\;\;${\rm{task-step}}\,({\rm{project}}\,({\it{i\/}}, {\it{ak\/}})\index{project}, {\it{i\/}})\index{task-step})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable ak-implements-active-task-step.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-implements-parallel-tasks \\ \index{ak-implements-parallel-tasks}
\=\+({\rm{good-ak}}\,({\it{ak\/}})\index{good-ak} $\wedge$ {\rm{finite-numberp}}\,({\it{i\/}}, {\rm{length}}\,({\rm{ak-pstates}}\,({\it{ak\/}})\index{ak-pstates})\index{length})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{project}}\,({\it{i\/}}, {\rm{ak-processor}}\,({\it{ak\/}}, {\it{oracle\/}})\index{ak-processor})\index{project} \\ 
$=$$\;\;\;\;${\rm{task-processor}}\,({\rm{project}}\,({\it{i\/}}, {\it{ak\/}})\index{project}, {\it{i\/}}, {\rm{control-oracle}}\,({\it{i\/}}, {\it{ak\/}}, {\it{oracle\/}})\index{control-oracle})\index{task-processor})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable ak-implements-parallel-tasks.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{asm-opcode-alist} \\  
\=\+{\sc{asm-opcode-alist}}\index{asm-opcode-alist} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{(}}{\tt{return}}{\tt{ .\ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{wait}}{\tt{ .\ }}{\tt{4}}{\tt{)}} \\ 
{\tt{(}}{\tt{run}}{\tt{ .\ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{br}}{\tt{ .\ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{brz}}{\tt{ .\ }}{\tt{10}}{\tt{)}} \\ 
{\tt{(}}{\tt{brnz}}{\tt{ .\ }}{\tt{6}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ .\ }}{\tt{14}}{\tt{)}} \\ 
{\tt{(}}{\tt{decr}}{\tt{ .\ }}{\tt{18}}{\tt{)}} \\ 
{\tt{(}}{\tt{decrm}}{\tt{ .\ }}{\tt{5}}{\tt{)}} \\ 
{\tt{(}}{\tt{incr}}{\tt{ .\ }}{\tt{22}}{\tt{)}} \\ 
{\tt{(}}{\tt{incrm}}{\tt{ .\ }}{\tt{7}}{\tt{)}} \\ 
{\tt{(}}{\tt{lbase}}{\tt{ .\ }}{\tt{26}}{\tt{)}} \\ 
{\tt{(}}{\tt{llimit}}{\tt{ .\ }}{\tt{30}}{\tt{)}} \\ 
{\tt{(}}{\tt{lpsw}}{\tt{ .\ }}{\tt{34}}{\tt{)}} \\ 
{\tt{(}}{\tt{post}}{\tt{ .\ }}{\tt{38}}{\tt{)}} \\ 
{\tt{(}}{\tt{svc}}{\tt{ .\ }}{\tt{42}}{\tt{)}} \\ 
{\tt{(}}{\tt{svcr}}{\tt{ .\ }}{\tt{46}}{\tt{)}} \\ 
{\tt{(}}{\tt{time}}{\tt{ .\ }}{\tt{58}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ .\ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{compare}}{\tt{ .\ }}{\tt{3}}{\tt{)}} \\ 
{\tt{(}}{\tt{mod}}{\tt{ .\ }}{\tt{9}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ .\ }}{\tt{11}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ .\ }}{\tt{13}}{\tt{)}} \\ 
{\tt{(}}{\tt{stout}}{\tt{ .\ }}{\tt{15}}{\tt{)}} \\ 
{\tt{(}}{\tt{testi}}{\tt{ .\ }}{\tt{50}}{\tt{)}} \\ 
{\tt{(}}{\tt{testo}}{\tt{ .\ }}{\tt{54}}{\tt{)}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{append-n-times} \\  
\=\+{\rm{append-n-times}}\,({\it{n\/}}, {\it{list\/}})\index{append-n-times} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{'}}{\tt{nil}} \\ 
{\bf else }{\rm{append}}\,({\it{list\/}}, {\rm{append-n-times}}\,({\it{n\/}} $-\;1$, {\it{list\/}})\index{append-n-times})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{lookup} \\  
\=\+{\rm{lookup}}\,({\it{x\/}}, {\it{alist\/}})\index{lookup} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{alist\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{car}}\,({\it{alist\/}})) $\wedge$ ({\it{x\/}} $=$ {\rm{car}}\,({\rm{car}}\,({\it{alist\/}}))) \\ 
{\bf then }{\rm{cdr}}\,({\rm{car}}\,({\it{alist\/}})) \\ 
{\bf else }{\rm{lookup}}\,({\it{x\/}}, {\rm{cdr}}\,({\it{alist\/}}))\index{lookup}$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{nil}}$\;${\bf  endif}\-\-
\end{tabbing}

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

\begin{tabbing}{\sc Definition}:\index{number-and-litatom-listp} \\  
\=\+{\rm{number-and-litatom-listp}}\,({\it{x\/}})\index{number-and-litatom-listp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{x\/}}) \\ 
{\bf then }\=\+(({\rm{car}}\,({\it{x\/}}) $\in\;${\bf{N}}${}$) $\vee$ {\rm{litatom}}\,({\rm{car}}\,({\it{x\/}}))) \\ 
$\wedge$$\;\;\;\;${\rm{number-and-litatom-listp}}\,({\rm{cdr}}\,({\it{x\/}}))\index{number-and-litatom-listp}\- \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{dc-formp} \\  
\=\+{\rm{dc-formp}}\,({\it{x\/}})\index{dc-formp} \\ 
$=$$\;\;\;\;$(\=\+{\rm{listp}}\,({\it{x\/}}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{car}}\,({\it{x\/}}) $=$ {\tt{'}}{\tt{dc}}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{car}}\,({\rm{cdr}}\,({\it{x\/}})) $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{x\/}}))) $\in\;${\bf{N}}${}$) \\ 
$\vee$$\;\;\;\;$(\=\+{\rm{litatom}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{x\/}})))) \\ 
$\vee$$\;\;\;\;$(\=\+{\rm{listp}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{x\/}})))) \\ 
$\vee$$\;\;\;\;${\rm{number-and-litatom-listp}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{x\/}}))))\index{number-and-litatom-listp})\-)\-)\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{translate-dc-arg} \\  
\=\+{\rm{translate-dc-arg}}\,({\it{arg\/}}, {\it{symtab\/}})\index{translate-dc-arg} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{arg\/}} $\in\;${\bf{N}}${}$$\;\;${\bf then }{\it{arg\/}} \\ 
{\bf elseif }{\rm{litatom}}\,({\it{arg\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{boundp}}\,({\it{arg\/}}, {\it{symtab\/}})\index{boundp}$\;\;${\bf then }{\rm{lookup}}\,({\it{arg\/}}, {\it{symtab\/}})\index{lookup} \\ 
{\bf else }{\it{arg\/}}$\;${\bf  endif}\- \\ 
{\bf else }{\it{arg\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{translate-dc-arglist} \\  
\=\+{\rm{translate-dc-arglist}}\,({\it{arglist\/}}, {\it{symtab\/}})\index{translate-dc-arglist} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{arglist\/}}) \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{translate-dc-arg}}\,({\rm{car}}\,({\it{arglist\/}}), {\it{symtab\/}})\index{translate-dc-arg}, \\ 
{\rm{translate-dc-arglist}}\,({\rm{cdr}}\,({\it{arglist\/}}), {\it{symtab\/}})\index{translate-dc-arglist})\- \\ 
{\bf else }{\tt{'}}{\tt{nil}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{translate-dc} \\  
\=\+{\rm{translate-dc}}\,({\it{dc-form\/}}, {\it{symtab\/}})\index{translate-dc} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{dc-formp}}\,({\it{dc-form\/}})\index{dc-formp} \\ 
{\bf then }{\rm{append-n-times}}\,(\=\+{\rm{car}}\,({\rm{cdr}}\,({\it{dc-form\/}})), \\ 
{\rm{translate-dc-arglist}}\,(\=\+\=\+{\bf if }{\rm{listp}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{dc-form\/}})))) \\ 
{\bf then }{\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{dc-form\/}}))) \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{dc-form\/}}))), \\ 
{\tt{'}}{\tt{nil}})\-$\;${\bf  endif}\-, \\ 
{\it{symtab\/}})\-\index{translate-dc-arglist})\-\index{append-n-times} \\ 
{\bf else }{\it{dc-form\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm-instruction-opcode} \\  
\=\+{\rm{asm-instruction-opcode}}\,({\it{instruction\/}})\index{asm-instruction-opcode} \\ 
$=$$\;\;\;\;${\rm{lookup}}\,(\=\+{\rm{car}}\,({\it{instruction\/}}), \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{(}}{\tt{return}}{\tt{ .\ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{wait}}{\tt{ .\ }}{\tt{4}}{\tt{)}} \\ 
{\tt{(}}{\tt{run}}{\tt{ .\ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{br}}{\tt{ .\ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{brz}}{\tt{ .\ }}{\tt{10}}{\tt{)}} \\ 
{\tt{(}}{\tt{brnz}}{\tt{ .\ }}{\tt{6}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ .\ }}{\tt{14}}{\tt{)}} \\ 
{\tt{(}}{\tt{decr}}{\tt{ .\ }}{\tt{18}}{\tt{)}} \\ 
{\tt{(}}{\tt{decrm}}{\tt{ .\ }}{\tt{5}}{\tt{)}} \\ 
{\tt{(}}{\tt{incr}}{\tt{ .\ }}{\tt{22}}{\tt{)}} \\ 
{\tt{(}}{\tt{incrm}}{\tt{ .\ }}{\tt{7}}{\tt{)}} \\ 
{\tt{(}}{\tt{lbase}}{\tt{ .\ }}{\tt{26}}{\tt{)}} \\ 
{\tt{(}}{\tt{llimit}}{\tt{ .\ }}{\tt{30}}{\tt{)}} \\ 
{\tt{(}}{\tt{lpsw}}{\tt{ .\ }}{\tt{34}}{\tt{)}} \\ 
{\tt{(}}{\tt{post}}{\tt{ .\ }}{\tt{38}}{\tt{)}} \\ 
{\tt{(}}{\tt{svc}}{\tt{ .\ }}{\tt{42}}{\tt{)}} \\ 
{\tt{(}}{\tt{svcr}}{\tt{ .\ }}{\tt{46}}{\tt{)}} \\ 
{\tt{(}}{\tt{time}}{\tt{ .\ }}{\tt{58}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ .\ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{compare}}{\tt{ .\ }}{\tt{3}}{\tt{)}} \\ 
{\tt{(}}{\tt{mod}}{\tt{ .\ }}{\tt{9}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ .\ }}{\tt{11}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ .\ }}{\tt{13}}{\tt{)}} \\ 
{\tt{(}}{\tt{stout}}{\tt{ .\ }}{\tt{15}}{\tt{)}} \\ 
{\tt{(}}{\tt{testi}}{\tt{ .\ }}{\tt{50}}{\tt{)}} \\ 
{\tt{(}}{\tt{testo}}{\tt{ .\ }}{\tt{54}}{\tt{)}}{\tt{)}}\-)\-\index{lookup}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm-instruction-mode1} \\  
\=\+{\rm{asm-instruction-mode1}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{asm-instruction-mode1} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\rm{car}}\,({\rm{cdr}}\,({\it{instruction\/}}))) \\ 
{\bf then }\=\+{\bf if }{\rm{boundp}}\,({\rm{car}}\,({\rm{car}}\,({\rm{cdr}}\,({\it{instruction\/}}))), {\it{symtab\/}})\index{boundp} \\ 
{\bf then }{\rm{lookup}}\,({\rm{car}}\,({\rm{car}}\,({\rm{cdr}}\,({\it{instruction\/}}))), {\it{symtab\/}})\index{lookup} \\ 
{\bf else }{\rm{car}}\,({\rm{car}}\,({\rm{cdr}}\,({\it{instruction\/}})))$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm-instruction-arg1} \\  
\=\+{\rm{asm-instruction-arg1}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{asm-instruction-arg1} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\rm{car}}\,({\rm{cdr}}\,({\it{instruction\/}}))) \\ 
{\bf then }\=\+{\bf if }{\rm{boundp}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{car}}\,({\rm{cdr}}\,({\it{instruction\/}})))), {\it{symtab\/}})\index{boundp} \\ 
{\bf then }{\rm{lookup}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{car}}\,({\rm{cdr}}\,({\it{instruction\/}})))), {\it{symtab\/}})\index{lookup} \\ 
{\bf else }{\rm{car}}\,({\rm{cdr}}\,({\rm{car}}\,({\rm{cdr}}\,({\it{instruction\/}}))))$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{boundp}}\,({\rm{car}}\,({\rm{cdr}}\,({\it{instruction\/}})), {\it{symtab\/}})\index{boundp} \\ 
{\bf then }{\rm{lookup}}\,({\rm{car}}\,({\rm{cdr}}\,({\it{instruction\/}})), {\it{symtab\/}})\index{lookup} \\ 
{\bf else }{\rm{car}}\,({\rm{cdr}}\,({\it{instruction\/}}))$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm-instruction-index1} \\  
\=\+{\rm{asm-instruction-index1}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{asm-instruction-index1} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\rm{car}}\,({\rm{cdr}}\,({\it{instruction\/}}))) \\ 
{\bf then }\=\+{\bf if }{\rm{boundp}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\rm{car}}\,({\rm{cdr}}\,({\it{instruction\/}}))))), {\it{symtab\/}})\index{boundp} \\ 
{\bf then }{\rm{lookup}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\rm{car}}\,({\rm{cdr}}\,({\it{instruction\/}}))))), {\it{symtab\/}})\index{lookup} \\ 
{\bf else }{\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\rm{car}}\,({\rm{cdr}}\,({\it{instruction\/}})))))$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm-instruction-mode2} \\  
\=\+{\rm{asm-instruction-mode2}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{asm-instruction-mode2} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{instruction\/}})))) \\ 
{\bf then }\=\+{\bf if }{\rm{boundp}}\,({\rm{car}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{instruction\/}})))), {\it{symtab\/}})\index{boundp} \\ 
{\bf then }{\rm{lookup}}\,({\rm{car}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{instruction\/}})))), {\it{symtab\/}})\index{lookup} \\ 
{\bf else }{\rm{car}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{instruction\/}}))))$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm-instruction-arg2} \\  
\=\+{\rm{asm-instruction-arg2}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{asm-instruction-arg2} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{instruction\/}})))) \\ 
{\bf then }\=\+{\bf if }{\rm{boundp}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{instruction\/}}))))), {\it{symtab\/}})\index{boundp} \\ 
{\bf then }{\rm{lookup}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{instruction\/}}))))), {\it{symtab\/}})\index{lookup} \\ 
{\bf else }{\rm{car}}\,({\rm{cdr}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{instruction\/}})))))$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{boundp}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{instruction\/}}))), {\it{symtab\/}})\index{boundp} \\ 
{\bf then }{\rm{lookup}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{instruction\/}}))), {\it{symtab\/}})\index{lookup} \\ 
{\bf else }{\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{instruction\/}})))$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm-instruction-index2} \\  
\=\+{\rm{asm-instruction-index2}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{asm-instruction-index2} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{instruction\/}})))) \\ 
{\bf then }\=\+{\bf if }{\rm{boundp}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{instruction\/}})))))), {\it{symtab\/}})\index{boundp} \\ 
{\bf then }{\rm{lookup}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{instruction\/}})))))), {\it{symtab\/}})\index{lookup} \\ 
{\bf else }{\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{instruction\/}}))))))$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm-good-arg} \\  
\=\+{\rm{asm-good-arg}}\,({\it{arg\/}}, {\it{mode\/}})\index{asm-good-arg} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\it{mode\/}} $=$ {\tt{'}}{\tt{0}}) $\vee$ ({\it{mode\/}} $=$ {\tt{'}}{\tt{2}})$\;\;${\bf then }{\rm{finite-numberp}}\,({\it{arg\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp} \\ 
{\bf else }{\rm{finite-numberp}}\,({\it{arg\/}}, {\tt{'}}{\tt{8}})\index{finite-numberp}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm-good-instruction} \\  
\=\+{\rm{asm-good-instruction}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{asm-good-instruction} \\ 
$=$$\;\;\;\;$(\=\+{\rm{boundp}}\,(\=\+{\rm{car}}\,({\it{instruction\/}}), \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{(}}{\tt{return}}{\tt{ .\ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{wait}}{\tt{ .\ }}{\tt{4}}{\tt{)}} \\ 
{\tt{(}}{\tt{run}}{\tt{ .\ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{br}}{\tt{ .\ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{brz}}{\tt{ .\ }}{\tt{10}}{\tt{)}} \\ 
{\tt{(}}{\tt{brnz}}{\tt{ .\ }}{\tt{6}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ .\ }}{\tt{14}}{\tt{)}} \\ 
{\tt{(}}{\tt{decr}}{\tt{ .\ }}{\tt{18}}{\tt{)}} \\ 
{\tt{(}}{\tt{decrm}}{\tt{ .\ }}{\tt{5}}{\tt{)}} \\ 
{\tt{(}}{\tt{incr}}{\tt{ .\ }}{\tt{22}}{\tt{)}} \\ 
{\tt{(}}{\tt{incrm}}{\tt{ .\ }}{\tt{7}}{\tt{)}} \\ 
{\tt{(}}{\tt{lbase}}{\tt{ .\ }}{\tt{26}}{\tt{)}} \\ 
{\tt{(}}{\tt{llimit}}{\tt{ .\ }}{\tt{30}}{\tt{)}} \\ 
{\tt{(}}{\tt{lpsw}}{\tt{ .\ }}{\tt{34}}{\tt{)}} \\ 
{\tt{(}}{\tt{post}}{\tt{ .\ }}{\tt{38}}{\tt{)}} \\ 
{\tt{(}}{\tt{svc}}{\tt{ .\ }}{\tt{42}}{\tt{)}} \\ 
{\tt{(}}{\tt{svcr}}{\tt{ .\ }}{\tt{46}}{\tt{)}} \\ 
{\tt{(}}{\tt{time}}{\tt{ .\ }}{\tt{58}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ .\ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{compare}}{\tt{ .\ }}{\tt{3}}{\tt{)}} \\ 
{\tt{(}}{\tt{mod}}{\tt{ .\ }}{\tt{9}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ .\ }}{\tt{11}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ .\ }}{\tt{13}}{\tt{)}} \\ 
{\tt{(}}{\tt{stout}}{\tt{ .\ }}{\tt{15}}{\tt{)}} \\ 
{\tt{(}}{\tt{testi}}{\tt{ .\ }}{\tt{50}}{\tt{)}} \\ 
{\tt{(}}{\tt{testo}}{\tt{ .\ }}{\tt{54}}{\tt{)}}{\tt{)}}\-)\-\index{boundp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{length}}\,({\it{instruction\/}})\index{length} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-nullary-instructionp}}\,({\rm{lookup}}\,(\=\+{\rm{car}}\,({\it{instruction\/}}), \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{(}}\=\+{\tt{return}} \\ 
{\tt{.\ }}{\tt{0}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{wait}}{\tt{ .\ }}{\tt{4}}{\tt{)}} \\ 
{\tt{(}}{\tt{run}}{\tt{ .\ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{br}}{\tt{ .\ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{brz}}{\tt{ .\ }}{\tt{10}}{\tt{)}} \\ 
{\tt{(}}{\tt{brnz}}{\tt{ .\ }}{\tt{6}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ .\ }}{\tt{14}}{\tt{)}} \\ 
{\tt{(}}{\tt{decr}}{\tt{ .\ }}{\tt{18}}{\tt{)}} \\ 
{\tt{(}}{\tt{decrm}}{\tt{ .\ }}{\tt{5}}{\tt{)}} \\ 
{\tt{(}}{\tt{incr}}{\tt{ .\ }}{\tt{22}}{\tt{)}} \\ 
{\tt{(}}{\tt{incrm}}{\tt{ .\ }}{\tt{7}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{lbase}} \\ 
{\tt{.\ }}{\tt{26}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{llimit}} \\ 
{\tt{.\ }}{\tt{30}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{lpsw}}{\tt{ .\ }}{\tt{34}}{\tt{)}} \\ 
{\tt{(}}{\tt{post}}{\tt{ .\ }}{\tt{38}}{\tt{)}} \\ 
{\tt{(}}{\tt{svc}}{\tt{ .\ }}{\tt{42}}{\tt{)}} \\ 
{\tt{(}}{\tt{svcr}}{\tt{ .\ }}{\tt{46}}{\tt{)}} \\ 
{\tt{(}}{\tt{time}}{\tt{ .\ }}{\tt{58}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ .\ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{compare}} \\ 
{\tt{.\ }}{\tt{3}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{mod}}{\tt{ .\ }}{\tt{9}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ .\ }}{\tt{11}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ .\ }}{\tt{13}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{stout}} \\ 
{\tt{.\ }}{\tt{15}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{testi}} \\ 
{\tt{.\ }}{\tt{50}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{testo}} \\ 
{\tt{.\ }}{\tt{54}}{\tt{)}}\-{\tt{)}}\-)\-\index{lookup})\index{tm-nullary-instructionp} \\ 
{\bf then }{\tt{'}}{\tt{1}} \\ 
{\bf elseif }{\rm{tm-unary-instructionp}}\,({\rm{lookup}}\,(\=\+{\rm{car}}\,({\it{instruction\/}}), \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{(}}\=\+{\tt{return}} \\ 
{\tt{.\ }}{\tt{0}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{wait}}{\tt{ .\ }}{\tt{4}}{\tt{)}} \\ 
{\tt{(}}{\tt{run}}{\tt{ .\ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{br}}{\tt{ .\ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{brz}}{\tt{ .\ }}{\tt{10}}{\tt{)}} \\ 
{\tt{(}}{\tt{brnz}}{\tt{ .\ }}{\tt{6}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{call}} \\ 
{\tt{.\ }}{\tt{14}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{decr}} \\ 
{\tt{.\ }}{\tt{18}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{decrm}} \\ 
{\tt{.\ }}{\tt{5}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{incr}} \\ 
{\tt{.\ }}{\tt{22}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{incrm}} \\ 
{\tt{.\ }}{\tt{7}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{lbase}} \\ 
{\tt{.\ }}{\tt{26}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{llimit}} \\ 
{\tt{.\ }}{\tt{30}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{lpsw}} \\ 
{\tt{.\ }}{\tt{34}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{post}} \\ 
{\tt{.\ }}{\tt{38}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{svc}}{\tt{ .\ }}{\tt{42}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{svcr}} \\ 
{\tt{.\ }}{\tt{46}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{time}} \\ 
{\tt{.\ }}{\tt{58}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{add}}{\tt{ .\ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{compare}} \\ 
{\tt{.\ }}{\tt{3}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{mod}}{\tt{ .\ }}{\tt{9}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{move}} \\ 
{\tt{.\ }}{\tt{11}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{mult}} \\ 
{\tt{.\ }}{\tt{13}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{stout}} \\ 
{\tt{.\ }}{\tt{15}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{testi}} \\ 
{\tt{.\ }}{\tt{50}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{testo}} \\ 
{\tt{.\ }}{\tt{54}}{\tt{)}}\-{\tt{)}}\-)\-\index{lookup})\index{tm-unary-instructionp} \\ 
{\bf then }{\tt{'}}{\tt{2}} \\ 
{\bf else }{\tt{'}}{\tt{3}}$\;${\bf  endif}\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,(\=\+{\rm{asm-instruction-mode1}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{symtab\/}})\-\index{asm-instruction-mode1}, \\ 
{\tt{'}}{\tt{4}})\-\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,(\=\+{\rm{asm-instruction-mode2}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{symtab\/}})\-\index{asm-instruction-mode2}, \\ 
{\tt{'}}{\tt{4}})\-\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{asm-good-arg}}\,(\=\+{\rm{asm-instruction-arg1}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{symtab\/}})\-\index{asm-instruction-arg1}, \\ 
{\rm{asm-instruction-mode1}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{symtab\/}})\-\index{asm-instruction-mode1})\-\index{asm-good-arg} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{asm-good-arg}}\,(\=\+{\rm{asm-instruction-arg2}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{symtab\/}})\-\index{asm-instruction-arg2}, \\ 
{\rm{asm-instruction-mode2}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{symtab\/}})\-\index{asm-instruction-mode2})\-\index{asm-good-arg} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,(\=\+{\rm{asm-instruction-index1}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{symtab\/}})\-\index{asm-instruction-index1}, \\ 
{\tt{'}}{\tt{8}})\-\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,(\=\+{\rm{asm-instruction-index2}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{symtab\/}})\-\index{asm-instruction-index2}, \\ 
{\tt{'}}{\tt{8}})\-\index{finite-numberp})\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm-pack-word1} \\  
\=\+{\rm{asm-pack-word1}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{asm-pack-word1} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{instruction\/}})\index{length} $=$ {\tt{'}}{\tt{1}} \\ 
{\bf then }{\rm{asm-instruction-opcode}}\,({\it{instruction\/}})\index{asm-instruction-opcode} \\ 
{\bf elseif }{\rm{length}}\,({\it{instruction\/}})\index{length} $=$ {\tt{'}}{\tt{2}} \\ 
{\bf then }\=\+{\rm{asm-instruction-opcode}}\,({\it{instruction\/}})\index{asm-instruction-opcode} \\ 
$+$$\;\;\;\;$(\=\+({\rm{asm-instruction-mode1}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{asm-instruction-mode1} $*$ {\tt{'}}{\tt{64}}) \\ 
$+$$\;\;\;\;$(\=\+{\rm{asm-instruction-index1}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{asm-instruction-index1} \\ 
$*$$\;\;\;\;${\tt{'}}{\tt{256}})\-)\-\- \\ 
{\bf else }\=\+{\rm{asm-instruction-opcode}}\,({\it{instruction\/}})\index{asm-instruction-opcode} \\ 
$+$$\;\;\;\;$(\=\+(\=\+{\rm{asm-instruction-mode1}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{asm-instruction-mode1} \\ 
$*$$\;\;\;\;${\tt{'}}{\tt{64}})\- \\ 
$+$$\;\;\;\;$(\=\+(\=\+{\rm{asm-instruction-index1}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{asm-instruction-index1} \\ 
$*$$\;\;\;\;${\tt{'}}{\tt{256}})\- \\ 
$+$$\;\;\;\;$(\=\+(\=\+{\rm{asm-instruction-mode2}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{symtab\/}})\-\index{asm-instruction-mode2} \\ 
$*$$\;\;\;\;${\tt{'}}{\tt{2048}})\- \\ 
$+$$\;\;\;\;$(\=\+{\rm{asm-instruction-index2}}\,(\=\+{\it{instruction\/}}, \\ 
{\it{symtab\/}})\-\index{asm-instruction-index2} \\ 
$*$$\;\;\;\;${\tt{'}}{\tt{8192}})\-)\-)\-)\-\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm-pack-instruction} \\  
\=\+{\rm{asm-pack-instruction}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{asm-pack-instruction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{instruction\/}})\index{length} $=$ {\tt{'}}{\tt{1}} \\ 
{\bf then }{\rm{cons}}\,({\rm{asm-pack-word1}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{asm-pack-word1}, {\tt{'}}{\tt{nil}}) \\ 
{\bf elseif }{\rm{length}}\,({\it{instruction\/}})\index{length} $=$ {\tt{'}}{\tt{2}} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\rm{asm-pack-word1}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{asm-pack-word1}, \\ 
{\rm{cons}}\,({\rm{asm-instruction-arg1}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{asm-instruction-arg1}, {\tt{'}}{\tt{nil}}))\- \\ 
{\bf else }{\rm{cons}}\,(\=\+{\rm{asm-pack-word1}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{asm-pack-word1}, \\ 
{\rm{cons}}\,(\=\+{\rm{asm-instruction-arg1}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{asm-instruction-arg1}, \\ 
{\rm{cons}}\,(\=\+{\rm{asm-instruction-arg2}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{asm-instruction-arg2}, \\ 
{\tt{'}}{\tt{nil}})\-)\-)\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{translate-instruction} \\  
\=\+{\rm{translate-instruction}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{translate-instruction} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{asm-good-instruction}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{asm-good-instruction} \\ 
{\bf then }{\rm{asm-pack-instruction}}\,({\it{instruction\/}}, {\it{symtab\/}})\index{asm-pack-instruction} \\ 
{\bf else }{\it{instruction\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{translate-source} \\  
\=\+{\rm{translate-source}}\,({\it{source\/}}, {\it{symtab\/}})\index{translate-source} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{source\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{litatom}}\,({\rm{car}}\,({\it{source\/}})) \\ 
{\bf then }{\rm{translate-source}}\,({\rm{cdr}}\,({\it{source\/}}), {\it{symtab\/}})\index{translate-source} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{car}}\,({\it{source\/}})) $\wedge$ ({\rm{car}}\,({\rm{car}}\,({\it{source\/}})) $=$ {\tt{'}}{\tt{dcl}}) \\ 
{\bf then }{\rm{translate-source}}\,({\rm{cdr}}\,({\it{source\/}}), {\it{symtab\/}})\index{translate-source} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{car}}\,({\it{source\/}})) $\wedge$ ({\rm{car}}\,({\rm{car}}\,({\it{source\/}})) $=$ {\tt{'}}{\tt{dc}}) \\ 
{\bf then }{\rm{append}}\,(\=\+{\rm{translate-dc}}\,({\rm{car}}\,({\it{source\/}}), {\it{symtab\/}})\index{translate-dc}, \\ 
{\rm{translate-source}}\,({\rm{cdr}}\,({\it{source\/}}), {\it{symtab\/}})\index{translate-source})\- \\ 
{\bf else }{\rm{append}}\,(\=\+{\rm{translate-instruction}}\,({\rm{car}}\,({\it{source\/}}), {\it{symtab\/}})\index{translate-instruction}, \\ 
{\rm{translate-source}}\,({\rm{cdr}}\,({\it{source\/}}), {\it{symtab\/}})\index{translate-source})\-$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{nil}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{incr-dc-position} \\  
\=\+{\rm{incr-dc-position}}\,({\it{dc-form\/}})\index{incr-dc-position} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{dc-form\/}})))) \\ 
{\bf then }{\rm{car}}\,({\rm{cdr}}\,({\it{dc-form\/}})) $*$ {\rm{length}}\,({\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\it{dc-form\/}}))))\index{length} \\ 
{\bf else }{\rm{car}}\,({\rm{cdr}}\,({\it{dc-form\/}}))$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{incr-instruction-position} \\  
\=\+{\rm{incr-instruction-position}}\,({\it{instruction\/}})\index{incr-instruction-position} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{boundp}}\,(\=\+{\rm{car}}\,({\it{instruction\/}}), \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{(}}{\tt{return}}{\tt{ .\ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{wait}}{\tt{ .\ }}{\tt{4}}{\tt{)}} \\ 
{\tt{(}}{\tt{run}}{\tt{ .\ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{br}}{\tt{ .\ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{brz}}{\tt{ .\ }}{\tt{10}}{\tt{)}} \\ 
{\tt{(}}{\tt{brnz}}{\tt{ .\ }}{\tt{6}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ .\ }}{\tt{14}}{\tt{)}} \\ 
{\tt{(}}{\tt{decr}}{\tt{ .\ }}{\tt{18}}{\tt{)}} \\ 
{\tt{(}}{\tt{decrm}}{\tt{ .\ }}{\tt{5}}{\tt{)}} \\ 
{\tt{(}}{\tt{incr}}{\tt{ .\ }}{\tt{22}}{\tt{)}} \\ 
{\tt{(}}{\tt{incrm}}{\tt{ .\ }}{\tt{7}}{\tt{)}} \\ 
{\tt{(}}{\tt{lbase}}{\tt{ .\ }}{\tt{26}}{\tt{)}} \\ 
{\tt{(}}{\tt{llimit}}{\tt{ .\ }}{\tt{30}}{\tt{)}} \\ 
{\tt{(}}{\tt{lpsw}}{\tt{ .\ }}{\tt{34}}{\tt{)}} \\ 
{\tt{(}}{\tt{post}}{\tt{ .\ }}{\tt{38}}{\tt{)}} \\ 
{\tt{(}}{\tt{svc}}{\tt{ .\ }}{\tt{42}}{\tt{)}} \\ 
{\tt{(}}{\tt{svcr}}{\tt{ .\ }}{\tt{46}}{\tt{)}} \\ 
{\tt{(}}{\tt{time}}{\tt{ .\ }}{\tt{58}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ .\ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{compare}}{\tt{ .\ }}{\tt{3}}{\tt{)}} \\ 
{\tt{(}}{\tt{mod}}{\tt{ .\ }}{\tt{9}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ .\ }}{\tt{11}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ .\ }}{\tt{13}}{\tt{)}} \\ 
{\tt{(}}{\tt{stout}}{\tt{ .\ }}{\tt{15}}{\tt{)}} \\ 
{\tt{(}}{\tt{testi}}{\tt{ .\ }}{\tt{50}}{\tt{)}} \\ 
{\tt{(}}{\tt{testo}}{\tt{ .\ }}{\tt{54}}{\tt{)}}{\tt{)}}\-)\-\index{boundp} \\ 
{\bf then }\=\+{\bf if }{\rm{tm-nullary-instructionp}}\,({\rm{lookup}}\,(\=\+{\rm{car}}\,({\it{instruction\/}}), \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{(}}{\tt{return}}{\tt{ .\ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{wait}}{\tt{ .\ }}{\tt{4}}{\tt{)}} \\ 
{\tt{(}}{\tt{run}}{\tt{ .\ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{br}}{\tt{ .\ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{brz}}{\tt{ .\ }}{\tt{10}}{\tt{)}} \\ 
{\tt{(}}{\tt{brnz}}{\tt{ .\ }}{\tt{6}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ .\ }}{\tt{14}}{\tt{)}} \\ 
{\tt{(}}{\tt{decr}}{\tt{ .\ }}{\tt{18}}{\tt{)}} \\ 
{\tt{(}}{\tt{decrm}}{\tt{ .\ }}{\tt{5}}{\tt{)}} \\ 
{\tt{(}}{\tt{incr}}{\tt{ .\ }}{\tt{22}}{\tt{)}} \\ 
{\tt{(}}{\tt{incrm}}{\tt{ .\ }}{\tt{7}}{\tt{)}} \\ 
{\tt{(}}{\tt{lbase}}{\tt{ .\ }}{\tt{26}}{\tt{)}} \\ 
{\tt{(}}{\tt{llimit}}{\tt{ .\ }}{\tt{30}}{\tt{)}} \\ 
{\tt{(}}{\tt{lpsw}}{\tt{ .\ }}{\tt{34}}{\tt{)}} \\ 
{\tt{(}}{\tt{post}}{\tt{ .\ }}{\tt{38}}{\tt{)}} \\ 
{\tt{(}}{\tt{svc}}{\tt{ .\ }}{\tt{42}}{\tt{)}} \\ 
{\tt{(}}{\tt{svcr}}{\tt{ .\ }}{\tt{46}}{\tt{)}} \\ 
{\tt{(}}{\tt{time}}{\tt{ .\ }}{\tt{58}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ .\ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{compare}}{\tt{ .\ }}{\tt{3}}{\tt{)}} \\ 
{\tt{(}}{\tt{mod}}{\tt{ .\ }}{\tt{9}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ .\ }}{\tt{11}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ .\ }}{\tt{13}}{\tt{)}} \\ 
{\tt{(}}{\tt{stout}}{\tt{ .\ }}{\tt{15}}{\tt{)}} \\ 
{\tt{(}}{\tt{testi}}{\tt{ .\ }}{\tt{50}}{\tt{)}} \\ 
{\tt{(}}{\tt{testo}}{\tt{ .\ }}{\tt{54}}{\tt{)}}{\tt{)}}\-)\-\index{lookup})\index{tm-nullary-instructionp}$\;\;${\bf then }{\tt{'}}{\tt{1}} \\ 
{\bf elseif }{\rm{tm-unary-instructionp}}\,({\rm{lookup}}\,(\=\+{\rm{car}}\,({\it{instruction\/}}), \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{(}}{\tt{return}}{\tt{ .\ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{wait}}{\tt{ .\ }}{\tt{4}}{\tt{)}} \\ 
{\tt{(}}{\tt{run}}{\tt{ .\ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{br}}{\tt{ .\ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{brz}}{\tt{ .\ }}{\tt{10}}{\tt{)}} \\ 
{\tt{(}}{\tt{brnz}}{\tt{ .\ }}{\tt{6}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ .\ }}{\tt{14}}{\tt{)}} \\ 
{\tt{(}}{\tt{decr}}{\tt{ .\ }}{\tt{18}}{\tt{)}} \\ 
{\tt{(}}{\tt{decrm}}{\tt{ .\ }}{\tt{5}}{\tt{)}} \\ 
{\tt{(}}{\tt{incr}}{\tt{ .\ }}{\tt{22}}{\tt{)}} \\ 
{\tt{(}}{\tt{incrm}}{\tt{ .\ }}{\tt{7}}{\tt{)}} \\ 
{\tt{(}}{\tt{lbase}}{\tt{ .\ }}{\tt{26}}{\tt{)}} \\ 
{\tt{(}}{\tt{llimit}}{\tt{ .\ }}{\tt{30}}{\tt{)}} \\ 
{\tt{(}}{\tt{lpsw}}{\tt{ .\ }}{\tt{34}}{\tt{)}} \\ 
{\tt{(}}{\tt{post}}{\tt{ .\ }}{\tt{38}}{\tt{)}} \\ 
{\tt{(}}{\tt{svc}}{\tt{ .\ }}{\tt{42}}{\tt{)}} \\ 
{\tt{(}}{\tt{svcr}}{\tt{ .\ }}{\tt{46}}{\tt{)}} \\ 
{\tt{(}}{\tt{time}}{\tt{ .\ }}{\tt{58}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ .\ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{compare}}{\tt{ .\ }}{\tt{3}}{\tt{)}} \\ 
{\tt{(}}{\tt{mod}}{\tt{ .\ }}{\tt{9}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ .\ }}{\tt{11}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ .\ }}{\tt{13}}{\tt{)}} \\ 
{\tt{(}}{\tt{stout}}{\tt{ .\ }}{\tt{15}}{\tt{)}} \\ 
{\tt{(}}{\tt{testi}}{\tt{ .\ }}{\tt{50}}{\tt{)}} \\ 
{\tt{(}}{\tt{testo}}{\tt{ .\ }}{\tt{54}}{\tt{)}}{\tt{)}}\-)\-\index{lookup})\index{tm-unary-instructionp} \\ 
{\bf then }{\tt{'}}{\tt{2}} \\ 
{\bf else }{\tt{'}}{\tt{3}}$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{build-symtab} \\  
\=\+{\rm{build-symtab}}\,({\it{source\/}}, {\it{symtab\/}}, {\it{position\/}})\index{build-symtab} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{source\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{litatom}}\,({\rm{car}}\,({\it{source\/}})) \\ 
{\bf then }{\rm{build-symtab}}\,(\=\+{\rm{cdr}}\,({\it{source\/}}), \\ 
{\rm{cons}}\,({\rm{cons}}\,({\rm{car}}\,({\it{source\/}}), {\it{position\/}}), {\it{symtab\/}}), \\ 
{\it{position\/}})\-\index{build-symtab} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{car}}\,({\it{source\/}})) $\wedge$ ({\rm{car}}\,({\rm{car}}\,({\it{source\/}})) $=$ {\tt{'}}{\tt{dcl}}) \\ 
{\bf then }{\rm{build-symtab}}\,(\=\+{\rm{cdr}}\,({\it{source\/}}), \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\rm{car}}\,({\rm{cdr}}\,({\rm{car}}\,({\it{source\/}}))), \\ 
{\rm{car}}\,({\rm{cdr}}\,({\rm{cdr}}\,({\rm{car}}\,({\it{source\/}})))))\-, \\ 
{\it{symtab\/}})\-, \\ 
{\it{position\/}})\-\index{build-symtab} \\ 
{\bf elseif }{\rm{listp}}\,({\rm{car}}\,({\it{source\/}})) $\wedge$ ({\rm{car}}\,({\rm{car}}\,({\it{source\/}})) $=$ {\tt{'}}{\tt{dc}}) \\ 
{\bf then }{\rm{build-symtab}}\,(\=\+{\rm{cdr}}\,({\it{source\/}}), \\ 
{\it{symtab\/}}, \\ 
{\it{position\/}} $+$ {\rm{incr-dc-position}}\,({\rm{car}}\,({\it{source\/}}))\index{incr-dc-position})\-\index{build-symtab} \\ 
{\bf else }{\rm{build-symtab}}\,(\=\+{\rm{cdr}}\,({\it{source\/}}), \\ 
{\it{symtab\/}}, \\ 
{\it{position\/}} $+$ {\rm{incr-instruction-position}}\,({\rm{car}}\,({\it{source\/}}))\index{incr-instruction-position})\-\index{build-symtab}$\;${\bf  endif}\- \\ 
{\bf else }{\it{symtab\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{find-duplicate-symbol} \\  
\=\+{\rm{find-duplicate-symbol}}\,({\it{symtab\/}}, {\it{already-seen\/}})\index{find-duplicate-symbol} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{symtab\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{listp}}\,({\rm{car}}\,({\it{symtab\/}})) \\ 
{\bf then }\=\+{\bf if }{\rm{car}}\,({\rm{car}}\,({\it{symtab\/}})) $\in$ {\it{already-seen\/}}$\;\;${\bf then }{\rm{car}}\,({\rm{car}}\,({\it{symtab\/}})) \\ 
{\bf else }{\rm{find-duplicate-symbol}}\,(\=\+{\rm{cdr}}\,({\it{symtab\/}}), \\ 
{\rm{cons}}\,(\=\+{\rm{car}}\,({\rm{car}}\,({\it{symtab\/}})), \\ 
{\it{already-seen\/}})\-)\-\index{find-duplicate-symbol}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{find-duplicate-symbol}}\,({\rm{cdr}}\,({\it{symtab\/}}), {\it{already-seen\/}})\index{find-duplicate-symbol}$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{*1*false}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{assembly-errorp} \\  
\=\+{\rm{assembly-errorp}}\,({\it{assembler-result\/}})\index{assembly-errorp} \\ 
$=$$\;\;\;\;$($\neg$ (\=\+{\rm{plistp}}\,({\it{assembler-result\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\it{assembler-result\/}})\index{length} $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$({\rm{car}}\,({\rm{cdr}}\,({\it{assembler-result\/}})) $=$ {\tt{'}}{\tt{*1*true}}))\-)\-)\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{find-non-finite-number} \\  
\=\+{\rm{find-non-finite-number}}\,({\it{l\/}})\index{find-non-finite-number} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}}) \\ 
{\bf then }\=\+{\bf if }{\rm{finite-numberp}}\,({\rm{car}}\,({\it{l\/}}), {\tt{'}}{\tt{65536}})\index{finite-numberp} \\ 
{\bf then }{\rm{find-non-finite-number}}\,({\rm{cdr}}\,({\it{l\/}}))\index{find-non-finite-number} \\ 
{\bf else }{\rm{car}}\,({\it{l\/}})$\;${\bf  endif}\- \\ 
{\bf else }{\tt{'}}{\tt{nil}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{assemble2} \\  
\=\+{\rm{assemble2}}\,({\it{memory\/}})\index{assemble2} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{finite-number-tablep}}\,({\tt{'}}{\tt{100}}, {\rm{table}}\,({\tt{'}}{\tt{100}}, {\it{memory\/}})\index{table}, {\tt{'}}{\tt{65536}})\index{finite-number-tablep} \\ 
{\bf then }{\rm{cons}}\,({\it{memory\/}}, {\tt{'}}{\tt{(}}{\tt{*1*true}}{\tt{)}}) \\ 
{\bf else }{\rm{cons}}\,(\=\+{\tt{'}}{\tt{nil}}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{assembly}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{error}}, \\ 
{\rm{cons}}\,(\=\+{\rm{find-non-finite-number}}\,({\it{memory\/}})\index{find-non-finite-number}, \\ 
{\tt{'}}{\tt{nil}})\-)\-)\-, \\ 
{\tt{'}}{\tt{nil}})\-)\-$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{assemble1} \\  
\=\+{\rm{assemble1}}\,({\it{source\/}}, {\it{symtab\/}})\index{assemble1} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{find-duplicate-symbol}}\,({\it{symtab\/}}, {\tt{'}}{\tt{nil}})\index{find-duplicate-symbol} \\ 
{\bf then }{\rm{cons}}\,(\=\+{\tt{'}}{\tt{nil}}, \\ 
{\rm{cons}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{assembly}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{error}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{duplicate}}, \\ 
{\rm{cons}}\,(\=\+{\tt{'}}{\tt{label}}, \\ 
{\rm{cons}}\,(\=\+{\rm{find-duplicate-symbol}}\,(\=\+{\it{symtab\/}}, \\ 
{\tt{'}}{\tt{nil}})\-\index{find-duplicate-symbol}, \\ 
{\tt{'}}{\tt{nil}})\-)\-)\-)\-)\-, \\ 
{\tt{'}}{\tt{nil}})\-)\- \\ 
{\bf else }{\rm{assemble2}}\,({\rm{translate-source}}\,({\it{source\/}}, {\it{symtab\/}})\index{translate-source})\index{assemble2}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{assemble} \\  
{\rm{assemble}}\,({\it{source\/}})\index{assemble} $=$ {\rm{assemble1}}\,({\it{source\/}}, {\rm{build-symtab}}\,({\it{source\/}}, {\tt{'}}{\tt{nil}}, {\tt{'}}{\tt{0}})\index{build-symtab})\index{assemble1}
\end{tabbing}


\noindent{\sc Event}:   Let us define the theory {\it{assembler}} to consist of the following events: assemble,
assemble1,
assemble2,
find-non-finite-number,
assembly-errorp,
find-duplicate-symbol,
build-symtab,
incr-instruction-position,
incr-dc-position,
translate-source,
translate-instruction,
asm-pack-instruction,
asm-pack-word1,
asm-good-instruction,
asm-good-arg,
asm-instruction-index2,
asm-instruction-arg2,
asm-instruction-mode2,
asm-instruction-index1,
asm-instruction-arg1,
asm-instruction-mode1,
asm-instruction-opcode,
translate-dc,
translate-dc-arglist,
translate-dc-arg,
dc-formp,
number-and-litatom-listp,
boundp,
append-n-times,
asm-opcode-alist.\index{assembler}

\addvspace{18pt}

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

\begin{tabbing}{\sc Definition}:\index{asm-reverse-opcode-alist} \\  
\=\+{\sc{asm-reverse-opcode-alist}}\index{asm-reverse-opcode-alist} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{(}}{\tt{0}}{\tt{ .\ }}{\tt{return}}{\tt{)}} \\ 
{\tt{(}}{\tt{4}}{\tt{ .\ }}{\tt{wait}}{\tt{)}} \\ 
{\tt{(}}{\tt{8}}{\tt{ .\ }}{\tt{run}}{\tt{)}} \\ 
{\tt{(}}{\tt{2}}{\tt{ .\ }}{\tt{br}}{\tt{)}} \\ 
{\tt{(}}{\tt{10}}{\tt{ .\ }}{\tt{brz}}{\tt{)}} \\ 
{\tt{(}}{\tt{6}}{\tt{ .\ }}{\tt{brnz}}{\tt{)}} \\ 
{\tt{(}}{\tt{14}}{\tt{ .\ }}{\tt{call}}{\tt{)}} \\ 
{\tt{(}}{\tt{18}}{\tt{ .\ }}{\tt{decr}}{\tt{)}} \\ 
{\tt{(}}{\tt{5}}{\tt{ .\ }}{\tt{decrm}}{\tt{)}} \\ 
{\tt{(}}{\tt{22}}{\tt{ .\ }}{\tt{incr}}{\tt{)}} \\ 
{\tt{(}}{\tt{7}}{\tt{ .\ }}{\tt{incrm}}{\tt{)}} \\ 
{\tt{(}}{\tt{26}}{\tt{ .\ }}{\tt{lbase}}{\tt{)}} \\ 
{\tt{(}}{\tt{30}}{\tt{ .\ }}{\tt{llimit}}{\tt{)}} \\ 
{\tt{(}}{\tt{34}}{\tt{ .\ }}{\tt{lpsw}}{\tt{)}} \\ 
{\tt{(}}{\tt{38}}{\tt{ .\ }}{\tt{post}}{\tt{)}} \\ 
{\tt{(}}{\tt{42}}{\tt{ .\ }}{\tt{svc}}{\tt{)}} \\ 
{\tt{(}}{\tt{46}}{\tt{ .\ }}{\tt{svcr}}{\tt{)}} \\ 
{\tt{(}}{\tt{58}}{\tt{ .\ }}{\tt{time}}{\tt{)}} \\ 
{\tt{(}}{\tt{1}}{\tt{ .\ }}{\tt{add}}{\tt{)}} \\ 
{\tt{(}}{\tt{3}}{\tt{ .\ }}{\tt{compare}}{\tt{)}} \\ 
{\tt{(}}{\tt{9}}{\tt{ .\ }}{\tt{mod}}{\tt{)}} \\ 
{\tt{(}}{\tt{11}}{\tt{ .\ }}{\tt{move}}{\tt{)}} \\ 
{\tt{(}}{\tt{13}}{\tt{ .\ }}{\tt{mult}}{\tt{)}} \\ 
{\tt{(}}{\tt{15}}{\tt{ .\ }}{\tt{stout}}{\tt{)}} \\ 
{\tt{(}}{\tt{50}}{\tt{ .\ }}{\tt{testi}}{\tt{)}} \\ 
{\tt{(}}{\tt{54}}{\tt{ .\ }}{\tt{testo}}{\tt{)}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{asm-symbolic-opcode} \\  
\=\+{\rm{asm-symbolic-opcode}}\,({\it{n\/}})\index{asm-symbolic-opcode} \\ 
$=$$\;\;\;\;${\rm{lookup}}\,(\=\+{\rm{tm-opcode}}\,({\it{n\/}})\index{tm-opcode}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{(}}{\tt{0}}{\tt{ .\ }}{\tt{return}}{\tt{)}} \\ 
{\tt{(}}{\tt{4}}{\tt{ .\ }}{\tt{wait}}{\tt{)}} \\ 
{\tt{(}}{\tt{8}}{\tt{ .\ }}{\tt{run}}{\tt{)}} \\ 
{\tt{(}}{\tt{2}}{\tt{ .\ }}{\tt{br}}{\tt{)}} \\ 
{\tt{(}}{\tt{10}}{\tt{ .\ }}{\tt{brz}}{\tt{)}} \\ 
{\tt{(}}{\tt{6}}{\tt{ .\ }}{\tt{brnz}}{\tt{)}} \\ 
{\tt{(}}{\tt{14}}{\tt{ .\ }}{\tt{call}}{\tt{)}} \\ 
{\tt{(}}{\tt{18}}{\tt{ .\ }}{\tt{decr}}{\tt{)}} \\ 
{\tt{(}}{\tt{5}}{\tt{ .\ }}{\tt{decrm}}{\tt{)}} \\ 
{\tt{(}}{\tt{22}}{\tt{ .\ }}{\tt{incr}}{\tt{)}} \\ 
{\tt{(}}{\tt{7}}{\tt{ .\ }}{\tt{incrm}}{\tt{)}} \\ 
{\tt{(}}{\tt{26}}{\tt{ .\ }}{\tt{lbase}}{\tt{)}} \\ 
{\tt{(}}{\tt{30}}{\tt{ .\ }}{\tt{llimit}}{\tt{)}} \\ 
{\tt{(}}{\tt{34}}{\tt{ .\ }}{\tt{lpsw}}{\tt{)}} \\ 
{\tt{(}}{\tt{38}}{\tt{ .\ }}{\tt{post}}{\tt{)}} \\ 
{\tt{(}}{\tt{42}}{\tt{ .\ }}{\tt{svc}}{\tt{)}} \\ 
{\tt{(}}{\tt{46}}{\tt{ .\ }}{\tt{svcr}}{\tt{)}} \\ 
{\tt{(}}{\tt{58}}{\tt{ .\ }}{\tt{time}}{\tt{)}} \\ 
{\tt{(}}{\tt{1}}{\tt{ .\ }}{\tt{add}}{\tt{)}} \\ 
{\tt{(}}{\tt{3}}{\tt{ .\ }}{\tt{compare}}{\tt{)}} \\ 
{\tt{(}}{\tt{9}}{\tt{ .\ }}{\tt{mod}}{\tt{)}} \\ 
{\tt{(}}{\tt{11}}{\tt{ .\ }}{\tt{move}}{\tt{)}} \\ 
{\tt{(}}{\tt{13}}{\tt{ .\ }}{\tt{mult}}{\tt{)}} \\ 
{\tt{(}}{\tt{15}}{\tt{ .\ }}{\tt{stout}}{\tt{)}} \\ 
{\tt{(}}{\tt{50}}{\tt{ .\ }}{\tt{testi}}{\tt{)}} \\ 
{\tt{(}}{\tt{54}}{\tt{ .\ }}{\tt{testo}}{\tt{)}}{\tt{)}}\-)\-\index{lookup}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-readyq-length}$\;\;$
{\sc{os-readyq-length}}\index{os-readyq-length} $=$ {\tt{'}}{\tt{20}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-task-table-length}$\;\;$
{\sc{os-task-table-length}}\index{os-task-table-length} $=$ {\tt{'}}{\tt{144}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-segment-table-length}$\;\;$
{\sc{os-segment-table-length}}\index{os-segment-table-length} $=$ {\tt{'}}{\tt{32}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-status-table-length}$\;\;$
{\sc{os-status-table-length}}\index{os-status-table-length} $=$ {\tt{'}}{\tt{32}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-ibuffer-length}$\;\;$
{\sc{os-ibuffer-length}}\index{os-ibuffer-length} $=$ {\tt{'}}{\tt{8}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-ibuffers-length}$\;\;$
{\sc{os-ibuffers-length}}\index{os-ibuffers-length} $=$ {\tt{'}}{\tt{128}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-obuffer-length}$\;\;$
{\sc{os-obuffer-length}}\index{os-obuffer-length} $=$ {\tt{'}}{\tt{8}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-obuffers-length}$\;\;$
{\sc{os-obuffers-length}}\index{os-obuffers-length} $=$ {\tt{'}}{\tt{128}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-mbuffer-length}$\;\;$
{\sc{os-mbuffer-length}}\index{os-mbuffer-length} $=$ {\tt{'}}{\tt{8}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-mbuffers-length}$\;\;$
{\sc{os-mbuffers-length}}\index{os-mbuffers-length} $=$ {\tt{'}}{\tt{2048}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-mbuffers-length-quarter}$\;\;$
{\sc{os-mbuffers-length-quarter}}\index{os-mbuffers-length-quarter} $=$ {\tt{'}}{\tt{512}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-length-is-divisible-by-4 \\ \index{os-mbuffers-length-is-divisible!-by-4}
{\tt{'}}{\tt{*1*true}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-source} \\  
\=\+{\sc{os-source}}\index{os-source} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{r0}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{r1}}{\tt{ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{r2}}{\tt{ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{3}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{r4}}{\tt{ }}{\tt{4}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{r5}}{\tt{ }}{\tt{5}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{r6}}{\tt{ }}{\tt{6}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{r7}}{\tt{ }}{\tt{7}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{interrupt-pc-field}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{interrupt-sp-field}}{\tt{ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{interrupt-flag-field}}{\tt{ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{svcid-addr}}{\tt{ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{input-devid-addr}}{\tt{ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{input-char-addr}}{\tt{ }}{\tt{9}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{output-devid-addr}}{\tt{ }}{\tt{9}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{charlub}}{\tt{ }}{\tt{256}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{send-svcid}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{receive-svcid}}{\tt{ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{tyo-svcid}}{\tt{ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{tyi-svcid}}{\tt{ }}{\tt{3}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{task-table-length}}{\tt{ }}{\tt{144}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{task-table-entry-length}}{\tt{ }}{\tt{9}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{pc-field}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{sp-field}}{\tt{ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{r2-field}}{\tt{ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{r3-field}}{\tt{ }}{\tt{3}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{r4-field}}{\tt{ }}{\tt{4}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{r5-field}}{\tt{ }}{\tt{5}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{r6-field}}{\tt{ }}{\tt{6}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{r7-field}}{\tt{ }}{\tt{7}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{flag-field}}{\tt{ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{readyq-length}}{\tt{ }}{\tt{20}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{qhead-field}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{qtail-field}}{\tt{ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{qcurrlength-field}}{\tt{ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{qmaxlength-field}}{\tt{ }}{\tt{3}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{qarray-field}}{\tt{ }}{\tt{4}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{segment-table-length}}{\tt{ }}{\tt{32}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{base-field}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{limit-field}}{\tt{ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{status-entry-length}}{\tt{ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{status-flag-field}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{status-taskid-field}}{\tt{ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{ready-status}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{error-status}}{\tt{ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{send-status}}{\tt{ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{receive-status}}{\tt{ }}{\tt{3}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{output-status}}{\tt{ }}{\tt{4}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{input-status}}{\tt{ }}{\tt{5}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{input-buffer-length}}{\tt{ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{output-buffer-length}}{\tt{ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{message-buffer-length}}{\tt{ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{source-multiplier}}{\tt{ }}{\tt{128}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{dest-multiplier}}{\tt{ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{dcl}}{\tt{ }}{\tt{taskidlub}}{\tt{ }}{\tt{16}}{\tt{)}} \\ 
{\tt{reg-save-area}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{clock-new-pc}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{1}}{\tt{ }}{\tt{clock-interrupt-handler}}{\tt{)}} \\ 
{\tt{error-new-pc}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{1}}{\tt{ }}{\tt{error-interrupt-handler}}{\tt{)}} \\ 
{\tt{svc-new-pc}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{1}}{\tt{ }}{\tt{svc-interrupt-handler}}{\tt{)}} \\ 
{\tt{input-new-pc}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{1}}{\tt{ }}{\tt{input-interrupt-handler}}{\tt{)}} \\ 
{\tt{output-new-pc}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{1}}{\tt{ }}{\tt{output-interrupt-handler}}{\tt{)}} \\ 
{\tt{interrupt-data}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{branch-address}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{1}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{time-slice}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{1}}{\tt{ }}{\tt{1000}}{\tt{)}} \\ 
{\tt{current-taskid}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{1}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{temp-r2}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{1}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{temp-r3}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{1}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{task-table}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{144}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{segment-table}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{32}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{readyq}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{20}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{status-table}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{32}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{ibuffers}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{128}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{obuffers}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{128}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{mbuffers}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{512}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{512}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{512}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{dc}}{\tt{ }}{\tt{512}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{save-state}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{temp-r2}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{temp-r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{readyq}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qfirst}}{\tt{)}} \\ 
{\tt{save-state-return}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{task-table-entry-length}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{task-table}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{move}} \\ 
{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r2}}{\tt{ }}{\tt{pc-field}}{\tt{)}} \\ 
{\tt{(}}{\tt{2}}{\tt{ }}{\tt{reg-save-area}}{\tt{ }}{\tt{interrupt-pc-field}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{move}} \\ 
{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r2}}{\tt{ }}{\tt{sp-field}}{\tt{)}} \\ 
{\tt{(}}{\tt{2}}{\tt{ }}{\tt{reg-save-area}}{\tt{ }}{\tt{interrupt-sp-field}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r2}}{\tt{ }}{\tt{r2-field}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{temp-r2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r2}}{\tt{ }}{\tt{r3-field}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{temp-r3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r2}}{\tt{ }}{\tt{r4-field}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r4}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r2}}{\tt{ }}{\tt{r5-field}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r5}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r2}}{\tt{ }}{\tt{r6-field}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r6}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r2}}{\tt{ }}{\tt{r7-field}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r7}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{flag-field}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{move}} \\ 
{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r2}}{\tt{)}} \\ 
{\tt{(}}{\tt{2}}{\tt{ }}{\tt{reg-save-area}}{\tt{ }}{\tt{interrupt-flag-field}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{temp-r2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{temp-r3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{return}}{\tt{)}} \\ 
{\tt{restore-state}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{task-table-entry-length}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{task-table}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{segment-table}}{\tt{)}} \\ 
{\tt{(}}{\tt{lbase}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{base-field}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{llimit}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{limit-field}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{flag-field}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{move}} \\ 
{\tt{(}}{\tt{2}}{\tt{ }}{\tt{reg-save-area}}{\tt{ }}{\tt{interrupt-pc-field}}{\tt{)}} \\ 
{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r2}}{\tt{ }}{\tt{pc-field}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{move}} \\ 
{\tt{(}}{\tt{2}}{\tt{ }}{\tt{reg-save-area}}{\tt{ }}{\tt{interrupt-sp-field}}{\tt{)}} \\ 
{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r2}}{\tt{ }}{\tt{sp-field}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}\=\+{\tt{move}} \\ 
{\tt{(}}{\tt{2}}{\tt{ }}{\tt{reg-save-area}}{\tt{ }}{\tt{interrupt-flag-field}}{\tt{)}} \\ 
{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r7}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r2}}{\tt{ }}{\tt{r7-field}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r6}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r2}}{\tt{ }}{\tt{r6-field}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r5}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r2}}{\tt{ }}{\tt{r5-field}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r4}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r2}}{\tt{ }}{\tt{r4-field}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r2}}{\tt{ }}{\tt{r3-field}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r2}}{\tt{ }}{\tt{r2-field}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{return}}{\tt{)}} \\ 
{\tt{clock-interrupt-handler}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{save-state}}{\tt{)}} \\ 
{\tt{trace-label1}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{readyq}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qfirst}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{dequeue}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{enqueue}}{\tt{)}} \\ 
{\tt{trace-label2}} \\ 
{\tt{(}}{\tt{br}}{\tt{ }}{\tt{dispatcher}}{\tt{)}} \\ 
{\tt{error-interrupt-handler}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{save-state}}{\tt{)}} \\ 
{\tt{trace-label3}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{readyq}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qfirst}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{dequeue}}{\tt{)}} \\ 
{\tt{trace-label4}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{status-entry-length}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{status-table}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r2}}{\tt{ }}{\tt{status-flag-field}}{\tt{)}}{\tt{ }}{\tt{error-status}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r2}}{\tt{ }}{\tt{status-taskid-field}}{\tt{)}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{br}}{\tt{ }}{\tt{dispatcher}}{\tt{)}} \\ 
{\tt{svc-interrupt-handler}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{save-state}}{\tt{)}} \\ 
{\tt{trace-label5}} \\ 
{\tt{(}}{\tt{mod}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{svcid-addr}}{\tt{)}}{\tt{ }}{\tt{4}}{\tt{)}} \\ 
{\tt{(}}{\tt{compare}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{svcid-addr}}{\tt{)}}{\tt{ }}{\tt{send-svcid}}{\tt{)}} \\ 
{\tt{(}}{\tt{brz}}{\tt{ }}{\tt{send-svc-handler}}{\tt{)}} \\ 
{\tt{(}}{\tt{compare}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{svcid-addr}}{\tt{)}}{\tt{ }}{\tt{receive-svcid}}{\tt{)}} \\ 
{\tt{(}}{\tt{brz}}{\tt{ }}{\tt{receive-svc-handler}}{\tt{)}} \\ 
{\tt{(}}{\tt{compare}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{svcid-addr}}{\tt{)}}{\tt{ }}{\tt{tyo-svcid}}{\tt{)}} \\ 
{\tt{(}}{\tt{brz}}{\tt{ }}{\tt{tyo-svc-handler}}{\tt{)}} \\ 
{\tt{(}}{\tt{br}}{\tt{ }}{\tt{tyi-svc-handler}}{\tt{)}} \\ 
{\tt{send-svc-handler}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r6}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{mod}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r6}}{\tt{)}}{\tt{ }}{\tt{taskidlub}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r7}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{readyq}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qfirst}}{\tt{)}} \\ 
{\tt{trace-label6}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{current-taskid}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r4}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r6}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r4}}{\tt{)}}{\tt{ }}{\tt{dest-multiplier}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{source-multiplier}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r4}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{mbuffers}}{\tt{)}} \\ 
{\tt{trace-label7}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qfullp}}{\tt{)}} \\ 
{\tt{(}}{\tt{brz}}{\tt{ }}{\tt{block-send}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r7}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{enqueue}}{\tt{)}} \\ 
{\tt{trace-label8}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r6}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{status-entry-length}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{status-table}}{\tt{)}} \\ 
{\tt{(}}{\tt{compare}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{status-flag-field}}{\tt{)}}{\tt{ }}{\tt{receive-status}}{\tt{)}} \\ 
{\tt{(}}{\tt{brnz}}{\tt{ }}{\tt{svc-resume-task}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{compare}} \\ 
{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{status-taskid-field}}{\tt{)}} \\ 
{\tt{(}}{\tt{2}}{\tt{ }}{\tt{current-taskid}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{brnz}}{\tt{ }}{\tt{svc-resume-task}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{status-flag-field}}{\tt{)}}{\tt{ }}{\tt{ready-status}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{status-taskid-field}}{\tt{)}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r6}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{readyq}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{enqueue}}{\tt{)}} \\ 
{\tt{trace-label9}} \\ 
{\tt{(}}{\tt{br}}{\tt{ }}{\tt{svc-resume-task}}{\tt{)}} \\ 
{\tt{block-send}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{readyq}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{dequeue}}{\tt{)}} \\ 
{\tt{trace-label10}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{current-taskid}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{status-entry-length}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{status-table}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{status-flag-field}}{\tt{)}}{\tt{ }}{\tt{send-status}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{status-taskid-field}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r6}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{br}}{\tt{ }}{\tt{dispatcher}}{\tt{)}} \\ 
{\tt{receive-svc-handler}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r6}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{mod}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r6}}{\tt{)}}{\tt{ }}{\tt{taskidlub}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{readyq}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qfirst}}{\tt{)}} \\ 
{\tt{trace-label11}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{current-taskid}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r4}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r4}}{\tt{)}}{\tt{ }}{\tt{dest-multiplier}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r6}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{source-multiplier}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r4}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{mbuffers}}{\tt{)}} \\ 
{\tt{trace-label12}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qemptyp}}{\tt{)}} \\ 
{\tt{(}}{\tt{brz}}{\tt{ }}{\tt{block-receive}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qfirst}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{dequeue}}{\tt{)}} \\ 
{\tt{trace-label13}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{current-taskid}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{task-table-entry-length}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{task-table}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{r3-field}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{)}} \\ 
{\tt{trace-label14}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r6}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{status-entry-length}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{status-table}}{\tt{)}} \\ 
{\tt{(}}{\tt{compare}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{status-flag-field}}{\tt{)}}{\tt{ }}{\tt{send-status}}{\tt{)}} \\ 
{\tt{(}}{\tt{brnz}}{\tt{ }}{\tt{svc-resume-task}}{\tt{)}} \\ 
{\tt{(}}\=\+{\tt{compare}} \\ 
{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{status-taskid-field}}{\tt{)}} \\ 
{\tt{(}}{\tt{2}}{\tt{ }}{\tt{current-taskid}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{brnz}}{\tt{ }}{\tt{svc-resume-task}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{status-flag-field}}{\tt{)}}{\tt{ }}{\tt{ready-status}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{status-taskid-field}}{\tt{)}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r6}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{readyq}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{enqueue}}{\tt{)}} \\ 
{\tt{trace-label15}} \\ 
{\tt{(}}{\tt{br}}{\tt{ }}{\tt{svc-resume-task}}{\tt{)}} \\ 
{\tt{block-receive}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{readyq}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{dequeue}}{\tt{)}} \\ 
{\tt{trace-label16}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{current-taskid}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{status-entry-length}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{status-table}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{status-flag-field}}{\tt{)}}{\tt{ }}{\tt{receive-status}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{status-taskid-field}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r6}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{br}}{\tt{ }}{\tt{dispatcher}}{\tt{)}} \\ 
{\tt{tyo-svc-handler}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r7}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{readyq}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qfirst}}{\tt{)}} \\ 
{\tt{trace-label17}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{current-taskid}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{output-buffer-length}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{obuffers}}{\tt{)}} \\ 
{\tt{trace-label18}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qfullp}}{\tt{)}} \\ 
{\tt{(}}{\tt{brz}}{\tt{ }}{\tt{block-tyo}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r7}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{enqueue}}{\tt{)}} \\ 
{\tt{trace-label19}} \\ 
{\tt{(}}{\tt{testo}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{current-taskid}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{brnz}}{\tt{ }}{\tt{svc-resume-task}}{\tt{)}} \\ 
{\tt{(}}{\tt{post}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{current-taskid}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{br}}{\tt{ }}{\tt{svc-resume-task}}{\tt{)}} \\ 
{\tt{block-tyo}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{readyq}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{dequeue}}{\tt{)}} \\ 
{\tt{trace-label20}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{current-taskid}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{status-entry-length}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{status-table}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{status-flag-field}}{\tt{)}}{\tt{ }}{\tt{output-status}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{status-taskid-field}}{\tt{)}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{br}}{\tt{ }}{\tt{dispatcher}}{\tt{)}} \\ 
{\tt{tyi-svc-handler}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{readyq}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qfirst}}{\tt{)}} \\ 
{\tt{trace-label21}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{current-taskid}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{input-buffer-length}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{ibuffers}}{\tt{)}} \\ 
{\tt{trace-label22}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qemptyp}}{\tt{)}} \\ 
{\tt{(}}{\tt{brz}}{\tt{ }}{\tt{block-tyi}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qfirst}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{dequeue}}{\tt{)}} \\ 
{\tt{trace-label23}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{current-taskid}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{task-table-entry-length}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{task-table}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{r3-field}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{br}}{\tt{ }}{\tt{svc-resume-task}}{\tt{)}} \\ 
{\tt{block-tyi}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{readyq}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{dequeue}}{\tt{)}} \\ 
{\tt{trace-label24}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{current-taskid}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{status-entry-length}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{status-table}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{status-flag-field}}{\tt{)}}{\tt{ }}{\tt{input-status}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{status-taskid-field}}{\tt{)}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{br}}{\tt{ }}{\tt{dispatcher}}{\tt{)}} \\ 
{\tt{input-interrupt-handler}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{branch-address}}{\tt{)}}{\tt{ }}{\tt{dispatcher}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{temp-r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{readyq}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qemptyp}}{\tt{)}} \\ 
{\tt{trace-label25}} \\ 
{\tt{(}}{\tt{brz}}{\tt{ }}{\tt{iih-skip-save-state}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{branch-address}}{\tt{)}}{\tt{ }}{\tt{resume-task}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{temp-r3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{save-state}}{\tt{)}} \\ 
{\tt{trace-label26}}{\tt{ }}{\tt{iih-skip-save-state}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r5}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{input-devid-addr}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r5}}{\tt{)}}{\tt{ }}{\tt{status-entry-length}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r5}}{\tt{)}}{\tt{ }}{\tt{status-table}}{\tt{)}} \\ 
{\tt{(}}{\tt{compare}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r5}}{\tt{ }}{\tt{status-flag-field}}{\tt{)}}{\tt{ }}{\tt{input-status}}{\tt{)}} \\ 
{\tt{(}}{\tt{brnz}}{\tt{ }}{\tt{check-for-full-input-buffer}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{input-devid-addr}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{readyq}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{enqueue}}{\tt{)}} \\ 
{\tt{trace-label27}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r5}}{\tt{ }}{\tt{status-flag-field}}{\tt{)}}{\tt{ }}{\tt{ready-status}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r5}}{\tt{ }}{\tt{status-taskid-field}}{\tt{)}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{trace-label28}}{\tt{ }}{\tt{check-for-full-input-buffer}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{input-devid-addr}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{input-buffer-length}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{ibuffers}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qfullp}}{\tt{)}} \\ 
{\tt{(}}{\tt{brnz}}{\tt{ }}{\tt{check-for-iport-error}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{input-char-addr}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{charlub}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qreplace}}{\tt{)}} \\ 
{\tt{trace-label29}} \\ 
{\tt{(}}{\tt{br}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{branch-address}}{\tt{)}}{\tt{)}} \\ 
{\tt{check-for-iport-error}} \\ 
{\tt{(}}{\tt{testi}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{input-devid-addr}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{brnz}}{\tt{ }}{\tt{enqueue-input-character}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{input-char-addr}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{charlub}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{enqueue}}{\tt{)}} \\ 
{\tt{trace-label30}} \\ 
{\tt{(}}{\tt{br}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{branch-address}}{\tt{)}}{\tt{)}} \\ 
{\tt{enqueue-input-character}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{input-char-addr}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{enqueue}}{\tt{)}} \\ 
{\tt{trace-label31}} \\ 
{\tt{(}}{\tt{br}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{branch-address}}{\tt{)}}{\tt{)}} \\ 
{\tt{output-interrupt-handler}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{branch-address}}{\tt{)}}{\tt{ }}{\tt{dispatcher}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{temp-r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{readyq}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qemptyp}}{\tt{)}} \\ 
{\tt{trace-label32}} \\ 
{\tt{(}}{\tt{brz}}{\tt{ }}{\tt{oih-skip-save-state}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{branch-address}}{\tt{)}}{\tt{ }}{\tt{resume-task}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{temp-r3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{save-state}}{\tt{)}} \\ 
{\tt{trace-label33}}{\tt{ }}{\tt{oih-skip-save-state}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r5}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{output-devid-addr}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r5}}{\tt{)}}{\tt{ }}{\tt{status-entry-length}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r5}}{\tt{)}}{\tt{ }}{\tt{status-table}}{\tt{)}} \\ 
{\tt{(}}{\tt{compare}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r5}}{\tt{ }}{\tt{status-flag-field}}{\tt{)}}{\tt{ }}{\tt{output-status}}{\tt{)}} \\ 
{\tt{(}}{\tt{brnz}}{\tt{ }}{\tt{check-for-empty-output-buffer}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{output-devid-addr}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{readyq}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{enqueue}}{\tt{)}} \\ 
{\tt{trace-label34}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r5}}{\tt{ }}{\tt{status-flag-field}}{\tt{)}}{\tt{ }}{\tt{ready-status}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r5}}{\tt{ }}{\tt{status-taskid-field}}{\tt{)}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{trace-label35}}{\tt{ }}{\tt{check-for-empty-output-buffer}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{output-devid-addr}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{mult}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{output-buffer-length}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{obuffers}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qemptyp}}{\tt{)}} \\ 
{\tt{(}}{\tt{brz}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{branch-address}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qfirst}}{\tt{)}} \\ 
{\tt{(}}{\tt{stout}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{output-devid-addr}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{dequeue}}{\tt{)}} \\ 
{\tt{trace-label36}} \\ 
{\tt{(}}{\tt{br}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{branch-address}}{\tt{)}}{\tt{)}} \\ 
{\tt{dispatcher}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{readyq}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qemptyp}}{\tt{)}} \\ 
{\tt{dispatcher-trace-label1}} \\ 
{\tt{(}}{\tt{brz}}{\tt{ }}{\tt{readyq-empty}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qfirst}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{restore-state}}{\tt{)}} \\ 
{\tt{dispatcher-trace-label2}} \\ 
{\tt{(}}{\tt{time}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{time-slice}}{\tt{ }}{\tt{0}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{lpsw}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{reg-save-area}}{\tt{)}}{\tt{)}} \\ 
{\tt{readyq-empty}} \\ 
{\tt{(}}{\tt{wait}}{\tt{)}} \\ 
{\tt{pc-after-wait}}{\tt{ }}{\tt{svc-resume-task}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{readyq}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qfirst}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{restore-state}}{\tt{)}} \\ 
{\tt{svc-resume-task-trace-label1}} \\ 
{\tt{(}}{\tt{svcr}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{reg-save-area}}{\tt{)}}{\tt{)}} \\ 
{\tt{resume-task}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{ }}{\tt{readyq}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{qfirst}}{\tt{)}} \\ 
{\tt{(}}{\tt{call}}{\tt{ }}{\tt{restore-state}}{\tt{)}} \\ 
{\tt{resume-task-trace-label1}} \\ 
{\tt{(}}{\tt{lpsw}}{\tt{ }}{\tt{(}}{\tt{2}}{\tt{ }}{\tt{reg-save-area}}{\tt{)}}{\tt{)}} \\ 
{\tt{enqueue}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r4}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r4}}{\tt{)}}{\tt{ }}{\tt{qarray-field}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r4}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{qtail-field}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r4}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{incr}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{qcurrlength-field}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{incrm}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{qtail-field}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{qmaxlength-field}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{return}}{\tt{)}} \\ 
{\tt{qreplace}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r4}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{qtail-field}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{decrm}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r4}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{qmaxlength-field}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r4}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r4}}{\tt{)}}{\tt{ }}{\tt{qarray-field}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r4}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{return}}{\tt{)}} \\ 
{\tt{dequeue}} \\ 
{\tt{(}}{\tt{decr}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{qcurrlength-field}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{incrm}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{qhead-field}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{qmaxlength-field}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{return}}{\tt{)}} \\ 
{\tt{qfirst}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r3}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{qarray-field}}{\tt{)}} \\ 
{\tt{(}}{\tt{add}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{qhead-field}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{move}}{\tt{ }}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r2}}{\tt{)}}{\tt{)}} \\ 
{\tt{(}}{\tt{return}}{\tt{)}} \\ 
{\tt{qemptyp}} \\ 
{\tt{(}}{\tt{compare}}{\tt{ }}{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{qcurrlength-field}}{\tt{)}}{\tt{ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{return}}{\tt{)}} \\ 
{\tt{qfullp}} \\ 
{\tt{(}}\=\+{\tt{compare}} \\ 
{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{qcurrlength-field}}{\tt{)}} \\ 
{\tt{(}}{\tt{3}}{\tt{ }}{\tt{r3}}{\tt{ }}{\tt{qmaxlength-field}}{\tt{)}}{\tt{)}}\- \\ 
{\tt{(}}{\tt{return}}{\tt{)}} \\ 
{\tt{end-of-os-source}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  clean-assembly \\ \index{clean-assembly}
{\tt{'}}{\tt{*1*true}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-symtab} \\  
\=\+{\sc{os-symtab}}\index{os-symtab} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{(}}{\tt{end-of-os-source}}{\tt{ .\ }}{\tt{3301}}{\tt{)}} \\ 
{\tt{(}}{\tt{qfullp}}{\tt{ .\ }}{\tt{3297}}{\tt{)}} \\ 
{\tt{(}}{\tt{qemptyp}}{\tt{ .\ }}{\tt{3293}}{\tt{)}} \\ 
{\tt{(}}{\tt{qfirst}}{\tt{ .\ }}{\tt{3280}}{\tt{)}} \\ 
{\tt{(}}{\tt{dequeue}}{\tt{ .\ }}{\tt{3274}}{\tt{)}} \\ 
{\tt{(}}{\tt{qreplace}}{\tt{ .\ }}{\tt{3258}}{\tt{)}} \\ 
{\tt{(}}{\tt{enqueue}}{\tt{ .\ }}{\tt{3240}}{\tt{)}} \\ 
{\tt{(}}{\tt{resume-task-trace-label1}}{\tt{ .\ }}{\tt{3238}}{\tt{)}} \\ 
{\tt{(}}{\tt{resume-task}}{\tt{ .\ }}{\tt{3231}}{\tt{)}} \\ 
{\tt{(}}{\tt{svc-resume-task-trace-label1}}{\tt{ .\ }}{\tt{3229}}{\tt{)}} \\ 
{\tt{(}}{\tt{svc-resume-task}}{\tt{ .\ }}{\tt{3222}}{\tt{)}} \\ 
{\tt{(}}{\tt{pc-after-wait}}{\tt{ .\ }}{\tt{3222}}{\tt{)}} \\ 
{\tt{(}}{\tt{readyq-empty}}{\tt{ .\ }}{\tt{3221}}{\tt{)}} \\ 
{\tt{(}}{\tt{dispatcher-trace-label2}}{\tt{ .\ }}{\tt{3217}}{\tt{)}} \\ 
{\tt{(}}{\tt{dispatcher-trace-label1}}{\tt{ .\ }}{\tt{3211}}{\tt{)}} \\ 
{\tt{(}}{\tt{dispatcher}}{\tt{ .\ }}{\tt{3206}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label36}}{\tt{ .\ }}{\tt{3204}}{\tt{)}} \\ 
{\tt{(}}{\tt{check-for-empty-output-buffer}}{\tt{ .\ }}{\tt{3184}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label35}}{\tt{ .\ }}{\tt{3184}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label34}}{\tt{ .\ }}{\tt{3178}}{\tt{)}} \\ 
{\tt{(}}{\tt{oih-skip-save-state}}{\tt{ .\ }}{\tt{3156}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label33}}{\tt{ .\ }}{\tt{3156}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label32}}{\tt{ .\ }}{\tt{3146}}{\tt{)}} \\ 
{\tt{(}}{\tt{output-interrupt-handler}}{\tt{ .\ }}{\tt{3135}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label31}}{\tt{ .\ }}{\tt{3133}}{\tt{)}} \\ 
{\tt{(}}{\tt{enqueue-input-character}}{\tt{ .\ }}{\tt{3128}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label30}}{\tt{ .\ }}{\tt{3126}}{\tt{)}} \\ 
{\tt{(}}{\tt{check-for-iport-error}}{\tt{ .\ }}{\tt{3114}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label29}}{\tt{ .\ }}{\tt{3112}}{\tt{)}} \\ 
{\tt{(}}{\tt{check-for-full-input-buffer}}{\tt{ .\ }}{\tt{3091}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label28}}{\tt{ .\ }}{\tt{3091}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label27}}{\tt{ .\ }}{\tt{3085}}{\tt{)}} \\ 
{\tt{(}}{\tt{iih-skip-save-state}}{\tt{ .\ }}{\tt{3063}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label26}}{\tt{ .\ }}{\tt{3063}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label25}}{\tt{ .\ }}{\tt{3053}}{\tt{)}} \\ 
{\tt{(}}{\tt{input-interrupt-handler}}{\tt{ .\ }}{\tt{3042}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label24}}{\tt{ .\ }}{\tt{3025}}{\tt{)}} \\ 
{\tt{(}}{\tt{block-tyi}}{\tt{ .\ }}{\tt{3020}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label23}}{\tt{ .\ }}{\tt{3006}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label22}}{\tt{ .\ }}{\tt{2998}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label21}}{\tt{ .\ }}{\tt{2986}}{\tt{)}} \\ 
{\tt{(}}{\tt{tyi-svc-handler}}{\tt{ .\ }}{\tt{2981}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label20}}{\tt{ .\ }}{\tt{2964}}{\tt{)}} \\ 
{\tt{(}}{\tt{block-tyo}}{\tt{ .\ }}{\tt{2959}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label19}}{\tt{ .\ }}{\tt{2951}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label18}}{\tt{ .\ }}{\tt{2942}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label17}}{\tt{ .\ }}{\tt{2930}}{\tt{)}} \\ 
{\tt{(}}{\tt{tyo-svc-handler}}{\tt{ .\ }}{\tt{2922}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label16}}{\tt{ .\ }}{\tt{2905}}{\tt{)}} \\ 
{\tt{(}}{\tt{block-receive}}{\tt{ .\ }}{\tt{2900}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label15}}{\tt{ .\ }}{\tt{2898}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label14}}{\tt{ .\ }}{\tt{2865}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label13}}{\tt{ .\ }}{\tt{2853}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label12}}{\tt{ .\ }}{\tt{2845}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label11}}{\tt{ .\ }}{\tt{2824}}{\tt{)}} \\ 
{\tt{(}}{\tt{receive-svc-handler}}{\tt{ .\ }}{\tt{2813}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label10}}{\tt{ .\ }}{\tt{2796}}{\tt{)}} \\ 
{\tt{(}}{\tt{block-send}}{\tt{ .\ }}{\tt{2791}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label9}}{\tt{ .\ }}{\tt{2789}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label8}}{\tt{ .\ }}{\tt{2756}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label7}}{\tt{ .\ }}{\tt{2747}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label6}}{\tt{ .\ }}{\tt{2726}}{\tt{)}} \\ 
{\tt{(}}{\tt{send-svc-handler}}{\tt{ .\ }}{\tt{2712}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label5}}{\tt{ .\ }}{\tt{2692}}{\tt{)}} \\ 
{\tt{(}}{\tt{svc-interrupt-handler}}{\tt{ .\ }}{\tt{2690}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label4}}{\tt{ .\ }}{\tt{2676}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label3}}{\tt{ .\ }}{\tt{2669}}{\tt{)}} \\ 
{\tt{(}}{\tt{error-interrupt-handler}}{\tt{ .\ }}{\tt{2667}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label2}}{\tt{ .\ }}{\tt{2665}}{\tt{)}} \\ 
{\tt{(}}{\tt{trace-label1}}{\tt{ .\ }}{\tt{2656}}{\tt{)}} \\ 
{\tt{(}}{\tt{clock-interrupt-handler}}{\tt{ .\ }}{\tt{2654}}{\tt{)}} \\ 
{\tt{(}}{\tt{restore-state}}{\tt{ .\ }}{\tt{2601}}{\tt{)}} \\ 
{\tt{(}}{\tt{save-state-return}}{\tt{ .\ }}{\tt{2558}}{\tt{)}} \\ 
{\tt{(}}{\tt{save-state}}{\tt{ .\ }}{\tt{2547}}{\tt{)}} \\ 
{\tt{(}}{\tt{mbuffers}}{\tt{ .\ }}{\tt{499}}{\tt{)}} \\ 
{\tt{(}}{\tt{obuffers}}{\tt{ .\ }}{\tt{371}}{\tt{)}} \\ 
{\tt{(}}{\tt{ibuffers}}{\tt{ .\ }}{\tt{243}}{\tt{)}} \\ 
{\tt{(}}{\tt{status-table}}{\tt{ .\ }}{\tt{211}}{\tt{)}} \\ 
{\tt{(}}{\tt{readyq}}{\tt{ .\ }}{\tt{191}}{\tt{)}} \\ 
{\tt{(}}{\tt{segment-table}}{\tt{ .\ }}{\tt{159}}{\tt{)}} \\ 
{\tt{(}}{\tt{task-table}}{\tt{ .\ }}{\tt{15}}{\tt{)}} \\ 
{\tt{(}}{\tt{temp-r3}}{\tt{ .\ }}{\tt{14}}{\tt{)}} \\ 
{\tt{(}}{\tt{temp-r2}}{\tt{ .\ }}{\tt{13}}{\tt{)}} \\ 
{\tt{(}}{\tt{current-taskid}}{\tt{ .\ }}{\tt{12}}{\tt{)}} \\ 
{\tt{(}}{\tt{time-slice}}{\tt{ .\ }}{\tt{11}}{\tt{)}} \\ 
{\tt{(}}{\tt{branch-address}}{\tt{ .\ }}{\tt{10}}{\tt{)}} \\ 
{\tt{(}}{\tt{interrupt-data}}{\tt{ .\ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{output-new-pc}}{\tt{ .\ }}{\tt{7}}{\tt{)}} \\ 
{\tt{(}}{\tt{input-new-pc}}{\tt{ .\ }}{\tt{6}}{\tt{)}} \\ 
{\tt{(}}{\tt{svc-new-pc}}{\tt{ .\ }}{\tt{5}}{\tt{)}} \\ 
{\tt{(}}{\tt{error-new-pc}}{\tt{ .\ }}{\tt{4}}{\tt{)}} \\ 
{\tt{(}}{\tt{clock-new-pc}}{\tt{ .\ }}{\tt{3}}{\tt{)}} \\ 
{\tt{(}}{\tt{reg-save-area}}{\tt{ .\ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{taskidlub}}{\tt{ .\ }}{\tt{16}}{\tt{)}} \\ 
{\tt{(}}{\tt{dest-multiplier}}{\tt{ .\ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{source-multiplier}}{\tt{ .\ }}{\tt{128}}{\tt{)}} \\ 
{\tt{(}}{\tt{message-buffer-length}}{\tt{ .\ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{output-buffer-length}}{\tt{ .\ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{input-buffer-length}}{\tt{ .\ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{input-status}}{\tt{ .\ }}{\tt{5}}{\tt{)}} \\ 
{\tt{(}}{\tt{output-status}}{\tt{ .\ }}{\tt{4}}{\tt{)}} \\ 
{\tt{(}}{\tt{receive-status}}{\tt{ .\ }}{\tt{3}}{\tt{)}} \\ 
{\tt{(}}{\tt{send-status}}{\tt{ .\ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{error-status}}{\tt{ .\ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{ready-status}}{\tt{ .\ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{status-taskid-field}}{\tt{ .\ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{status-flag-field}}{\tt{ .\ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{status-entry-length}}{\tt{ .\ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{limit-field}}{\tt{ .\ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{base-field}}{\tt{ .\ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{segment-table-length}}{\tt{ .\ }}{\tt{32}}{\tt{)}} \\ 
{\tt{(}}{\tt{qarray-field}}{\tt{ .\ }}{\tt{4}}{\tt{)}} \\ 
{\tt{(}}{\tt{qmaxlength-field}}{\tt{ .\ }}{\tt{3}}{\tt{)}} \\ 
{\tt{(}}{\tt{qcurrlength-field}}{\tt{ .\ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{qtail-field}}{\tt{ .\ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{qhead-field}}{\tt{ .\ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{readyq-length}}{\tt{ .\ }}{\tt{20}}{\tt{)}} \\ 
{\tt{(}}{\tt{flag-field}}{\tt{ .\ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{r7-field}}{\tt{ .\ }}{\tt{7}}{\tt{)}} \\ 
{\tt{(}}{\tt{r6-field}}{\tt{ .\ }}{\tt{6}}{\tt{)}} \\ 
{\tt{(}}{\tt{r5-field}}{\tt{ .\ }}{\tt{5}}{\tt{)}} \\ 
{\tt{(}}{\tt{r4-field}}{\tt{ .\ }}{\tt{4}}{\tt{)}} \\ 
{\tt{(}}{\tt{r3-field}}{\tt{ .\ }}{\tt{3}}{\tt{)}} \\ 
{\tt{(}}{\tt{r2-field}}{\tt{ .\ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{sp-field}}{\tt{ .\ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{pc-field}}{\tt{ .\ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{task-table-entry-length}}{\tt{ .\ }}{\tt{9}}{\tt{)}} \\ 
{\tt{(}}{\tt{task-table-length}}{\tt{ .\ }}{\tt{144}}{\tt{)}} \\ 
{\tt{(}}{\tt{tyi-svcid}}{\tt{ .\ }}{\tt{3}}{\tt{)}} \\ 
{\tt{(}}{\tt{tyo-svcid}}{\tt{ .\ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{receive-svcid}}{\tt{ .\ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{send-svcid}}{\tt{ .\ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{charlub}}{\tt{ .\ }}{\tt{256}}{\tt{)}} \\ 
{\tt{(}}{\tt{output-devid-addr}}{\tt{ .\ }}{\tt{9}}{\tt{)}} \\ 
{\tt{(}}{\tt{input-char-addr}}{\tt{ .\ }}{\tt{9}}{\tt{)}} \\ 
{\tt{(}}{\tt{input-devid-addr}}{\tt{ .\ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{svcid-addr}}{\tt{ .\ }}{\tt{8}}{\tt{)}} \\ 
{\tt{(}}{\tt{interrupt-flag-field}}{\tt{ .\ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{interrupt-sp-field}}{\tt{ .\ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{interrupt-pc-field}}{\tt{ .\ }}{\tt{0}}{\tt{)}} \\ 
{\tt{(}}{\tt{r7}}{\tt{ .\ }}{\tt{7}}{\tt{)}} \\ 
{\tt{(}}{\tt{r6}}{\tt{ .\ }}{\tt{6}}{\tt{)}} \\ 
{\tt{(}}{\tt{r5}}{\tt{ .\ }}{\tt{5}}{\tt{)}} \\ 
{\tt{(}}{\tt{r4}}{\tt{ .\ }}{\tt{4}}{\tt{)}} \\ 
{\tt{(}}{\tt{r3}}{\tt{ .\ }}{\tt{3}}{\tt{)}} \\ 
{\tt{(}}{\tt{r2}}{\tt{ .\ }}{\tt{2}}{\tt{)}} \\ 
{\tt{(}}{\tt{r1}}{\tt{ .\ }}{\tt{1}}{\tt{)}} \\ 
{\tt{(}}{\tt{r0}}{\tt{ .\ }}{\tt{0}}{\tt{)}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-task-table-address}$\;\;$
{\sc{os-task-table-address}}\index{os-task-table-address} $=$ {\tt{'}}{\tt{15}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-readyq-address}$\;\;$
{\sc{os-readyq-address}}\index{os-readyq-address} $=$ {\tt{'}}{\tt{191}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-segment-table-address}$\;\;$
{\sc{os-segment-table-address}}\index{os-segment-table-address} $=$ {\tt{'}}{\tt{159}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-status-table-address}$\;\;$
{\sc{os-status-table-address}}\index{os-status-table-address} $=$ {\tt{'}}{\tt{211}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-ibuffers-address}$\;\;$
{\sc{os-ibuffers-address}}\index{os-ibuffers-address} $=$ {\tt{'}}{\tt{243}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-obuffers-address}$\;\;$
{\sc{os-obuffers-address}}\index{os-obuffers-address} $=$ {\tt{'}}{\tt{371}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-mbuffers-address}$\;\;$
{\sc{os-mbuffers-address}}\index{os-mbuffers-address} $=$ {\tt{'}}{\tt{499}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-clock-interrupt-handler-addre!ss}$\;\;$
{\sc{os-clock-interrupt-handler-address}}\index{os-clock-interrupt-handler-addre!ss} $=$ {\tt{'}}{\tt{2654}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-error-handler-address}$\;\;$
{\sc{os-error-handler-address}}\index{os-error-handler-address} $=$ {\tt{'}}{\tt{2667}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-handler-address}$\;\;$
{\sc{os-svc-handler-address}}\index{os-svc-handler-address} $=$ {\tt{'}}{\tt{2690}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-input-interrupt-handler-addre!ss}$\;\;$
{\sc{os-input-interrupt-handler-address}}\index{os-input-interrupt-handler-addre!ss} $=$ {\tt{'}}{\tt{3042}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-output-interrupt-handler-add!ress}$\;\;$
{\sc{os-output-interrupt-handler-address}}\index{os-output-interrupt-handler-add!ress} $=$ {\tt{'}}{\tt{3135}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-code-address}$\;\;$
{\sc{os-code-address}}\index{os-code-address} $=$ {\tt{'}}{\tt{2547}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-save-state-return-address}$\;\;$
{\sc{os-save-state-return-address}}\index{os-save-state-return-address} $=$ {\tt{'}}{\tt{2558}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-dispatcher-return-address}$\;\;$
{\sc{os-dispatcher-return-address}}\index{os-dispatcher-return-address} $=$ {\tt{'}}{\tt{nil}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-slice-address}$\;\;$
{\sc{os-time-slice-address}}\index{os-time-slice-address} $=$ {\tt{'}}{\tt{11}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-code-length}$\;\;$
{\sc{os-code-length}}\index{os-code-length} $=$ {\tt{'}}{\tt{754}}
\end{tabbing}

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

\begin{tabbing}{\sc Definition}:\index{firstn-n-times} \\  
\=\+{\rm{firstn-n-times}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{firstn-n-times} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{n\/}} $\simeq {\tt{0}}$$\;\;${\bf then }{\tt{'}}{\tt{nil}} \\ 
{\bf else }{\rm{append}}\,({\rm{firstn}}\,({\it{k\/}}, {\it{l\/}})\index{firstn}, {\rm{firstn-n-times}}\,({\it{n\/}} $-\;1$, {\it{k\/}}, {\rm{nthcdr}}\,({\it{k\/}}, {\it{l\/}})\index{nthcdr})\index{firstn-n-times})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{firstn-with-small-recursion} \\  
\=\+{\rm{firstn-with-small-recursion}}\,({\it{n\/}}, {\it{l\/}}, {\it{max\/}})\index{firstn-with-small-recursion} \\ 
$=$$\;\;\;\;${\rm{append}}\,(\=\+{\rm{firstn}}\,({\it{n\/}} ${}${\bf{mod}}${}$ {\it{max\/}}, {\it{l\/}})\index{firstn}, \\ 
{\rm{firstn-n-times}}\,({\it{n\/}} $\div$ {\it{max\/}}, {\it{max\/}}, {\rm{nthcdr}}\,({\it{n\/}} ${}${\bf{mod}}${}$ {\it{max\/}}, {\it{l\/}})\index{nthcdr})\index{firstn-n-times})\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{nthcdr-with-small-recursion} \\  
\=\+{\rm{nthcdr-with-small-recursion}}\,({\it{n\/}}, {\it{l\/}}, {\it{max\/}})\index{nthcdr-with-small-recursion} \\ 
$=$$\;\;\;\;${\rm{nthcdr}}\,({\it{n\/}} ${}${\bf{mod}}${}$ {\it{max\/}}, {\rm{nthcdr-n-times}}\,({\it{n\/}} $\div$ {\it{max\/}}, {\it{max\/}}, {\it{l\/}})\index{nthcdr-n-times})\index{nthcdr}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{getseg-with-small-recursion} \\  
\=\+{\rm{getseg-with-small-recursion}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}}, {\it{max\/}})\index{getseg-with-small-recursion} \\ 
$=$$\;\;\;\;${\rm{firstn-with-small-recursion}}\,(\=\+{\it{k\/}}, \\ 
{\rm{nthcdr-with-small-recursion}}\,({\it{n\/}}, {\it{l\/}}, {\it{max\/}})\index{nthcdr-with-small-recursion}, \\ 
{\it{max\/}})\-\index{firstn-with-small-recursion}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-machine-code} \\  
\=\+{\sc{os-machine-code}}\index{os-machine-code} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{2187}}{\tt{ }}{\tt{13}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2187}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{15}} \\ 
{\tt{4299}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{12747}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{4811}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{13}}{\tt{ }}{\tt{5067}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3275}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{3531}} \\ 
{\tt{2}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{3787}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{4043}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{7}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{20683}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{13}} \\ 
{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{15}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{159}} \\ 
{\tt{218}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{478}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{6283}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{14731}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{6795}} \\ 
{\tt{0}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{63563}}{\tt{ }}{\tt{7}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{55371}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{47179}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{38987}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{30795}}{\tt{ }}{\tt{3}} \\ 
{\tt{2}}{\tt{ }}{\tt{22603}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{2547}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{14}} \\ 
{\tt{3240}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3206}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{2547}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2}} \\ 
{\tt{65}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{1}}{\tt{ }}{\tt{459}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3206}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{2547}}{\tt{ }}{\tt{137}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{131}} \\ 
{\tt{8}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{2712}}{\tt{ }}{\tt{131}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{1}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{2813}}{\tt{ }}{\tt{131}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{2922}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2981}} \\ 
{\tt{2123}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{73}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{16}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{7}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{2187}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{2}} \\ 
{\tt{2123}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{128}}{\tt{ }}{\tt{2113}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{499}} \\ 
{\tt{14}}{\tt{ }}{\tt{3297}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{2791}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{7}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3240}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}} \\ 
{\tt{3}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{195}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{4547}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{459}}{\tt{ }}{\tt{3}} \\ 
{\tt{0}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3240}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}} \\ 
{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2507}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3206}} \\ 
{\tt{2123}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{73}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{16}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{2187}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{2}} \\ 
{\tt{77}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{128}}{\tt{ }}{\tt{2113}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{499}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3293}} \\ 
{\tt{10}}{\tt{ }}{\tt{2900}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{15}} \\ 
{\tt{3019}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{195}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3222}} \\ 
{\tt{4547}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{459}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}} \\ 
{\tt{14}}{\tt{ }}{\tt{3240}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}} \\ 
{\tt{3}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2507}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3206}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{7}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}} \\ 
{\tt{3280}}{\tt{ }}{\tt{2187}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{371}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3297}}{\tt{ }}{\tt{10}} \\ 
{\tt{2959}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{7}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3240}}{\tt{ }}{\tt{182}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{166}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{75}} \\ 
{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{459}} \\ 
{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3206}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{2187}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}} \\ 
{\tt{8}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{243}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3293}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{3020}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{12}} \\ 
{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{15}}{\tt{ }}{\tt{3019}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{4171}} \\ 
{\tt{3}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{459}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3206}}{\tt{ }}{\tt{139}}{\tt{ }}{\tt{10}} \\ 
{\tt{3206}}{\tt{ }}{\tt{2187}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3293}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{3063}}{\tt{ }}{\tt{139}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{3231}} \\ 
{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{2547}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{195}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{6}} \\ 
{\tt{3091}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3240}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{459}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{4171}} \\ 
{\tt{3}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{243}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3297}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3114}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{256}} \\ 
{\tt{14}}{\tt{ }}{\tt{3258}}{\tt{ }}{\tt{130}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{178}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3128}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{256}}{\tt{ }}{\tt{14}} \\ 
{\tt{3240}}{\tt{ }}{\tt{130}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3240}}{\tt{ }}{\tt{130}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{139}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{3206}}{\tt{ }}{\tt{2187}} \\ 
{\tt{14}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3293}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{3156}}{\tt{ }}{\tt{139}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{3231}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{14}} \\ 
{\tt{14}}{\tt{ }}{\tt{2547}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{195}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3184}}{\tt{ }}{\tt{4171}} \\ 
{\tt{2}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3240}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{459}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{8}} \\ 
{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{371}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3293}}{\tt{ }}{\tt{138}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{2191}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{130}} \\ 
{\tt{10}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3293}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{3221}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{2601}}{\tt{ }}{\tt{186}}{\tt{ }}{\tt{11}} \\ 
{\tt{162}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{2601}}{\tt{ }}{\tt{174}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}} \\ 
{\tt{3280}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{2601}}{\tt{ }}{\tt{162}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{14401}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2251}}{\tt{ }}{\tt{4}} \\ 
{\tt{2}}{\tt{ }}{\tt{726}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{31175}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{14411}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{30789}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2113}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{65}} \\ 
{\tt{4}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{2251}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{722}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{30919}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{4}} \\ 
{\tt{6209}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{6219}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{707}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{31427}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-limit}$\;\;$
{\sc{os-limit}}\index{os-limit} $=$ {\tt{'}}{\tt{3311}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-task-table} \\  
{\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table} $=$ {\rm{getseg}}\,({\tt{'}}{\tt{15}}, {\tt{'}}{\tt{144}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getseg}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-readyq}$\;\;$
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq} $=$ {\rm{getseg}}\,({\tt{'}}{\tt{191}}, {\tt{'}}{\tt{20}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getseg}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-segment-table} \\  
{\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table} $=$ {\rm{getseg}}\,({\tt{'}}{\tt{159}}, {\tt{'}}{\tt{32}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getseg}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-status-table} \\  
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table} $=$ {\rm{getseg}}\,({\tt{'}}{\tt{211}}, {\tt{'}}{\tt{32}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getseg}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-ibuffers} \\  
{\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers} $=$ {\rm{getseg}}\,({\tt{'}}{\tt{243}}, {\tt{'}}{\tt{128}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getseg}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-obuffers} \\  
{\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers} $=$ {\rm{getseg}}\,({\tt{'}}{\tt{371}}, {\tt{'}}{\tt{128}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getseg}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-mbuffers} \\  
{\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers} $=$ {\rm{getseg}}\,({\tt{'}}{\tt{499}}, {\tt{'}}{\tt{2048}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getseg}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-code}$\;\;$
{\rm{os-code}}\,({\it{os\/}})\index{os-code} $=$ {\rm{getseg}}\,({\tt{'}}{\tt{2547}}, {\tt{'}}{\tt{754}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getseg}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-os-task-table \\ \index{length-os-task-table}
{\rm{length}}\,({\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\index{length} $=$ {\tt{'}}{\tt{144}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-os-task-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-os-task-table \\ \index{plistp-os-task-table}
{\rm{plistp}}\,({\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-os-task-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-os-readyq \\ \index{length-os-readyq}
{\rm{length}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{length} $=$ {\tt{'}}{\tt{20}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-os-readyq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-os-readyq \\ \index{plistp-os-readyq}
{\rm{plistp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-os-readyq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-os-segment-table \\ \index{length-os-segment-table}
{\rm{length}}\,({\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{length} $=$ {\tt{'}}{\tt{32}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-os-segment-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-os-segment-table \\ \index{plistp-os-segment-table}
{\rm{plistp}}\,({\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-os-segment-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-os-status-table \\ \index{length-os-status-table}
{\rm{length}}\,({\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{length} $=$ {\tt{'}}{\tt{32}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-os-status-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-os-status-table \\ \index{plistp-os-status-table}
{\rm{plistp}}\,({\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-os-status-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-os-ibuffers \\ \index{length-os-ibuffers}
{\rm{length}}\,({\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{length} $=$ {\tt{'}}{\tt{128}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-os-ibuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-os-ibuffers \\ \index{plistp-os-ibuffers}
{\rm{plistp}}\,({\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-os-ibuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-os-obuffers \\ \index{length-os-obuffers}
{\rm{length}}\,({\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\index{length} $=$ {\tt{'}}{\tt{128}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-os-obuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-os-obuffers \\ \index{plistp-os-obuffers}
{\rm{plistp}}\,({\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-os-obuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-os-mbuffers \\ \index{length-os-mbuffers}
{\rm{length}}\,({\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{length} $=$ {\tt{'}}{\tt{2048}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-os-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-os-mbuffers \\ \index{plistp-os-mbuffers}
{\rm{plistp}}\,({\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-os-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-current-taskid-address}$\;\;$
{\sc{os-current-taskid-address}}\index{os-current-taskid-address} $=$ {\tt{'}}{\tt{12}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label1}$\;\;$
{\sc{os-trace-label1}}\index{os-trace-label1} $=$ {\tt{'}}{\tt{2656}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label2}$\;\;$
{\sc{os-trace-label2}}\index{os-trace-label2} $=$ {\tt{'}}{\tt{2665}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label3}$\;\;$
{\sc{os-trace-label3}}\index{os-trace-label3} $=$ {\tt{'}}{\tt{2669}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label4}$\;\;$
{\sc{os-trace-label4}}\index{os-trace-label4} $=$ {\tt{'}}{\tt{2676}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label5}$\;\;$
{\sc{os-trace-label5}}\index{os-trace-label5} $=$ {\tt{'}}{\tt{2692}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label6}$\;\;$
{\sc{os-trace-label6}}\index{os-trace-label6} $=$ {\tt{'}}{\tt{2726}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label7}$\;\;$
{\sc{os-trace-label7}}\index{os-trace-label7} $=$ {\tt{'}}{\tt{2747}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label8}$\;\;$
{\sc{os-trace-label8}}\index{os-trace-label8} $=$ {\tt{'}}{\tt{2756}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label9}$\;\;$
{\sc{os-trace-label9}}\index{os-trace-label9} $=$ {\tt{'}}{\tt{2789}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label10}$\;\;$
{\sc{os-trace-label10}}\index{os-trace-label10} $=$ {\tt{'}}{\tt{2796}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-receive-handler-address}$\;\;$
{\sc{os-svc-receive-handler-address}}\index{os-svc-receive-handler-address} $=$ {\tt{'}}{\tt{2813}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label11}$\;\;$
{\sc{os-trace-label11}}\index{os-trace-label11} $=$ {\tt{'}}{\tt{2824}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label12}$\;\;$
{\sc{os-trace-label12}}\index{os-trace-label12} $=$ {\tt{'}}{\tt{2845}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label13}$\;\;$
{\sc{os-trace-label13}}\index{os-trace-label13} $=$ {\tt{'}}{\tt{2853}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label14}$\;\;$
{\sc{os-trace-label14}}\index{os-trace-label14} $=$ {\tt{'}}{\tt{2865}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label15}$\;\;$
{\sc{os-trace-label15}}\index{os-trace-label15} $=$ {\tt{'}}{\tt{2898}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label16}$\;\;$
{\sc{os-trace-label16}}\index{os-trace-label16} $=$ {\tt{'}}{\tt{2905}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-tyo-handler-address}$\;\;$
{\sc{os-svc-tyo-handler-address}}\index{os-svc-tyo-handler-address} $=$ {\tt{'}}{\tt{2922}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label17}$\;\;$
{\sc{os-trace-label17}}\index{os-trace-label17} $=$ {\tt{'}}{\tt{2930}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label18}$\;\;$
{\sc{os-trace-label18}}\index{os-trace-label18} $=$ {\tt{'}}{\tt{2942}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label19}$\;\;$
{\sc{os-trace-label19}}\index{os-trace-label19} $=$ {\tt{'}}{\tt{2951}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label20}$\;\;$
{\sc{os-trace-label20}}\index{os-trace-label20} $=$ {\tt{'}}{\tt{2964}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-tyi-handler-address}$\;\;$
{\sc{os-svc-tyi-handler-address}}\index{os-svc-tyi-handler-address} $=$ {\tt{'}}{\tt{2981}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label21}$\;\;$
{\sc{os-trace-label21}}\index{os-trace-label21} $=$ {\tt{'}}{\tt{2986}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label22}$\;\;$
{\sc{os-trace-label22}}\index{os-trace-label22} $=$ {\tt{'}}{\tt{2998}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label23}$\;\;$
{\sc{os-trace-label23}}\index{os-trace-label23} $=$ {\tt{'}}{\tt{3006}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label24}$\;\;$
{\sc{os-trace-label24}}\index{os-trace-label24} $=$ {\tt{'}}{\tt{3025}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label25}$\;\;$
{\sc{os-trace-label25}}\index{os-trace-label25} $=$ {\tt{'}}{\tt{3053}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label26}$\;\;$
{\sc{os-trace-label26}}\index{os-trace-label26} $=$ {\tt{'}}{\tt{3063}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label27}$\;\;$
{\sc{os-trace-label27}}\index{os-trace-label27} $=$ {\tt{'}}{\tt{3085}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label28}$\;\;$
{\sc{os-trace-label28}}\index{os-trace-label28} $=$ {\tt{'}}{\tt{3091}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label29}$\;\;$
{\sc{os-trace-label29}}\index{os-trace-label29} $=$ {\tt{'}}{\tt{3112}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label30}$\;\;$
{\sc{os-trace-label30}}\index{os-trace-label30} $=$ {\tt{'}}{\tt{3126}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label31}$\;\;$
{\sc{os-trace-label31}}\index{os-trace-label31} $=$ {\tt{'}}{\tt{3133}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label32}$\;\;$
{\sc{os-trace-label32}}\index{os-trace-label32} $=$ {\tt{'}}{\tt{3146}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label33}$\;\;$
{\sc{os-trace-label33}}\index{os-trace-label33} $=$ {\tt{'}}{\tt{3156}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label34}$\;\;$
{\sc{os-trace-label34}}\index{os-trace-label34} $=$ {\tt{'}}{\tt{3178}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label35}$\;\;$
{\sc{os-trace-label35}}\index{os-trace-label35} $=$ {\tt{'}}{\tt{3184}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-trace-label36}$\;\;$
{\sc{os-trace-label36}}\index{os-trace-label36} $=$ {\tt{'}}{\tt{3204}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-dispatcher-trace-label1}$\;\;$
{\sc{os-dispatcher-trace-label1}}\index{os-dispatcher-trace-label1} $=$ {\tt{'}}{\tt{3211}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-dispatcher-trace-label2}$\;\;$
{\sc{os-dispatcher-trace-label2}}\index{os-dispatcher-trace-label2} $=$ {\tt{'}}{\tt{3217}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-resume-task-address}$\;\;$
{\sc{os-svc-resume-task-address}}\index{os-svc-resume-task-address} $=$ {\tt{'}}{\tt{3222}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-resume-task-trace-label1}$\;\;$
{\sc{os-svc-resume-task-trace-label1}}\index{os-svc-resume-task-trace-label1} $=$ {\tt{'}}{\tt{3229}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-resume-task-address}$\;\;$
{\sc{os-resume-task-address}}\index{os-resume-task-address} $=$ {\tt{'}}{\tt{3231}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-resume-task-trace-label1}$\;\;$
{\sc{os-resume-task-trace-label1}}\index{os-resume-task-trace-label1} $=$ {\tt{'}}{\tt{3238}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-pc-after-wait}$\;\;$
{\sc{os-pc-after-wait}}\index{os-pc-after-wait} $=$ {\tt{'}}{\tt{3222}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-temp-r2-address}$\;\;$
{\sc{os-temp-r2-address}}\index{os-temp-r2-address} $=$ {\tt{'}}{\tt{13}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-temp-r3-address}$\;\;$
{\sc{os-temp-r3-address}}\index{os-temp-r3-address} $=$ {\tt{'}}{\tt{14}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-dispatcher-address}$\;\;$
{\sc{os-dispatcher-address}}\index{os-dispatcher-address} $=$ {\tt{'}}{\tt{3206}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-dispatcher-pc-after-wait}$\;\;$
{\sc{os-dispatcher-pc-after-wait}}\index{os-dispatcher-pc-after-wait} $=$ {\tt{'}}{\tt{3222}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-dispatcher-qemptyp-return-ad!dress}$\;\;$
{\sc{os-dispatcher-qemptyp-return-address}}\index{os-dispatcher-qemptyp-return-ad!dress} $=$ {\tt{'}}{\tt{3211}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-restore-state-address}$\;\;$
{\sc{os-restore-state-address}}\index{os-restore-state-address} $=$ {\tt{'}}{\tt{2601}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-os-code \\ \index{length-os-code}
{\rm{length}}\,({\rm{os-code}}\,({\it{os\/}})\index{os-code})\index{length} $=$ {\tt{'}}{\tt{754}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-os-code.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-os-code \\ \index{plistp-os-code}
{\rm{plistp}}\,({\rm{os-code}}\,({\it{os\/}})\index{os-code})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-os-code.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{finite-number-queuep} \\  
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep} \\ 
$=$$\;\;\;\;$(\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth} $=$ {\it{capacity\/}}) \\ 
$\wedge$$\;\;\;\;${\rm{finite-number-listp}}\,({\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\it{capacity\/}}, {\it{queue\/}})\index{getseg}, {\it{lub\/}})\index{finite-number-listp})\-)\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  array-queuep-finite-number-queue \\ \index{array-queuep-finite-number-queue}
{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep} $\rightarrow$ {\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep}
\end{tabbing}


\noindent{\sc Event}:   Disable array-queuep-finite-number-queue.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qmaxlength-field \\ \index{finite-number-queue-qmaxlength-!field}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth} $=$ {\it{capacity\/}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qmaxlength-field.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-qarray \\ \index{finite-number-listp-qarray}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-listp}}\,({\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\it{capacity\/}}, {\it{queue\/}})\index{getseg}, {\it{lub\/}})\index{finite-number-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-qarray.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-finite-number-queue \\ \index{length-finite-number-queue}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$({\rm{length}}\,({\it{queue\/}})\index{length} $=$ ({\tt{'}}{\tt{4}} $+$ {\it{capacity\/}}))\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  plistp-finite-number-queue \\ \index{plistp-finite-number-queue}
{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep} $\rightarrow$ {\rm{plistp}}\,({\it{queue\/}})\index{plistp}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qhead-size \\ \index{finite-number-queue-qhead-size}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$(({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth} $<$ {\it{capacity\/}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qhead-size.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qtail-size \\ \index{finite-number-queue-qtail-size}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$(({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth} $<$ {\it{capacity\/}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qtail-size.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qcurrlength-size \\ \index{finite-number-queue-qcurrlength!-size}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$(({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $<$ ($1\;+$ {\it{capacity\/}})))\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qcurrlength-size.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qmaxlength-value \\ \index{finite-number-queue-qmaxlength-v!alue}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth} $=$ {\it{capacity\/}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qmaxlength-value.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qarray-after-enq \\ \index{finite-number-queue-qarray-afte!r-enq}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\it{capacity\/}}, {\rm{array-enq}}\,({\it{item\/}}, {\it{queue\/}})\index{array-enq})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,({\it{item\/}}, {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, {\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\it{capacity\/}}, {\it{queue\/}})\index{getseg})\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qarray-after-enq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-array-enq \\ \index{finite-number-queuep-array-enq}
\=\+(\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{array-qfullp}}\,({\it{queue\/}})\index{array-qfullp}) $\wedge$ {\rm{finite-numberp}}\,({\it{item\/}}, {\it{lub\/}})\index{finite-numberp}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,({\rm{array-enq}}\,({\it{item\/}}, {\it{queue\/}})\index{array-enq}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-array-enq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qarray-after-deq \\ \index{finite-number-queue-qarray-afte!r-deq}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$({\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\it{capacity\/}}, {\rm{array-deq}}\,({\it{queue\/}})\index{array-deq})\index{getseg} $=$ {\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\it{capacity\/}}, {\it{queue\/}})\index{getseg})\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qarray-after-deq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-array-deq \\ \index{finite-number-queuep-array-deq}
\=\+({\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,({\rm{array-deq}}\,({\it{queue\/}})\index{array-deq}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-array-deq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qfirst-finite-number-queue \\ \index{array-qfirst-finite-number-queue}
\=\+({\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst} $<$ {\it{lub\/}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qfirst-finite-number-queue.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  remainder-array-qfirst-finite-number-queue \\ \index{remainder-array-qfirst-finite-n!umber-queue}
\=\+({\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst} ${}${\bf{mod}}${}$ {\it{lub\/}}) $=$ {\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst})\-
\end{tabbing}


\noindent{\sc Event}:   Disable remainder-array-qfirst-finite-number-queue.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{finite-number-queuep-facts}} to consist of the following events: finite-number-queue-qmaxlength-value,
finite-number-queue-qcurrlength-size,
finite-number-queue-qtail-size,
finite-number-queue-qhead-size,
remainder-array-qfirst-finite-number-queue,
array-qfirst-finite-number-queue,
finite-number-queuep-array-deq,
finite-number-queue-qarray-after-deq,
finite-number-queuep-array-enq,
finite-number-queue-qarray-after-enq,
plistp-finite-number-queue,
length-finite-number-queue,
finite-number-listp-qarray,
finite-number-queue-qmaxlength-field,
array-queuep-finite-number-queue.\index{finite-number-queuep-facts}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{finite-number-queue-listp} \\  
\=\+{\rm{finite-number-queue-listp}}\,({\it{list\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-listp} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{list\/}}) \\ 
{\bf then }\=\+{\rm{finite-number-queuep}}\,({\rm{car}}\,({\it{list\/}}), {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep} \\ 
$\wedge$$\;\;\;\;${\rm{finite-number-queue-listp}}\,({\rm{cdr}}\,({\it{list\/}}), {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-listp}\- \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-getnth \\ \index{finite-number-queuep-getnth}
\=\+({\rm{finite-number-queue-listp}}\,({\it{l\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-listp} $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-getnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-putnth \\ \index{finite-number-queue-listp-putnt!h}
\=\+(\=\+{\rm{finite-number-queue-listp}}\,({\it{l\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-listp} \\ 
$\wedge$$\;\;\;\;${\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,({\rm{putnth}}\,({\it{queue\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-putnth.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{finite-number-queue-tablep} \\  
\=\+{\rm{finite-number-queue-tablep}}\,({\it{n\/}}, {\it{l\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-tablep} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{l\/}}) \\ 
{\bf then }\=\+{\rm{plistp}}\,({\rm{car}}\,({\it{l\/}}))\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\rm{car}}\,({\it{l\/}}))\index{length} $=$ {\it{n\/}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-number-queue-listp}}\,({\rm{car}}\,({\it{l\/}}), {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-listp} \\ 
$\wedge$$\;\;\;\;${\rm{finite-number-queue-tablep}}\,(\=\+{\it{n\/}}, \\ 
{\rm{cdr}}\,({\it{l\/}}), \\ 
{\it{capacity\/}}, \\ 
{\it{lub\/}})\-\index{finite-number-queue-tablep})\-)\-\- \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-getnth \\ \index{finite-number-queue-listp-getnt!h}
\=\+({\rm{finite-number-queue-tablep}}\,({\it{n\/}}, {\it{l\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-tablep} $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{length} $=$ {\it{n\/}}) \\ 
$\wedge$$\;\;\;\;${\rm{finite-number-queue-listp}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-listp})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-getnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-getnth2 \\ \index{finite-number-queuep-getnth2}
\=\+(\=\+{\rm{finite-number-queue-tablep}}\,({\it{n\/}}, {\it{l\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-tablep} \\ 
$\wedge$$\;\;\;\;$(({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) $\wedge$ ({\it{j\/}} $<$ {\it{n\/}})))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,({\rm{getnth2}}\,({\it{i\/}}, {\it{j\/}}, {\it{l\/}})\index{getnth2}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-getnth2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-tablep-putnth \\ \index{finite-number-queue-tablep-putnt!h}
\=\+(\=\+{\rm{finite-number-queue-tablep}}\,({\it{n\/}}, {\it{l\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-tablep} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-number-queue-listp}}\,({\it{s\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-listp} \\ 
$\wedge$$\;\;\;\;$({\rm{plistp}}\,({\it{s\/}})\index{plistp} $\wedge$ ({\rm{length}}\,({\it{s\/}})\index{length} $=$ {\it{n\/}})))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-tablep}}\,({\it{n\/}}, {\rm{putnth}}\,({\it{s\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-tablep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-tablep-putnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-tablep-putnth2 \\ \index{finite-number-queue-tablep-putnt!h2}
\=\+(\=\+{\rm{finite-number-queue-tablep}}\,({\it{n\/}}, {\it{l\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-tablep} \\ 
$\wedge$$\;\;\;\;$(({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) $\wedge$ {\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-tablep}}\,({\it{n\/}}, {\rm{putnth2}}\,({\it{queue\/}}, {\it{i\/}}, {\it{j\/}}, {\it{l\/}})\index{putnth2}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-tablep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-tablep-putnth2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-nthcdr \\ \index{finite-number-queue-listp-nthcd!r}
\=\+{\rm{finite-number-queue-listp}}\,({\it{l\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-listp} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,({\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-nthcdr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-firstn \\ \index{finite-number-queue-listp-first!n}
\=\+{\rm{finite-number-queue-listp}}\,({\it{l\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-listp} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{l\/}})\index{firstn}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-firstn.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-getseg \\ \index{finite-number-queue-listp-getse!g}
\=\+(\=\+\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ ({\it{n\/}} $+$ {\it{k\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;${\rm{finite-number-queue-listp}}\,({\it{l\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-listp})\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-getseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  divisor-not-lessp \\ \index{divisor-not-lessp}
(({\it{n\/}} $\not\simeq {\tt{0}}$) $\wedge$ (({\it{a\/}} $\not\simeq {\tt{0}}$) $\wedge$ {\rm{divides}}\,({\it{n\/}}, {\it{a\/}})\index{divides})) $\rightarrow$ ({\it{a\/}} $\not<$ {\it{n\/}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  divides-not-lessp-instance \\ \index{divides-not-lessp-instance}
\=\+(({\it{n\/}} $\not\simeq {\tt{0}}$) $\wedge$ ({\rm{listp}}\,({\it{l\/}}) $\wedge$ (({\rm{length}}\,({\it{l\/}})\index{length} ${}${\bf{mod}}${}$ {\it{n\/}}) $=$ {\tt{'}}{\tt{0}}))) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{length}}\,({\it{l\/}})\index{length} $<$ {\it{n\/}}) $=$ {\tt{'}}{\tt{*1*false}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable divides-not-lessp-instance.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-tablep-table \\ \index{finite-number-queue-tablep-table}
\=\+(\=\+({\it{n\/}} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{length}}\,({\it{l\/}})\index{length} ${}${\bf{mod}}${}$ {\it{n\/}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;${\rm{finite-number-queue-listp}}\,({\it{l\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-listp})\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-tablep}}\,({\it{n\/}}, {\rm{table}}\,({\it{n\/}}, {\it{l\/}})\index{table}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-tablep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-tablep-table.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-current-taskid}$\;\;$
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-ready-set} \\  
{\rm{os-ready-set}}\,({\it{os\/}})\index{os-ready-set} $=$ {\rm{index-ready-set}}\,({\tt{'}}{\tt{0}}, {\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\index{index-ready-set}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-readyq-qarray} \\  
\=\+{\rm{os-readyq-qarray}}\,({\it{os\/}})\index{os-readyq-qarray} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{getnth}, {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{getseg}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN GOOD-OS
 (OS)
 (AND
  (GOOD-TM OS)
  (AND
   (EQUAL (TM-SLIMIT OS) '3311)
   (AND
    (EQUAL (OS-CODE OS)
           '(2187 13 2 2187 14 3 75 3 191 14 3280 77 2 9 65 2 15 4299 2 0
                  12747 2 0 4811 2 13 5067 2 14 3275 2 4 3531 2 5 3787 2 6
                  4043 2 7 65 2 8 20683 2 0 4171 2 13 4171 3 14 0 2123 3 2 77
                  2 9 65 2 15 77 3 2 65 3 159 218 3 478 3 2123 3 2 65 3 8
                  6283 0 2 14731 0 2 6795 0 3 63563 7 2 55371 6 2 47179 5 2
                  38987 4 2 30795 3 2 22603 2 2 0 14 2547 75 3 191 14 3280 14
                  3274 14 3240 2 3206 14 2547 75 3 191 14 3280 14 3274 77 2 2
                  65 2 211 203 2 1 459 2 0 2 3206 14 2547 137 8 4 131 8 0 10
                  2712 131 8 1 10 2813 131 8 2 10 2922 2 2981 2123 6 2 73 6
                  16 2123 7 3 75 3 191 14 3280 2187 12 2 2123 4 6 77 4 8 2123
                  3 2 77 3 128 2113 3 4 65 3 499 14 3297 10 2791 2123 2 7 14
                  3240 2123 3 6 77 3 2 65 3 211 195 3 3 6 3222 4547 3 12 6
                  3222 203 3 0 459 3 0 2123 2 6 75 3 191 14 3240 2 3222 75 3
                  191 14 3274 4171 3 12 77 3 2 65 3 211 203 3 2 2507 3 6 2
                  3206 2123 6 2 73 6 16 75 3 191 14 3280 2187 12 2 2123 4 2
                  77 4 8 2123 3 6 77 3 128 2113 3 4 65 3 499 14 3293 10 2900
                  14 3280 14 3274 4171 3 12 77 3 9 65 3 15 3019 3 2 2123 3 6
                  77 3 2 65 3 211 195 3 2 6 3222 4547 3 12 6 3222 203 3 0 459
                  3 0 2123 2 6 75 3 191 14 3240 2 3222 75 3 191 14 3274 4171
                  3 12 77 3 2 65 3 211 203 3 3 2507 3 6 2 3206 2123 7 3 75 3
                  191 14 3280 2187 12 2 2123 3 2 77 3 8 65 3 371 14 3297 10
                  2959 2123 2 7 14 3240 182 12 6 3222 166 12 2 3222 75 3 191
                  14 3274 4171 3 12 77 3 2 65 3 211 203 3 4 459 3 0 2 3206 75
                  3 191 14 3280 2187 12 2 2123 3 2 77 3 8 65 3 243 14 3293 10
                  3020 14 3280 14 3274 4171 3 12 77 3 9 65 3 15 3019 3 2 2
                  3222 75 3 191 14 3274 4171 3 12 77 3 2 65 3 211 203 3 5 459
                  3 0 2 3206 139 10 3206 2187 14 3 75 3 191 14 3293 10 3063
                  139 10 3231 4171 3 14 14 2547 4171 5 8 77 5 2 65 5 211 195
                  5 5 6 3091 4171 2 8 75 3 191 14 3240 203 5 0 459 5 0 4171 3
                  8 77 3 8 65 3 243 14 3297 6 3114 4171 2 9 65 2 256 14 3258
                  130 10 178 8 6 3128 4171 2 9 65 2 256 14 3240 130 10 4171 2
                  9 14 3240 130 10 139 10 3206 2187 14 3 75 3 191 14 3293 10
                  3156 139 10 3231 4171 3 14 14 2547 4171 5 9 77 5 2 65 5 211
                  195 5 4 6 3184 4171 2 9 75 3 191 14 3240 203 5 0 459 5 0
                  4171 3 9 77 3 8 65 3 371 14 3293 138 10 14 3280 2191 9 2 14
                  3274 130 10 75 3 191 14 3293 10 3221 14 3280 14 2601 186 11
                  162 0 4 75 3 191 14 3280 14 2601 174 0 75 3 191 14 3280 14
                  2601 162 0 2123 4 3 65 4 4 14401 4 3 2251 4 2 726 3 31175 3
                  3 0 14411 4 3 30789 4 3 2113 4 3 65 4 4 2251 4 2 0 722 3
                  30919 3 3 0 2123 2 3 65 2 4 6209 2 3 6219 2 2 0 707 3 0 0
                  31427 3 3 0))
    (AND
     (EQUAL (GETNTH '3 (TM-MEMORY OS))
            '2654)
     (AND
      (EQUAL (GETNTH '4 (TM-MEMORY OS))
             '2667)
      (AND
       (EQUAL (GETNTH '5 (TM-MEMORY OS))
              '2690)
       (AND
        (EQUAL (GETNTH '6 (TM-MEMORY OS))
               '3042)
        (AND
         (EQUAL (GETNTH '7 (TM-MEMORY OS))
                '3135)
         (AND
          (EQUAL (GETNTH '11 (TM-MEMORY OS))
                 '1000)
          (AND
           (NOT (TM-IN-SUPERVISOR-MODE OS))
           (AND
            (GOOD-CPU-LIST (TABLE '9 (OS-TASK-TABLE OS)))
            (AND
             (GOOD-STATUS-LIST (TABLE '2 (OS-STATUS-TABLE OS)))
             (AND
              (FINITE-NUMBER-QUEUEP (OS-READYQ OS)
                                    '16
                                    '16)
              (AND
               (MUTUALLY-DISJOINT (TABLE '2 (OS-SEGMENT-TABLE OS)))
               (AND
                (DISJOINT-EVERYWHERE '0
                                     '3311
                                     (TABLE '2 (OS-SEGMENT-TABLE OS)))
                (AND
                 (FINITE-SEGMENT-TABLEP (TABLE '2 (OS-SEGMENT-TABLE OS))
                                        '65536)
                 (AND
                  (FINITE-NUMBER-QUEUE-LISTP (TABLE '8 (OS-IBUFFERS OS))
                                             '4
                                             '65536)
                  (AND
                   (FINITE-NUMBER-QUEUE-LISTP (TABLE '8 (OS-OBUFFERS OS))
                                              '4
                                              '65536)
                   (AND
                    (FINITE-NUMBER-QUEUE-LISTP (TABLE '8 (OS-MBUFFERS OS))
                                               '4
                                               '65536)
                    (AND
                     (PERMUTATION (MAPUP-QUEUE (OS-READYQ OS))
                                  (OS-READY-SET OS))
                     (AND
                      (IFF (TM-WAITING OS)
                           (ARRAY-QEMPTYP (OS-READYQ OS)))
                      (IMPLIES
                       (NOT (TM-WAITING OS))
                       (AND
                        (EQUAL
                             (TM-BASE OS)
                             (BASE (GETNTH (OS-CURRENT-TASKID OS)
                                           (TABLE '2 (OS-SEGMENT-TABLE OS)))))
                        (EQUAL
                         (TM-LIMIT OS)
                         (LIMIT
                          (GETNTH
                           (OS-CURRENT-TASKID OS)
                           (TABLE '2
                               (OS-SEGMENT-TABLE OS))))))))))))))))))))))))))))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  good-tm-os \\ \index{good-tm-os}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-tm}}\,({\it{os\/}})\index{good-tm}
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os \\ \index{tm-slimit-os}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ ({\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit} $=$ {\tt{'}}{\tt{3311}})
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os \\ \index{os-code-os}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-code}}\,({\it{os\/}})\index{os-code} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{2187}}{\tt{ }}{\tt{13}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2187}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{65}} \\ 
{\tt{2}}{\tt{ }}{\tt{15}}{\tt{ }}{\tt{4299}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{12747}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{4811}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{13}}{\tt{ }}{\tt{5067}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{14}} \\ 
{\tt{3275}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{3531}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{3787}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{4043}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{7}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{8}} \\ 
{\tt{20683}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{13}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{2}} \\ 
{\tt{9}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{15}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{159}}{\tt{ }}{\tt{218}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{478}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}} \\ 
{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{6283}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{14731}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{6795}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{63563}}{\tt{ }}{\tt{7}} \\ 
{\tt{2}}{\tt{ }}{\tt{55371}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{47179}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{38987}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{30795}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}} \\ 
{\tt{22603}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{2547}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}} \\ 
{\tt{14}}{\tt{ }}{\tt{3240}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3206}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{2547}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{14}} \\ 
{\tt{3274}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{1}}{\tt{ }}{\tt{459}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3206}}{\tt{ }}{\tt{14}} \\ 
{\tt{2547}}{\tt{ }}{\tt{137}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{131}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{2712}}{\tt{ }}{\tt{131}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{1}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{2813}} \\ 
{\tt{131}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{2922}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2981}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{73}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{16}}{\tt{ }}{\tt{2123}} \\ 
{\tt{7}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{2187}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{4}} \\ 
{\tt{8}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{128}}{\tt{ }}{\tt{2113}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{499}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3297}} \\ 
{\tt{10}}{\tt{ }}{\tt{2791}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{7}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3240}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}} \\ 
{\tt{211}}{\tt{ }}{\tt{195}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{4547}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}} \\ 
{\tt{459}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3240}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}} \\ 
{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}} \\ 
{\tt{2507}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3206}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{73}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{16}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}} \\ 
{\tt{3280}}{\tt{ }}{\tt{2187}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}} \\ 
{\tt{128}}{\tt{ }}{\tt{2113}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{499}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3293}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{2900}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}} \\ 
{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{15}}{\tt{ }}{\tt{3019}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2123}} \\ 
{\tt{3}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{195}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{4547}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{12}} \\ 
{\tt{6}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{459}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}} \\ 
{\tt{3240}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}} \\ 
{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2507}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3206}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{7}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{75}} \\ 
{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{2187}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}} \\ 
{\tt{371}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3297}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{2959}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{7}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3240}}{\tt{ }}{\tt{182}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{6}} \\ 
{\tt{3222}}{\tt{ }}{\tt{166}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{12}} \\ 
{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{459}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3206}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}} \\ 
{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{2187}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{243}} \\ 
{\tt{14}}{\tt{ }}{\tt{3293}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{3020}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{77}} \\ 
{\tt{3}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{15}}{\tt{ }}{\tt{3019}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}} \\ 
{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{459}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2}} \\ 
{\tt{3206}}{\tt{ }}{\tt{139}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{3206}}{\tt{ }}{\tt{2187}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3293}}{\tt{ }}{\tt{10}} \\ 
{\tt{3063}}{\tt{ }}{\tt{139}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{3231}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{2547}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{77}} \\ 
{\tt{5}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{195}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3091}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}} \\ 
{\tt{14}}{\tt{ }}{\tt{3240}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{459}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}} \\ 
{\tt{243}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3297}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3114}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{256}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3258}} \\ 
{\tt{130}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{178}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3128}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{256}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3240}} \\ 
{\tt{130}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3240}}{\tt{ }}{\tt{130}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{139}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{3206}} \\ 
{\tt{2187}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3293}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{3156}}{\tt{ }}{\tt{139}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{3231}} \\ 
{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{2547}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{195}} \\ 
{\tt{5}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3184}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3240}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{0}} \\ 
{\tt{459}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{371}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3293}}{\tt{ }}{\tt{138}} \\ 
{\tt{10}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{2191}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{130}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}} \\ 
{\tt{3293}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{3221}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{2601}}{\tt{ }}{\tt{186}}{\tt{ }}{\tt{11}}{\tt{ }}{\tt{162}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{75}} \\ 
{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{2601}}{\tt{ }}{\tt{174}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}} \\ 
{\tt{14}}{\tt{ }}{\tt{2601}}{\tt{ }}{\tt{162}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{14401}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2251}} \\ 
{\tt{4}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{726}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{31175}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{14411}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{30789}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2113}} \\ 
{\tt{4}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{2251}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{722}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{30919}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2123}} \\ 
{\tt{2}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{6209}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{6219}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{707}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{31427}} \\ 
{\tt{3}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{)}}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-clock-new-pc \\ \index{os-clock-new-pc}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ ({\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth} $=$ {\tt{'}}{\tt{2654}})
\end{tabbing}


\noindent{\sc Event}:   Disable os-clock-new-pc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-error-new-pc \\ \index{os-error-new-pc}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ ({\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth} $=$ {\tt{'}}{\tt{2667}})
\end{tabbing}


\noindent{\sc Event}:   Disable os-error-new-pc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-svc-new-pc \\ \index{os-svc-new-pc}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ ({\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth} $=$ {\tt{'}}{\tt{2690}})
\end{tabbing}


\noindent{\sc Event}:   Disable os-svc-new-pc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-input-new-pc \\ \index{os-input-new-pc}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ ({\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth} $=$ {\tt{'}}{\tt{3042}})
\end{tabbing}


\noindent{\sc Event}:   Disable os-input-new-pc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-output-new-pc \\ \index{os-output-new-pc}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ ({\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth} $=$ {\tt{'}}{\tt{3135}})
\end{tabbing}


\noindent{\sc Event}:   Disable os-output-new-pc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-time-slice \\ \index{os-time-slice}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ ({\rm{getnth}}\,({\tt{'}}{\tt{11}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth} $=$ {\tt{'}}{\tt{1000}})
\end{tabbing}


\noindent{\sc Event}:   Disable os-time-slice.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-not-in-supervisor-mode \\ \index{os-not-in-supervisor-mode}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ ($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{os\/}})\index{tm-in-supervisor-mode})
\end{tabbing}


\noindent{\sc Event}:   Disable os-not-in-supervisor-mode.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os \\ \index{tm-base-os}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-base}}\,({\it{os\/}})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os \\ \index{tm-limit-os}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\it{os\/}})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-cpu-list-os-task-table \\ \index{good-cpu-list-os-task-table}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-cpu-list}}\,({\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\index{table})\index{good-cpu-list}
\end{tabbing}


\noindent{\sc Event}:   Disable good-cpu-list-os-task-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-status-list-os-status-table \\ \index{good-status-list-os-status-table}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-status-list}}\,({\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\index{good-status-list}
\end{tabbing}


\noindent{\sc Event}:   Disable good-status-list-os-status-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-os-readyq \\ \index{finite-number-queuep-os-readyq}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{finite-number-queuep}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq}, {\tt{'}}{\tt{16}}, {\tt{'}}{\tt{16}})\index{finite-number-queuep}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-os-readyq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mutually-disjoint-os-segment-table \\ \index{mutually-disjoint-os-segment-ta!ble}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{mutually-disjoint}}\,({\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\index{mutually-disjoint}
\end{tabbing}


\noindent{\sc Event}:   Disable mutually-disjoint-os-segment-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  disjoint-everywhere-os-segment-table \\ \index{disjoint-everywhere-os-segment-t!able}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;${\rm{disjoint-everywhere}}\,({\tt{'}}{\tt{0}}, {\tt{'}}{\tt{3311}}, {\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\index{disjoint-everywhere}\-
\end{tabbing}


\noindent{\sc Event}:   Disable disjoint-everywhere-os-segment-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-segment-tablep-os-segment-table \\ \index{finite-segment-tablep-os-segment!-table}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-segment-tablep}}\,({\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table}, {\tt{'}}{\tt{65536}})\index{finite-segment-tablep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-segment-tablep-os-segment-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-ibuffers \\ \index{finite-number-queue-listp-os-ib!uffers}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,({\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{table}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-ibuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-obuffers \\ \index{finite-number-queue-listp-os-ob!uffers}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,({\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\index{table}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-obuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-mbuffers \\ \index{finite-number-queue-listp-os-mb!uffers}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,({\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-tablep-os-mbuffers \\ \index{finite-number-queue-tablep-os-m!buffers}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-tablep}}\,(\=\+{\tt{'}}{\tt{16}}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{16}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\index{table}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queue-tablep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-tablep-os-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-qarray-os-ready-set \\ \index{permutation-os-readyq-qarray-os!-ready-set}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{permutation}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue}, {\rm{os-ready-set}}\,({\it{os\/}})\index{os-ready-set})\index{permutation}
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-qarray-os-ready-set.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-waiting-iff-array-qemptyp-os-readyq \\ \index{tm-waiting-iff-array-qemptyp-os!-readyq}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\leftrightarrow$ {\rm{array-qemptyp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qemptyp})
\end{tabbing}


\noindent{\sc Event}:   Disable tm-waiting-iff-array-qemptyp-os-readyq.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-taskid}$\;\;$
{\rm{os-taskid}}\,({\it{os\/}})\index{os-taskid} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-numberp-os-taskid \\ \index{finite-numberp-os-taskid}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{os-taskid}}\,({\it{os\/}})\index{os-taskid}, {\tt{'}}{\tt{16}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-os-taskid.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{good-os-properties}} to consist of the following events: finite-numberp-os-taskid,
tm-waiting-iff-array-qemptyp-os-readyq,
permutation-os-readyq-qarray-os-ready-set,
finite-number-queue-tablep-os-mbuffers,
finite-number-queue-listp-os-mbuffers,
finite-number-queue-listp-os-obuffers,
finite-number-queue-listp-os-ibuffers,
finite-segment-tablep-os-segment-table,
disjoint-everywhere-os-segment-table,
mutually-disjoint-os-segment-table,
finite-number-queuep-os-readyq,
good-status-list-os-status-table,
good-cpu-list-os-task-table,
tm-limit-os,
tm-base-os,
os-not-in-supervisor-mode,
os-time-slice,
os-output-new-pc,
os-input-new-pc,
os-svc-new-pc,
os-error-new-pc,
os-clock-new-pc,
os-code-os,
tm-slimit-os,
good-tm-os.\index{good-os-properties}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-finite-number-queue-corollary \\ \index{length-finite-number-queue-coro!llary}
{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{16}}, {\tt{'}}{\tt{16}})\index{finite-number-queuep} $\rightarrow$ ({\rm{length}}\,({\it{queue\/}})\index{length} $=$ {\tt{'}}{\tt{20}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-finite-number-queue-corollary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-finite-number-queue-corollary \\ \index{plistp-finite-number-queue-coro!llary}
{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{16}}, {\tt{'}}{\tt{16}})\index{finite-number-queuep} $\rightarrow$ {\rm{plistp}}\,({\it{queue\/}})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-finite-number-queue-corollary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-queuep-finite-number-queue-corollary \\ \index{array-queuep-finite-number-queue!-corollary}
{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{16}}, {\tt{'}}{\tt{16}})\index{finite-number-queuep} $\rightarrow$ {\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep}
\end{tabbing}


\noindent{\sc Event}:   Disable array-queuep-finite-number-queue-corollary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qhead-size-corollary \\ \index{finite-number-queue-qhead-size-!corollary}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{16}}, {\tt{'}}{\tt{16}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$(({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth} $<$ {\tt{'}}{\tt{16}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qhead-size-corollary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qtail-size-corollary \\ \index{finite-number-queue-qtail-size-!corollary}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{16}}, {\tt{'}}{\tt{16}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$(({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth} $<$ {\tt{'}}{\tt{16}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qtail-size-corollary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qcurrlength-size-corollary \\ \index{finite-number-queue-qcurrlength!-size-corollary}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{16}}, {\tt{'}}{\tt{16}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$(({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $<$ {\tt{'}}{\tt{17}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qcurrlength-size-corollary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qmaxlength-value-corollary \\ \index{finite-number-queue-qmaxlength-v!alue-corollary}
{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{16}}, {\tt{'}}{\tt{16}})\index{finite-number-queuep} $\rightarrow$ ({\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth} $=$ {\tt{'}}{\tt{16}})
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qmaxlength-value-corollary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-array-enq-finite-number-queue-corollary \\ \index{finite-number-queuep-array-enq-!finite-number-queue-corollary}
\=\+(\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{16}}, {\tt{'}}{\tt{16}})\index{finite-number-queuep} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{array-qfullp}}\,({\it{queue\/}})\index{array-qfullp}) $\wedge$ (({\it{item\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{item\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,({\rm{array-enq}}\,({\it{item\/}}, {\it{queue\/}})\index{array-enq}, {\tt{'}}{\tt{16}}, {\tt{'}}{\tt{16}})\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-array-enq-finite-number-queue-corollary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-array-deq-finite-number-queue-corollary \\ \index{finite-number-queuep-array-deq-!finite-number-queue-corollary}
\=\+({\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{16}}, {\tt{'}}{\tt{16}})\index{finite-number-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,({\rm{array-deq}}\,({\it{queue\/}})\index{array-deq}, {\tt{'}}{\tt{16}}, {\tt{'}}{\tt{16}})\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-array-deq-finite-number-queue-corollary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qfirst-finite-number-queue-corollary \\ \index{array-qfirst-finite-number-queue!-corollary}
\=\+({\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{16}}, {\tt{'}}{\tt{16}})\index{finite-number-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst} $<$ {\tt{'}}{\tt{16}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qfirst-finite-number-queue-corollary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  remainder-array-qfirst-finite-number-queue-corollary \\ \index{remainder-array-qfirst-finite-n!umber-queue-corollary}
\=\+({\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{16}}, {\tt{'}}{\tt{16}})\index{finite-number-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{16}}) $=$ {\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst})\-
\end{tabbing}


\noindent{\sc Event}:   Disable remainder-array-qfirst-finite-number-queue-corollary.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{finite-number-queue-corollaries}} to consist of the following events: remainder-array-qfirst-finite-number-queue-corollary,
array-qfirst-finite-number-queue-corollary,
finite-number-queuep-array-deq-finite-number-queue-corollary,
finite-number-queuep-array-enq-finite-number-queue-corollary,
finite-number-queue-qmaxlength-value-corollary,
finite-number-queue-qcurrlength-size-corollary,
finite-number-queue-qtail-size-corollary,
finite-number-queue-qhead-size-corollary,
array-queuep-finite-number-queue-corollary,
plistp-finite-number-queue-corollary,
length-finite-number-queue-corollary.\index{finite-number-queue-corollaries}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-finite-number-queue-corollary-for-mbuffers \\ \index{length-finite-number-queue-coro!llary-for-mbuffers}
{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} $\rightarrow$ ({\rm{length}}\,({\it{queue\/}})\index{length} $=$ {\tt{'}}{\tt{8}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-finite-number-queue-corollary-for-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-finite-number-queue-corollary-for-mbuffers \\ \index{plistp-finite-number-queue-coro!llary-for-mbuffers}
{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} $\rightarrow$ {\rm{plistp}}\,({\it{queue\/}})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-finite-number-queue-corollary-for-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-queuep-finite-number-queue-corollary-for-mbuffers \\ \index{array-queuep-finite-number-queue!-corollary-for-mbuffers}
{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} $\rightarrow$ {\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep}
\end{tabbing}


\noindent{\sc Event}:   Disable array-queuep-finite-number-queue-corollary-for-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qhead-size-corollary-for-mbuffers \\ \index{finite-number-queue-qhead-size-!corollary-for-mbuffers}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$(({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth} $<$ {\tt{'}}{\tt{4}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qhead-size-corollary-for-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qtail-size-corollary-for-mbuffers \\ \index{finite-number-queue-qtail-size-!corollary-for-mbuffers}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$(({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth} $<$ {\tt{'}}{\tt{4}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qtail-size-corollary-for-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qcurrlength-size-corollary-for-mbuffers \\ \index{finite-number-queue-qcurrlength!-size-corollary-for-mbuffers}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$(({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $<$ {\tt{'}}{\tt{5}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qcurrlength-size-corollary-for-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qmaxlength-value-corollary-for-mbuffers \\ \index{finite-number-queue-qmaxlength-v!alue-corollary-for-mbuffers}
{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} $\rightarrow$ ({\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth} $=$ {\tt{'}}{\tt{4}})
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qmaxlength-value-corollary-for-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-array-enq-finite-number-queue-corollary-for-mbuffers \\ \index{finite-number-queuep-array-enq-!finite-number-queue-corollary-for-mbuffers}
\=\+(\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{array-qfullp}}\,({\it{queue\/}})\index{array-qfullp}) $\wedge$ (({\it{item\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{item\/}} $<$ {\tt{'}}{\tt{65536}}))))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,({\rm{array-enq}}\,({\it{item\/}}, {\it{queue\/}})\index{array-enq}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-array-enq-finite-number-queue-corollary-for-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-array-deq-finite-number-queue-corollary-for-mbuffers \\ \index{finite-number-queuep-array-deq-!finite-number-queue-corollary-for-mbuffers}
\=\+({\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,({\rm{array-deq}}\,({\it{queue\/}})\index{array-deq}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-array-deq-finite-number-queue-corollary-for-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qfirst-finite-number-queue-corollary-for-mbuffers \\ \index{array-qfirst-finite-number-queue!-corollary-for-mbuffers}
\=\+({\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst} $<$ {\tt{'}}{\tt{65536}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qfirst-finite-number-queue-corollary-for-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  remainder-array-qfirst-finite-number-queue-corollary-for-mbuffers \\ \index{remainder-array-qfirst-finite-n!umber-queue-corollary-for-mbuffers}
\=\+({\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{65536}}) $=$ {\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst})\-
\end{tabbing}


\noindent{\sc Event}:   Disable remainder-array-qfirst-finite-number-queue-corollary-for-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-getnth-corollary \\ \index{finite-number-queue-listp-getnt!h-corollary}
\=\+({\rm{finite-number-queue-tablep}}\,({\tt{'}}{\tt{16}}, {\it{l\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queue-tablep} $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{length}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{length} $=$ {\tt{'}}{\tt{16}}) \\ 
$\wedge$$\;\;\;\;${\rm{finite-number-queue-listp}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queue-listp})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-getnth-corollary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-getnth2-corollary \\ \index{finite-number-queuep-getnth2-co!rollary}
\=\+(\=\+{\rm{finite-number-queue-tablep}}\,({\tt{'}}{\tt{16}}, {\it{l\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queue-tablep} \\ 
$\wedge$$\;\;\;\;$(({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) $\wedge$ ({\it{j\/}} $<$ {\tt{'}}{\tt{16}})))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,({\rm{getnth2}}\,({\it{i\/}}, {\it{j\/}}, {\it{l\/}})\index{getnth2}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-getnth2-corollary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-tablep-putnth-corollary \\ \index{finite-number-queue-tablep-putnt!h-corollary}
\=\+(\=\+{\rm{finite-number-queue-tablep}}\,({\tt{'}}{\tt{16}}, {\it{l\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queue-tablep} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-number-queue-listp}}\,({\it{s\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queue-listp} \\ 
$\wedge$$\;\;\;\;$({\rm{plistp}}\,({\it{s\/}})\index{plistp} $\wedge$ ({\rm{length}}\,({\it{s\/}})\index{length} $=$ {\tt{'}}{\tt{16}})))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-tablep}}\,({\tt{'}}{\tt{16}}, {\rm{putnth}}\,({\it{s\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queue-tablep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-tablep-putnth-corollary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-tablep-putnth2-corollary \\ \index{finite-number-queue-tablep-putnt!h2-corollary}
\=\+(\=\+{\rm{finite-number-queue-tablep}}\,({\tt{'}}{\tt{16}}, {\it{l\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queue-tablep} \\ 
$\wedge$$\;\;\;\;$(({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) $\wedge$ {\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-tablep}}\,({\tt{'}}{\tt{16}}, {\rm{putnth2}}\,({\it{queue\/}}, {\it{i\/}}, {\it{j\/}}, {\it{l\/}})\index{putnth2}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queue-tablep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-tablep-putnth2-corollary.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{finite-number-queue-tablep-corollaries}} to consist of the following events: finite-number-queue-tablep-putnth2-corollary,
finite-number-queue-tablep-putnth-corollary,
finite-number-queuep-getnth2-corollary,
finite-number-queue-listp-getnth-corollary,
remainder-array-qfirst-finite-number-queue-corollary-for-mbuffers,
array-qfirst-finite-number-queue-corollary-for-mbuffers,
finite-number-queuep-array-deq-finite-number-queue-corollary-for-mbuffers,
finite-number-queuep-array-enq-finite-number-queue-corollary-for-mbuffers,
finite-number-queue-qmaxlength-value-corollary-for-mbuffers,
finite-number-queue-qcurrlength-size-corollary-for-mbuffers,
finite-number-queue-qtail-size-corollary-for-mbuffers,
finite-number-queue-qhead-size-corollary-for-mbuffers,
array-queuep-finite-number-queue-corollary-for-mbuffers,
plistp-finite-number-queue-corollary-for-mbuffers,
length-finite-number-queue-corollary-for-mbuffers.\index{finite-number-queue-tablep-coro!llaries}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  number-of-ready-tasks-equals-length-os-readyq \\ \index{number-of-ready-tasks-equals-le!ngth-os-readyq}
\=\+{\rm{permutation}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue}, {\rm{os-ready-set}}\,({\it{os\/}})\index{os-ready-set})\index{permutation} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{number-of-ready-tasks}}\,({\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\index{number-of-ready-tasks} \\ 
$=$$\;\;\;\;${\rm{length}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{length})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable number-of-ready-tasks-equals-length-os-readyq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-waiting-to-sendp-implies-readyq-not-full \\ \index{os-waiting-to-sendp-implies-rea!dyq-not-full}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\it{destid\/}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\it{destid\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp})\-)\- \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  os-waiting-to-receivep-implies-readyq-not-full \\ \index{os-waiting-to-receivep-implies-!readyq-not-full}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\it{destid\/}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} $=$ {\tt{'}}{\tt{3}}) \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\it{destid\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp})\-)\- \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  os-waiting-to-inputp-implies-readyq-not-full \\ \index{os-waiting-to-inputp-implies-re!adyq-not-full}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\it{destid\/}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} $=$ {\tt{'}}{\tt{5}}) \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\it{destid\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp})\-)\- \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  os-waiting-to-outputp-implies-readyq-not-full \\ \index{os-waiting-to-outputp-implies-re!adyq-not-full}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\it{destid\/}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} $=$ {\tt{'}}{\tt{4}}) \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\it{destid\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp})\-)\- \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qarray-after-qreplace \\ \index{finite-number-queue-qarray-afte!r-qreplace}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\it{capacity\/}}, {\rm{array-qreplace}}\,({\it{item\/}}, {\it{queue\/}})\index{array-qreplace})\index{getseg} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\it{item\/}}, \\ 
{\rm{decr-mod}}\,({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})\index{decr-mod}, \\ 
{\rm{getseg}}\,({\tt{'}}{\tt{4}}, {\it{capacity\/}}, {\it{queue\/}})\index{getseg})\-\index{putnth})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-array-qreplace \\ \index{finite-number-queuep-array-qrep!lace}
\=\+(\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp}) $\wedge$ {\rm{finite-numberp}}\,({\it{item\/}}, {\it{lub\/}})\index{finite-numberp}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,({\rm{array-qreplace}}\,({\it{item\/}}, {\it{queue\/}})\index{array-qreplace}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-array-qreplace.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-qarray-os-ready-set-corollary \\ \index{permutation-os-readyq-qarray-os!-ready-set-corollary}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue}, \\ 
{\rm{index-ready-set}}\,({\tt{'}}{\tt{0}}, {\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\index{index-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-qarray-os-ready-set-corollary.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{mapup-cpu} \\  
\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}$\;\;${\bf then }{\rm{getnth}}\,({\it{taskid\/}}, {\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\index{table})\index{getnth} \\ 
{\bf elseif }{\it{taskid\/}} $=$ {\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}$\;\;${\bf then }{\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu} \\ 
{\bf else }{\rm{getnth}}\,({\it{taskid\/}}, {\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\index{table})\index{getnth}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{mapup-regs} \\  
{\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs} $=$ {\rm{getseg}}\,({\tt{'}}{\tt{0}}, {\tt{'}}{\tt{8}}, {\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\index{getseg}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{mapup-cc} \\  
{\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc} $=$ {\rm{tm-unpack-cc}}\,({\rm{getnth}}\,({\tt{'}}{\tt{8}}, {\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\index{getnth})\index{tm-unpack-cc}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{mapup-error} \\  
\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{tm-unpack-error}}\,({\rm{getnth}}\,({\tt{'}}{\tt{8}}, {\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\index{getnth})\index{tm-unpack-error}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{mapup-svcflag} \\  
\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{tm-unpack-svcflag}}\,({\rm{getnth}}\,({\tt{'}}{\tt{8}}, {\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\index{getnth})\index{tm-unpack-svcflag}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{mapup-svcid} \\  
\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{tm-unpack-svcid}}\,({\rm{getnth}}\,({\tt{'}}{\tt{8}}, {\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\index{getnth})\index{tm-unpack-svcid}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{mapup-base} \\  
\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,({\it{taskid\/}}, {\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\index{getnth})\index{base}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{mapup-limit} \\  
\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,({\it{taskid\/}}, {\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\index{getnth})\index{limit}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{mapup-task} \\  
\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory}, \\ 
{\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs}, \\ 
{\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc}, \\ 
{\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error}, \\ 
{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag}, \\ 
{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid}, \\ 
{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\index{mapup-address-space}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{mapup-tasks} \\  
\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $<$ {\tt{'}}{\tt{16}} \\ 
{\bf then }{\rm{cons}}\,({\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task}, {\rm{mapup-tasks}}\,($1\;+$ {\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks}) \\ 
{\bf else }{\tt{'}}{\tt{nil}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{mapup-os-tasks}$\;\;$
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks} $=$ {\rm{mapup-tasks}}\,({\tt{'}}{\tt{0}}, {\it{os\/}})\index{mapup-tasks}
\end{tabbing}

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

\begin{tabbing}{\sc Definition}:\index{mapup-os-ibuffers} \\  
{\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers} $=$ {\rm{mapup-queue-list}}\,({\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{table})\index{mapup-queue-list}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{mapup-os-obuffers} \\  
{\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers} $=$ {\rm{mapup-queue-list}}\,({\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\index{table})\index{mapup-queue-list}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{mapup-os-mbuffers} \\  
\=\+{\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{table}}\,({\tt{'}}{\tt{16}}, {\rm{mapup-queue-list}}\,({\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\index{mapup-queue-list})\index{table}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{mapup-os} \\  
\=\+{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak}}\,(\=\+{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks}, \\ 
{\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers}, \\ 
{\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers}, \\ 
{\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers}, \\ 
{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table}, \\ 
{\rm{tm-rwstate}}\,({\it{os\/}})\index{tm-rwstate}, \\ 
{\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}, \\ 
{\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\-\index{ak}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-mapup-queue-list \\ \index{length-mapup-queue-list}
{\rm{length}}\,({\rm{mapup-queue-list}}\,({\it{l\/}})\index{mapup-queue-list})\index{length} $=$ {\rm{length}}\,({\it{l\/}})\index{length}
\end{tabbing}


\noindent{\sc Event}:   Disable length-mapup-queue-list.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-mapup-queue-list \\ \index{getnth-mapup-queue-list}
\=\+({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\it{i\/}}, {\rm{mapup-queue-list}}\,({\it{l\/}})\index{mapup-queue-list})\index{getnth} $=$ {\rm{mapup-queue}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{mapup-queue})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-mapup-queue-list.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-list-putnth \\ \index{mapup-queue-list-putnth}
\=\+{\rm{mapup-queue-list}}\,({\rm{putnth}}\,({\it{v\/}}, {\it{i\/}}, {\it{l\/}})\index{putnth})\index{mapup-queue-list} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,({\rm{mapup-queue}}\,({\it{v\/}})\index{mapup-queue}, {\it{i\/}}, {\rm{mapup-queue-list}}\,({\it{l\/}})\index{mapup-queue-list})\index{putnth}\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-list-putnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-getnth \\ \index{mapup-queue-getnth}
\=\+({\rm{finite-number-queue-listp}}\,({\it{l\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queue-listp} $\wedge$ ({\it{id\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{mapup-queue}}\,({\rm{getnth}}\,({\it{id\/}}, {\it{l\/}})\index{getnth})\index{mapup-queue} $=$ {\rm{getnth}}\,({\it{id\/}}, {\rm{mapup-queue-list}}\,({\it{l\/}})\index{mapup-queue-list})\index{getnth})\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-getnth.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-mapup-tasks \\ \index{length-mapup-tasks}
{\rm{length}}\,({\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\index{length} $=$ ({\tt{'}}{\tt{16}} $-$ {\it{taskid\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-mapup-tasks.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-mapup-os-tasks \\ \index{length-mapup-os-tasks}
{\rm{length}}\,({\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\index{length} $=$ {\tt{'}}{\tt{16}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-mapup-os-tasks.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-mapup-cpu \\ \index{length-mapup-cpu}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{length}}\,({\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\index{length} $=$ {\tt{'}}{\tt{9}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-mapup-cpu.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-mapup-cpu \\ \index{finite-number-listp-mapup-cpu}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-listp}}\,({\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu}, {\tt{'}}{\tt{65536}})\index{finite-number-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-mapup-cpu.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-mapup-base \\ \index{numberp-mapup-base}
({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) $\rightarrow$ ({\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base} $\in\;${\bf{N}}${}$)
\end{tabbing}


\noindent{\sc Event}:   Disable numberp-mapup-base.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-mapup-limit \\ \index{numberp-mapup-limit}
({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) $\rightarrow$ ({\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit} $\in\;${\bf{N}}${}$)
\end{tabbing}


\noindent{\sc Event}:   Disable numberp-mapup-limit.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-mapup-regs \\ \index{plistp-mapup-regs}
{\rm{plistp}}\,({\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-mapup-regs.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-mapup-regs \\ \index{length-mapup-regs}
{\rm{length}}\,({\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\index{length} $=$ {\tt{'}}{\tt{8}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-mapup-regs.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-mapup-regs \\ \index{finite-number-listp-mapup-regs}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-listp}}\,({\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs}, {\tt{'}}{\tt{65536}})\index{finite-number-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-mapup-regs.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-mapup-cc \\ \index{finite-numberp-mapup-cc}
{\rm{finite-numberp}}\,({\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc}, {\tt{'}}{\tt{4}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-mapup-cc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-mapup-error \\ \index{finite-numberp-mapup-error}
{\rm{finite-numberp}}\,({\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error}, {\tt{'}}{\tt{64}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-mapup-error.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-mapup-svcflag \\ \index{finite-numberp-mapup-svcflag}
{\rm{finite-numberp}}\,({\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag}, {\tt{'}}{\tt{2}})\index{finite-numberp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-mapup-svcflag.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-mapup-svcid \\ \index{finite-numberp-mapup-svcid}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid}, {\tt{'}}{\tt{128}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-mapup-svcid.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  leq-plus-base-limit-getnth \\ \index{leq-plus-base-limit-getnth}
\=\+({\rm{finite-segment-tablep}}\,({\it{l\/}}, {\it{max\/}})\index{finite-segment-tablep} $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;$\=\+{\bf if }{\it{max\/}} $<$ ({\rm{base}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{base} $+$ {\rm{limit}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{limit})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  leq-plus-base-limit-getnth-corollary \\ \index{leq-plus-base-limit-getnth-coro!llary}
\=\+({\rm{finite-segment-tablep}}\,({\it{l\/}}, {\tt{'}}{\tt{65536}})\index{finite-segment-tablep} $\wedge$ ({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length})) \\ 
$\rightarrow$$\;\;\;\;$({\tt{'}}{\tt{65536}} $\not<$ ({\rm{base}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{base} $+$ {\rm{limit}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{limit}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable leq-plus-base-limit-getnth-corollary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  leq-plus-mapup-base-mapup-limit \\ \index{leq-plus-mapup-base-mapup-limit}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$({\tt{'}}{\tt{65536}} $\not<$ ({\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base} $+$ {\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable leq-plus-mapup-base-mapup-limit.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-tm-memory-mapup-task \\ \index{length-tm-memory-mapup-task}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{length}}\,({\rm{tm-memory}}\,({\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\index{tm-memory})\index{length} $=$ {\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-
\end{tabbing}


\noindent{\sc Event}:   Disable length-tm-memory-mapup-task.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-mapup-task \\ \index{good-address-space-mapup-task}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{finite-numberp}}\,({\it{taskid\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space}}\,(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task}, \\ 
{\rm{length}}\,({\rm{tm-memory}}\,({\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\index{tm-memory})\index{length})\-\index{good-address-space}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-mapup-task.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-list-mapup-tasks \\ \index{good-address-space-list-mapup-t!asks}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{finite-numberp}}\,({\it{taskid\/}}, {\tt{'}}{\tt{16}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-address-space-list}}\,({\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\index{good-address-space-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-list-mapup-tasks.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-address-space-list-mapup-os-tasks \\ \index{good-address-space-list-mapup-o!s-tasks}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-address-space-list}}\,({\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\index{good-address-space-list}
\end{tabbing}


\noindent{\sc Event}:   Disable good-address-space-list-mapup-os-tasks.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-mapup-os-ibuffers \\ \index{length-mapup-os-ibuffers}
{\rm{length}}\,({\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\index{length} $=$ {\tt{'}}{\tt{16}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-mapup-os-ibuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-mapup-queue \\ \index{good-task-buffer-mapup-queue}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-task-buffer}}\,({\rm{mapup-queue}}\,({\it{queue\/}})\index{mapup-queue}, {\it{capacity\/}})\index{good-task-buffer}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-mapup-queue.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-list-mapup-queue-list \\ \index{good-task-buffer-list-mapup-que!ue-list}
\=\+{\rm{finite-number-queue-listp}}\,({\it{l\/}}, {\it{capacity\/}}, {\tt{'}}{\tt{65536}})\index{finite-number-queue-listp} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-task-buffer-list}}\,({\rm{mapup-queue-list}}\,({\it{l\/}})\index{mapup-queue-list}, {\it{capacity\/}})\index{good-task-buffer-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-list-mapup-queue-list.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-list-mapup-os-ibuffers \\ \index{good-task-buffer-list-mapup-os-i!buffers}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-task-buffer-list}}\,({\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers}, {\tt{'}}{\tt{4}})\index{good-task-buffer-list}
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-list-mapup-os-ibuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-mapup-os-obuffers \\ \index{length-mapup-os-obuffers}
{\rm{length}}\,({\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\index{length} $=$ {\tt{'}}{\tt{16}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-mapup-os-obuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-list-mapup-os-obuffers \\ \index{good-task-buffer-list-mapup-os-!obuffers}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-task-buffer-list}}\,({\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers}, {\tt{'}}{\tt{4}})\index{good-task-buffer-list}
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-list-mapup-os-obuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-mapup-os-mbuffers \\ \index{length-mapup-os-mbuffers}
{\rm{length}}\,({\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\index{length} $=$ {\tt{'}}{\tt{16}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-mapup-os-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-list-nthcdr \\ \index{good-task-buffer-list-nthcdr}
\=\+{\rm{good-task-buffer-list}}\,({\it{l\/}}, {\it{capacity\/}})\index{good-task-buffer-list} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-task-buffer-list}}\,({\rm{nthcdr}}\,({\it{n\/}}, {\it{l\/}})\index{nthcdr}, {\it{capacity\/}})\index{good-task-buffer-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-list-nthcdr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-list-firstn \\ \index{good-task-buffer-list-firstn}
\=\+{\rm{good-task-buffer-list}}\,({\it{l\/}}, {\it{capacity\/}})\index{good-task-buffer-list} \\ 
$\rightarrow$$\;\;\;\;${\rm{good-task-buffer-list}}\,({\rm{firstn}}\,({\it{n\/}}, {\it{l\/}})\index{firstn}, {\it{capacity\/}})\index{good-task-buffer-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-list-firstn.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-list-getseg \\ \index{good-task-buffer-list-getseg}
\=\+(\=\+{\rm{good-task-buffer-list}}\,({\it{l\/}}, {\it{capacity\/}})\index{good-task-buffer-list} \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ {\it{n\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }({\rm{length}}\,({\it{l\/}})\index{length} $-$ {\it{n\/}}) $<$ {\it{k\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-task-buffer-list}}\,({\rm{getseg}}\,({\it{n\/}}, {\it{k\/}}, {\it{l\/}})\index{getseg}, {\it{capacity\/}})\index{good-task-buffer-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-list-getseg.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-table-table \\ \index{good-task-buffer-table-table}
\=\+(\=\+{\rm{good-task-buffer-list}}\,({\it{l\/}}, {\it{capacity\/}})\index{good-task-buffer-list} \\ 
$\wedge$$\;\;\;\;$((({\rm{length}}\,({\it{l\/}})\index{length} ${}${\bf{mod}}${}$ {\it{n\/}}) $=$ {\tt{'}}{\tt{0}}) $\wedge$ ({\it{n\/}} $\not\simeq {\tt{0}}$)))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-task-buffer-table}}\,({\rm{table}}\,({\it{n\/}}, {\it{l\/}})\index{table}, {\it{n\/}}, {\it{capacity\/}})\index{good-task-buffer-table}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-table-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-task-buffer-table-mapup-os-mbuffers \\ \index{good-task-buffer-table-mapup-os!-mbuffers}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-task-buffer-table}}\,({\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers}, {\tt{'}}{\tt{16}}, {\tt{'}}{\tt{4}})\index{good-task-buffer-table}
\end{tabbing}


\noindent{\sc Event}:   Disable good-task-buffer-table-mapup-os-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-mapup-finite-number-queue \\ \index{finite-number-listp-mapup-finite!-number-queue}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\it{capacity\/}}, {\it{lub\/}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-listp}}\,({\rm{mapup-queue}}\,({\it{queue\/}})\index{mapup-queue}, {\it{lub\/}})\index{finite-number-listp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-number-listp-mapup-finite-number-queue-corollary \\ \index{finite-number-listp-mapup-finite!-number-queue-corollary}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{finite-number-listp}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue}, {\tt{'}}{\tt{16}})\index{finite-number-listp}
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-listp-mapup-finite-number-queue-corollary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-ready-set-mapup-os \\ \index{ak-ready-set-mapup-os}
{\rm{ak-ready-set}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-ready-set} $=$ {\rm{os-ready-set}}\,({\it{os\/}})\index{os-ready-set}
\end{tabbing}


\noindent{\sc Event}:   Disable ak-ready-set-mapup-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-ak-mapup-os \\ \index{good-ak-mapup-os}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-ak}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{good-ak}
\end{tabbing}


\noindent{\sc Event}:   Disable good-ak-mapup-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-qemptyp-mapup-queue-os-readyq \\ \index{not-qemptyp-mapup-queue-os-read!yq}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{qemptyp}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qemptyp})\-
\end{tabbing}


\noindent{\sc Event}:   Disable not-qemptyp-mapup-queue-os-readyq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-qfirst-mapup-queue-os-readyq \\ \index{lessp-qfirst-mapup-queue-os-rea!dyq}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst} $<$ {\tt{'}}{\tt{16}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-qfirst-mapup-queue-os-readyq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-set-error \\ \index{good-os-tm-set-error}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{finite-numberp}}\,({\it{error\/}}, {\tt{'}}{\tt{64}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-set-error}}\,({\it{error\/}}, {\it{os\/}})\index{tm-set-error})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-set-error.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-set-pc \\ \index{good-os-tm-set-pc}
({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{finite-numberp}}\,({\it{pc\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp}) $\rightarrow$ {\rm{good-os}}\,({\rm{tm-set-pc}}\,({\it{pc\/}}, {\it{os\/}})\index{tm-set-pc})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-set-pc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-set-sp \\ \index{good-os-tm-set-sp}
({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{finite-numberp}}\,({\it{sp\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp}) $\rightarrow$ {\rm{good-os}}\,({\rm{tm-set-sp}}\,({\it{sp\/}}, {\it{os\/}})\index{tm-set-sp})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-set-sp.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-set-cc \\ \index{good-os-tm-set-cc}
({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{finite-numberp}}\,({\it{cc\/}}, {\tt{'}}{\tt{4}})\index{finite-numberp}) $\rightarrow$ {\rm{good-os}}\,({\rm{tm-set-cc}}\,({\it{cc\/}}, {\it{os\/}})\index{tm-set-cc})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-set-cc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-set-svcflag \\ \index{good-os-tm-set-svcflag}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{finite-numberp}}\,({\it{svcflag\/}}, {\tt{'}}{\tt{2}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-set-svcflag}}\,({\it{svcflag\/}}, {\it{os\/}})\index{tm-set-svcflag})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-set-svcflag.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-set-svcid \\ \index{good-os-tm-set-svcid}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{finite-numberp}}\,({\it{svcid\/}}, {\tt{'}}{\tt{128}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-set-svcid}}\,({\it{svcid\/}}, {\it{os\/}})\index{tm-set-svcid})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-set-svcid.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-store-in-regmem \\ \index{good-os-tm-store-in-regmem}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{finite-numberp}}\,({\it{value\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-store-in-regmem}}\,({\it{value\/}}, {\it{addr\/}}, {\it{os\/}})\index{tm-store-in-regmem})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-store-in-regmem.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-equal-plus-base-limit-0 \\ \index{not-equal-plus-base-limit-0}
\=\+(\=\+{\rm{good-tm}}\,({\it{tm\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{tm\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr\/}}, {\it{tm\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$({\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} $\not=$ {\tt{'}}{\tt{1}}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(({\rm{tm-base}}\,({\it{tm\/}})\index{tm-base} $+$ {\rm{tm-limit}}\,({\it{tm\/}})\index{tm-limit}) $\not=$ {\tt{'}}{\tt{0}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equality-of-getseg-backchain-corollary \\ \index{equality-of-getseg-backchain-co!rollary}
\=\+(\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{os\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{nested-intervals}}\,({\tt{'}}{\tt{0}}, {\tt{'}}{\tt{3311}}, {\it{i\/}}, {\it{j\/}})\index{nested-intervals} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{disjoint-everywhere}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\tt{'}}{\tt{3311}}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{disjoint-everywhere} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
$<$$\;\;\;\;${\rm{length}}\,({\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\index{table})\index{length})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\it{os\/}})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-limit}}\,({\it{os\/}})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\index{table})\-\index{getnth})\index{limit})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,(\=\+{\it{addr\/}}, \\ 
{\it{os\/}})\-\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{1}})\-)\-)\-)\-)\-)\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\it{i\/}}, \\ 
{\it{j\/}}, \\ 
{\rm{putnth}}\,(\=\+{\it{value\/}}, \\ 
{\rm{tm-base}}\,({\it{os\/}})\index{tm-base} $+$ {\rm{real-addr-num}}\,({\it{addr\/}})\index{real-addr-num}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{putnth})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\it{i\/}}, {\it{j\/}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable equality-of-getseg-backchain-corollary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  equality-of-getnth-backchain-corollary \\ \index{equality-of-getnth-backchain-co!rollary}
\=\+(\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-in-supervisor-mode}}\,({\it{os\/}})\index{tm-in-supervisor-mode}) \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\it{i\/}} $<$ {\tt{'}}{\tt{0}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$(\=\+(({\it{i\/}} $-$ {\tt{'}}{\tt{0}}) $<$ {\tt{'}}{\tt{3311}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{disjoint-everywhere}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\tt{'}}{\tt{3311}}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\index{table})\-\index{disjoint-everywhere} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
$<$$\;\;\;\;${\rm{length}}\,({\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\index{table})\index{length})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\it{os\/}})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{tm-limit}}\,({\it{os\/}})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\index{table})\-\index{getnth})\index{limit})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,(\=\+{\it{addr\/}}, \\ 
{\it{os\/}})\-\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{1}})\-)\-)\-)\-)\-)\-)\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\it{i\/}}, \\ 
{\rm{putnth}}\,(\=\+{\it{value\/}}, \\ 
{\rm{tm-base}}\,({\it{os\/}})\index{tm-base} $+$ {\rm{real-addr-num}}\,({\it{addr\/}})\index{real-addr-num}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{putnth})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\it{i\/}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable equality-of-getnth-backchain-corollary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-store-in-memory \\ \index{good-os-tm-store-in-memory}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} $\not\simeq {\tt{0}}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{real-addr-source}}\,({\it{addr\/}})\index{real-addr-source} $\not=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-good-address}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-good-address} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\it{value\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-store-in-memory}}\,({\it{value\/}}, {\rm{real-addr-num}}\,({\it{addr\/}})\index{real-addr-num}, {\it{os\/}})\index{tm-store-in-memory})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-store-in-memory.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-store \\ \index{good-os-tm-store}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$({\rm{tm-good-address}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-good-address} $\wedge$ {\rm{finite-numberp}}\,({\it{value\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-store}}\,({\it{value\/}}, {\it{addr\/}}, {\it{os\/}})\index{tm-store})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-store.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-add \\ \index{good-os-tm-execute-add}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{os\/}})\index{tm-good-address})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-execute-add}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{os\/}})\index{tm-execute-add})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-add.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-branch \\ \index{good-os-tm-execute-branch}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-good-address}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-execute-branch}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-execute-branch})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-branch.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-branch-on-zero \\ \index{good-os-tm-execute-branch-on-ze!ro}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-good-address}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-execute-branch-on-zero}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-execute-branch-on-zero})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-branch-on-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-branch-not-zero \\ \index{good-os-tm-execute-branch-not-ze!ro}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-good-address}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-execute-branch-not-zero}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-execute-branch-not-zero})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-branch-not-zero.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-call \\ \index{good-os-tm-execute-call}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-good-address})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-execute-call}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-execute-call})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-call.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-compare \\ \index{good-os-tm-execute-compare}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{os\/}})\index{tm-good-address}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-execute-compare}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{os\/}})\index{tm-execute-compare})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-compare.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-decr \\ \index{good-os-tm-execute-decr}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-good-address})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-execute-decr}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-execute-decr})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-decr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-decr-mod \\ \index{good-os-tm-execute-decr-mod}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{os\/}})\index{tm-good-address})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-execute-decr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{os\/}})\index{tm-execute-decr-mod})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-decr-mod.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-incr \\ \index{good-os-tm-execute-incr}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-good-address})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-execute-incr}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-execute-incr})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-incr.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-incr-mod \\ \index{good-os-tm-execute-incr-mod}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{os\/}})\index{tm-good-address})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-execute-incr-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{os\/}})\index{tm-execute-incr-mod})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-incr-mod.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-load-base \\ \index{good-os-tm-execute-load-base}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-os}}\,({\rm{tm-execute-load-base}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-execute-load-base})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-load-base.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-load-limit \\ \index{good-os-tm-execute-load-limit}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-os}}\,({\rm{tm-execute-load-limit}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-execute-load-limit})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-load-limit.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-load-psw \\ \index{good-os-tm-execute-load-psw}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-os}}\,({\rm{tm-execute-load-psw}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-execute-load-psw})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-load-psw.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-mod \\ \index{good-os-tm-execute-mod}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{os\/}})\index{tm-good-address})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-execute-mod}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{os\/}})\index{tm-execute-mod})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-mod.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-move \\ \index{good-os-tm-execute-move}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$({\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{os\/}})\index{tm-good-address} $\wedge$ {\rm{tm-good-address}}\,({\it{addr2\/}}, {\it{os\/}})\index{tm-good-address}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-execute-move}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{os\/}})\index{tm-execute-move})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-move.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-multiply \\ \index{good-os-tm-execute-multiply}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{tm-good-address}}\,({\it{addr1\/}}, {\it{os\/}})\index{tm-good-address})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-execute-multiply}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{os\/}})\index{tm-execute-multiply})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-multiply.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-return \\ \index{good-os-tm-execute-return}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-os}}\,({\rm{tm-execute-return}}\,({\it{os\/}})\index{tm-execute-return})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-return.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-post-output-interrupt \\ \index{good-os-tm-execute-post-output-i!nterrupt}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-os}}\,({\rm{tm-execute-post-output-interrupt}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-execute-post-output-interrupt})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-post-output-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-run \\ \index{good-os-tm-execute-run}
({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) $\rightarrow$ {\rm{good-os}}\,({\rm{tm-execute-run}}\,({\it{os\/}})\index{tm-execute-run})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-run.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-set-clock \\ \index{good-os-tm-execute-set-clock}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-os}}\,({\rm{tm-execute-set-clock}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-execute-set-clock})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-set-clock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-start-output \\ \index{good-os-tm-execute-start-output}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-os}}\,({\rm{tm-execute-start-output}}\,({\it{addr1\/}}, {\it{addr2\/}}, {\it{os\/}})\index{tm-execute-start-output})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-start-output.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-svc \\ \index{good-os-tm-execute-svc}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-good-address}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-good-address}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-execute-svc}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-execute-svc})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-svc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-svc-return \\ \index{good-os-tm-execute-svc-return}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-os}}\,({\rm{tm-execute-svc-return}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-execute-svc-return})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-svc-return.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-test-iport \\ \index{good-os-tm-execute-test-iport}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-os}}\,({\rm{tm-execute-test-iport}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-execute-test-iport})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-test-iport.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-test-oport \\ \index{good-os-tm-execute-test-oport}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-os}}\,({\rm{tm-execute-test-oport}}\,({\it{addr\/}}, {\it{os\/}})\index{tm-execute-test-oport})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-test-oport.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-wait \\ \index{good-os-tm-execute-wait}
({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) $\rightarrow$ {\rm{good-os}}\,({\rm{tm-execute-wait}}\,({\it{os\/}})\index{tm-execute-wait})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-wait.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-nullary \\ \index{good-os-tm-execute-nullary}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-execute-nullary}}\,({\it{opcode\/}}, {\it{os\/}})\index{tm-execute-nullary})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-nullary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-unary \\ \index{good-os-tm-execute-unary}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-execute-unary}}\,({\it{opcode\/}}, {\it{addr\/}}, {\it{os\/}})\index{tm-execute-unary})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-unary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-binary \\ \index{good-os-tm-execute-binary}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-execute-binary}}\,({\it{opcode\/}}, {\it{addr1\/}}, {\it{addr2\/}}, {\it{os\/}})\index{tm-execute-binary})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-binary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute-instruction \\ \index{good-os-tm-execute-instruction}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-execute-instruction}}\,({\it{instruction\/}}, {\it{os\/}})\index{tm-execute-instruction})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute-instruction.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-execute \\ \index{good-os-tm-execute}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-execute}}\,({\it{instruction\/}}, {\it{os\/}})\index{tm-execute})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-decrement-clock \\ \index{good-os-tm-decrement-clock}
({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) $\rightarrow$ {\rm{good-os}}\,({\rm{tm-decrement-clock}}\,({\it{os\/}})\index{tm-decrement-clock})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-decrement-clock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-fetch-execute \\ \index{good-os-tm-fetch-execute}
({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) $\rightarrow$ {\rm{good-os}}\,({\rm{tm-fetch-execute}}\,({\it{os\/}})\index{tm-fetch-execute})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-fetch-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-set-iports \\ \index{good-os-tm-set-iports}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\it{iports\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(({\rm{length}}\,({\it{iports\/}})\index{length} $=$ {\tt{'}}{\tt{16}}) $\wedge$ {\rm{good-tm-iport-array}}\,({\it{iports\/}})\index{good-tm-iport-array}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-set-iports}}\,({\it{iports\/}}, {\it{os\/}})\index{tm-set-iports})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-set-iports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-set-oports \\ \index{good-os-tm-set-oports}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\it{oports\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;$(({\rm{length}}\,({\it{oports\/}})\index{length} $=$ {\tt{'}}{\tt{16}}) $\wedge$ {\rm{good-tm-oport-array}}\,({\it{oports\/}})\index{good-tm-oport-array}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{tm-set-oports}}\,({\it{oports\/}}, {\it{os\/}})\index{tm-set-oports})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-set-oports.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-tm-post-interrupt \\ \index{good-os-tm-post-interrupt}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-os}}\,({\rm{tm-post-interrupt}}\,({\it{interrupt\/}}, {\it{os\/}})\index{tm-post-interrupt})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-tm-post-interrupt.

\addvspace{18pt}

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

\begin{tabbing}{\sc Theorem}:  mutually-disjoint-segments-are-disjoint-case1 \\ \index{mutually-disjoint-segments-are-!disjoint-case1}
\=\+(\=\+{\rm{mutually-disjoint}}\,({\it{l\/}})\index{mutually-disjoint} \\ 
$\wedge$$\;\;\;\;$(({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) $\wedge$ (({\it{j\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) $\wedge$ ({\rm{fix}}\,({\it{i\/}}) $<$ {\rm{fix}}\,({\it{j\/}})))))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{disjoint}}\,(\=\+{\rm{base}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{base}, \\ 
{\rm{limit}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{limit}, \\ 
{\rm{base}}\,({\rm{getnth}}\,({\it{j\/}}, {\it{l\/}})\index{getnth})\index{base}, \\ 
{\rm{limit}}\,({\rm{getnth}}\,({\it{j\/}}, {\it{l\/}})\index{getnth})\index{limit})\-\index{disjoint}\-
\end{tabbing}


\noindent{\sc Event}:   Disable mutually-disjoint-segments-are-disjoint-case1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mutually-disjoint-segments-are-disjoint \\ \index{mutually-disjoint-segments-are-!disjoint}
\=\+(\=\+{\rm{mutually-disjoint}}\,({\it{l\/}})\index{mutually-disjoint} \\ 
$\wedge$$\;\;\;\;$(({\it{i\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) $\wedge$ (({\it{j\/}} $<$ {\rm{length}}\,({\it{l\/}})\index{length}) $\wedge$ ({\rm{fix}}\,({\it{i\/}}) $\not=$ {\rm{fix}}\,({\it{j\/}})))))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{disjoint}}\,(\=\+{\rm{base}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{base}, \\ 
{\rm{limit}}\,({\rm{getnth}}\,({\it{i\/}}, {\it{l\/}})\index{getnth})\index{limit}, \\ 
{\rm{base}}\,({\rm{getnth}}\,({\it{j\/}}, {\it{l\/}})\index{getnth})\index{base}, \\ 
{\rm{limit}}\,({\rm{getnth}}\,({\it{j\/}}, {\it{l\/}})\index{getnth})\index{limit})\-\index{disjoint}\-
\end{tabbing}


\noindent{\sc Event}:   Disable mutually-disjoint-segments-are-disjoint.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  numberp-os-current-taskid \\ \index{numberp-os-current-taskid}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid} $<$ {\tt{'}}{\tt{16}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable numberp-os-current-taskid.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-fetch-execute-mapup-address-space-separation \\ \index{tm-fetch-execute-mapup-address-!space-separation}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}) \\ 
$\wedge$$\;\;\;\;$({\it{taskid\/}} $\not=$ {\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\rm{tm-fetch-execute}}\,({\it{os\/}})\index{tm-fetch-execute})\index{tm-memory}, \\ 
{\it{regs\/}}, \\ 
{\it{cc\/}}, \\ 
{\it{error\/}}, \\ 
{\it{svcflag\/}}, \\ 
{\it{svcid\/}}, \\ 
{\rm{base}}\,({\rm{getnth}}\,(\=\+{\it{taskid\/}}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base}, \\ 
{\rm{limit}}\,({\rm{getnth}}\,(\=\+{\it{taskid\/}}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-\index{mapup-address-space} \\ 
$=$$\;\;\;\;${\rm{mapup-address-space}}\,(\=\+{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory}, \\ 
{\it{regs\/}}, \\ 
{\it{cc\/}}, \\ 
{\it{error\/}}, \\ 
{\it{svcflag\/}}, \\ 
{\it{svcid\/}}, \\ 
{\rm{base}}\,({\rm{getnth}}\,(\=\+{\it{taskid\/}}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\index{table})\-\index{getnth})\index{base}, \\ 
{\rm{limit}}\,({\rm{getnth}}\,(\=\+{\it{taskid\/}}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\index{table})\-\index{getnth})\index{limit})\-\index{mapup-address-space})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-fetch-execute-mapup-address-space-separation.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-tm-reglength-tm-cpu \\ \index{getnth-tm-reglength-tm-cpu}
\=\+{\rm{getnth}}\,({\tt{'}}{\tt{8}}, {\rm{tm-cpu}}\,({\it{tm\/}})\index{tm-cpu})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{tm-pack-psw}}\,({\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, {\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, {\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, {\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\index{tm-pack-psw}\-
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-tm-reglength-tm-cpu.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-tm-fetch-execute \\ \index{os-ibuffers-tm-fetch-execute}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{tm-fetch-execute}}\,({\it{os\/}})\index{tm-fetch-execute})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-tm-fetch-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-tm-fetch-execute \\ \index{os-obuffers-tm-fetch-execute}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{tm-fetch-execute}}\,({\it{os\/}})\index{tm-fetch-execute})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-tm-fetch-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-tm-fetch-execute \\ \index{os-mbuffers-tm-fetch-execute}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{tm-fetch-execute}}\,({\it{os\/}})\index{tm-fetch-execute})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-tm-fetch-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-tm-fetch-execute \\ \index{os-readyq-tm-fetch-execute}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-readyq}}\,({\rm{tm-fetch-execute}}\,({\it{os\/}})\index{tm-fetch-execute})\index{os-readyq} $=$ {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-tm-fetch-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-tm-fetch-execute \\ \index{os-status-table-tm-fetch-execute}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-status-table}}\,({\rm{tm-fetch-execute}}\,({\it{os\/}})\index{tm-fetch-execute})\index{os-status-table} $=$ {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-tm-fetch-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-tm-fetch-execute \\ \index{os-task-table-tm-fetch-execute}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-task-table}}\,({\rm{tm-fetch-execute}}\,({\it{os\/}})\index{tm-fetch-execute})\index{os-task-table} $=$ {\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-tm-fetch-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-tm-fetch-execute \\ \index{os-segment-table-tm-fetch-execute}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-segment-table}}\,({\rm{tm-fetch-execute}}\,({\it{os\/}})\index{tm-fetch-execute})\index{os-segment-table} $=$ {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-tm-fetch-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-current-taskid-tm-fetch-execute \\ \index{os-current-taskid-tm-fetch-exec!ute}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-current-taskid}}\,({\rm{tm-fetch-execute}}\,({\it{os\/}})\index{tm-fetch-execute})\index{os-current-taskid} $=$ {\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-current-taskid-tm-fetch-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-waiting-tm-fetch-execute \\ \index{tm-waiting-tm-fetch-execute}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ ({\rm{tm-waiting}}\,({\rm{tm-fetch-execute}}\,({\it{os\/}})\index{tm-fetch-execute})\index{tm-waiting} $=$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})
\end{tabbing}


\noindent{\sc Event}:   Disable tm-waiting-tm-fetch-execute.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{good-os-properties-crock}} to consist of the following events: finite-numberp-os-taskid,
tm-waiting-iff-array-qemptyp-os-readyq,
permutation-os-readyq-qarray-os-ready-set,
finite-number-queue-tablep-os-mbuffers,
finite-number-queue-listp-os-obuffers,
finite-number-queue-listp-os-ibuffers,
finite-segment-tablep-os-segment-table,
disjoint-everywhere-os-segment-table,
mutually-disjoint-os-segment-table,
finite-number-queuep-os-readyq,
good-status-list-os-status-table,
good-cpu-list-os-task-table,
os-not-in-supervisor-mode,
os-time-slice,
os-output-new-pc,
os-input-new-pc,
os-svc-new-pc,
os-error-new-pc,
os-clock-new-pc,
os-code-os,
tm-slimit-os,
good-tm-os.\index{good-os-properties-crock}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  times-commutativity-associativity-crock \\ \index{times-commutativity-associativit!y-crock}
({\it{a\/}} $*$ ({\it{c\/}} $*$ {\it{b\/}})) $=$ (({\it{a\/}} $*$ {\it{b\/}}) $*$ {\it{c\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable times-commutativity-associativity-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-unpack-cc-tm-pack-psw \\ \index{tm-unpack-cc-tm-pack-psw}
\=\+{\rm{finite-numberp}}\,({\it{cc\/}}, {\tt{'}}{\tt{4}})\index{finite-numberp} \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-unpack-cc}}\,({\rm{tm-pack-psw}}\,({\it{cc\/}}, {\it{error\/}}, {\it{svcflag\/}}, {\it{svcid\/}})\index{tm-pack-psw})\index{tm-unpack-cc} $=$ {\it{cc\/}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-unpack-cc-tm-pack-psw.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  remainder-plus-plus-times \\ \index{remainder-plus-plus-times}
(({\it{a\/}} $+$ ({\it{b\/}} $+$ ({\it{j\/}} $*$ {\it{i\/}}))) ${}${\bf{mod}}${}$ {\it{j\/}}) $=$ (({\it{a\/}} $+$ {\it{b\/}}) ${}${\bf{mod}}${}$ {\it{j\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable remainder-plus-plus-times.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-unpack-error-tm-pack-psw \\ \index{tm-unpack-error-tm-pack-psw}
\=\+({\rm{finite-numberp}}\,({\it{cc\/}}, {\tt{'}}{\tt{4}})\index{finite-numberp} $\wedge$ {\rm{finite-numberp}}\,({\it{error\/}}, {\tt{'}}{\tt{64}})\index{finite-numberp}) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-unpack-error}}\,({\rm{tm-pack-psw}}\,({\it{cc\/}}, {\it{error\/}}, {\it{svcflag\/}}, {\it{svcid\/}})\index{tm-pack-psw})\index{tm-unpack-error} $=$ {\it{error\/}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-unpack-error-tm-pack-psw.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  remainder-plus-plus-plus-times \\ \index{remainder-plus-plus-plus-times}
(({\it{a\/}} $+$ ({\it{b\/}} $+$ ({\it{c\/}} $+$ ({\it{i\/}} $*$ {\it{j\/}})))) ${}${\bf{mod}}${}$ {\it{j\/}}) $=$ (({\it{a\/}} $+$ ({\it{b\/}} $+$ {\it{c\/}})) ${}${\bf{mod}}${}$ {\it{j\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable remainder-plus-plus-plus-times.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable quotient-plus-plus-times.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-unpack-svcflag-tm-pack-psw \\ \index{tm-unpack-svcflag-tm-pack-psw}
\=\+(\=\+{\rm{finite-numberp}}\,({\it{cc\/}}, {\tt{'}}{\tt{4}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$({\rm{finite-numberp}}\,({\it{error\/}}, {\tt{'}}{\tt{64}})\index{finite-numberp} $\wedge$ {\rm{finite-numberp}}\,({\it{svcflag\/}}, {\tt{'}}{\tt{2}})\index{finite-numberp}))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-unpack-svcflag}}\,({\rm{tm-pack-psw}}\,({\it{cc\/}}, {\it{error\/}}, {\it{svcflag\/}}, {\it{svcid\/}})\index{tm-pack-psw})\index{tm-unpack-svcflag} $=$ {\it{svcflag\/}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-unpack-svcflag-tm-pack-psw.

\addvspace{18pt}

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


\noindent{\sc Event}:   Disable quotient-plus-plus-plus-times.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-unpack-svcid-tm-pack-psw \\ \index{tm-unpack-svcid-tm-pack-psw}
\=\+(\=\+{\rm{finite-numberp}}\,({\it{cc\/}}, {\tt{'}}{\tt{4}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{finite-numberp}}\,({\it{error\/}}, {\tt{'}}{\tt{64}})\index{finite-numberp} \\ 
$\wedge$$\;\;\;\;$({\rm{finite-numberp}}\,({\it{svcflag\/}}, {\tt{'}}{\tt{2}})\index{finite-numberp} $\wedge$ {\rm{finite-numberp}}\,({\it{svcid\/}}, {\tt{'}}{\tt{128}})\index{finite-numberp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-unpack-svcid}}\,({\rm{tm-pack-psw}}\,({\it{cc\/}}, {\it{error\/}}, {\it{svcflag\/}}, {\it{svcid\/}})\index{tm-pack-psw})\index{tm-unpack-svcid} $=$ {\it{svcid\/}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-unpack-svcid-tm-pack-psw.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-current-task-tm-fetch-execute \\ \index{mapup-current-task-tm-fetch-exe!cute}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, {\rm{tm-fetch-execute}}\,({\it{os\/}})\index{tm-fetch-execute})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{tm-fetch-execute}}\,({\rm{mapup-task}}\,({\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, {\it{os\/}})\index{mapup-task})\index{tm-fetch-execute})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-current-task-tm-fetch-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-separation \\ \index{mapup-task-separation}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}) \\ 
$\wedge$$\;\;\;\;$({\it{taskid\/}} $\not=$ {\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{tm-fetch-execute}}\,({\it{os\/}})\index{tm-fetch-execute})\index{mapup-task} $=$ {\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-separation.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-tm-fetch-execute-casesplit \\ \index{mapup-task-tm-fetch-execute-case!split}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{tm-fetch-execute}}\,({\it{os\/}})\index{tm-fetch-execute})\index{mapup-task} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid} \\ 
{\bf then }{\rm{tm-fetch-execute}}\,({\rm{mapup-task}}\,({\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, {\it{os\/}})\index{mapup-task})\index{tm-fetch-execute} \\ 
{\bf else }{\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-tm-fetch-execute-casesplit.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-tm-fetch-execute-case1 \\ \index{mapup-tasks-tm-fetch-execute-ca!se1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid} $<$ {\it{taskid\/}})))\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{tm-fetch-execute}}\,({\it{os\/}})\index{tm-fetch-execute})\index{mapup-tasks} $=$ {\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-tm-fetch-execute-case1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-mapup-tasks \\ \index{getnth-mapup-tasks}
\=\+(\=\+({\it{i\/}} $<$ {\tt{'}}{\tt{16}}) \\ 
$\wedge$$\;\;\;\;$(\=\+\=\+{\bf if }{\it{i\/}} $<$ {\it{j\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;$(({\it{j\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{i\/}} $\in\;${\bf{N}}${}$)))\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\it{i\/}} $-$ {\it{j\/}}, {\rm{mapup-tasks}}\,({\it{j\/}}, {\it{os\/}})\index{mapup-tasks})\index{getnth} $=$ {\rm{mapup-task}}\,({\it{i\/}}, {\it{os\/}})\index{mapup-task})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  getnth-mapup-tasks-corollary2 \\ \index{getnth-mapup-tasks-corollary2}
\=\+(({\it{i\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{i\/}} $\in\;${\bf{N}}${}$)) \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{mapup-tasks}}\,({\it{i\/}}, {\it{os\/}})\index{mapup-tasks})\index{getnth} $=$ {\rm{mapup-task}}\,({\it{i\/}}, {\it{os\/}})\index{mapup-task})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-mapup-tasks-corollary2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-tm-fetch-execute-case2 \\ \index{mapup-tasks-tm-fetch-execute-ca!se2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid} $<$ {\it{taskid\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{tm-fetch-execute}}\,({\it{os\/}})\index{tm-fetch-execute})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-fetch-execute}}\,({\rm{getnth}}\,(\=\+\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid} \\ 
$-$$\;\;\;\;${\it{taskid\/}}\-, \\ 
{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\index{getnth})\index{tm-fetch-execute}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid} $-$ {\it{taskid\/}}, \\ 
{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-tm-fetch-execute-case2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  difference-zero-arg2 \\ \index{difference-zero-arg2}
({\it{n\/}} $-$ {\tt{'}}{\tt{0}}) $=$ {\rm{fix}}\,({\it{n\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable difference-zero-arg2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-tm-fetch-execute \\ \index{mapup-os-tasks-tm-fetch-execute}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{tm-fetch-execute}}\,({\it{os\/}})\index{tm-fetch-execute})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-fetch-execute}}\,({\rm{getnth}}\,(\=\+{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{getnth})\index{tm-fetch-execute}, \\ 
{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-tm-fetch-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-tm-fetch-execute \\ \index{correctness-of-tm-fetch-execute}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{tm-clock-interruptp}}\,({\it{os\/}})\index{tm-clock-interruptp}))) \\ 
$\rightarrow$$\;\;\;\;$({\rm{mapup-os}}\,({\rm{tm-fetch-execute}}\,({\it{os\/}})\index{tm-fetch-execute})\index{mapup-os} $=$ {\rm{ak-private-step}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-private-step})\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-tm-fetch-execute.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-array-enq \\ \index{contract-array-enq}
\=\+({\it{maxlength\/}} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{putnth}}\,(\=\+{\rm{incr-mod}}\,({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, {\it{maxlength\/}})\index{incr-mod}, \\ 
{\tt{'}}{\tt{1}}, \\ 
{\rm{putnth}}\,(\=\+$1\;+$ {\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth}, \\ 
{\tt{'}}{\tt{2}}, \\ 
{\rm{putnth}}\,({\it{item\/}}, {\tt{'}}{\tt{4}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, {\it{queue\/}})\index{putnth})\-\index{putnth})\-\index{putnth} \\ 
$=$$\;\;\;\;${\rm{array-enq}}\,({\it{item\/}}, {\it{queue\/}})\index{array-enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable contract-array-enq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-array-enq-instance \\ \index{contract-array-enq-instance}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\it{maxlength\/}} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{putnth}}\,(\=\+{\rm{incr-mod}}\,({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, {\it{maxlength\/}})\index{incr-mod}, \\ 
{\tt{'}}{\tt{1}}, \\ 
{\rm{putnth}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\tt{'}}{\tt{2}}, \\ 
{\rm{putnth}}\,({\it{item\/}}, {\tt{'}}{\tt{4}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, {\it{queue\/}})\index{putnth})\-\index{putnth})\-\index{putnth} \\ 
$=$$\;\;\;\;${\rm{array-enq}}\,({\it{item\/}}, {\it{queue\/}})\index{array-enq})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable contract-array-enq-instance.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-array-deq \\ \index{contract-array-deq}
\=\+({\it{maxlength\/}} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{putnth}}\,(\=\+{\rm{incr-mod}}\,({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth}, {\it{maxlength\/}})\index{incr-mod}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $-\;1$, {\tt{'}}{\tt{2}}, {\it{queue\/}})\index{putnth})\-\index{putnth} \\ 
$=$$\;\;\;\;${\rm{array-deq}}\,({\it{queue\/}})\index{array-deq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable contract-array-deq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-array-qfirst \\ \index{contract-array-qfirst}
{\rm{getnth}}\,({\tt{'}}{\tt{4}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth}, {\it{queue\/}})\index{getnth} $=$ {\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst}
\end{tabbing}


\noindent{\sc Event}:   Disable contract-array-qfirst.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-array-qreplace \\ \index{contract-array-qreplace}
\=\+(\=\+{\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp}) $\wedge$ ({\it{maxlength\/}} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{putnth}}\,({\it{item\/}}, {\tt{'}}{\tt{4}} $+$ {\rm{decr-mod}}\,({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}, {\it{maxlength\/}})\index{decr-mod}, {\it{queue\/}})\index{putnth} \\ 
$=$$\;\;\;\;${\rm{array-qreplace}}\,({\it{item\/}}, {\it{queue\/}})\index{array-qreplace})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable contract-array-qreplace.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{contract-queues}} to consist of the following events: contract-array-qfirst,
contract-array-enq-instance,
contract-array-qreplace,
contract-array-enq,
contract-array-deq.\index{contract-queues}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{tick}$\;\;$
{\rm{tick}}\,({\it{n\/}})\index{tick} $=$ {\rm{fixlength}}\,({\it{n\/}}, {\tt{'}}{\tt{nil}}, {\tt{'}}{\tt{tick}})\index{fixlength}
\end{tabbing}

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

\begin{tabbing}{\sc Theorem}:  getnth-os-code \\ \index{getnth-os-code}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\it{n\/}}, {\rm{os-code}}\,({\it{os\/}})\index{os-code})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\it{n\/}}, \\ 
{\tt{'}}{\tt{(}}\=\+{\tt{2187}}{\tt{ }}{\tt{13}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2187}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{77}} \\ 
{\tt{2}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{15}}{\tt{ }}{\tt{4299}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{12747}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{4811}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{13}} \\ 
{\tt{5067}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3275}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{3531}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{3787}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{4043}} \\ 
{\tt{2}}{\tt{ }}{\tt{7}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{20683}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{13}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{14}} \\ 
{\tt{0}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{15}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{159}} \\ 
{\tt{218}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{478}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{6283}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2}} \\ 
{\tt{14731}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{6795}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{63563}}{\tt{ }}{\tt{7}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{55371}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{2}} \\ 
{\tt{47179}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{38987}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{30795}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{22603}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2}} \\ 
{\tt{0}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{2547}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{14}} \\ 
{\tt{3240}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3206}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{2547}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{14}} \\ 
{\tt{3274}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{1}}{\tt{ }}{\tt{459}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2}} \\ 
{\tt{3206}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{2547}}{\tt{ }}{\tt{137}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{131}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{2712}}{\tt{ }}{\tt{131}} \\ 
{\tt{8}}{\tt{ }}{\tt{1}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{2813}}{\tt{ }}{\tt{131}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{2922}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2981}}{\tt{ }}{\tt{2123}} \\ 
{\tt{6}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{73}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{16}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{7}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}} \\ 
{\tt{2187}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}} \\ 
{\tt{128}}{\tt{ }}{\tt{2113}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{499}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3297}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{2791}} \\ 
{\tt{2123}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{7}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3240}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{211}} \\ 
{\tt{195}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{4547}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}} \\ 
{\tt{459}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3240}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3222}} \\ 
{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}} \\ 
{\tt{211}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2507}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3206}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{73}} \\ 
{\tt{6}}{\tt{ }}{\tt{16}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{2187}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{2}} \\ 
{\tt{77}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{128}}{\tt{ }}{\tt{2113}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}} \\ 
{\tt{499}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3293}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{2900}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{4171}} \\ 
{\tt{3}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{15}}{\tt{ }}{\tt{3019}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{77}} \\ 
{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{195}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{4547}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{6}} \\ 
{\tt{3222}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{459}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}} \\ 
{\tt{14}}{\tt{ }}{\tt{3240}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}} \\ 
{\tt{12}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2507}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{2}} \\ 
{\tt{3206}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{7}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{2187}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{2}} \\ 
{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{371}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3297}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{2959}} \\ 
{\tt{2123}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{7}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3240}}{\tt{ }}{\tt{182}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{166}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{2}} \\ 
{\tt{3222}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}} \\ 
{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{459}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3206}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}} \\ 
{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{2187}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}} \\ 
{\tt{243}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3293}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{3020}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{4171}} \\ 
{\tt{3}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{15}}{\tt{ }}{\tt{3019}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3222}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}} \\ 
{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{203}} \\ 
{\tt{3}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{459}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3206}}{\tt{ }}{\tt{139}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{3206}}{\tt{ }}{\tt{2187}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3}} \\ 
{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3293}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{3063}}{\tt{ }}{\tt{139}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{3231}}{\tt{ }}{\tt{4171}} \\ 
{\tt{3}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{2547}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{195}} \\ 
{\tt{5}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3091}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3240}}{\tt{ }}{\tt{203}} \\ 
{\tt{5}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{459}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{243}}{\tt{ }}{\tt{14}} \\ 
{\tt{3297}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3114}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{256}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3258}}{\tt{ }}{\tt{130}} \\ 
{\tt{10}}{\tt{ }}{\tt{178}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3128}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{256}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3240}} \\ 
{\tt{130}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3240}}{\tt{ }}{\tt{130}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{139}}{\tt{ }}{\tt{10}} \\ 
{\tt{3206}}{\tt{ }}{\tt{2187}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3293}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{3156}} \\ 
{\tt{139}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{3231}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{2547}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{9}} \\ 
{\tt{77}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{211}}{\tt{ }}{\tt{195}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{6}}{\tt{ }}{\tt{3184}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{9}} \\ 
{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3240}}{\tt{ }}{\tt{203}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{459}}{\tt{ }}{\tt{5}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{4171}}{\tt{ }}{\tt{3}} \\ 
{\tt{9}}{\tt{ }}{\tt{77}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{371}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3293}}{\tt{ }}{\tt{138}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}} \\ 
{\tt{2191}}{\tt{ }}{\tt{9}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3274}}{\tt{ }}{\tt{130}}{\tt{ }}{\tt{10}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3293}} \\ 
{\tt{10}}{\tt{ }}{\tt{3221}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{2601}}{\tt{ }}{\tt{186}}{\tt{ }}{\tt{11}}{\tt{ }}{\tt{162}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{4}} \\ 
{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{2601}}{\tt{ }}{\tt{174}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{75}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{191}} \\ 
{\tt{14}}{\tt{ }}{\tt{3280}}{\tt{ }}{\tt{14}}{\tt{ }}{\tt{2601}}{\tt{ }}{\tt{162}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{4}} \\ 
{\tt{14401}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2251}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{726}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{31175}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}} \\ 
{\tt{14411}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{30789}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{2113}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{4}}{\tt{ }}{\tt{2251}} \\ 
{\tt{4}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{722}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{30919}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{2123}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{65}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{4}} \\ 
{\tt{6209}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{6219}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{707}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{31427}}{\tt{ }}{\tt{3}}{\tt{ }}{\tt{3}} \\ 
{\tt{0}}{\tt{)}}\-)\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-os-code.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{tracing-lemmas}} to consist of the following events: getnth-os-code,
open-up-tm-processor,
tick,
tm-processor-with-null-oracle.\index{tracing-lemmas}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{os-segment-lengths}} to consist of the following events: length-os-task-table,
plistp-os-task-table,
length-os-segment-table,
plistp-os-segment-table,
length-os-readyq,
plistp-os-readyq,
length-os-status-table,
plistp-os-status-table,
length-os-ibuffers,
plistp-os-ibuffers,
length-os-obuffers,
plistp-os-obuffers,
length-os-mbuffers,
plistp-os-mbuffers,
length-os-code,
plistp-os-code.\index{os-segment-lengths}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{trace-arithmetic}} to consist of the following events: canonicalize-plus-terms1,
canonicalize-plus-terms2,
canonicalize-plus-terms3,
commutativity-of-plus,
commutativity-of-times,
difference-x-x,
difference-plus2,
difference-plus-cancellation2-instance,
plus-0-arg1,
times-1,
yet-another-difference-plus-crock,
lessp-remainder2.\index{trace-arithmetic}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{finite-number-queue-corollaries1}} to consist of the following events: remainder-array-qfirst-finite-number-queue-corollary,
array-qfirst-finite-number-queue-corollary,
finite-number-queuep-array-deq-finite-number-queue-corollary,
finite-number-queuep-array-enq-finite-number-queue-corollary,
finite-number-queue-qmaxlength-value-corollary,
finite-number-queue-qcurrlength-size-corollary,
finite-number-queue-qtail-size-corollary,
finite-number-queue-qhead-size-corollary,
array-queuep-finite-number-queue-corollary.\index{finite-number-queue-corollaries!1}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{good-os-properties1}} to consist of the following events: finite-numberp-os-taskid,
permutation-os-readyq-qarray-os-ready-set,
finite-number-queue-listp-os-mbuffers,
finite-number-queue-tablep-os-mbuffers,
finite-number-queue-listp-os-obuffers,
finite-number-queue-listp-os-ibuffers,
finite-segment-tablep-os-segment-table,
disjoint-everywhere-os-segment-table,
mutually-disjoint-os-segment-table,
finite-number-queuep-os-readyq,
good-status-list-os-status-table,
good-cpu-list-os-task-table,
tm-limit-os,
tm-base-os,
os-not-in-supervisor-mode,
os-time-slice,
os-output-new-pc,
os-input-new-pc,
os-svc-new-pc,
os-error-new-pc,
os-clock-new-pc,
tm-slimit-os,
good-tm-os.\index{good-os-properties1}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{memory-reference}} to consist of the following events: getnth-putnth-coincidence,
getnth-putnth-non-interference,
getnth-after-putseg,
getnth-before-putseg,
getnth-putseg-coincidence,
putnth-coincidence,
putnth-non-interference-corollary1,
putnth-non-interference-corollary2,
putnth-after-putseg,
putnth-putseg-coincidence,
length-getseg,
length-putseg,
length-putnth.\index{memory-reference}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{trace-array-queue-facts}} to consist of the following events: array-qcurrlength-in-an-empty-queue,
array-qcurrlength-in-a-non-empty-queue,
array-qcurrlength-in-a-non-full-queue,
array-qcurrlength-in-a-full-queue,
not-array-qfullp-array-deq,
not-array-qemptyp-array-enq,
array-queuep-array-deq,
plistp-array-deq,
length-array-deq,
array-queuep-array-enq,
plistp-array-enq,
length-array-enq,
length-array-qarray,
plistp-array-qarray,
lessp-qcurrlength-add1-qmaxlength,
lessp-qtail-qmaxlength,
lessp-qhead-qmaxlength,
qmaxlength-greater-than-zero,
qmaxlength-non-zero,
numberp-qmaxlength,
numberp-qcurrlength,
numberp-qtail,
numberp-qhead.\index{trace-array-queue-facts}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-readyq-qarray-address}$\;\;$
{\sc{os-readyq-qarray-address}}\index{os-readyq-qarray-address} $=$ {\tt{'}}{\tt{195}}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  os-readyq-address-facts \\ \index{os-readyq-address-facts}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{16}}, {\tt{'}}{\tt{16}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$(\=\+((({\tt{'}}{\tt{195}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth}) $<$ {\tt{'}}{\tt{65536}}) $=$ {\tt{'}}{\tt{*1*true}}) \\ 
$\wedge$$\;\;\;\;$((({\tt{'}}{\tt{195}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth}) $<$ {\tt{'}}{\tt{65536}}) $=$ {\tt{'}}{\tt{*1*true}}))\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-address-facts.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-pack-psw-tm-unpack-fields1 \\ \index{tm-pack-psw-tm-unpack-fields1}
\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{tm-unpack-cc}}\,({\it{n\/}})\index{tm-unpack-cc}, \\ 
{\rm{tm-unpack-error}}\,({\it{n\/}})\index{tm-unpack-error}, \\ 
{\rm{tm-unpack-svcflag}}\,({\it{n\/}})\index{tm-unpack-svcflag}, \\ 
{\rm{tm-unpack-svcid}}\,({\it{n\/}})\index{tm-unpack-svcid})\-\index{tm-pack-psw} \\ 
$=$$\;\;\;\;$(\=\+({\it{n\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{256}}) \\ 
$+$$\;\;\;\;$(\=\+({\tt{'}}{\tt{256}} $*$ (({\it{n\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{512}}) $\div$ {\tt{'}}{\tt{256}})) \\ 
$+$$\;\;\;\;$({\tt{'}}{\tt{512}} $*$ ({\it{n\/}} $\div$ {\tt{'}}{\tt{512}})))\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-pack-psw-tm-unpack-fields1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-pack-psw-tm-unpack-fields2 \\ \index{tm-pack-psw-tm-unpack-fields2}
\=\+(\=\+({\it{n\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{256}}) \\ 
$+$$\;\;\;\;$(\=\+({\tt{'}}{\tt{256}} $*$ (({\it{n\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{512}}) $\div$ {\tt{'}}{\tt{256}})) \\ 
$+$$\;\;\;\;$({\tt{'}}{\tt{512}} $*$ ({\it{n\/}} $\div$ {\tt{'}}{\tt{512}})))\-)\- \\ 
$=$$\;\;\;\;$(({\it{n\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{512}}) $+$ ({\tt{'}}{\tt{512}} $*$ ({\it{n\/}} $\div$ {\tt{'}}{\tt{512}})))\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-pack-psw-tm-unpack-fields2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-pack-psw-tm-unpack-fields \\ \index{tm-pack-psw-tm-unpack-fields}
\=\+({\it{n\/}} $\in\;${\bf{N}}${}$) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{tm-unpack-cc}}\,({\it{n\/}})\index{tm-unpack-cc}, \\ 
{\rm{tm-unpack-error}}\,({\it{n\/}})\index{tm-unpack-error}, \\ 
{\rm{tm-unpack-svcflag}}\,({\it{n\/}})\index{tm-unpack-svcflag}, \\ 
{\rm{tm-unpack-svcid}}\,({\it{n\/}})\index{tm-unpack-svcid})\-\index{tm-pack-psw} \\ 
$=$$\;\;\;\;${\it{n\/}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-pack-psw-tm-unpack-fields.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  list-of-getnths9 \\ \index{list-of-getnths9}
\=\+({\rm{plistp}}\,({\it{l\/}})\index{plistp} $\wedge$ ({\rm{length}}\,({\it{l\/}})\index{length} $=$ {\tt{'}}{\tt{9}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,({\rm{getnth}}\,({\tt{'}}{\tt{8}}, {\it{l\/}})\index{getnth}, {\tt{'}}{\tt{nil}}))\-)\-)\-)\-)\-)\-)\-)\- \\ 
$=$$\;\;\;\;${\it{l\/}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable list-of-getnths9.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA CONTRACT-CPU
 (REWRITE)
 (IMPLIES
  (GOOD-CPU CPU)
  (EQUAL
   (CONS
    (GETNTH '0 CPU)
    (CONS
     (GETNTH '1 CPU)
     (CONS
      (GETNTH '2 CPU)
      (CONS
       (GETNTH '3 CPU)
       (CONS
        (GETNTH '4 CPU)
        (CONS
            (GETNTH '5 CPU)
            (CONS (GETNTH '6 CPU)
                  (CONS (GETNTH '7 CPU)
                        (CONS (TM-PACK-PSW (TM-UNPACK-CC (GETNTH '8 CPU))
                                           (TM-UNPACK-ERROR (GETNTH '8 CPU))
                                           (TM-UNPACK-SVCFLAG (GETNTH '8 CPU))
                                           (TM-UNPACK-SVCID (GETNTH '8 CPU)))
                              'NIL)))))))))
   CPU))
 ((ENABLE TM-PACK-PSW-TM-UNPACK-FIELDS GOOD-CPU LIST-OF-GETNTHS9
          FINITE-NUMBERP-GETNTH OPEN-UP-GETNTH OPEN-UP-GETNTH-ON-ZERO)
  (USE (A-FINITE-NUMBER-IS-A-NUMBER (N (GETNTH '8 CPU))
                                    (LUB '65536)))
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable contract-cpu.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  list-of-putnths8 \\ \index{list-of-putnths8}
\=\+({\rm{plistp}}\,({\it{l\/}})\index{plistp} $\wedge$ ({\rm{length}}\,({\it{l\/}})\index{length} $=$ {\tt{'}}{\tt{8}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{putnth}}\,(\=\+{\it{a\/}}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\it{b\/}}, \\ 
{\tt{'}}{\tt{1}}, \\ 
{\rm{putnth}}\,(\=\+{\it{c\/}}, \\ 
{\tt{'}}{\tt{2}}, \\ 
{\rm{putnth}}\,(\=\+{\it{d\/}}, \\ 
{\tt{'}}{\tt{3}}, \\ 
{\rm{putnth}}\,(\=\+{\it{w\/}}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\rm{putnth}}\,(\=\+{\it{x\/}}, \\ 
{\tt{'}}{\tt{5}}, \\ 
{\rm{putnth}}\,(\=\+{\it{y\/}}, \\ 
{\tt{'}}{\tt{6}}, \\ 
{\rm{putnth}}\,({\it{z\/}}, {\tt{'}}{\tt{7}}, {\it{l\/}})\index{putnth})\-\index{putnth})\-\index{putnth})\-\index{putnth})\-\index{putnth})\-\index{putnth})\-\index{putnth})\-\index{putnth} \\ 
$=$$\;\;\;\;${\rm{cons}}\,(\=\+{\it{a\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{b\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{c\/}}, \\ 
{\rm{cons}}\,({\it{d\/}}, {\rm{cons}}\,({\it{w\/}}, {\rm{cons}}\,({\it{x\/}}, {\rm{cons}}\,({\it{y\/}}, {\rm{cons}}\,({\it{z\/}}, {\tt{'}}{\tt{nil}}))))))\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable list-of-putnths8.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-list-of-getnths8 \\ \index{contract-list-of-getnths8}
\=\+(\=\+({\it{n\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ ({\tt{'}}{\tt{8}} $+$ {\it{n\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\it{n\/}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{1}} $+$ {\it{n\/}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}} $+$ {\it{n\/}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}} $+$ {\it{n\/}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}} $+$ {\it{n\/}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{5}} $+$ {\it{n\/}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{6}} $+$ {\it{n\/}}, {\it{l\/}})\index{getnth}, \\ 
{\rm{cons}}\,({\rm{getnth}}\,({\tt{'}}{\tt{7}} $+$ {\it{n\/}}, {\it{l\/}})\index{getnth}, {\tt{'}}{\tt{nil}}))\-)\-)\-)\-)\-)\-)\- \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\it{n\/}}, {\tt{'}}{\tt{8}}, {\it{l\/}})\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable contract-list-of-getnths8.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-sequence-of-putnths8 \\ \index{contract-sequence-of-putnths8}
\=\+(\=\+({\it{n\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ ({\tt{'}}{\tt{9}} $+$ {\it{n\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{putnth}}\,(\=\+{\it{v0\/}}, \\ 
{\it{n\/}}, \\ 
{\rm{putnth}}\,(\=\+{\it{v1\/}}, \\ 
{\tt{'}}{\tt{1}} $+$ {\it{n\/}}, \\ 
{\rm{putnth}}\,(\=\+{\it{v2\/}}, \\ 
{\tt{'}}{\tt{2}} $+$ {\it{n\/}}, \\ 
{\rm{putnth}}\,(\=\+{\it{v3\/}}, \\ 
{\tt{'}}{\tt{3}} $+$ {\it{n\/}}, \\ 
{\rm{putnth}}\,(\=\+{\it{v4\/}}, \\ 
{\tt{'}}{\tt{4}} $+$ {\it{n\/}}, \\ 
{\rm{putnth}}\,(\=\+{\it{v5\/}}, \\ 
{\tt{'}}{\tt{5}} $+$ {\it{n\/}}, \\ 
{\rm{putnth}}\,(\=\+{\it{v6\/}}, \\ 
{\tt{'}}{\tt{6}} $+$ {\it{n\/}}, \\ 
{\rm{putnth}}\,(\=\+{\it{v7\/}}, \\ 
{\tt{'}}{\tt{7}} $+$ {\it{n\/}}, \\ 
{\rm{putnth}}\,(\=\+{\it{v8\/}}, \\ 
\=\+{\tt{'}}{\tt{8}} \\ 
$+$$\;\;\;\;${\it{n\/}}\-, \\ 
{\it{l\/}})\-\index{putnth})\-\index{putnth})\-\index{putnth})\-\index{putnth})\-\index{putnth})\-\index{putnth})\-\index{putnth})\-\index{putnth})\-\index{putnth} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,(\=\+{\rm{cons}}\,(\=\+{\it{v0\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{v1\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{v2\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{v3\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{v4\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{v5\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{v6\/}}, \\ 
{\rm{cons}}\,(\=\+{\it{v7\/}}, \\ 
{\rm{cons}}\,({\it{v8\/}}, {\tt{'}}{\tt{nil}}))\-)\-)\-)\-)\-)\-)\-)\-, \\ 
{\it{n\/}}, \\ 
{\it{l\/}})\-\index{putseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable contract-sequence-of-putnths8.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 CONTRACT-PUTNTHS-INTO-TASK-TABLE
 (REWRITE)
 (IMPLIES
  (AND (GOOD-TM OS) (LESSP ID '16))
  (EQUAL
   (PUTNTH
    (GETNTH '0 (TM-REGS OS))
    (TIMES '9 ID)
    (PUTNTH
     (GETNTH '1 (TM-REGS OS))
     (PLUS '1 (TIMES '9 ID))
     (PUTNTH
      (GETNTH '2 (TM-REGS OS))
      (PLUS '2 (TIMES '9 ID))
      (PUTNTH
       (GETNTH '3 (TM-REGS OS))
       (PLUS '3 (TIMES '9 ID))
       (PUTNTH
        (GETNTH '4 (TM-REGS OS))
        (PLUS '4 (TIMES '9 ID))
        (PUTNTH
         (GETNTH '5 (TM-REGS OS))
         (PLUS '5 (TIMES '9 ID))
         (PUTNTH
               (GETNTH '6 (TM-REGS OS))
               (PLUS '6 (TIMES '9 ID))
               (PUTNTH (GETNTH '7 (TM-REGS OS))
                       (PLUS '7 (TIMES '9 ID))
                       (PUTNTH (PLUS (TM-CC OS)
                                     (PLUS (TIMES '4 (TM-ERROR OS))
                                           (PLUS (TIMES '256 (TM-SVCFLAG OS))
                                                 (TIMES '512 (TM-SVCID OS)))))
                               (PLUS '8 (TIMES '9 ID))
                               (OS-TASK-TABLE OS))))))))))
   (PUTSEG (TM-CPU OS)
           (TIMES '9 ID)
           (OS-TASK-TABLE OS))))
 ((ENABLE TM-CPU TM-R0 TM-R1 TM-R2 TM-R3 TM-R4 TM-R5 TM-R6 TM-R7 TM-PACK-PSW
          COMMUTATIVITY-OF-PLUS COMMUTATIVITY-OF-TIMES
          CONTRACT-SEQUENCE-OF-PUTNTHS8 LENGTH-OS-TASK-TABLE)
  (ENABLE-THEORY GOOD-TM-PROPERTIES GROUND-ZERO)
  (DISABLE PLUS TIMES)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable contract-putnths-into-task-table.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 CONTRACT-PUTNTHS-INTO-REGMEM
 (REWRITE)
 (IMPLIES
  (AND (GOOD-TM OS)
       (AND (EQUAL (LENGTH TASK-TABLE) '144)
            (AND (NUMBERP TASKID)
                 (LESSP TASKID '16))))
  (EQUAL
   (PUTNTH
    (GETNTH (TIMES '9 TASKID) TASK-TABLE)
    '0
    (PUTNTH
     (GETNTH (PLUS '1 (TIMES '9 TASKID))
             TASK-TABLE)
     '1
     (PUTNTH
      (GETNTH (PLUS '2 (TIMES '9 TASKID))
              TASK-TABLE)
      '2
      (PUTNTH
          (GETNTH (PLUS '3 (TIMES '9 TASKID))
                  TASK-TABLE)
          '3
          (PUTNTH (GETNTH (PLUS '4 (TIMES '9 TASKID))
                          TASK-TABLE)
                  '4
                  (PUTNTH (GETNTH (PLUS '5 (TIMES '9 TASKID))
                                  TASK-TABLE)
                          '5
                          (PUTNTH (GETNTH (PLUS '6 (TIMES '9 TASKID))
                                          TASK-TABLE)
                                  '6
                                  (PUTNTH (GETNTH (PLUS '7 (TIMES '9 TASKID))
                                                  TASK-TABLE)
                                          '7
                                          (TM-REGS OS)))))))))
   (GETSEG '0
           '8
           (GETNTH TASKID
                   (TABLE '9 TASK-TABLE)))))
 ((ENABLE-THEORY GOOD-TM-PROPERTIES GROUND-ZERO)
  (ENABLE LIST-OF-PUTNTHS8 LENGTH-TABLE CONTRACT-LIST-OF-GETNTHS8 GETNTH-TABLE
          COMMUTATIVITY-OF-TIMES GETSEG-GETSEG PLUS-0)
  (DISABLE PLUS TIMES)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable contract-putnths-into-regmem.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 OS-TASK-TABLE-ADDRESS-FACTS
 (REWRITE)
 (IMPLIES
  (LESSP ID '16)
  (AND
    (EQUAL (LESSP (PLUS '15 (TIMES '9 ID))
                  '65536)
           '*1*TRUE)
    (AND (EQUAL (LESSP (PLUS '16 (TIMES '9 ID))
                       '65536)
                '*1*TRUE)
         (AND (EQUAL (LESSP (PLUS '17 (TIMES '9 ID))
                            '65536)
                     '*1*TRUE)
              (AND (EQUAL (LESSP (PLUS '18 (TIMES '9 ID))
                                 '65536)
                          '*1*TRUE)
                   (AND (EQUAL (LESSP (PLUS '19 (TIMES '9 ID))
                                      '65536)
                               '*1*TRUE)
                        (AND (EQUAL (LESSP (PLUS '20 (TIMES '9 ID))
                                           '65536)
                                    '*1*TRUE)
                             (AND (EQUAL (LESSP (PLUS '21 (TIMES '9 ID))
                                                '65536)
                                         '*1*TRUE)
                                  (AND (EQUAL (LESSP (PLUS '22 (TIMES '9 ID))
                                                     '65536)
                                              '*1*TRUE)
                                       (EQUAL (LESSP (PLUS '23 (TIMES '9 ID))
                                                     '65536)
                                              '*1*TRUE))))))))))
 ((ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable os-task-table-address-facts.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-new-task-table} \\  
\=\+{\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,(\=\+{\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu}, \\ 
{\tt{'}}{\tt{9}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\-\index{putseg}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-new-regs} \\  
\=\+{\rm{os-new-regs}}\,({\it{taskid\/}}, {\it{tm\/}})\index{os-new-regs} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,({\tt{'}}{\tt{0}}, {\tt{'}}{\tt{8}}, {\rm{getnth}}\,({\it{taskid\/}}, {\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-new-task-table}}\,({\it{tm\/}})\index{os-new-task-table})\index{table})\index{getnth})\index{getseg}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-new-flags} \\  
\=\+{\rm{os-new-flags}}\,({\it{taskid\/}}, {\it{tm\/}})\index{os-new-flags} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{8}}, {\rm{getnth}}\,({\it{taskid\/}}, {\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-new-task-table}}\,({\it{tm\/}})\index{os-new-task-table})\index{table})\index{getnth})\index{getnth}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-new-cc} \\  
{\rm{os-new-cc}}\,({\it{taskid\/}}, {\it{tm\/}})\index{os-new-cc} $=$ {\rm{tm-unpack-cc}}\,({\rm{os-new-flags}}\,({\it{taskid\/}}, {\it{tm\/}})\index{os-new-flags})\index{tm-unpack-cc}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-new-error} \\  
{\rm{os-new-error}}\,({\it{taskid\/}}, {\it{tm\/}})\index{os-new-error} $=$ {\rm{tm-unpack-error}}\,({\rm{os-new-flags}}\,({\it{taskid\/}}, {\it{tm\/}})\index{os-new-flags})\index{tm-unpack-error}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-new-svcflag} \\  
{\rm{os-new-svcflag}}\,({\it{taskid\/}}, {\it{tm\/}})\index{os-new-svcflag} $=$ {\rm{tm-unpack-svcflag}}\,({\rm{os-new-flags}}\,({\it{taskid\/}}, {\it{tm\/}})\index{os-new-flags})\index{tm-unpack-svcflag}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-new-svcid} \\  
{\rm{os-new-svcid}}\,({\it{taskid\/}}, {\it{tm\/}})\index{os-new-svcid} $=$ {\rm{tm-unpack-svcid}}\,({\rm{os-new-flags}}\,({\it{taskid\/}}, {\it{tm\/}})\index{os-new-flags})\index{tm-unpack-svcid}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-new-base} \\  
\=\+{\rm{os-new-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{os-new-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,({\it{taskid\/}}, {\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\index{getnth})\index{base}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-new-limit} \\  
\=\+{\rm{os-new-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{os-new-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,({\it{taskid\/}}, {\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\index{getnth})\index{limit}\-
\end{tabbing}


\noindent{\sc Event}:   Let us define the theory {\it{os-new-cpu}} to consist of the following events: os-new-base,
os-new-cc,
os-new-error,
os-new-flags,
os-new-limit,
os-new-regs,
os-new-svcflag,
os-new-svcid.\index{os-new-cpu}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-cpu-list-os-new-task-table \\ \index{good-cpu-list-os-new-task-table}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-cpu-list}}\,({\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\index{table})\index{good-cpu-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-cpu-list-os-new-task-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-address-facts \\ \index{os-segment-table-address-facts}
\=\+({\it{id\/}} $<$ {\tt{'}}{\tt{16}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+((({\tt{'}}{\tt{159}} $+$ ({\tt{'}}{\tt{2}} $*$ {\it{id\/}})) $<$ {\tt{'}}{\tt{65536}}) $=$ {\tt{'}}{\tt{*1*true}}) \\ 
$\wedge$$\;\;\;\;$(\=\+((({\tt{'}}{\tt{160}} $+$ ({\tt{'}}{\tt{2}} $*$ {\it{id\/}})) $<$ {\tt{'}}{\tt{65536}}) $=$ {\tt{'}}{\tt{*1*true}}) \\ 
$\wedge$$\;\;\;\;$(\=\+((({\tt{'}}{\tt{2}} $*$ {\it{id\/}}) $<$ {\tt{'}}{\tt{32}}) $=$ {\tt{'}}{\tt{*1*true}}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\tt{'}}{\tt{1}} $+$ ({\tt{'}}{\tt{2}} $*$ {\it{id\/}})) $<$ {\tt{'}}{\tt{32}}) \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-address-facts.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-os-new-base-expression \\ \index{contract-os-new-base-expression}
\=\+(({\tt{'}}{\tt{2}} $*$ {\it{taskid\/}}) $<$ {\tt{'}}{\tt{32}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\it{taskid\/}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,({\it{taskid\/}}, {\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\index{getnth})\index{base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable contract-os-new-base-expression.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-os-new-limit-expression \\ \index{contract-os-new-limit-expressio!n}
\=\+(({\tt{'}}{\tt{1}} $+$ ({\tt{'}}{\tt{2}} $*$ {\it{taskid\/}})) $<$ {\tt{'}}{\tt{32}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{1}} $+$ ({\tt{'}}{\tt{2}} $*$ {\it{taskid\/}}), {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,({\it{taskid\/}}, {\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\index{getnth})\index{limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable contract-os-new-limit-expression.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{access-os-segment-table}} to consist of the following events: os-segment-table-address-facts,
contract-os-new-base-expression,
contract-os-new-limit-expression.\index{access-os-segment-table}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-sequence-of-putnths2 \\ \index{contract-sequence-of-putnths2}
\=\+(\=\+({\it{n\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{length}}\,({\it{l\/}})\index{length} $<$ ({\tt{'}}{\tt{2}} $+$ {\it{n\/}})$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{putnth}}\,({\it{a\/}}, {\it{n\/}}, {\rm{putnth}}\,({\it{b\/}}, {\tt{'}}{\tt{1}} $+$ {\it{n\/}}, {\it{l\/}})\index{putnth})\index{putnth} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,({\rm{cons}}\,({\it{a\/}}, {\rm{cons}}\,({\it{b\/}}, {\tt{'}}{\tt{nil}})), {\it{n\/}}, {\it{l\/}})\index{putseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable contract-sequence-of-putnths2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-putnths-into-status-table \\ \index{contract-putnths-into-status-ta!ble}
\=\+({\it{i\/}} $<$ {\tt{'}}{\tt{16}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{putnth}}\,({\it{a\/}}, {\tt{'}}{\tt{2}} $*$ {\it{i\/}}, {\rm{putnth}}\,({\it{b\/}}, {\tt{'}}{\tt{1}} $+$ ({\tt{'}}{\tt{2}} $*$ {\it{i\/}}), {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{putnth})\index{putnth} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,({\rm{cons}}\,({\it{a\/}}, {\rm{cons}}\,({\it{b\/}}, {\tt{'}}{\tt{nil}})), {\tt{'}}{\tt{2}} $*$ {\it{i\/}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{putseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable contract-putnths-into-status-table.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-address-facts \\ \index{os-status-table-address-facts}
\=\+({\it{id\/}} $<$ {\tt{'}}{\tt{16}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+((({\tt{'}}{\tt{2}} $*$ {\it{id\/}}) $<$ {\tt{'}}{\tt{65536}}) $=$ {\tt{'}}{\tt{*1*true}}) \\ 
$\wedge$$\;\;\;\;$(\=\+((({\tt{'}}{\tt{211}} $+$ ({\tt{'}}{\tt{2}} $*$ {\it{id\/}})) $<$ {\tt{'}}{\tt{65536}}) $=$ {\tt{'}}{\tt{*1*true}}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+(({\tt{'}}{\tt{212}} $+$ ({\tt{'}}{\tt{2}} $*$ {\it{id\/}})) $<$ {\tt{'}}{\tt{65536}}) \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+((({\tt{'}}{\tt{2}} $*$ {\it{id\/}}) $<$ {\tt{'}}{\tt{32}}) $=$ {\tt{'}}{\tt{*1*true}}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+(($1\;+$ ({\tt{'}}{\tt{2}} $*$ {\it{id\/}})) $<$ {\tt{'}}{\tt{32}}) \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+(\=\+({\tt{'}}{\tt{1}} $+$ ({\tt{'}}{\tt{2}} $*$ {\it{id\/}})) \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{32}})\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\tt{'}}{\tt{32}} \\ 
$<$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\it{id\/}})\-)\-)\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*false}})\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-address-facts.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  access-os-status-table-crock \\ \index{access-os-status-table-crock}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ ({\it{id\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\it{id\/}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\it{id\/}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} $<$ {\tt{'}}{\tt{65536}}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{getnth}}\,({\tt{'}}{\tt{1}} $+$ ({\tt{'}}{\tt{2}} $*$ {\it{id\/}}), {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}} $+$ ({\tt{'}}{\tt{2}} $*$ {\it{id\/}}), \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{65536}})\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable access-os-status-table-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-getnth-os-status-table \\ \index{finite-numberp-getnth-os-status!-table}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ ({\it{i\/}} $<$ {\tt{'}}{\tt{32}})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{getnth}}\,({\it{i\/}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth}, {\tt{'}}{\tt{65536}})\index{finite-numberp}\-
\end{tabbing}


\noindent{\sc Event}:   Let us define the theory {\it{access-os-status-table}} to consist of the following events: contract-putnths-into-status-table,
os-status-table-address-facts,
access-os-status-table-crock.\index{access-os-status-table}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-update-status} \\  
\=\+{\rm{os-update-status}}\,({\it{id\/}}, {\it{status\/}}, {\it{flag\/}}, {\it{os\/}})\index{os-update-status} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,({\rm{cons}}\,({\it{status\/}}, {\rm{cons}}\,({\it{flag\/}}, {\tt{'}}{\tt{nil}})), {\tt{'}}{\tt{2}} $*$ {\it{id\/}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{putseg}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  re-associate-times \\ \index{re-associate-times}
(($1\;+$ {\it{a\/}}) $*$ (($1\;+$ {\it{b\/}}) $*$ {\it{c\/}})) $=$ ((($1\;+$ {\it{a\/}}) $*$ ($1\;+$ {\it{b\/}})) $*$ {\it{c\/}})
\end{tabbing}


\noindent{\sc Event}:   Disable re-associate-times.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  limited-associativity-of-plus \\ \index{limited-associativity-of-plus}
((($1\;+$ {\it{a\/}}) $+$ ({\it{b\/}} $+$ {\it{c\/}})) $+$ {\it{d\/}}) $=$ (($1\;+$ {\it{a\/}}) $+$ (({\it{b\/}} $+$ {\it{c\/}}) $+$ {\it{d\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable limited-associativity-of-plus.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{finite-number-queue-corollaries-for-mbuffers}} to consist of the following events: remainder-array-qfirst-finite-number-queue-corollary-for-mbuffers,
array-qfirst-finite-number-queue-corollary-for-mbuffers,
finite-number-queuep-array-deq-finite-number-queue-corollary-for-mbuffers,
finite-number-queuep-array-enq-finite-number-queue-corollary-for-mbuffers,
finite-number-queue-qmaxlength-value-corollary-for-mbuffers,
finite-number-queue-qcurrlength-size-corollary-for-mbuffers,
finite-number-queue-qtail-size-corollary-for-mbuffers,
finite-number-queue-qhead-size-corollary-for-mbuffers,
array-queuep-finite-number-queue-corollary-for-mbuffers,
plistp-finite-number-queue-corollary-for-mbuffers,
length-finite-number-queue-corollary-for-mbuffers.\index{finite-number-queue-corollaries!-for-mbuffers}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{finite-number-queue-corollaries-for-mbuffers1}} to consist of the following events: remainder-array-qfirst-finite-number-queue-corollary-for-mbuffers,
array-qfirst-finite-number-queue-corollary-for-mbuffers,
finite-number-queuep-array-deq-finite-number-queue-corollary-for-mbuffers,
finite-number-queuep-array-enq-finite-number-queue-corollary-for-mbuffers,
finite-number-queue-qcurrlength-size-corollary-for-mbuffers,
finite-number-queue-qtail-size-corollary-for-mbuffers,
finite-number-queue-qhead-size-corollary-for-mbuffers,
array-queuep-finite-number-queue-corollary-for-mbuffers,
plistp-finite-number-queue-corollary-for-mbuffers,
length-finite-number-queue-corollary-for-mbuffers.\index{finite-number-queue-corollaries!-for-mbuffers1}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-mbuffer-source-multiplier}$\;\;$
{\sc{os-mbuffer-source-multiplier}}\index{os-mbuffer-source-multiplier} $=$ {\tt{'}}{\tt{128}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-mbuffer-dest-multiplier}$\;\;$
{\sc{os-mbuffer-dest-multiplier}}\index{os-mbuffer-dest-multiplier} $=$ {\tt{'}}{\tt{8}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-mbuffers-address-plus-qtail-!field}$\;\;$
{\sc{os-mbuffers-address-plus-qtail-field}}\index{os-mbuffers-address-plus-qtail-!field} $=$ {\tt{'}}{\tt{500}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-mbuffers-address-plus-qcurrle!ngth-field}$\;\;$
{\sc{os-mbuffers-address-plus-qcurrlength-field}}\index{os-mbuffers-address-plus-qcurrle!ngth-field} $=$ {\tt{'}}{\tt{501}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-mbuffers-address-plus-qmaxle!ngth-field}$\;\;$
{\sc{os-mbuffers-address-plus-qmaxlength-field}}\index{os-mbuffers-address-plus-qmaxle!ngth-field} $=$ {\tt{'}}{\tt{502}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-mbuffers-address-plus-qarray!-field}$\;\;$
{\sc{os-mbuffers-address-plus-qarray-field}}\index{os-mbuffers-address-plus-qarray!-field} $=$ {\tt{'}}{\tt{503}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-current-mbuffer} \\  
\=\+{\rm{os-current-mbuffer}}\,({\it{sid\/}}, {\it{did\/}}, {\it{os\/}})\index{os-current-mbuffer} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(({\tt{'}}{\tt{16}} $*$ {\it{sid\/}}) $+$ {\it{did\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\index{getnth}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-current-mbuffer \\ \index{finite-number-queuep-current-mb!uffer}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (({\it{sid\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{did\/}} $<$ {\tt{'}}{\tt{16}}))) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,(\=\+{\rm{getnth}}\,(\=\+({\tt{'}}{\tt{16}} $*$ {\it{sid\/}}) $+$ {\it{did\/}}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\-\index{getnth}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-current-mbuffer.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-current-mbuffer-for-receive \\ \index{finite-number-queuep-current-mb!uffer-for-receive}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (({\it{sid\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{did\/}} $<$ {\tt{'}}{\tt{16}}))) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,(\=\+{\rm{getnth}}\,(\=\+{\it{did\/}} $+$ ({\tt{'}}{\tt{16}} $*$ {\it{sid\/}}), \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\-\index{getnth}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-current-mbuffer-for-receive.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  re-associate-times1 \\ \index{re-associate-times1}
({\tt{'}}{\tt{8}} $*$ ({\it{b\/}} $+$ ({\tt{'}}{\tt{16}} $*$ {\it{a\/}}))) $=$ (({\tt{'}}{\tt{8}} $*$ {\it{b\/}}) $+$ ({\tt{'}}{\tt{128}} $*$ {\it{a\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable re-associate-times1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-os-mbuffer-address \\ \index{rewrite-os-mbuffer-address}
\=\+(\=\+({\tt{'}}{\tt{8}} $*$ ({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\rm{tm-regs}}\,({\it{os\/}})\index{tm-regs})\index{getnth} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{16}})) \\ 
$+$$\;\;\;\;$({\tt{'}}{\tt{128}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}))\- \\ 
$=$$\;\;\;\;$(\=\+{\tt{'}}{\tt{8}} \\ 
$*$$\;\;\;\;$(\=\+({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\rm{tm-regs}}\,({\it{os\/}})\index{tm-regs})\index{getnth} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{16}}) \\ 
$+$$\;\;\;\;$({\tt{'}}{\tt{16}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}))\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-os-mbuffer-address.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-os-mbuffer-address1 \\ \index{rewrite-os-mbuffer-address1}
\=\+(\=\+({\tt{'}}{\tt{8}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}) \\ 
$+$$\;\;\;\;$({\tt{'}}{\tt{128}} $*$ ({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\rm{tm-regs}}\,({\it{os\/}})\index{tm-regs})\index{getnth} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{16}})))\- \\ 
$=$$\;\;\;\;$(\=\+{\tt{'}}{\tt{8}} \\ 
$*$$\;\;\;\;$(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
$+$$\;\;\;\;$({\tt{'}}{\tt{16}} $*$ ({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\rm{tm-regs}}\,({\it{os\/}})\index{tm-regs})\index{getnth} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{16}})))\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-os-mbuffer-address1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-address-facts1 \\ \index{os-mbuffers-address-facts1}
\=\+({\it{i\/}} $<$ {\tt{'}}{\tt{16}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+((({\tt{'}}{\tt{8}} $*$ {\it{i\/}}) $<$ {\tt{'}}{\tt{65536}}) $=$ {\tt{'}}{\tt{*1*true}}) \\ 
$\wedge$$\;\;\;\;$(\=\+((({\tt{'}}{\tt{128}} $*$ {\it{i\/}}) $<$ {\tt{'}}{\tt{2048}}) $=$ {\tt{'}}{\tt{*1*true}}) \\ 
$\wedge$$\;\;\;\;$(\=\+((({\tt{'}}{\tt{128}} $*$ {\it{i\/}}) $<$ {\tt{'}}{\tt{65536}}) $=$ {\tt{'}}{\tt{*1*true}}) \\ 
$\wedge$$\;\;\;\;$((({\tt{'}}{\tt{16}} $*$ {\it{i\/}}) $<$ {\tt{'}}{\tt{256}}) $=$ {\tt{'}}{\tt{*1*true}}))\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-address-facts1.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 OS-MBUFFERS-ADDRESS-FACTS2
 (REWRITE)
 (IMPLIES
  (AND (LESSP I '16) (LESSP J '16))
  (AND
   (EQUAL (LESSP (PLUS (TIMES '8 J) (TIMES '128 I))
                 '65536)
          '*1*TRUE)
   (AND
    (EQUAL (LESSP (PLUS '500
                        (PLUS (TIMES '8 J) (TIMES '128 I)))
                  '65536)
           '*1*TRUE)
    (AND
     (EQUAL (LESSP (PLUS '499
                         (PLUS (TIMES '8 J) (TIMES '128 I)))
                   '65536)
            '*1*TRUE)
     (AND
      (EQUAL (LESSP (PLUS '501
                          (PLUS (TIMES '8 J) (TIMES '128 I)))
                    '65536)
             '*1*TRUE)
      (AND
       (EQUAL (LESSP (PLUS '502
                           (PLUS (TIMES '8 J) (TIMES '128 I)))
                     '65536)
              '*1*TRUE)
       (AND
        (EQUAL (LESSP (PLUS '503
                            (PLUS (TIMES '8 J) (TIMES '128 I)))
                      '65536)
               '*1*TRUE)
        (AND
            (EQUAL (LESSP (PLUS '1
                                (PLUS (TIMES '8 J) (TIMES '128 I)))
                          '2048)
                   '*1*TRUE)
            (AND (EQUAL (LESSP (PLUS '2
                                     (PLUS (TIMES '8 J) (TIMES '128 I)))
                               '2048)
                        '*1*TRUE)
                 (AND (EQUAL (LESSP (PLUS '3
                                          (PLUS (TIMES '8 J) (TIMES '128 I)))
                                    '2048)
                             '*1*TRUE)
                      (EQUAL (LESSP (PLUS '4
                                          (PLUS (TIMES '8 J) (TIMES '128 I)))
                                    '2048)
                             '*1*TRUE)))))))))))
 ((ENABLE COMMUTATIVITY-OF-PLUS)
  (ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable os-mbuffers-address-facts2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-address-facts3 \\ \index{os-mbuffers-address-facts3}
\=\+(({\it{i\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{j\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(((({\tt{'}}{\tt{16}} $*$ {\it{j\/}}) $+$ {\it{i\/}}) $<$ {\tt{'}}{\tt{256}}) $=$ {\tt{'}}{\tt{*1*true}}) \\ 
$\wedge$$\;\;\;\;$(\=\+((({\tt{'}}{\tt{8}} $*$ ({\it{i\/}} $+$ ({\tt{'}}{\tt{16}} $*$ {\it{j\/}}))) $<$ {\tt{'}}{\tt{2048}}) $=$ {\tt{'}}{\tt{*1*true}}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+(({\tt{'}}{\tt{8}} $*$ (({\tt{'}}{\tt{16}} $*$ {\it{j\/}}) $+$ {\it{i\/}})) $<$ {\tt{'}}{\tt{2048}}) \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+(\=\+{\tt{'}}{\tt{2048}} \\ 
$<$$\;\;\;\;$(\=\+{\tt{'}}{\tt{8}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{8}} \\ 
$*$$\;\;\;\;$(({\tt{'}}{\tt{16}} $*$ {\it{j\/}}) $+$ {\it{i\/}}))\-)\-)\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*false}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+(\=\+(({\tt{'}}{\tt{8}} $*$ {\it{j\/}}) $+$ ({\tt{'}}{\tt{128}} $*$ {\it{i\/}})) \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{2048}})\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+(\=\+{\tt{'}}{\tt{2048}} \\ 
$<$$\;\;\;\;$(\=\+{\tt{'}}{\tt{8}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{8}} \\ 
$*$$\;\;\;\;$({\it{i\/}} $+$ (\=\+{\tt{'}}{\tt{16}} \\ 
$*$$\;\;\;\;${\it{j\/}})\-))\-)\-)\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*false}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+({\it{i\/}} $+$ ({\tt{'}}{\tt{16}} $*$ {\it{j\/}})) \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{256}})\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\-)\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-address-facts3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-getnth-from-current-mbuffer \\ \index{finite-numberp-getnth-from-curre!nt-mbuffer}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ (({\it{sid\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ (({\it{did\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{i\/}} $<$ {\tt{'}}{\tt{8}})))) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-numberp}}\,(\=\+{\rm{getnth}}\,(\=\+{\it{i\/}}, \\ 
{\rm{getnth}}\,(\=\+({\tt{'}}{\tt{16}} $*$ {\it{sid\/}}) $+$ {\it{did\/}}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\-\index{getnth})\-\index{getnth}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-numberp}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-numberp-getnth-from-current-mbuffer1 \\ \index{finite-numberp-getnth-from-curre!nt-mbuffer1}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ (({\it{sid\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ (({\it{did\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{i\/}} $<$ {\tt{'}}{\tt{8}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{getnth}}\,({\it{i\/}}, {\rm{getnth}}\,(({\tt{'}}{\tt{16}} $*$ {\it{sid\/}}) $+$ {\it{did\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\index{getnth})\index{getnth} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\it{i\/}}, \\ 
{\rm{getnth}}\,(\=\+({\tt{'}}{\tt{16}} $*$ {\it{sid\/}}) $+$ {\it{did\/}}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\-\index{getnth})\-\index{getnth} \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{65536}})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-getnth-from-current-mbuffer1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  access-current-os-mbuffer-fields \\ \index{access-current-os-mbuffer-field!s}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (({\it{sid\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{did\/}} $<$ {\tt{'}}{\tt{16}}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{getnth}}\,(({\tt{'}}{\tt{16}} $*$ {\it{sid\/}}) $+$ {\it{did\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\index{getnth})\-\index{getnth} \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{65535}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{getnth}}\,(\=\+({\tt{'}}{\tt{16}} $*$ {\it{sid\/}}) $+$ {\it{did\/}}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\-\index{getnth})\-\index{getnth} \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{65535}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{3}}, \\ 
{\rm{getnth}}\,(\=\+({\tt{'}}{\tt{16}} $*$ {\it{sid\/}}) $+$ {\it{did\/}}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\-\index{getnth})\-\index{getnth} \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{65535}})\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable access-current-os-mbuffer-fields.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-plus-fact-for-mbuffers1 \\ \index{lessp-plus-fact-for-mbuffers1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{sid\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{did\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+(\=\+{\tt{'}}{\tt{4}} \\ 
$+$$\;\;\;\;$(\=\+(({\tt{'}}{\tt{8}} $*$ {\it{did\/}}) $+$ ({\tt{'}}{\tt{128}} $*$ {\it{sid\/}})) \\ 
$+$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{getnth}}\,(\=\+({\tt{'}}{\tt{16}} $*$ {\it{sid\/}}) $+$ {\it{did\/}}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\-\index{getnth})\-\index{getnth})\-)\- \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{2048}})\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-plus-fact-for-mbuffers1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-plus-fact-for-mbuffers2 \\ \index{lessp-plus-fact-for-mbuffers2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{sid\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{did\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+(\=\+{\tt{'}}{\tt{503}} \\ 
$+$$\;\;\;\;$(\=\+(({\tt{'}}{\tt{8}} $*$ {\it{did\/}}) $+$ ({\tt{'}}{\tt{128}} $*$ {\it{sid\/}})) \\ 
$+$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{getnth}}\,(\=\+({\tt{'}}{\tt{16}} $*$ {\it{sid\/}}) $+$ {\it{did\/}}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\-\index{getnth})\-\index{getnth})\-)\- \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{65536}})\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-plus-fact-for-mbuffers2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  index-within-length-of-mbuffer \\ \index{index-within-length-of-mbuffer}
\=\+(\=\+\=\+{\bf if }{\tt{'}}{\tt{4}} $<$ {\it{i\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;${\rm{finite-number-queuep}}\,(\=\+{\rm{getnth}}\,(\=\+\=\+({\tt{'}}{\tt{16}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}) \\ 
$+$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\rm{tm-regs}}\,({\it{os\/}})\index{tm-regs})\index{getnth} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{16}})\-, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\-\index{getnth}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queuep})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+({\it{i\/}} $+$ {\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{getnth}}\,(\=\+\=\+({\tt{'}}{\tt{16}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}) \\ 
$+$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\rm{tm-regs}}\,({\it{os\/}})\index{tm-regs})\index{getnth} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{16}})\-, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\-\index{getnth})\-\index{getnth}) \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{8}})\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable index-within-length-of-mbuffer.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-plus-fact-for-mbuffers-for-receive1 \\ \index{lessp-plus-fact-for-mbuffers-fo!r-receive1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{sid\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{did\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+(\=\+{\tt{'}}{\tt{4}} \\ 
$+$$\;\;\;\;$(\=\+(({\tt{'}}{\tt{8}} $*$ {\it{did\/}}) $+$ ({\tt{'}}{\tt{128}} $*$ {\it{sid\/}})) \\ 
$+$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+{\it{did\/}} $+$ ({\tt{'}}{\tt{16}} $*$ {\it{sid\/}}), \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\-\index{getnth})\-\index{getnth})\-)\- \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{2048}})\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-plus-fact-for-mbuffers-for-receive1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-plus-fact-for-mbuffers-for-receive2 \\ \index{lessp-plus-fact-for-mbuffers-fo!r-receive2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{sid\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{did\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+(\=\+{\tt{'}}{\tt{503}} \\ 
$+$$\;\;\;\;$(\=\+(({\tt{'}}{\tt{8}} $*$ {\it{did\/}}) $+$ ({\tt{'}}{\tt{128}} $*$ {\it{sid\/}})) \\ 
$+$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+{\it{did\/}} $+$ ({\tt{'}}{\tt{16}} $*$ {\it{sid\/}}), \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\-\index{getnth})\-\index{getnth})\-)\- \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{65536}})\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-plus-fact-for-mbuffers-for-receive2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  access-current-os-mbuffer-fields-for-receive \\ \index{access-current-os-mbuffer-field!s-for-receive}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (({\it{i\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{j\/}} $<$ {\tt{'}}{\tt{16}}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{getnth}}\,({\it{i\/}} $+$ ({\tt{'}}{\tt{16}} $*$ {\it{j\/}}), {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\index{getnth})\index{getnth} \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{65535}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{getnth}}\,({\it{i\/}} $+$ ({\tt{'}}{\tt{16}} $*$ {\it{j\/}}), {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\index{getnth})\-\index{getnth} \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{65535}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{3}}, \\ 
{\rm{getnth}}\,(\=\+{\it{i\/}} $+$ ({\tt{'}}{\tt{16}} $*$ {\it{j\/}}), \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\-\index{getnth})\-\index{getnth} \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{65535}})\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable access-current-os-mbuffer-fields-for-receive.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  index-within-length-of-mbuffer-for-receive \\ \index{index-within-length-of-mbuffer-!for-receive}
\=\+(\=\+\=\+{\bf if }{\tt{'}}{\tt{4}} $<$ {\it{i\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;${\rm{finite-number-queuep}}\,(\=\+{\rm{getnth}}\,(\=\+\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{16}} \\ 
$*$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\rm{tm-regs}}\,({\it{os\/}})\index{tm-regs})\index{getnth} \\ 
${}${\bf{mod}}${}$$\;\;\;\;${\tt{'}}{\tt{16}})\-)\-\-, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\-\index{getnth}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queuep})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+({\it{i\/}} $+$ {\rm{getnth}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{16}} \\ 
$*$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\rm{tm-regs}}\,({\it{os\/}})\index{tm-regs})\index{getnth} \\ 
${}${\bf{mod}}${}$$\;\;\;\;${\tt{'}}{\tt{16}})\-)\-\-, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\-\index{getnth})\-\index{getnth}) \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{8}})\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable index-within-length-of-mbuffer-for-receive.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  access-current-mbuffer \\ \index{access-current-mbuffer}
\=\+(({\it{sid\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ (({\it{did\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{i\/}} $<$ {\tt{'}}{\tt{8}}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\it{i\/}} $+$ (({\tt{'}}{\tt{8}} $*$ {\it{did\/}}) $+$ ({\tt{'}}{\tt{128}} $*$ {\it{sid\/}})), {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\it{i\/}}, {\rm{os-current-mbuffer}}\,({\it{sid\/}}, {\it{did\/}}, {\it{os\/}})\index{os-current-mbuffer})\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable access-current-mbuffer.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-putnth-into-current-mbuffer \\ \index{contract-putnth-into-current-mb!uffer}
\=\+(\=\+(({\it{i\/}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\rm{os-current-mbuffer}}\,({\it{sid\/}}, {\it{did\/}}, {\it{os\/}})\index{os-current-mbuffer})\index{getnth}) $<$ {\tt{'}}{\tt{8}}) \\ 
$\wedge$$\;\;\;\;$(({\it{sid\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{did\/}} $<$ {\tt{'}}{\tt{16}})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{putnth}}\,(\=\+{\it{value\/}}, \\ 
{\it{i\/}} $+$ (\=\+(({\tt{'}}{\tt{8}} $*$ {\it{did\/}}) $+$ ({\tt{'}}{\tt{128}} $*$ {\it{sid\/}})) \\ 
$+$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{getnth}}\,(\=\+({\tt{'}}{\tt{16}} $*$ {\it{sid\/}}) $+$ {\it{did\/}}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\-\index{getnth})\-\index{getnth})\-, \\ 
{\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-\index{putnth} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,(\=\+{\rm{putnth}}\,(\=\+{\it{value\/}}, \\ 
{\it{i\/}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\rm{os-current-mbuffer}}\,({\it{sid\/}}, {\it{did\/}}, {\it{os\/}})\index{os-current-mbuffer})\index{getnth}, \\ 
{\rm{os-current-mbuffer}}\,({\it{sid\/}}, {\it{did\/}}, {\it{os\/}})\index{os-current-mbuffer})\-\index{putnth}, \\ 
({\tt{'}}{\tt{8}} $*$ {\it{did\/}}) $+$ ({\tt{'}}{\tt{128}} $*$ {\it{sid\/}}), \\ 
{\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-\index{putseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable contract-putnth-into-current-mbuffer.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  associativity-of-plus-crock \\ \index{associativity-of-plus-crock}
\=\+(\=\+{\tt{'}}{\tt{4}} \\ 
$+$$\;\;\;\;$(\=\+({\tt{'}}{\tt{8}} $*$ {\it{i\/}}) \\ 
$+$$\;\;\;\;$(\=\+({\tt{'}}{\tt{128}} $*$ {\it{j\/}}) \\ 
$+$$\;\;\;\;${\rm{getnth}}\,(({\tt{'}}{\tt{8}} $*$ {\it{i\/}}) $+$ ({\tt{'}}{\tt{128}} $*$ {\it{j\/}}), {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{getnth})\-)\-)\- \\ 
$=$$\;\;\;\;$(\=\+({\tt{'}}{\tt{8}} $*$ {\it{i\/}}) \\ 
$+$$\;\;\;\;$(\=\+({\tt{'}}{\tt{128}} $*$ {\it{j\/}}) \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{4}} \\ 
$+$$\;\;\;\;${\rm{getnth}}\,(\=\+({\tt{'}}{\tt{8}} $*$ {\it{i\/}}) $+$ ({\tt{'}}{\tt{128}} $*$ {\it{j\/}}), \\ 
{\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-\index{getnth})\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable associativity-of-plus-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-getnth-from-current-mbuffer-for-receive \\ \index{contract-getnth-from-current-mb!uffer-for-receive}
\=\+(\=\+(({\tt{'}}{\tt{4}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{os-current-mbuffer}}\,({\it{sid\/}}, {\it{did\/}}, {\it{os\/}})\index{os-current-mbuffer})\index{getnth}) $<$ {\tt{'}}{\tt{8}}) \\ 
$\wedge$$\;\;\;\;$(({\it{sid\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{did\/}} $<$ {\tt{'}}{\tt{16}})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{4}} \\ 
$+$$\;\;\;\;$(\=\+(({\tt{'}}{\tt{8}} $*$ {\it{did\/}}) $+$ ({\tt{'}}{\tt{128}} $*$ {\it{sid\/}})) \\ 
$+$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+{\it{did\/}} $+$ ({\tt{'}}{\tt{16}} $*$ {\it{sid\/}}), \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\-\index{getnth})\-\index{getnth})\-\-, \\ 
{\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{4}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{os-current-mbuffer}}\,({\it{sid\/}}, {\it{did\/}}, {\it{os\/}})\index{os-current-mbuffer})\index{getnth}, \\ 
{\rm{os-current-mbuffer}}\,({\it{sid\/}}, {\it{did\/}}, {\it{os\/}})\index{os-current-mbuffer})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable contract-getnth-from-current-mbuffer-for-receive.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  access-current-mbuffer-qhead \\ \index{access-current-mbuffer-qhead}
\=\+(({\it{sid\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{did\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getnth}}\,(({\tt{'}}{\tt{8}} $*$ {\it{did\/}}) $+$ ({\tt{'}}{\tt{128}} $*$ {\it{sid\/}}), {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{os-current-mbuffer}}\,({\it{sid\/}}, {\it{did\/}}, {\it{os\/}})\index{os-current-mbuffer})\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable access-current-mbuffer-qhead.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-putnth-into-current-mbuffer-for-receive1 \\ \index{contract-putnth-into-current-mb!uffer-for-receive1}
\=\+(({\it{i\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{i\/}} $<$ {\tt{'}}{\tt{4}}) $\wedge$ (({\it{sid\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{did\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{putnth}}\,(\=\+{\it{value\/}}, \\ 
{\it{i\/}} $+$ (({\tt{'}}{\tt{8}} $*$ {\it{did\/}}) $+$ ({\tt{'}}{\tt{128}} $*$ {\it{sid\/}})), \\ 
{\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-\index{putnth} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,(\=\+{\rm{putnth}}\,({\it{value\/}}, {\it{i\/}}, {\rm{os-current-mbuffer}}\,({\it{sid\/}}, {\it{did\/}}, {\it{os\/}})\index{os-current-mbuffer})\index{putnth}, \\ 
({\tt{'}}{\tt{8}} $*$ {\it{did\/}}) $+$ ({\tt{'}}{\tt{128}} $*$ {\it{sid\/}}), \\ 
{\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-\index{putseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable contract-putnth-into-current-mbuffer-for-receive1.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-mbuffers-with-enqueued-messa!ge} \\  
\=\+{\rm{os-mbuffers-with-enqueued-message}}\,({\it{os\/}})\index{os-mbuffers-with-enqueued-messa!ge} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,(\=\+{\rm{array-enq}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-regs}}\,({\it{os\/}})\index{tm-regs})\index{getnth}, \\ 
{\rm{os-current-mbuffer}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\rm{tm-regs}}\,({\it{os\/}})\index{tm-regs})\index{getnth} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{16}}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\-\index{array-enq}, \\ 
\=\+({\tt{'}}{\tt{8}} $*$ ({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\rm{tm-regs}}\,({\it{os\/}})\index{tm-regs})\index{getnth} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{16}})) \\ 
$+$$\;\;\;\;$({\tt{'}}{\tt{128}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst})\-, \\ 
{\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-\index{putseg}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-os-mbuffers-with-enqueued-message \\ \index{length-os-mbuffers-with-enqueue!d-message}
{\rm{length}}\,({\rm{os-mbuffers-with-enqueued-message}}\,({\it{os\/}})\index{os-mbuffers-with-enqueued-messa!ge})\index{length} $=$ {\tt{'}}{\tt{2048}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-os-mbuffers-with-enqueued-message.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-os-mbuffers-with-enqueued-message \\ \index{plistp-os-mbuffers-with-enqueue!d-message}
{\rm{plistp}}\,({\rm{os-mbuffers-with-enqueued-message}}\,({\it{os\/}})\index{os-mbuffers-with-enqueued-messa!ge})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-os-mbuffers-with-enqueued-message.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-mbuffers-with-dequeued-messa!ge} \\  
\=\+{\rm{os-mbuffers-with-dequeued-message}}\,({\it{os\/}})\index{os-mbuffers-with-dequeued-messa!ge} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,(\=\+{\rm{array-deq}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-deq}, \\ 
\=\+({\tt{'}}{\tt{8}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}) \\ 
$+$$\;\;\;\;$({\tt{'}}{\tt{128}} $*$ ({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\rm{tm-regs}}\,({\it{os\/}})\index{tm-regs})\index{getnth} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{16}}))\-, \\ 
{\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-\index{putseg}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-os-mbuffers-with-dequeued-message \\ \index{length-os-mbuffers-with-dequeue!d-message}
{\rm{length}}\,({\rm{os-mbuffers-with-dequeued-message}}\,({\it{os\/}})\index{os-mbuffers-with-dequeued-messa!ge})\index{length} $=$ {\tt{'}}{\tt{2048}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-os-mbuffers-with-dequeued-message.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-os-mbuffers-with-dequeued-message \\ \index{plistp-os-mbuffers-with-dequeue!d-message}
{\rm{plistp}}\,({\rm{os-mbuffers-with-dequeued-message}}\,({\it{os\/}})\index{os-mbuffers-with-dequeued-messa!ge})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-os-mbuffers-with-dequeued-message.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-array-qfullp-mbuffers-instance \\ \index{correctness-of-array-qfullp-mbu!ffers-instance}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ ({\tt{'}}{\tt{4}} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{array-qfullp}}\,({\it{queue\/}})\index{array-qfullp} $=$ {\rm{qfullp}}\,({\rm{mapup-queue}}\,({\it{queue\/}})\index{mapup-queue}, {\tt{'}}{\tt{4}})\index{qfullp})\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-array-qfullp-mbuffers-instance.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-getnth2-os-mbuffers \\ \index{mapup-queue-getnth2-os-mbuffers}
\=\+(({\it{i\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{j\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{getnth2}}\,({\it{i\/}}, {\it{j\/}}, {\rm{table}}\,({\tt{'}}{\tt{16}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\index{table})\index{getnth2})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{getnth2}}\,({\it{i\/}}, {\it{j\/}}, {\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\index{getnth2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-getnth2-os-mbuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-current-mbuffer-rewrite-to-getnth2 \\ \index{os-current-mbuffer-rewrite-to-get!nth2}
\=\+(({\it{sid\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{did\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getnth}}\,(({\tt{'}}{\tt{16}} $*$ {\it{sid\/}}) $+$ {\it{did\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth2}}\,({\it{sid\/}}, {\it{did\/}}, {\rm{table}}\,({\tt{'}}{\tt{16}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\index{table})\index{getnth2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-current-mbuffer-rewrite-to-getnth2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  limited-associativity-of-plus2 \\ \index{limited-associativity-of-plus2}
((($1\;+$ {\it{a\/}}) $+$ {\it{b\/}}) $+$ {\it{c\/}}) $=$ (($1\;+$ {\it{a\/}}) $+$ ({\it{b\/}} $+$ {\it{c\/}}))
\end{tabbing}


\noindent{\sc Event}:   Disable limited-associativity-of-plus2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-finite-number-queue-corollary-for-ibuffers \\ \index{length-finite-number-queue-coro!llary-for-ibuffers}
{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} $\rightarrow$ ({\rm{length}}\,({\it{queue\/}})\index{length} $=$ {\tt{'}}{\tt{8}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-finite-number-queue-corollary-for-ibuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-finite-number-queue-corollary-for-ibuffers \\ \index{plistp-finite-number-queue-coro!llary-for-ibuffers}
{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} $\rightarrow$ {\rm{plistp}}\,({\it{queue\/}})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-finite-number-queue-corollary-for-ibuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-queuep-finite-number-queue-corollary-for-ibuffers \\ \index{array-queuep-finite-number-queue!-corollary-for-ibuffers}
{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} $\rightarrow$ {\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep}
\end{tabbing}


\noindent{\sc Event}:   Disable array-queuep-finite-number-queue-corollary-for-ibuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qhead-size-corollary-for-ibuffers \\ \index{finite-number-queue-qhead-size-!corollary-for-ibuffers}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$(({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth} $<$ {\tt{'}}{\tt{4}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qhead-size-corollary-for-ibuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qtail-size-corollary-for-ibuffers \\ \index{finite-number-queue-qtail-size-!corollary-for-ibuffers}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$(({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth} $<$ {\tt{'}}{\tt{4}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qtail-size-corollary-for-ibuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qcurrlength-size-corollary-for-ibuffers \\ \index{finite-number-queue-qcurrlength!-size-corollary-for-ibuffers}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$(({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $<$ {\tt{'}}{\tt{5}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qcurrlength-size-corollary-for-ibuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qmaxlength-value-corollary-for-ibuffers \\ \index{finite-number-queue-qmaxlength-v!alue-corollary-for-ibuffers}
{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} $\rightarrow$ ({\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth} $=$ {\tt{'}}{\tt{4}})
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qmaxlength-value-corollary-for-ibuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-array-enq-finite-number-queue-corollary-for-ibuffers \\ \index{finite-number-queuep-array-enq-!finite-number-queue-corollary-for-ibuffers}
\=\+(\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{array-qfullp}}\,({\it{queue\/}})\index{array-qfullp}) $\wedge$ (({\it{item\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{item\/}} $<$ {\tt{'}}{\tt{65536}}))))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,({\rm{array-enq}}\,({\it{item\/}}, {\it{queue\/}})\index{array-enq}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-array-enq-finite-number-queue-corollary-for-ibuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-array-deq-finite-number-queue-corollary-for-ibuffers \\ \index{finite-number-queuep-array-deq-!finite-number-queue-corollary-for-ibuffers}
\=\+({\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,({\rm{array-deq}}\,({\it{queue\/}})\index{array-deq}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-array-deq-finite-number-queue-corollary-for-ibuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qfirst-finite-number-queue-corollary-for-ibuffers \\ \index{array-qfirst-finite-number-queue!-corollary-for-ibuffers}
\=\+({\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst} $<$ {\tt{'}}{\tt{65536}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qfirst-finite-number-queue-corollary-for-ibuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  remainder-array-qfirst-finite-number-queue-corollary-for-ibuffers \\ \index{remainder-array-qfirst-finite-n!umber-queue-corollary-for-ibuffers}
\=\+({\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{65536}}) $=$ {\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst})\-
\end{tabbing}


\noindent{\sc Event}:   Disable remainder-array-qfirst-finite-number-queue-corollary-for-ibuffers.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{finite-number-queue-corollaries-for-ibuffers}} to consist of the following events: remainder-array-qfirst-finite-number-queue-corollary-for-ibuffers,
array-qfirst-finite-number-queue-corollary-for-ibuffers,
finite-number-queuep-array-deq-finite-number-queue-corollary-for-ibuffers,
finite-number-queuep-array-enq-finite-number-queue-corollary-for-ibuffers,
finite-number-queue-qmaxlength-value-corollary-for-ibuffers,
finite-number-queue-qcurrlength-size-corollary-for-ibuffers,
finite-number-queue-qtail-size-corollary-for-ibuffers,
finite-number-queue-qhead-size-corollary-for-ibuffers,
array-queuep-finite-number-queue-corollary-for-ibuffers,
plistp-finite-number-queue-corollary-for-ibuffers,
length-finite-number-queue-corollary-for-ibuffers.\index{finite-number-queue-corollaries!-for-ibuffers}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{finite-number-queue-corollaries-for-ibuffers1}} to consist of the following events: remainder-array-qfirst-finite-number-queue-corollary-for-ibuffers,
array-qfirst-finite-number-queue-corollary-for-ibuffers,
finite-number-queuep-array-deq-finite-number-queue-corollary-for-ibuffers,
finite-number-queuep-array-enq-finite-number-queue-corollary-for-ibuffers,
finite-number-queue-qcurrlength-size-corollary-for-ibuffers,
finite-number-queue-qtail-size-corollary-for-ibuffers,
finite-number-queue-qhead-size-corollary-for-ibuffers,
array-queuep-finite-number-queue-corollary-for-ibuffers,
plistp-finite-number-queue-corollary-for-ibuffers,
length-finite-number-queue-corollary-for-ibuffers.\index{finite-number-queue-corollaries!-for-ibuffers1}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-ibuffers-address-plus-qtail-!field}$\;\;$
{\sc{os-ibuffers-address-plus-qtail-field}}\index{os-ibuffers-address-plus-qtail-!field} $=$ {\tt{'}}{\tt{244}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-ibuffers-address-plus-qcurrle!ngth-field}$\;\;$
{\sc{os-ibuffers-address-plus-qcurrlength-field}}\index{os-ibuffers-address-plus-qcurrle!ngth-field} $=$ {\tt{'}}{\tt{245}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-ibuffers-address-plus-qmaxle!ngth-field}$\;\;$
{\sc{os-ibuffers-address-plus-qmaxlength-field}}\index{os-ibuffers-address-plus-qmaxle!ngth-field} $=$ {\tt{'}}{\tt{246}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-ibuffers-address-plus-qarray!-field}$\;\;$
{\sc{os-ibuffers-address-plus-qarray-field}}\index{os-ibuffers-address-plus-qarray!-field} $=$ {\tt{'}}{\tt{247}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-current-ibuffer} \\  
{\rm{os-current-ibuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-ibuffer} $=$ {\rm{getnth}}\,({\it{id\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{table})\index{getnth}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-current-ibuffer \\ \index{finite-number-queuep-current-ib!uffer}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{id\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,(\=\+{\rm{getnth}}\,({\it{id\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{table})\index{getnth}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-current-ibuffer.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-array-qreplace-corollary-for-ibuffers \\ \index{finite-number-queuep-array-qrep!lace-corollary-for-ibuffers}
\=\+(\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp}) $\wedge$ {\rm{finite-numberp}}\,({\it{item\/}}, {\tt{'}}{\tt{65536}})\index{finite-numberp}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,({\rm{array-qreplace}}\,({\it{item\/}}, {\it{queue\/}})\index{array-qreplace}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-array-qreplace-corollary-for-ibuffers.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 OS-IBUFFERS-ADDRESS-FACTS
 (REWRITE)
 (IMPLIES
  (LESSP I '16)
  (AND
   (EQUAL (LESSP (TIMES '8 I) '128)
          '*1*TRUE)
   (AND
    (EQUAL (LESSP '128 (PLUS '8 (TIMES '8 I)))
           '*1*FALSE)
    (AND
     (EQUAL (LESSP (TIMES '8 I) '65536)
            '*1*TRUE)
     (AND
      (EQUAL (LESSP (PLUS '243 (TIMES '8 I))
                    '65536)
             '*1*TRUE)
      (AND
       (EQUAL (LESSP (PLUS '244 (TIMES '8 I))
                     '65536)
              '*1*TRUE)
       (AND
         (EQUAL (LESSP (PLUS '245 (TIMES '8 I))
                       '65536)
                '*1*TRUE)
         (AND (EQUAL (LESSP (PLUS '246 (TIMES '8 I))
                            '65536)
                     '*1*TRUE)
              (AND (EQUAL (LESSP (PLUS '247 (TIMES '8 I))
                                 '65536)
                          '*1*TRUE)
                   (AND (EQUAL (LESSP (PLUS '1 (TIMES '8 I)) '128)
                               '*1*TRUE)
                        (AND (EQUAL (LESSP (PLUS '2 (TIMES '8 I)) '128)
                                    '*1*TRUE)
                             (AND (EQUAL (LESSP (PLUS '3 (TIMES '8 I)) '128)
                                         '*1*TRUE)
                                  (EQUAL (LESSP (PLUS '4 (TIMES '8 I)) '128)
                                         '*1*TRUE)))))))))))))
 ((ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable os-ibuffers-address-facts.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-plus-facts-for-ibuffers \\ \index{lessp-plus-facts-for-ibuffers}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ({\it{id\/}} $<$ {\tt{'}}{\tt{16}}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+(\=\+(\=\+{\tt{'}}{\tt{4}} \\ 
$+$$\;\;\;\;$(\=\+({\tt{'}}{\tt{8}} $*$ {\it{id\/}}) \\ 
$+$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{getnth}}\,({\it{id\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{table})\index{getnth})\index{getnth})\-)\- \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{128}})\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+(\=\+{\tt{'}}{\tt{247}} \\ 
$+$$\;\;\;\;$(\=\+({\tt{'}}{\tt{8}} $*$ {\it{id\/}}) \\ 
$+$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,({\it{id\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{table})\index{getnth})\-\index{getnth})\-)\- \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{65536}})\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-plus-facts-for-ibuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  index-within-length-of-ibuffer \\ \index{index-within-length-of-ibuffer}
\=\+(\=\+\=\+{\bf if }{\tt{'}}{\tt{4}} $<$ {\it{i\/}}$\;\;${\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\- \\ 
$\wedge$$\;\;\;\;${\rm{finite-number-queuep}}\,(\=\+{\rm{getnth}}\,({\it{id\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{table})\index{getnth}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queuep})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(({\it{i\/}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{getnth}}\,({\it{id\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{table})\index{getnth})\index{getnth}) $<$ {\tt{'}}{\tt{8}}) \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable index-within-length-of-ibuffer.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-qmaxlength-field-os-current-ibuffer-tm-wordlub \\ \index{lessp-qmaxlength-field-os-curre!nt-ibuffer-tm-wordlub}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ ({\it{id\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{getnth}}\,({\it{id\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{table})\index{getnth})\index{getnth} $<$ {\tt{'}}{\tt{65536}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-qmaxlength-field-os-current-ibuffer-tm-wordlub.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  qreplace-address-fact \\ \index{qreplace-address-fact}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+(\=\+(\=\+{\tt{'}}{\tt{243}} \\ 
$+$$\;\;\;\;$(\=\+({\tt{'}}{\tt{8}} $*$ {\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}) \\ 
$+$$\;\;\;\;${\rm{decr-mod}}\,(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{table})\-\index{getnth})\-\index{getnth}, \\ 
{\tt{'}}{\tt{4}})\-\index{decr-mod})\-)\- \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{65536}})\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+(\=\+(\=\+{\tt{'}}{\tt{247}} \\ 
$+$$\;\;\;\;$(\=\+(\=\+{\tt{'}}{\tt{8}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port})\- \\ 
$+$$\;\;\;\;${\rm{decr-mod}}\,(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-\index{table})\-\index{getnth})\-\index{getnth}, \\ 
{\tt{'}}{\tt{4}})\-\index{decr-mod})\-)\- \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{65536}})\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+(\=\+{\tt{'}}{\tt{4}} \\ 
$+$$\;\;\;\;$(\=\+(\=\+{\tt{'}}{\tt{8}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port})\- \\ 
$+$$\;\;\;\;${\rm{decr-mod}}\,(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-\index{table})\-\index{getnth})\-\index{getnth}, \\ 
{\tt{'}}{\tt{4}})\-\index{decr-mod})\-)\- \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{128}})\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable qreplace-address-fact.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  more-ibuffer-address-facts \\ \index{more-ibuffer-address-facts}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+(\=\+(\=\+{\tt{'}}{\tt{243}} \\ 
$+$$\;\;\;\;$(\=\+({\tt{'}}{\tt{8}} $*$ {\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}) \\ 
$+$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{table})\-\index{getnth})\-\index{getnth})\-)\- \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{65536}})\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+(\=\+(\=\+{\tt{'}}{\tt{247}} \\ 
$+$$\;\;\;\;$(\=\+(\=\+{\tt{'}}{\tt{8}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port})\- \\ 
$+$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{table})\-\index{getnth})\-\index{getnth})\-)\- \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{65536}})\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+(\=\+{\tt{'}}{\tt{4}} \\ 
$+$$\;\;\;\;$(\=\+(\=\+{\tt{'}}{\tt{8}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port})\- \\ 
$+$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-\index{table})\-\index{getnth})\-\index{getnth})\-)\- \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{128}})\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable more-ibuffer-address-facts.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  access-current-ibuffer \\ \index{access-current-ibuffer}
\=\+(({\it{id\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{i\/}} $<$ {\tt{'}}{\tt{8}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\it{i\/}} $+$ ({\tt{'}}{\tt{8}} $*$ {\it{id\/}}), {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\it{i\/}}, {\rm{os-current-ibuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-ibuffer})\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable access-current-ibuffer.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-getnth-from-current-ibuffer \\ \index{contract-getnth-from-current-ib!uffer}
\=\+((({\tt{'}}{\tt{4}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{os-current-ibuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-ibuffer})\index{getnth}) $<$ {\tt{'}}{\tt{8}}) $\wedge$ ({\it{id\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{4}} \\ 
$+$$\;\;\;\;$(\=\+({\tt{'}}{\tt{8}} $*$ {\it{id\/}}) \\ 
$+$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,({\it{id\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{table})\index{getnth})\-\index{getnth})\-\-, \\ 
{\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{4}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{os-current-ibuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-ibuffer})\index{getnth}, \\ 
{\rm{os-current-ibuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-ibuffer})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable contract-getnth-from-current-ibuffer.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  access-current-ibuffer-qhead \\ \index{access-current-ibuffer-qhead}
\=\+({\it{id\/}} $<$ {\tt{'}}{\tt{16}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{8}} $*$ {\it{id\/}}, {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{os-current-ibuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-ibuffer})\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable access-current-ibuffer-qhead.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-putnth-into-current-ibuffer \\ \index{contract-putnth-into-current-ib!uffer}
\=\+(({\it{i\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{i\/}} $<$ {\tt{'}}{\tt{4}}) $\wedge$ ({\it{id\/}} $<$ {\tt{'}}{\tt{16}}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{putnth}}\,({\it{value\/}}, {\it{i\/}} $+$ ({\tt{'}}{\tt{8}} $*$ {\it{id\/}}), {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{putnth} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,(\=\+{\rm{putnth}}\,({\it{value\/}}, {\it{i\/}}, {\rm{os-current-ibuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-ibuffer})\index{putnth}, \\ 
{\tt{'}}{\tt{8}} $*$ {\it{id\/}}, \\ 
{\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-\index{putseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable contract-putnth-into-current-ibuffer.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-putnth-into-current-ibuffer1 \\ \index{contract-putnth-into-current-ib!uffer1}
\=\+(\=\+(({\it{i\/}} $+$ {\rm{decr-mod}}\,({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\rm{os-current-ibuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-ibuffer})\index{getnth}, {\tt{'}}{\tt{4}})\index{decr-mod}) $<$ {\tt{'}}{\tt{8}}) \\ 
$\wedge$$\;\;\;\;$({\it{id\/}} $<$ {\tt{'}}{\tt{16}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{putnth}}\,(\=\+{\it{value\/}}, \\ 
{\it{i\/}} $+$ (\=\+({\tt{'}}{\tt{8}} $*$ {\it{id\/}}) \\ 
$+$$\;\;\;\;${\rm{decr-mod}}\,(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{getnth}}\,(\=\+{\it{id\/}}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-\index{table})\-\index{getnth})\-\index{getnth}, \\ 
{\tt{'}}{\tt{4}})\-\index{decr-mod})\-, \\ 
{\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-\index{putnth} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,(\=\+{\rm{putnth}}\,(\=\+{\it{value\/}}, \\ 
{\it{i\/}} $+$ {\rm{decr-mod}}\,(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{os-current-ibuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-ibuffer})\-\index{getnth}, \\ 
{\tt{'}}{\tt{4}})\-\index{decr-mod}, \\ 
{\rm{os-current-ibuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-ibuffer})\-\index{putnth}, \\ 
{\tt{'}}{\tt{8}} $*$ {\it{id\/}}, \\ 
{\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-\index{putseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable contract-putnth-into-current-ibuffer1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-putnth-into-current-ibuffer2 \\ \index{contract-putnth-into-current-ib!uffer2}
\=\+((({\it{i\/}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\rm{os-current-ibuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-ibuffer})\index{getnth}) $<$ {\tt{'}}{\tt{8}}) $\wedge$ ({\it{id\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{putnth}}\,(\=\+{\it{value\/}}, \\ 
{\it{i\/}} $+$ (\=\+({\tt{'}}{\tt{8}} $*$ {\it{id\/}}) \\ 
$+$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{getnth}}\,({\it{id\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{table})\index{getnth})\-\index{getnth})\-, \\ 
{\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-\index{putnth} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,(\=\+{\rm{putnth}}\,(\=\+{\it{value\/}}, \\ 
{\it{i\/}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\rm{os-current-ibuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-ibuffer})\index{getnth}, \\ 
{\rm{os-current-ibuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-ibuffer})\-\index{putnth}, \\ 
{\tt{'}}{\tt{8}} $*$ {\it{id\/}}, \\ 
{\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-\index{putseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable contract-putnth-into-current-ibuffer2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-ibuffers-with-dequeued-chara!cter} \\  
\=\+{\rm{os-ibuffers-with-dequeued-character}}\,({\it{os\/}})\index{os-ibuffers-with-dequeued-chara!cter} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,(\=\+{\rm{array-deq}}\,({\rm{os-current-ibuffer}}\,({\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, {\it{os\/}})\index{os-current-ibuffer})\index{array-deq}, \\ 
{\tt{'}}{\tt{8}} $*$ {\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-\index{putseg}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-os-ibuffers-with-dequeued-character \\ \index{length-os-ibuffers-with-dequeue!d-character}
{\rm{length}}\,({\rm{os-ibuffers-with-dequeued-character}}\,({\it{os\/}})\index{os-ibuffers-with-dequeued-chara!cter})\index{length} $=$ {\tt{'}}{\tt{128}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-os-ibuffers-with-dequeued-character.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-os-ibuffers-with-dequeued-character \\ \index{plistp-os-ibuffers-with-dequeue!d-character}
{\rm{plistp}}\,({\rm{os-ibuffers-with-dequeued-character}}\,({\it{os\/}})\index{os-ibuffers-with-dequeued-chara!cter})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-os-ibuffers-with-dequeued-character.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-ibuffers-with-qreplaced-over!flow-character} \\  
\=\+{\rm{os-ibuffers-with-qreplaced-overflow-character}}\,({\it{os\/}})\index{os-ibuffers-with-qreplaced-over!flow-character} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,(\=\+{\rm{array-qreplace}}\,(\=\+{\rm{tm-overflow-char}}\,({\rm{tm-ichar}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{getnth})\index{tm-ichar})\index{tm-overflow-char}, \\ 
{\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{table})\-\index{getnth})\-\index{array-qreplace}, \\ 
{\tt{'}}{\tt{8}} $*$ {\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-\index{putseg}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-os-ibuffers-with-qreplaced-overflow-character \\ \index{length-os-ibuffers-with-qreplace!d-overflow-character}
{\rm{length}}\,({\rm{os-ibuffers-with-qreplaced-overflow-character}}\,({\it{os\/}})\index{os-ibuffers-with-qreplaced-over!flow-character})\index{length} $=$ {\tt{'}}{\tt{128}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-os-ibuffers-with-qreplaced-overflow-character.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-os-ibuffers-with-qreplaced-overflow-character \\ \index{plistp-os-ibuffers-with-qreplace!d-overflow-character}
{\rm{plistp}}\,({\rm{os-ibuffers-with-qreplaced-overflow-character}}\,({\it{os\/}})\index{os-ibuffers-with-qreplaced-over!flow-character})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-os-ibuffers-with-qreplaced-overflow-character.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-ibuffers-with-enqueued-overf!low-character} \\  
\=\+{\rm{os-ibuffers-with-enqueued-overflow-character}}\,({\it{os\/}})\index{os-ibuffers-with-enqueued-overf!low-character} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,(\=\+{\rm{array-enq}}\,(\=\+{\rm{tm-overflow-char}}\,({\rm{tm-ichar}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{getnth})\index{tm-ichar})\index{tm-overflow-char}, \\ 
{\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{table})\-\index{getnth})\-\index{array-enq}, \\ 
{\tt{'}}{\tt{8}} $*$ {\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-\index{putseg}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-os-ibuffers-with-enqueued-overflow-character \\ \index{length-os-ibuffers-with-enqueue!d-overflow-character}
{\rm{length}}\,({\rm{os-ibuffers-with-enqueued-overflow-character}}\,({\it{os\/}})\index{os-ibuffers-with-enqueued-overf!low-character})\index{length} $=$ {\tt{'}}{\tt{128}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-os-ibuffers-with-enqueued-overflow-character.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-os-ibuffers-with-enqueued-overflow-character \\ \index{plistp-os-ibuffers-with-enqueue!d-overflow-character}
{\rm{plistp}}\,({\rm{os-ibuffers-with-enqueued-overflow-character}}\,({\it{os\/}})\index{os-ibuffers-with-enqueued-overf!low-character})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-os-ibuffers-with-enqueued-overflow-character.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-ibuffers-with-enqueued-chara!cter} \\  
\=\+{\rm{os-ibuffers-with-enqueued-character}}\,({\it{os\/}})\index{os-ibuffers-with-enqueued-chara!cter} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,(\=\+{\rm{array-enq}}\,(\=\+{\rm{tm-ichar}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{getnth})\index{tm-ichar}, \\ 
{\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{table})\-\index{getnth})\-\index{array-enq}, \\ 
{\tt{'}}{\tt{8}} $*$ {\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-\index{putseg}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-os-ibuffers-with-enqueued-character \\ \index{length-os-ibuffers-with-enqueue!d-character}
{\rm{length}}\,({\rm{os-ibuffers-with-enqueued-character}}\,({\it{os\/}})\index{os-ibuffers-with-enqueued-chara!cter})\index{length} $=$ {\tt{'}}{\tt{128}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-os-ibuffers-with-enqueued-character.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-os-ibuffers-with-enqueued-character \\ \index{plistp-os-ibuffers-with-enqueue!d-character}
{\rm{plistp}}\,({\rm{os-ibuffers-with-enqueued-character}}\,({\it{os\/}})\index{os-ibuffers-with-enqueued-chara!cter})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-os-ibuffers-with-enqueued-character.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-getnth-for-ibuffers \\ \index{mapup-queue-getnth-for-ibuffers}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{id\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{table})\index{getnth})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\it{id\/}}, {\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-getnth-for-ibuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  length-finite-number-queue-corollary-for-obuffers \\ \index{length-finite-number-queue-coro!llary-for-obuffers}
{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} $\rightarrow$ ({\rm{length}}\,({\it{queue\/}})\index{length} $=$ {\tt{'}}{\tt{8}})
\end{tabbing}


\noindent{\sc Event}:   Disable length-finite-number-queue-corollary-for-obuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-finite-number-queue-corollary-for-obuffers \\ \index{plistp-finite-number-queue-coro!llary-for-obuffers}
{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} $\rightarrow$ {\rm{plistp}}\,({\it{queue\/}})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-finite-number-queue-corollary-for-obuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-queuep-finite-number-queue-corollary-for-obuffers \\ \index{array-queuep-finite-number-queue!-corollary-for-obuffers}
{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} $\rightarrow$ {\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep}
\end{tabbing}


\noindent{\sc Event}:   Disable array-queuep-finite-number-queue-corollary-for-obuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qhead-size-corollary-for-obuffers \\ \index{finite-number-queue-qhead-size-!corollary-for-obuffers}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$(({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\it{queue\/}})\index{getnth} $<$ {\tt{'}}{\tt{4}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qhead-size-corollary-for-obuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qtail-size-corollary-for-obuffers \\ \index{finite-number-queue-qtail-size-!corollary-for-obuffers}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$(({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\it{queue\/}})\index{getnth} $<$ {\tt{'}}{\tt{4}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qtail-size-corollary-for-obuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qcurrlength-size-corollary-for-obuffers \\ \index{finite-number-queue-qcurrlength!-size-corollary-for-obuffers}
\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} \\ 
$\rightarrow$$\;\;\;\;$(({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{getnth}}\,({\tt{'}}{\tt{2}}, {\it{queue\/}})\index{getnth} $<$ {\tt{'}}{\tt{5}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qcurrlength-size-corollary-for-obuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-qmaxlength-value-corollary-for-obuffers \\ \index{finite-number-queue-qmaxlength-v!alue-corollary-for-obuffers}
{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} $\rightarrow$ ({\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth} $=$ {\tt{'}}{\tt{4}})
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-qmaxlength-value-corollary-for-obuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-array-enq-finite-number-queue-corollary-for-obuffers \\ \index{finite-number-queuep-array-enq-!finite-number-queue-corollary-for-obuffers}
\=\+(\=\+{\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{array-qfullp}}\,({\it{queue\/}})\index{array-qfullp}) $\wedge$ (({\it{item\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{item\/}} $<$ {\tt{'}}{\tt{65536}}))))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,({\rm{array-enq}}\,({\it{item\/}}, {\it{queue\/}})\index{array-enq}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-array-enq-finite-number-queue-corollary-for-obuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-array-deq-finite-number-queue-corollary-for-obuffers \\ \index{finite-number-queuep-array-deq-!finite-number-queue-corollary-for-obuffers}
\=\+({\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,({\rm{array-deq}}\,({\it{queue\/}})\index{array-deq}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-array-deq-finite-number-queue-corollary-for-obuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qfirst-finite-number-queue-corollary-for-obuffers \\ \index{array-qfirst-finite-number-queue!-corollary-for-obuffers}
\=\+({\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst} $<$ {\tt{'}}{\tt{65536}}))\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qfirst-finite-number-queue-corollary-for-obuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  remainder-array-qfirst-finite-number-queue-corollary-for-obuffers \\ \index{remainder-array-qfirst-finite-n!umber-queue-corollary-for-obuffers}
\=\+({\rm{finite-number-queuep}}\,({\it{queue\/}}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{65536}})\index{finite-number-queuep} $\wedge$ ($\neg$ {\rm{array-qemptyp}}\,({\it{queue\/}})\index{array-qemptyp})) \\ 
$\rightarrow$$\;\;\;\;$(({\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{65536}}) $=$ {\rm{array-qfirst}}\,({\it{queue\/}})\index{array-qfirst})\-
\end{tabbing}


\noindent{\sc Event}:   Disable remainder-array-qfirst-finite-number-queue-corollary-for-obuffers.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{finite-number-queue-corollaries-for-obuffers}} to consist of the following events: remainder-array-qfirst-finite-number-queue-corollary-for-obuffers,
array-qfirst-finite-number-queue-corollary-for-obuffers,
finite-number-queuep-array-deq-finite-number-queue-corollary-for-obuffers,
finite-number-queuep-array-enq-finite-number-queue-corollary-for-obuffers,
finite-number-queue-qmaxlength-value-corollary-for-obuffers,
finite-number-queue-qcurrlength-size-corollary-for-obuffers,
finite-number-queue-qtail-size-corollary-for-obuffers,
finite-number-queue-qhead-size-corollary-for-obuffers,
array-queuep-finite-number-queue-corollary-for-obuffers,
plistp-finite-number-queue-corollary-for-obuffers,
length-finite-number-queue-corollary-for-obuffers.\index{finite-number-queue-corollaries!-for-obuffers}

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{finite-number-queue-corollaries-for-obuffers1}} to consist of the following events: remainder-array-qfirst-finite-number-queue-corollary-for-obuffers,
array-qfirst-finite-number-queue-corollary-for-obuffers,
finite-number-queuep-array-deq-finite-number-queue-corollary-for-obuffers,
finite-number-queuep-array-enq-finite-number-queue-corollary-for-obuffers,
finite-number-queue-qcurrlength-size-corollary-for-obuffers,
finite-number-queue-qtail-size-corollary-for-obuffers,
finite-number-queue-qhead-size-corollary-for-obuffers,
array-queuep-finite-number-queue-corollary-for-obuffers,
plistp-finite-number-queue-corollary-for-obuffers,
length-finite-number-queue-corollary-for-obuffers.\index{finite-number-queue-corollaries!-for-obuffers1}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-obuffers-address-plus-qtail-!field}$\;\;$
{\sc{os-obuffers-address-plus-qtail-field}}\index{os-obuffers-address-plus-qtail-!field} $=$ {\tt{'}}{\tt{372}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-obuffers-address-plus-qcurrle!ngth-field}$\;\;$
{\sc{os-obuffers-address-plus-qcurrlength-field}}\index{os-obuffers-address-plus-qcurrle!ngth-field} $=$ {\tt{'}}{\tt{373}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-obuffers-address-plus-qmaxle!ngth-field}$\;\;$
{\sc{os-obuffers-address-plus-qmaxlength-field}}\index{os-obuffers-address-plus-qmaxle!ngth-field} $=$ {\tt{'}}{\tt{374}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-obuffers-address-plus-qarray!-field}$\;\;$
{\sc{os-obuffers-address-plus-qarray-field}}\index{os-obuffers-address-plus-qarray!-field} $=$ {\tt{'}}{\tt{375}}
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-current-obuffer} \\  
{\rm{os-current-obuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-obuffer} $=$ {\rm{getnth}}\,({\it{id\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\index{table})\index{getnth}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-current-obuffer \\ \index{finite-number-queuep-current-ob!uffer}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{id\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,(\=\+{\rm{getnth}}\,({\it{id\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\index{table})\index{getnth}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-current-obuffer.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 OS-OBUFFERS-ADDRESS-FACTS
 (REWRITE)
 (IMPLIES
  (LESSP I '16)
  (AND
   (EQUAL (LESSP (TIMES '8 I) '65536)
          '*1*TRUE)
   (AND
    (EQUAL (LESSP (PLUS '371 (TIMES '8 I))
                  '65536)
           '*1*TRUE)
    (AND
     (EQUAL (LESSP (PLUS '372 (TIMES '8 I))
                   '65536)
            '*1*TRUE)
     (AND
         (EQUAL (LESSP (PLUS '373 (TIMES '8 I))
                       '65536)
                '*1*TRUE)
         (AND (EQUAL (LESSP (PLUS '374 (TIMES '8 I))
                            '65536)
                     '*1*TRUE)
              (AND (EQUAL (LESSP (PLUS '375 (TIMES '8 I))
                                 '65536)
                          '*1*TRUE)
                   (AND (EQUAL (LESSP (PLUS '1 (TIMES '8 I)) '128)
                               '*1*TRUE)
                        (AND (EQUAL (LESSP (PLUS '2 (TIMES '8 I)) '128)
                                    '*1*TRUE)
                             (AND (EQUAL (LESSP (PLUS '3 (TIMES '8 I)) '128)
                                         '*1*TRUE)
                                  (EQUAL (LESSP (PLUS '4 (TIMES '8 I)) '128)
                                         '*1*TRUE)))))))))))
 ((ENABLE-THEORY GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable os-obuffers-address-facts.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-plus-facts-for-obuffers \\ \index{lessp-plus-facts-for-obuffers}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ({\it{id\/}} $<$ {\tt{'}}{\tt{16}}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+(\=\+(\=\+{\tt{'}}{\tt{4}} \\ 
$+$$\;\;\;\;$(\=\+({\tt{'}}{\tt{8}} $*$ {\it{id\/}}) \\ 
$+$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\rm{getnth}}\,({\it{id\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\index{table})\index{getnth})\index{getnth})\-)\- \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{128}})\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+(\=\+{\tt{'}}{\tt{375}} \\ 
$+$$\;\;\;\;$(\=\+({\tt{'}}{\tt{8}} $*$ {\it{id\/}}) \\ 
$+$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{getnth}}\,({\it{id\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\index{table})\index{getnth})\-\index{getnth})\-)\- \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{65536}})\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-plus-facts-for-obuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-qmaxlength-field-os-current-obuffer-tm-wordlub \\ \index{lessp-qmaxlength-field-os-curre!nt-obuffer-tm-wordlub}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ ({\it{id\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{getnth}}\,({\it{id\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\index{table})\index{getnth})\index{getnth} $<$ {\tt{'}}{\tt{65536}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-qmaxlength-field-os-current-obuffer-tm-wordlub.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  obuffer-address-facts \\ \index{obuffer-address-facts}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+(\=\+{\tt{'}}{\tt{375}} \\ 
$+$$\;\;\;\;$(\=\+({\tt{'}}{\tt{8}} $*$ {\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}) \\ 
$+$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\index{table})\-\index{getnth})\-\index{getnth})\-)\- \\ 
$<$$\;\;\;\;${\tt{'}}{\tt{65536}})\- \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{*1*true}})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable obuffer-address-facts.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  access-current-obuffer \\ \index{access-current-obuffer}
\=\+(({\it{id\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{i\/}} $<$ {\tt{'}}{\tt{8}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\it{i\/}} $+$ ({\tt{'}}{\tt{8}} $*$ {\it{id\/}}), {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\it{i\/}}, {\rm{os-current-obuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-obuffer})\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable access-current-obuffer.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-getnth-from-current-obuffer \\ \index{contract-getnth-from-current-ob!uffer}
\=\+((({\tt{'}}{\tt{4}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\rm{os-current-obuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-obuffer})\index{getnth}) $<$ {\tt{'}}{\tt{8}}) $\wedge$ ({\it{id\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{4}} \\ 
$+$$\;\;\;\;$(\=\+({\tt{'}}{\tt{8}} $*$ {\it{id\/}}) \\ 
$+$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{getnth}}\,({\it{id\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\index{table})\index{getnth})\-\index{getnth})\-\-, \\ 
{\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{4}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\rm{os-current-obuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-obuffer})\index{getnth}, \\ 
{\rm{os-current-obuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-obuffer})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable contract-getnth-from-current-obuffer.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-putnth-into-current-obuffer \\ \index{contract-putnth-into-current-ob!uffer}
\=\+((({\it{i\/}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\rm{os-current-obuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-obuffer})\index{getnth}) $<$ {\tt{'}}{\tt{8}}) $\wedge$ ({\it{id\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{putnth}}\,(\=\+{\it{value\/}}, \\ 
{\it{i\/}} $+$ (\=\+({\tt{'}}{\tt{8}} $*$ {\it{id\/}}) \\ 
$+$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{getnth}}\,({\it{id\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\index{table})\index{getnth})\-\index{getnth})\-, \\ 
{\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-\index{putnth} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,(\=\+{\rm{putnth}}\,(\=\+{\it{value\/}}, \\ 
{\it{i\/}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{1}}, {\rm{os-current-obuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-obuffer})\index{getnth}, \\ 
{\rm{os-current-obuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-obuffer})\-\index{putnth}, \\ 
{\tt{'}}{\tt{8}} $*$ {\it{id\/}}, \\ 
{\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-\index{putseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable contract-putnth-into-current-obuffer.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-putnth-into-current-obuffer1 \\ \index{contract-putnth-into-current-ob!uffer1}
\=\+(({\it{i\/}} $\in\;${\bf{N}}${}$) $\wedge$ (({\it{i\/}} $<$ {\tt{'}}{\tt{4}}) $\wedge$ ({\it{id\/}} $<$ {\tt{'}}{\tt{16}}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{putnth}}\,({\it{value\/}}, {\it{i\/}} $+$ ({\tt{'}}{\tt{8}} $*$ {\it{id\/}}), {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\index{putnth} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,(\=\+{\rm{putnth}}\,({\it{value\/}}, {\it{i\/}}, {\rm{os-current-obuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-obuffer})\index{putnth}, \\ 
{\tt{'}}{\tt{8}} $*$ {\it{id\/}}, \\ 
{\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-\index{putseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable contract-putnth-into-current-obuffer1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  contract-getnth-from-current-obuffer1 \\ \index{contract-getnth-from-current-ob!uffer1}
\=\+((({\tt{'}}{\tt{4}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{os-current-obuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-obuffer})\index{getnth}) $<$ {\tt{'}}{\tt{8}}) $\wedge$ ({\it{id\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{4}} \\ 
$+$$\;\;\;\;$(\=\+({\tt{'}}{\tt{8}} $*$ {\it{id\/}}) \\ 
$+$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,({\it{id\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\index{table})\index{getnth})\-\index{getnth})\-\-, \\ 
{\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{4}} $+$ {\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{os-current-obuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-obuffer})\index{getnth}, \\ 
{\rm{os-current-obuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-obuffer})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable contract-getnth-from-current-obuffer1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  access-current-obuffer-qhead \\ \index{access-current-obuffer-qhead}
\=\+({\it{id\/}} $<$ {\tt{'}}{\tt{16}}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{8}} $*$ {\it{id\/}}, {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{0}}, {\rm{os-current-obuffer}}\,({\it{id\/}}, {\it{os\/}})\index{os-current-obuffer})\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable access-current-obuffer-qhead.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-obuffers-with-enqueued-chara!cter} \\  
\=\+{\rm{os-obuffers-with-enqueued-character}}\,({\it{os\/}})\index{os-obuffers-with-enqueued-chara!cter} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,(\=\+{\rm{array-enq}}\,(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-regs}}\,({\it{os\/}})\index{tm-regs})\index{getnth}, \\ 
{\rm{os-current-obuffer}}\,({\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, {\it{os\/}})\index{os-current-obuffer})\-\index{array-enq}, \\ 
{\tt{'}}{\tt{8}} $*$ {\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-\index{putseg}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-os-obuffers-with-enqueued-character \\ \index{length-os-obuffers-with-enqueue!d-character}
{\rm{length}}\,({\rm{os-obuffers-with-enqueued-character}}\,({\it{os\/}})\index{os-obuffers-with-enqueued-chara!cter})\index{length} $=$ {\tt{'}}{\tt{128}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-os-obuffers-with-enqueued-character.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-os-obuffers-with-enqueued-character \\ \index{plistp-os-obuffers-with-enqueue!d-character}
{\rm{plistp}}\,({\rm{os-obuffers-with-enqueued-character}}\,({\it{os\/}})\index{os-obuffers-with-enqueued-chara!cter})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-os-obuffers-with-enqueued-character.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-obuffers-with-dequeued-chara!cter} \\  
\=\+{\rm{os-obuffers-with-dequeued-character}}\,({\it{os\/}})\index{os-obuffers-with-dequeued-chara!cter} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,(\=\+{\rm{array-deq}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-deq}, \\ 
{\tt{'}}{\tt{8}} $*$ {\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-\index{putseg}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-os-obuffers-with-dequeued-character \\ \index{length-os-obuffers-with-dequeue!d-character}
{\rm{length}}\,({\rm{os-obuffers-with-dequeued-character}}\,({\it{os\/}})\index{os-obuffers-with-dequeued-chara!cter})\index{length} $=$ {\tt{'}}{\tt{128}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-os-obuffers-with-dequeued-character.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-os-obuffers-with-dequeued-character \\ \index{plistp-os-obuffers-with-dequeue!d-character}
{\rm{plistp}}\,({\rm{os-obuffers-with-dequeued-character}}\,({\it{os\/}})\index{os-obuffers-with-dequeued-chara!cter})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-os-obuffers-with-dequeued-character.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  restore-regs \\ \index{restore-regs}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{getseg}}\,(\=\+{\tt{'}}{\tt{9}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{9}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu}, \\ 
{\tt{'}}{\tt{9}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\-\index{putseg})\-\index{getseg})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{tm-regs}}\,({\it{os\/}})\index{tm-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable restore-regs.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  restore-regs1 \\ \index{restore-regs1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu}, \\ 
{\tt{'}}{\tt{9}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\-\index{putseg})\-\index{table})\-\index{getnth})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{tm-regs}}\,({\it{os\/}})\index{tm-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable restore-regs1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  restore-cc \\ \index{restore-cc}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{8}} $+$ ({\tt{'}}{\tt{9}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}), \\ 
{\rm{putseg}}\,(\=\+{\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu}, \\ 
{\tt{'}}{\tt{9}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\-\index{putseg})\-\index{getnth} \\ 
${}${\bf{mod}}${}$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$=$$\;\;\;\;${\rm{tm-cc}}\,({\it{os\/}})\index{tm-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable restore-cc.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  restore-error \\ \index{restore-error}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{8}} $+$ ({\tt{'}}{\tt{9}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}), \\ 
{\rm{putseg}}\,(\=\+{\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu}, \\ 
{\tt{'}}{\tt{9}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\-\index{putseg})\-\index{getnth} \\ 
${}${\bf{mod}}${}$$\;\;\;\;${\tt{'}}{\tt{256}})\- \\ 
$\div$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$=$$\;\;\;\;${\rm{tm-error}}\,({\it{os\/}})\index{tm-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable restore-error.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  restore-svcflag \\ \index{restore-svcflag}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{8}} $+$ ({\tt{'}}{\tt{9}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}), \\ 
{\rm{putseg}}\,(\=\+{\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu}, \\ 
{\tt{'}}{\tt{9}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\-\index{putseg})\-\index{getnth} \\ 
${}${\bf{mod}}${}$$\;\;\;\;${\tt{'}}{\tt{512}})\- \\ 
$\div$$\;\;\;\;${\tt{'}}{\tt{256}})\- \\ 
$=$$\;\;\;\;${\rm{tm-svcflag}}\,({\it{os\/}})\index{tm-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable restore-svcflag.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  restore-svcid \\ \index{restore-svcid}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{8}} $+$ ({\tt{'}}{\tt{9}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}), \\ 
{\rm{putseg}}\,(\=\+{\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu}, \\ 
{\tt{'}}{\tt{9}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\-\index{putseg})\-\index{getnth} \\ 
$\div$$\;\;\;\;${\tt{'}}{\tt{512}})\- \\ 
$=$$\;\;\;\;${\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable restore-svcid.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-task-table-with-delivered-ch!aracter} \\  
\=\+{\rm{os-task-table-with-delivered-character}}\,({\it{os\/}})\index{os-task-table-with-delivered-ch!aracter} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,(\=\+{\rm{putnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{table})\-\index{getnth})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{3}}, \\ 
{\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu})\-\index{putnth}, \\ 
{\tt{'}}{\tt{9}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\-\index{putseg}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-os-task-table-with-delivered-character \\ \index{length-os-task-table-with-delive!red-character}
{\rm{length}}\,({\rm{os-task-table-with-delivered-character}}\,({\it{os\/}})\index{os-task-table-with-delivered-ch!aracter})\index{length} $=$ {\tt{'}}{\tt{144}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-os-task-table-with-delivered-character.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-os-task-table-with-delivered-character \\ \index{plistp-os-task-table-with-delive!red-character}
{\rm{plistp}}\,({\rm{os-task-table-with-delivered-character}}\,({\it{os\/}})\index{os-task-table-with-delivered-ch!aracter})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-os-task-table-with-delivered-character.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  restore-regs-for-tyi-svc-return \\ \index{restore-regs-for-tyi-svc-return}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-task-table-with-delivered-character}}\,({\it{os\/}})\index{os-task-table-with-delivered-ch!aracter})\index{table})\-\index{getnth})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\index{table})\-\index{getnth})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{3}}, \\ 
{\rm{tm-regs}}\,({\it{os\/}})\index{tm-regs})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable restore-regs-for-tyi-svc-return.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  restore-cc-for-tyi-svc-return \\ \index{restore-cc-for-tyi-svc-return}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{8}} $+$ ({\tt{'}}{\tt{9}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}), \\ 
{\rm{os-task-table-with-delivered-character}}\,({\it{os\/}})\index{os-task-table-with-delivered-ch!aracter})\-\index{getnth} \\ 
${}${\bf{mod}}${}$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$=$$\;\;\;\;${\rm{tm-cc}}\,({\it{os\/}})\index{tm-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable restore-cc-for-tyi-svc-return.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  restore-error-for-tyi-svc-return \\ \index{restore-error-for-tyi-svc-retur!n}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{8}} $+$ ({\tt{'}}{\tt{9}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}), \\ 
{\rm{os-task-table-with-delivered-character}}\,({\it{os\/}})\index{os-task-table-with-delivered-ch!aracter})\-\index{getnth} \\ 
${}${\bf{mod}}${}$$\;\;\;\;${\tt{'}}{\tt{256}})\- \\ 
$\div$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$=$$\;\;\;\;${\rm{tm-error}}\,({\it{os\/}})\index{tm-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable restore-error-for-tyi-svc-return.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  restore-svcid-for-tyi-svc-return \\ \index{restore-svcid-for-tyi-svc-retur!n}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{8}} $+$ ({\tt{'}}{\tt{9}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}), \\ 
{\rm{os-task-table-with-delivered-character}}\,({\it{os\/}})\index{os-task-table-with-delivered-ch!aracter})\-\index{getnth} \\ 
$\div$$\;\;\;\;${\tt{'}}{\tt{512}})\- \\ 
$=$$\;\;\;\;${\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable restore-svcid-for-tyi-svc-return.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-task-table-with-delivered-me!ssage} \\  
\=\+{\rm{os-task-table-with-delivered-message}}\,({\it{os\/}})\index{os-task-table-with-delivered-me!ssage} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,(\=\+{\rm{putnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{getnth}}\,(\=\+\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{16}} \\ 
$*$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{tm-regs}}\,({\it{os\/}})\index{tm-regs})\-\index{getnth} \\ 
${}${\bf{mod}}${}$$\;\;\;\;${\tt{'}}{\tt{16}})\-)\-\-, \\ 
{\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\index{table})\-\index{getnth})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{3}}, \\ 
{\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu})\-\index{putnth}, \\ 
{\tt{'}}{\tt{9}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\-\index{putseg}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  length-os-task-table-with-delivered-message \\ \index{length-os-task-table-with-delive!red-message}
{\rm{length}}\,({\rm{os-task-table-with-delivered-message}}\,({\it{os\/}})\index{os-task-table-with-delivered-me!ssage})\index{length} $=$ {\tt{'}}{\tt{144}}
\end{tabbing}


\noindent{\sc Event}:   Disable length-os-task-table-with-delivered-message.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  plistp-os-task-table-with-delivered-message \\ \index{plistp-os-task-table-with-delive!red-message}
{\rm{plistp}}\,({\rm{os-task-table-with-delivered-message}}\,({\it{os\/}})\index{os-task-table-with-delivered-me!ssage})\index{plistp}
\end{tabbing}


\noindent{\sc Event}:   Disable plistp-os-task-table-with-delivered-message.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  restore-regs-for-receive-svc-return \\ \index{restore-regs-for-receive-svc-ret!urn}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-task-table-with-delivered-message}}\,({\it{os\/}})\index{os-task-table-with-delivered-me!ssage})\index{table})\-\index{getnth})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{3}}, \\ 
{\rm{tm-regs}}\,({\it{os\/}})\index{tm-regs})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable restore-regs-for-receive-svc-return.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  restore-cc-for-receive-svc-return \\ \index{restore-cc-for-receive-svc-retu!rn}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{8}} $+$ ({\tt{'}}{\tt{9}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}), \\ 
{\rm{os-task-table-with-delivered-message}}\,({\it{os\/}})\index{os-task-table-with-delivered-me!ssage})\-\index{getnth} \\ 
${}${\bf{mod}}${}$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$=$$\;\;\;\;${\rm{tm-cc}}\,({\it{os\/}})\index{tm-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable restore-cc-for-receive-svc-return.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  restore-error-for-receive-svc-return \\ \index{restore-error-for-receive-svc-ret!urn}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{8}} $+$ ({\tt{'}}{\tt{9}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}), \\ 
{\rm{os-task-table-with-delivered-message}}\,({\it{os\/}})\index{os-task-table-with-delivered-me!ssage})\-\index{getnth} \\ 
${}${\bf{mod}}${}$$\;\;\;\;${\tt{'}}{\tt{256}})\- \\ 
$\div$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$=$$\;\;\;\;${\rm{tm-error}}\,({\it{os\/}})\index{tm-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable restore-error-for-receive-svc-return.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  restore-svcid-for-receive-svc-return \\ \index{restore-svcid-for-receive-svc-ret!urn}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{8}} $+$ ({\tt{'}}{\tt{9}} $*$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}), \\ 
{\rm{os-task-table-with-delivered-message}}\,({\it{os\/}})\index{os-task-table-with-delivered-me!ssage})\-\index{getnth} \\ 
$\div$$\;\;\;\;${\tt{'}}{\tt{512}})\- \\ 
$=$$\;\;\;\;${\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable restore-svcid-for-receive-svc-return.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{executable-fns}} to consist of the following events: *1*greaterp,
*1*leq,
*1*geq,
*1*member,
*1*iff,
*1*ord-lessp,
*1*ordinalp,
*1*assoc,
*1*pairlist,
*1*subrp,
*1*apply-subr,
*1*formals,
*1*body,
*1*fix-cost,
*1*strip-cars,
*1*sum-cdrs,
*1*v\&c\$,
*1*v\&c-apply\$,
*1*eval\$,
*1*quantifier-initial-value,
*1*add-to-set,
*1*append,
*1*max,
*1*union,
*1*quantifier-operation,
*1*for,
*1*exp,
*1*divides,
*1*number-and-list-induction,
*1*double-number-induction,
*1*double-number-double-list-induction,
*1*lessp-quotient-induction,
*1*min,
*1*lessp-quotient-quotient-induction,
*1*length,
*1*insert,
*1*occurrences,
*1*remove,
*1*permutation,
*1*plistp,
*1*setp,
*1*sorted,
*1*transitivity-of-permutation-induction,
*1*setp-permutation-induction,
*1*getnth,
*1*putnth,
*1*getseg,
*1*putseg,
*1*fixlength,
*1*firstn,
*1*nthcdr,
*1*getnth-getseg-induction,
*1*integer-induction-instance,
*1*getseg-putseg-induction,
*1*nested-intervals,
*1*strange-induction,
*1*getnth2,
*1*putnth2,
*1*reverse,
*1*finite-numberp,
*1*number-listp,
*1*finite-number-listp,
*1*non-zero-listp,
*1*tablep,
*1*table,
*1*flatten,
*1*integer-nthcdr-induction,
*1*finite-number-tablep,
*1*nonlast,
*1*incr-mod,
*1*decr-mod,
*1*qfirst,
*1*enq,
*1*deq,
*1*qemptyp,
*1*qfullp,
*1*qreplace,
*1*qhead-field,
*1*qtail-field,
*1*qcurrlength-field,
*1*qmaxlength-field,
*1*qarray-field,
*1*delta,
*1*array-qindex-relation,
*1*array-queuep,
*1*array-enq,
*1*array-deq,
*1*array-qfirst,
*1*array-qfullp,
*1*array-qemptyp,
*1*array-nonlast,
*1*array-qreplace,
*1*delta-segment,
*1*mapup-queue,
*1*qfirst2,
*1*enq2,
*1*deq2,
*1*qfullp2,
*1*qemptyp2,
*1*tm-wordsize,
*1*tm-wordlub,
*1*alu-result,
*1*alu-value,
*1*alu-carry,
*1*tm-alu-decr,
*1*tm-alu-decr-mod,
*1*tm-alu-difference,
*1*tm-alu-incr,
*1*tm-alu-incr-mod,
*1*tm-alu-mod,
*1*tm-alu-mult,
*1*tm-alu-plus,
*1*tm-incr,
*1*tm-incrn,
*1*tm-decr,
*1*tm-shellp,
*1*tm-memory,
*1*tm-regs,
*1*tm-cc,
*1*tm-error,
*1*tm-svcflag,
*1*tm-svcid,
*1*tm-base,
*1*tm-limit,
*1*tm-slimit,
*1*tm-svmode,
*1*tm-rwstate,
*1*tm-clock,
*1*tm-iports,
*1*tm-oports,
*1*tm-regsize,
*1*tm-charsize,
*1*tm-ccsize,
*1*tm-errorsize,
*1*tm-svcflagsize,
*1*tm-svcidsize,
*1*tm-cclub,
*1*tm-errorlub,
*1*tm-svcflaglub,
*1*tm-svcidlub,
*1*tm-reglength,
*1*tm-memlength,
*1*tm-charlub,
*1*tm-port-length,
*1*tm-pc-address,
*1*tm-sp-address,
*1*tm-set-memory,
*1*tm-set-regs,
*1*tm-set-cc,
*1*tm-set-error,
*1*tm-set-svcflag,
*1*tm-set-svcid,
*1*tm-set-base,
*1*tm-set-limit,
*1*tm-set-slimit,
*1*tm-set-svmode,
*1*tm-set-rwstate,
*1*tm-set-clock,
*1*tm-set-iports,
*1*tm-set-oports,
*1*tm-pc,
*1*tm-set-pc,
*1*tm-sp,
*1*tm-set-sp,
*1*tm-non-zero-no-carry-condition,
*1*tm-zero-no-carry-condition,
*1*tm-non-zero-carry-condition,
*1*tm-zero-carry-condition,
*1*tm-cc-value,
*1*tm-cc-divisor,
*1*tm-error-divisor,
*1*tm-svcflag-divisor,
*1*tm-pack-psw,
*1*tm-unpack-cc,
*1*tm-unpack-error,
*1*tm-unpack-svcflag,
*1*tm-unpack-svcid,
*1*tm-register-save-area-addr,
*1*tm-clock-new-pc-addr,
*1*tm-error-new-pc-addr,
*1*tm-svc-new-pc-addr,
*1*tm-input-new-pc-addr,
*1*tm-output-new-pc-addr,
*1*tm-svcid-addr,
*1*tm-input-devid-addr,
*1*tm-input-char-addr,
*1*tm-output-devid-addr,
*1*tm-no-error,
*1*tm-halt-status,
*1*tm-opcode-error,
*1*tm-privilege-error,
*1*tm-stack-overflow-error,
*1*tm-stack-underflow-error,
*1*tm-address-error,
*1*tm-pc-address-error,
*1*tm-supervisor-mode,
*1*tm-user-mode,
*1*tm-in-supervisor-mode,
*1*tm-wait-state,
*1*tm-run-state,
*1*tm-waiting,
*1*tm-svc,
*1*tm-no-svc,
*1*tm-cleared-svcflag,
*1*tm-iportp,
*1*tm-iinterrupt-flag,
*1*tm-ierror-flag,
*1*tm-ichar,
*1*tm-oportp,
*1*tm-ointerrupt-flag,
*1*tm-obusy-flag,
*1*tm-ochar,
*1*tm-iport-errorp,
*1*tm-clear-input-interrupt,
*1*tm-post-input-interrupt,
*1*tm-oport-idlep,
*1*tm-start-output,
*1*tm-post-output-interrupt,
*1*tm-clear-output-interrupt,
*1*real-addr,
*1*real-addr-source,
*1*real-addr-num,
*1*tm-arg-mode,
*1*tm-arg-datum,
*1*tm-arg-index,
*1*tm-fix-word,
*1*tm-fix-reg-address,
*1*tm-compute-address,
*1*tm-good-address,
*1*tm-incr-address,
*1*tm-incrn-address,
*1*tm-fetch-from-memory,
*1*tm-store-in-memory,
*1*tm-fetch-from-regmem,
*1*tm-store-in-regmem,
*1*tm-fetch,
*1*tm-store,
*1*tm-stack-overflowp,
*1*tm-stack-underflowp,
*1*tm-execute-add,
*1*tm-execute-branch,
*1*tm-execute-branch-on-zero,
*1*tm-execute-branch-not-zero,
*1*tm-execute-call,
*1*tm-execute-compare,
*1*tm-execute-decr,
*1*tm-execute-decr-mod,
*1*tm-execute-incr,
*1*tm-execute-incr-mod,
*1*tm-execute-load-base,
*1*tm-execute-load-limit,
*1*tm-execute-load-psw,
*1*tm-execute-mod,
*1*tm-execute-move,
*1*tm-execute-multiply,
*1*tm-execute-post-output-interrupt,
*1*tm-execute-return,
*1*tm-execute-run,
*1*tm-execute-set-clock,
*1*tm-execute-start-output,
*1*tm-execute-svc,
*1*tm-execute-svc-return,
*1*tm-execute-test-iport,
*1*tm-execute-test-oport,
*1*tm-execute-wait,
*1*tm-opcode-size,
*1*tm-mode-size,
*1*tm-index-size,
*1*tm-opcode-divisor,
*1*tm-mode1-divisor,
*1*tm-index1-divisor,
*1*tm-mode2-divisor,
*1*tm-opcode,
*1*tm-mode1,
*1*tm-index1,
*1*tm-mode2,
*1*tm-index2,
*1*tm-nullary-instructionp,
*1*tm-unary-instructionp,
*1*tm-datum1,
*1*tm-datum2,
*1*tm-arg1,
*1*tm-arg2,
*1*tm-return-opcode,
*1*tm-wait-opcode,
*1*tm-run-opcode,
*1*tm-execute-nullary,
*1*tm-br-opcode,
*1*tm-brnz-opcode,
*1*tm-brz-opcode,
*1*tm-call-opcode,
*1*tm-decr-opcode,
*1*tm-incr-opcode,
*1*tm-lbase-opcode,
*1*tm-llimit-opcode,
*1*tm-lpsw-opcode,
*1*tm-post-opcode,
*1*tm-svc-opcode,
*1*tm-svc-return-opcode,
*1*tm-testi-opcode,
*1*tm-testo-opcode,
*1*tm-time-opcode,
*1*tm-execute-unary,
*1*tm-add-opcode,
*1*tm-compare-opcode,
*1*tm-decr-mod-opcode,
*1*tm-incr-mod-opcode,
*1*tm-mod-opcode,
*1*tm-move-opcode,
*1*tm-mult-opcode,
*1*tm-stout-opcode,
*1*tm-execute-binary,
*1*tm-execute-instruction,
*1*tm-fetch-opcode,
*1*tm-fetch-arg1,
*1*tm-fetch-arg2,
*1*tm-execute,
*1*tm-decrement-clock,
*1*tm-good-pc-address,
*1*tm-fetch-execute,
*1*tm-fetch-new-pc-on-interrupt,
*1*tm-store-old-psw-on-interrupt,
*1*tm-clock-interruptp,
*1*tm-execute-clock-interrupt,
*1*tm-errorp,
*1*tm-execute-error-interrupt,
*1*tm-svc-interruptp,
*1*tm-store-svcid-on-interrupt,
*1*tm-execute-svc-interrupt,
*1*tm-overflow-char,
*1*tm-some-input-interruptp,
*1*tm-input-interruptp,
*1*tm-interrupting-input-port,
*1*tm-store-interrupting-input-device,
*1*tm-execute-input-interrupt,
*1*tm-some-output-interruptp,
*1*tm-output-interruptp,
*1*tm-interrupting-output-port,
*1*tm-store-interrupting-output-device,
*1*tm-execute-output-interrupt,
*1*tm-device-input-eventp,
*1*tm-idevid,
*1*tm-idatum,
*1*tm-device-output-eventp,
*1*tm-odevid,
*1*tm-post-interrupt,
*1*tm-step,
*1*tm-processor.\index{executable-fns}

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-intended-clock-interrupt} \\  
\=\+{\rm{os-intended-clock-interrupt}}\,({\it{tm\/}})\index{os-intended-clock-interrupt} \\ 
$=$$\;\;\;\;${\rm{tm-set-memory}}\,(\=\+{\rm{putnth}}\,(\=\+{\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp}, \\ 
{\tt{'}}{\tt{1}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{2}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-task-table}}\,({\it{tm\/}})\index{os-task-table}, \\ 
{\tt{'}}{\tt{15}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-segment-table}}\,({\it{tm\/}})\index{os-segment-table}, \\ 
{\tt{'}}{\tt{159}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-readyq}}\,({\it{tm\/}})\index{os-readyq}, \\ 
{\tt{'}}{\tt{191}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-code}}\,({\it{tm\/}})\index{os-code}, \\ 
{\tt{'}}{\tt{2547}}, \\ 
{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\-\index{putseg})\-\index{putseg})\-\index{putseg})\-\index{putseg})\-\index{putnth})\-\index{putnth})\-\index{putnth}, \\ 
{\rm{tm-set-pc}}\,(\=\+{\tt{'}}{\tt{2654}}, \\ 
{\rm{tm-set-sp}}\,(\=\+{\tt{'}}{\tt{3310}}, \\ 
{\rm{tm-set-svmode}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{tm-set-error}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-set-rwstate}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\it{tm\/}})\-\index{tm-set-rwstate})\-\index{tm-set-error})\-\index{tm-set-svmode})\-\index{tm-set-sp})\-\index{tm-set-pc})\-\index{tm-set-memory}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equivalence-of-clock-interrupt-expressions \\ \index{equivalence-of-clock-interrupt-e!xpressions}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}))) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-execute-clock-interrupt}}\,({\it{os\/}})\index{tm-execute-clock-interrupt} $=$ {\rm{os-intended-clock-interrupt}}\,({\it{os\/}})\index{os-intended-clock-interrupt})\-
\end{tabbing}


\noindent{\sc Event}:   Disable equivalence-of-clock-interrupt-expressions.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-clock-interrupt-han!dler-thru-save-state} \\  
\=\+{\rm{os-time-for-clock-interrupt-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-clock-interrupt-han!dler-thru-save-state} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-CLOCK-INTERRUPT-HANDLER-THRU-SAVE-STATE
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-R2 OS)
      '13
      (PUTNTH
       (TM-R3 OS)
       '14
       (PUTSEG
              (OS-NEW-TASK-TABLE OS)
              '15
              (PUTSEG (OS-SEGMENT-TABLE OS)
                      '159
                      (PUTSEG (OS-READYQ OS)
                              '191
                              (PUTSEG (OS-CODE OS)
                                      '2547
                                      (PUTNTH '2558
                                              '3309
                                              (PUTNTH '2656
                                                      '3310
                                                      (TM-MEMORY OS))))))))))))
  (PUTNTH '2656
          '0
          (PUTNTH '3310
                  '1
                  (PUTNTH (TM-R2 OS)
                          '2
                          (PUTNTH (TM-R3 OS)
                                  '3
                                  (TM-REGS OS)))))
  (TM-CC-VALUE (TM-ALU-PLUS (PLUS '15
                                  (TIMES '9
                                         (ARRAY-QFIRST (OS-READYQ OS))))
                            '8))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-clock-interrupt-handler-thru-save-state \\ \index{trace-clock-interrupt-handler-t!hru-save-state}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-clock-interrupt}}\,({\it{os\/}})\index{os-intended-clock-interrupt}, \\ 
{\rm{os-time-for-clock-interrupt-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-clock-interrupt-han!dler-thru-save-state})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-clock-interrupt-handler-thru-save-state}}\,({\it{os\/}})\index{os-clock-interrupt-handler-thru!-save-state})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-clock-interrupt-handler-thru-save-state.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-clock-interrupt-han!dler-to-dispatcher} \\  
\=\+{\rm{os-time-for-clock-interrupt-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-clock-interrupt-han!dler-to-dispatcher} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-CLOCK-INTERRUPT-HANDLER-TO-DISPATCHER
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-R2 OS)
      '13
      (PUTNTH
       (TM-R3 OS)
       '14
       (PUTSEG
              (OS-NEW-TASK-TABLE OS)
              '15
              (PUTSEG (OS-SEGMENT-TABLE OS)
                      '159
                      (PUTSEG (ARRAY-ENQ (ARRAY-QFIRST (OS-READYQ OS))
                                         (ARRAY-DEQ (OS-READYQ OS)))
                              '191
                              (PUTSEG (OS-CODE OS)
                                      '2547
                                      (PUTNTH '2558
                                              '3309
                                              (PUTNTH '2665
                                                      '3310
                                                      (TM-MEMORY OS))))))))))))
  (PUTNTH '3206
     '0
     (PUTNTH '3310
             '1
             (PUTNTH (ARRAY-QFIRST (OS-READYQ OS))
                     '2
                     (PUTNTH '191
                             '3
                             (PUTNTH (PLUS '195
                                           (GETNTH '1
                                                   (ARRAY-DEQ (OS-READYQ OS))))
                                     '4
                                     (TM-REGS OS))))))
  (TM-CC-VALUE (TM-ALU-INCR-MOD (GETNTH '1
                                        (ARRAY-DEQ (OS-READYQ OS)))
                                '16))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-clock-interrupt-handler-to-dispatcher \\ \index{trace-clock-interrupt-handler-t!o-dispatcher}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-clock-interrupt-handler-thru-save-state}}\,({\it{os\/}})\index{os-clock-interrupt-handler-thru!-save-state}, \\ 
{\rm{os-time-for-clock-interrupt-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-clock-interrupt-han!dler-to-dispatcher})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-clock-interrupt-handler-to-dispatcher}}\,({\it{os\/}})\index{os-clock-interrupt-handler-to-di!spatcher})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-clock-interrupt-handler-to-dispatcher.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-clock-interrupt-han!dler-to-restore-state} \\  
\=\+{\rm{os-time-for-clock-interrupt-handler-to-restore-state}}\,({\it{os\/}})\index{os-time-for-clock-interrupt-han!dler-to-restore-state} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-CLOCK-INTERRUPT-HANDLER-TO-RESTORE-STATE
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-R2 OS)
      '13
      (PUTNTH
       (TM-R3 OS)
       '14
       (PUTSEG
              (OS-NEW-TASK-TABLE OS)
              '15
              (PUTSEG (OS-SEGMENT-TABLE OS)
                      '159
                      (PUTSEG (ARRAY-ENQ (ARRAY-QFIRST (OS-READYQ OS))
                                         (ARRAY-DEQ (OS-READYQ OS)))
                              '191
                              (PUTSEG (OS-CODE OS)
                                      '2547
                                      (PUTNTH '2558
                                              '3309
                                              (PUTNTH '3217
                                                      '3310
                                                      (TM-MEMORY OS))))))))))))
  (PUTNTH '2601
     '0
     (PUTNTH '3309
             '1
             (PUTNTH (ARRAY-QFIRST (ARRAY-ENQ (ARRAY-QFIRST (OS-READYQ OS))
                                              (ARRAY-DEQ (OS-READYQ OS))))
                     '2
                     (PUTNTH '191
                             '3
                             (PUTNTH (PLUS '195
                                           (GETNTH '1
                                                   (ARRAY-DEQ (OS-READYQ OS))))
                                     '4
                                     (TM-REGS OS))))))
  (TM-CC-VALUE (TM-ALU-PLUS '195
                            (GETNTH '0
                                    (ARRAY-ENQ (ARRAY-QFIRST (OS-READYQ OS))
                                               (ARRAY-DEQ (OS-READYQ OS))))))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-clock-interrupt-handler-to-restore-state \\ \index{trace-clock-interrupt-handler-t!o-restore-state}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-clock-interrupt-handler-to-dispatcher}}\,({\it{os\/}})\index{os-clock-interrupt-handler-to-di!spatcher}, \\ 
{\rm{os-time-for-clock-interrupt-handler-to-restore-state}}\,({\it{os\/}})\index{os-time-for-clock-interrupt-han!dler-to-restore-state})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-clock-interrupt-handler-to-restore-state}}\,({\it{os\/}})\index{os-clock-interrupt-handler-to-re!store-state})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-clock-interrupt-handler-to-restore-state.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-clock-new-readyq} \\  
\=\+{\rm{os-clock-new-readyq}}\,({\it{os\/}})\index{os-clock-new-readyq} \\ 
$=$$\;\;\;\;${\rm{array-enq}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-enq}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-clock-interrupt-han!dler-to-finish} \\  
\=\+{\rm{os-time-for-clock-interrupt-handler-to-finish}}\,({\it{os\/}})\index{os-time-for-clock-interrupt-han!dler-to-finish} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-CLOCK-INTERRUPT-HANDLER
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS)))
           (OS-NEW-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS))))
            (OS-NEW-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS))))
             (OS-NEW-TASK-TABLE OS))
     '2
     (PUTNTH
      (TM-R2 OS)
      '13
      (PUTNTH
       (TM-R3 OS)
       '14
       (PUTSEG
              (OS-NEW-TASK-TABLE OS)
              '15
              (PUTSEG (OS-SEGMENT-TABLE OS)
                      '159
                      (PUTSEG (OS-CLOCK-NEW-READYQ OS)
                              '191
                              (PUTSEG (OS-CODE OS)
                                      '2547
                                      (PUTNTH '2558
                                              '3309
                                              (PUTNTH '3217
                                                      '3310
                                                      (TM-MEMORY OS))))))))))))
  (OS-NEW-REGS (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS))
               OS)
  (OS-NEW-CC (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS))
             OS)
  (OS-NEW-ERROR (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS))
                OS)
  (OS-NEW-SVCFLAG (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS))
                  OS)
  (OS-NEW-SVCID (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS))
                OS)
  (OS-NEW-BASE (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS))
               OS)
  (OS-NEW-LIMIT (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS))
                OS)
  (TM-SLIMIT OS)
  '0
  '0
  '1000
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-clock-interrupt-handler-to-finish \\ \index{trace-clock-interrupt-handler-t!o-finish}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-clock-interrupt-handler-to-restore-state}}\,({\it{os\/}})\index{os-clock-interrupt-handler-to-re!store-state}, \\ 
{\rm{os-time-for-clock-interrupt-handler-to-finish}}\,({\it{os\/}})\index{os-time-for-clock-interrupt-han!dler-to-finish})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-clock-interrupt-handler-to-finish.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-cih-time1} \\  
\=\+{\rm{os-cih-time1}}\,({\it{os\/}})\index{os-cih-time1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-cih-time2} \\  
\=\+{\rm{os-cih-time2}}\,({\it{os\/}})\index{os-cih-time2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-clock-interrupt-han!dler} \\  
\=\+{\rm{os-time-for-clock-interrupt-handler}}\,({\it{os\/}})\index{os-time-for-clock-interrupt-han!dler} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-clock-trace1 \\ \index{rewrite-clock-trace1}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-clock-interrupt}}\,({\it{os\/}})\index{os-intended-clock-interrupt}, \\ 
{\rm{os-time-for-clock-interrupt-handler}}\,({\it{os\/}})\index{os-time-for-clock-interrupt-han!dler})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-clock-interrupt}}\,({\it{os\/}})\index{os-intended-clock-interrupt}, \\ 
{\rm{os-time-for-clock-interrupt-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-clock-interrupt-han!dler-thru-save-state})\-\index{tm-processor}, \\ 
{\rm{os-cih-time1}}\,({\it{os\/}})\index{os-cih-time1})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-clock-trace1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-clock-trace2 \\ \index{rewrite-clock-trace2}
\=\+{\rm{tm-processor}}\,({\rm{os-clock-interrupt-handler-thru-save-state}}\,({\it{os\/}})\index{os-clock-interrupt-handler-thru!-save-state}, {\rm{os-cih-time1}}\,({\it{os\/}})\index{os-cih-time1})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-clock-interrupt-handler-thru-save-state}}\,({\it{os\/}})\index{os-clock-interrupt-handler-thru!-save-state}, \\ 
{\rm{os-time-for-clock-interrupt-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-clock-interrupt-han!dler-to-dispatcher})\-\index{tm-processor}, \\ 
{\rm{os-cih-time2}}\,({\it{os\/}})\index{os-cih-time2})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-clock-trace2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-clock-trace3 \\ \index{rewrite-clock-trace3}
\=\+{\rm{tm-processor}}\,({\rm{os-clock-interrupt-handler-to-dispatcher}}\,({\it{os\/}})\index{os-clock-interrupt-handler-to-di!spatcher}, {\rm{os-cih-time2}}\,({\it{os\/}})\index{os-cih-time2})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-clock-interrupt-handler-to-dispatcher}}\,({\it{os\/}})\index{os-clock-interrupt-handler-to-di!spatcher}, \\ 
{\rm{os-time-for-clock-interrupt-handler-to-restore-state}}\,({\it{os\/}})\index{os-time-for-clock-interrupt-han!dler-to-restore-state})\-\index{tm-processor}, \\ 
{\rm{os-time-for-clock-interrupt-handler-to-finish}}\,({\it{os\/}})\index{os-time-for-clock-interrupt-han!dler-to-finish})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-clock-trace3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-clock-interrupt-handler \\ \index{trace-clock-interrupt-handler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-clock-interrupt}}\,({\it{os\/}})\index{os-intended-clock-interrupt}, \\ 
{\rm{os-time-for-clock-interrupt-handler}}\,({\it{os\/}})\index{os-time-for-clock-interrupt-han!dler})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-intended-error-interrupt} \\  
\=\+{\rm{os-intended-error-interrupt}}\,({\it{tm\/}})\index{os-intended-error-interrupt} \\ 
$=$$\;\;\;\;${\rm{tm-set-memory}}\,(\=\+{\rm{putnth}}\,(\=\+{\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp}, \\ 
{\tt{'}}{\tt{1}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{2}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-task-table}}\,({\it{tm\/}})\index{os-task-table}, \\ 
{\tt{'}}{\tt{15}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-segment-table}}\,({\it{tm\/}})\index{os-segment-table}, \\ 
{\tt{'}}{\tt{159}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-readyq}}\,({\it{tm\/}})\index{os-readyq}, \\ 
{\tt{'}}{\tt{191}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-status-table}}\,({\it{tm\/}})\index{os-status-table}, \\ 
{\tt{'}}{\tt{211}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-code}}\,({\it{tm\/}})\index{os-code}, \\ 
{\tt{'}}{\tt{2547}}, \\ 
{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\-\index{putseg})\-\index{putseg})\-\index{putseg})\-\index{putseg})\-\index{putseg})\-\index{putnth})\-\index{putnth})\-\index{putnth}, \\ 
{\rm{tm-set-pc}}\,(\=\+{\tt{'}}{\tt{2667}}, \\ 
{\rm{tm-set-sp}}\,(\=\+{\tt{'}}{\tt{3310}}, \\ 
{\rm{tm-set-svmode}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{tm-set-error}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-set-rwstate}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\it{tm\/}})\-\index{tm-set-rwstate})\-\index{tm-set-error})\-\index{tm-set-svmode})\-\index{tm-set-sp})\-\index{tm-set-pc})\-\index{tm-set-memory}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equivalence-of-error-interrupt-expressions \\ \index{equivalence-of-error-interrupt-e!xpressions}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-execute-error-interrupt}}\,({\it{os\/}})\index{tm-execute-error-interrupt} $=$ {\rm{os-intended-error-interrupt}}\,({\it{os\/}})\index{os-intended-error-interrupt})\-
\end{tabbing}


\noindent{\sc Event}:   Disable equivalence-of-error-interrupt-expressions.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-error-handler-thru-!save-state} \\  
\=\+{\rm{os-time-for-error-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-error-handler-thru-!save-state} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-ERROR-HANDLER-THRU-SAVE-STATE
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-R2 OS)
      '13
      (PUTNTH
       (TM-R3 OS)
       '14
       (PUTSEG
        (OS-NEW-TASK-TABLE OS)
        '15
        (PUTSEG
             (OS-SEGMENT-TABLE OS)
             '159
             (PUTSEG (OS-READYQ OS)
                     '191
                     (PUTSEG (OS-STATUS-TABLE OS)
                             '211
                             (PUTSEG (OS-CODE OS)
                                     '2547
                                     (PUTNTH '2558
                                             '3309
                                             (PUTNTH '2669
                                                     '3310
                                                     (TM-MEMORY OS)))))))))))))
  (PUTNTH '2669
          '0
          (PUTNTH '3310
                  '1
                  (PUTNTH (TM-R2 OS)
                          '2
                          (PUTNTH (TM-R3 OS)
                                  '3
                                  (TM-REGS OS)))))
  (TM-CC-VALUE (TM-ALU-PLUS (PLUS '15
                                  (TIMES '9
                                         (ARRAY-QFIRST (OS-READYQ OS))))
                            '8))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-error-handler-thru-save-state \\ \index{trace-error-handler-thru-save-st!ate}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-error-interrupt}}\,({\it{os\/}})\index{os-intended-error-interrupt}, \\ 
{\rm{os-time-for-error-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-error-handler-thru-!save-state})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-error-handler-thru-save-state}}\,({\it{os\/}})\index{os-error-handler-thru-save-state})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-error-handler-thru-save-state.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-error-handler-to-di!spatcher} \\  
\=\+{\rm{os-time-for-error-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-error-handler-to-di!spatcher} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-ERROR-HANDLER-TO-DISPATCHER
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-R2 OS)
      '13
      (PUTNTH
       (TM-R3 OS)
       '14
       (PUTSEG
        (OS-NEW-TASK-TABLE OS)
        '15
        (PUTSEG
             (OS-SEGMENT-TABLE OS)
             '159
             (PUTSEG (ARRAY-DEQ (OS-READYQ OS))
                     '191
                     (PUTSEG (OS-UPDATE-STATUS (ARRAY-QFIRST (OS-READYQ OS))
                                               '1
                                               '0
                                               OS)
                             '211
                             (PUTSEG (OS-CODE OS)
                                     '2547
                                     (PUTNTH '2558
                                             '3309
                                             (PUTNTH '2676
                                                     '3310
                                                     (TM-MEMORY OS)))))))))))))
  (PUTNTH '3206
          '0
          (PUTNTH '3310
                  '1
                  (PUTNTH (PLUS '211
                                (TIMES '2
                                       (ARRAY-QFIRST (OS-READYQ OS))))
                          '2
                          (PUTNTH '191 '3 (TM-REGS OS)))))
  (TM-CC-VALUE (TM-ALU-PLUS (TIMES '2
                                   (ARRAY-QFIRST (OS-READYQ OS)))
                            '211))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-error-handler-to-dispatcher \\ \index{trace-error-handler-to-dispatche!r}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-error-handler-thru-save-state}}\,({\it{os\/}})\index{os-error-handler-thru-save-state}, \\ 
{\rm{os-time-for-error-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-error-handler-to-di!spatcher})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-error-handler-to-dispatcher}}\,({\it{os\/}})\index{os-error-handler-to-dispatcher})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-error-handler-to-dispatcher.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-error-handler-to-wait!-state} \\  
\=\+{\rm{os-time-for-error-handler-to-wait-state}}\,({\it{os\/}})\index{os-time-for-error-handler-to-wait!-state} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-ERROR-HANDLER-PATH1
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-R2 OS)
      '13
      (PUTNTH
       (TM-R3 OS)
       '14
       (PUTSEG
        (OS-NEW-TASK-TABLE OS)
        '15
        (PUTSEG
             (OS-SEGMENT-TABLE OS)
             '159
             (PUTSEG (ARRAY-DEQ (OS-READYQ OS))
                     '191
                     (PUTSEG (OS-UPDATE-STATUS (ARRAY-QFIRST (OS-READYQ OS))
                                               '1
                                               '0
                                               OS)
                             '211
                             (PUTSEG (OS-CODE OS)
                                     '2547
                                     (PUTNTH '2558
                                             '3309
                                             (PUTNTH '3211
                                                     '3310
                                                     (TM-MEMORY OS)))))))))))))
  (PUTNTH '3222
          '0
          (PUTNTH '3310
                  '1
                  (PUTNTH (PLUS '211
                                (TIMES '2
                                       (ARRAY-QFIRST (OS-READYQ OS))))
                          '2
                          (PUTNTH '191 '3 (TM-REGS OS)))))
  '1
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '1
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-error-handler-to-wait-state \\ \index{trace-error-handler-to-wait-state}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-error-handler-to-dispatcher}}\,({\it{os\/}})\index{os-error-handler-to-dispatcher}, \\ 
{\rm{os-time-for-error-handler-to-wait-state}}\,({\it{os\/}})\index{os-time-for-error-handler-to-wait!-state})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-error-handler-to-wait-state.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-error-handler-to-re!store-state} \\  
\=\+{\rm{os-time-for-error-handler-to-restore-state}}\,({\it{os\/}})\index{os-time-for-error-handler-to-re!store-state} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-ERROR-HANDLER-TO-RESTORE-STATE
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-R2 OS)
      '13
      (PUTNTH
       (TM-R3 OS)
       '14
       (PUTSEG
        (OS-NEW-TASK-TABLE OS)
        '15
        (PUTSEG
             (OS-SEGMENT-TABLE OS)
             '159
             (PUTSEG (ARRAY-DEQ (OS-READYQ OS))
                     '191
                     (PUTSEG (OS-UPDATE-STATUS (ARRAY-QFIRST (OS-READYQ OS))
                                               '1
                                               '0
                                               OS)
                             '211
                             (PUTSEG (OS-CODE OS)
                                     '2547
                                     (PUTNTH '2558
                                             '3309
                                             (PUTNTH '3217
                                                     '3310
                                                     (TM-MEMORY OS)))))))))))))
  (PUTNTH '2601
          '0
          (PUTNTH '3309
                  '1
                  (PUTNTH (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                          '2
                          (PUTNTH '191 '3 (TM-REGS OS)))))
  (TM-CC-VALUE (TM-ALU-PLUS '195
                            (GETNTH '0
                                    (ARRAY-DEQ (OS-READYQ OS)))))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-error-handler-to-restore-state \\ \index{trace-error-handler-to-restore-!state}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-error-handler-to-dispatcher}}\,({\it{os\/}})\index{os-error-handler-to-dispatcher}, \\ 
{\rm{os-time-for-error-handler-to-restore-state}}\,({\it{os\/}})\index{os-time-for-error-handler-to-re!store-state})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-error-handler-to-restore-state}}\,({\it{os\/}})\index{os-error-handler-to-restore-state})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-error-handler-to-restore-state.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-error-handler-to-fi!nish} \\  
\=\+{\rm{os-time-for-error-handler-to-finish}}\,({\it{os\/}})\index{os-time-for-error-handler-to-fi!nish} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-ERROR-HANDLER-PATH2
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS))))
           (OS-NEW-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))))
            (OS-NEW-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))))
             (OS-NEW-TASK-TABLE OS))
     '2
     (PUTNTH
      (TM-R2 OS)
      '13
      (PUTNTH
       (TM-R3 OS)
       '14
       (PUTSEG
        (OS-NEW-TASK-TABLE OS)
        '15
        (PUTSEG
             (OS-SEGMENT-TABLE OS)
             '159
             (PUTSEG (ARRAY-DEQ (OS-READYQ OS))
                     '191
                     (PUTSEG (OS-UPDATE-STATUS (ARRAY-QFIRST (OS-READYQ OS))
                                               '1
                                               '0
                                               OS)
                             '211
                             (PUTSEG (OS-CODE OS)
                                     '2547
                                     (PUTNTH '2558
                                             '3309
                                             (PUTNTH '3217
                                                     '3310
                                                     (TM-MEMORY OS)))))))))))))
  (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
               OS)
  (OS-NEW-CC (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
             OS)
  (OS-NEW-ERROR (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                OS)
  (OS-NEW-SVCFLAG (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                  OS)
  (OS-NEW-SVCID (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                OS)
  (OS-NEW-BASE (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
               OS)
  (OS-NEW-LIMIT (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                OS)
  (TM-SLIMIT OS)
  '0
  '0
  '1000
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-error-handler-to-finish \\ \index{trace-error-handler-to-finish}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-error-handler-to-restore-state}}\,({\it{os\/}})\index{os-error-handler-to-restore-state}, \\ 
{\rm{os-time-for-error-handler-to-finish}}\,({\it{os\/}})\index{os-time-for-error-handler-to-fi!nish})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-error-handler-to-finish.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-error-time1} \\  
\=\+{\rm{os-error-time1}}\,({\it{os\/}})\index{os-error-time1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-error-handler-path1} \\  
\=\+{\rm{os-time-for-error-handler-path1}}\,({\it{os\/}})\index{os-time-for-error-handler-path1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-error-trace1 \\ \index{rewrite-error-trace1}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-error-interrupt}}\,({\it{os\/}})\index{os-intended-error-interrupt}, \\ 
{\rm{os-time-for-error-handler-path1}}\,({\it{os\/}})\index{os-time-for-error-handler-path1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-error-interrupt}}\,({\it{os\/}})\index{os-intended-error-interrupt}, \\ 
{\rm{os-time-for-error-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-error-handler-thru-!save-state})\-\index{tm-processor}, \\ 
{\rm{os-error-time1}}\,({\it{os\/}})\index{os-error-time1})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-error-trace1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-error-trace2 \\ \index{rewrite-error-trace2}
\=\+{\rm{tm-processor}}\,({\rm{os-error-handler-thru-save-state}}\,({\it{os\/}})\index{os-error-handler-thru-save-state}, {\rm{os-error-time1}}\,({\it{os\/}})\index{os-error-time1})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-error-handler-thru-save-state}}\,({\it{os\/}})\index{os-error-handler-thru-save-state}, \\ 
{\rm{os-time-for-error-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-error-handler-to-di!spatcher})\-\index{tm-processor}, \\ 
{\rm{os-time-for-error-handler-to-wait-state}}\,({\it{os\/}})\index{os-time-for-error-handler-to-wait!-state})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-error-trace2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-error-handler-path1 \\ \index{trace-error-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-error-interrupt}}\,({\it{os\/}})\index{os-intended-error-interrupt}, \\ 
{\rm{os-time-for-error-handler-path1}}\,({\it{os\/}})\index{os-time-for-error-handler-path1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-error-time2} \\  
\=\+{\rm{os-error-time2}}\,({\it{os\/}})\index{os-error-time2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-error-time3} \\  
\=\+{\rm{os-error-time3}}\,({\it{os\/}})\index{os-error-time3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-error-handler-path2} \\  
\=\+{\rm{os-time-for-error-handler-path2}}\,({\it{os\/}})\index{os-time-for-error-handler-path2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-error-trace3 \\ \index{rewrite-error-trace3}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-error-interrupt}}\,({\it{os\/}})\index{os-intended-error-interrupt}, \\ 
{\rm{os-time-for-error-handler-path2}}\,({\it{os\/}})\index{os-time-for-error-handler-path2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-error-interrupt}}\,({\it{os\/}})\index{os-intended-error-interrupt}, \\ 
{\rm{os-time-for-error-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-error-handler-thru-!save-state})\-\index{tm-processor}, \\ 
{\rm{os-error-time2}}\,({\it{os\/}})\index{os-error-time2})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-error-trace3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-error-trace4 \\ \index{rewrite-error-trace4}
\=\+{\rm{tm-processor}}\,({\rm{os-error-handler-thru-save-state}}\,({\it{os\/}})\index{os-error-handler-thru-save-state}, {\rm{os-error-time2}}\,({\it{os\/}})\index{os-error-time2})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-error-handler-thru-save-state}}\,({\it{os\/}})\index{os-error-handler-thru-save-state}, \\ 
{\rm{os-time-for-error-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-error-handler-to-di!spatcher})\-\index{tm-processor}, \\ 
{\rm{os-error-time3}}\,({\it{os\/}})\index{os-error-time3})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-error-trace4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-error-trace5 \\ \index{rewrite-error-trace5}
\=\+{\rm{tm-processor}}\,({\rm{os-error-handler-to-dispatcher}}\,({\it{os\/}})\index{os-error-handler-to-dispatcher}, {\rm{os-error-time3}}\,({\it{os\/}})\index{os-error-time3})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-error-handler-to-dispatcher}}\,({\it{os\/}})\index{os-error-handler-to-dispatcher}, \\ 
{\rm{os-time-for-error-handler-to-restore-state}}\,({\it{os\/}})\index{os-time-for-error-handler-to-re!store-state})\-\index{tm-processor}, \\ 
{\rm{os-time-for-error-handler-to-finish}}\,({\it{os\/}})\index{os-time-for-error-handler-to-fi!nish})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-error-trace5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-error-handler-path2 \\ \index{trace-error-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-error-interrupt}}\,({\it{os\/}})\index{os-intended-error-interrupt}, \\ 
{\rm{os-time-for-error-handler-path2}}\,({\it{os\/}})\index{os-time-for-error-handler-path2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-error-handler} \\  
\=\+{\rm{os-time-for-error-handler}}\,({\it{os\/}})\index{os-time-for-error-handler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp} \\ 
{\bf then }{\rm{os-time-for-error-handler-path1}}\,({\it{os\/}})\index{os-time-for-error-handler-path1} \\ 
{\bf else }{\rm{os-time-for-error-handler-path2}}\,({\it{os\/}})\index{os-time-for-error-handler-path2}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-error-handler} \\  
\=\+{\rm{os-error-handler}}\,({\it{os\/}})\index{os-error-handler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp} \\ 
{\bf then }{\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1} \\ 
{\bf else }{\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  trace-os-error-handler \\ \index{trace-os-error-handler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-error-interrupt}}\,({\it{os\/}})\index{os-intended-error-interrupt}, \\ 
{\rm{os-time-for-error-handler}}\,({\it{os\/}})\index{os-time-for-error-handler})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-error-handler}}\,({\it{os\/}})\index{os-error-handler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-os-error-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-intended-svc-send-interrupt} \\  
\=\+{\rm{os-intended-svc-send-interrupt}}\,({\it{tm\/}})\index{os-intended-svc-send-interrupt} \\ 
$=$$\;\;\;\;${\rm{tm-set-memory}}\,(\=\+{\rm{putnth}}\,(\=\+{\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp}, \\ 
{\tt{'}}{\tt{1}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{2}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-task-table}}\,({\it{tm\/}})\index{os-task-table}, \\ 
{\tt{'}}{\tt{15}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-segment-table}}\,({\it{tm\/}})\index{os-segment-table}, \\ 
{\tt{'}}{\tt{159}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-readyq}}\,({\it{tm\/}})\index{os-readyq}, \\ 
{\tt{'}}{\tt{191}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-status-table}}\,({\it{tm\/}})\index{os-status-table}, \\ 
{\tt{'}}{\tt{211}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-mbuffers}}\,({\it{tm\/}})\index{os-mbuffers}, \\ 
{\tt{'}}{\tt{499}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-code}}\,({\it{tm\/}})\index{os-code}, \\ 
{\tt{'}}{\tt{2547}}, \\ 
{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\-\index{putseg})\-\index{putseg})\-\index{putseg})\-\index{putseg})\-\index{putseg})\-\index{putseg})\-\index{putnth})\-\index{putnth})\-\index{putnth})\-\index{putnth}, \\ 
{\rm{tm-set-pc}}\,(\=\+{\tt{'}}{\tt{2690}}, \\ 
{\rm{tm-set-sp}}\,(\=\+{\tt{'}}{\tt{3310}}, \\ 
{\rm{tm-set-svmode}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{tm-set-error}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-set-rwstate}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\it{tm\/}})\-\index{tm-set-rwstate})\-\index{tm-set-error})\-\index{tm-set-svmode})\-\index{tm-set-sp})\-\index{tm-set-pc})\-\index{tm-set-memory}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equivalence-of-svc-send-interrupt-expressions \\ \index{equivalence-of-svc-send-interrupt!-expressions}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}))) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-execute-svc-interrupt}}\,({\it{os\/}})\index{tm-execute-svc-interrupt} $=$ {\rm{os-intended-svc-send-interrupt}}\,({\it{os\/}})\index{os-intended-svc-send-interrupt})\-
\end{tabbing}


\noindent{\sc Event}:   Disable equivalence-of-svc-send-interrupt-expressions.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-send-handler-th!ru-save-state} \\  
\=\+{\rm{os-time-for-svc-send-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-th!ru-save-state} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-SEND-HANDLER-THRU-SAVE-STATE
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-SVCID OS)
      '8
      (PUTNTH
       (TM-R2 OS)
       '13
       (PUTNTH
        (TM-R3 OS)
        '14
        (PUTSEG
         (OS-NEW-TASK-TABLE OS)
         '15
         (PUTSEG
          (OS-SEGMENT-TABLE OS)
          '159
          (PUTSEG
           (OS-READYQ OS)
           '191
           (PUTSEG (OS-STATUS-TABLE OS)
                   '211
                   (PUTSEG (OS-MBUFFERS OS)
                           '499
                           (PUTSEG (OS-CODE OS)
                                   '2547
                                   (PUTNTH '2558
                                           '3309
                                           (PUTNTH '2692
                                                   '3310
                                                   (TM-MEMORY OS)))))))))))))))
  (PUTNTH '2692
          '0
          (PUTNTH '3310
                  '1
                  (PUTNTH (TM-R2 OS)
                          '2
                          (PUTNTH (TM-R3 OS)
                                  '3
                                  (TM-REGS OS)))))
  (TM-CC-VALUE (TM-ALU-PLUS (PLUS '15
                                  (TIMES '9
                                         (ARRAY-QFIRST (OS-READYQ OS))))
                            '8))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-send-handler-thru-save-state \\ \index{trace-svc-send-handler-thru-save!-state}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-send-interrupt}}\,({\it{os\/}})\index{os-intended-svc-send-interrupt}, \\ 
{\rm{os-time-for-svc-send-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-th!ru-save-state})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-send-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-send-handler-thru-save-st!ate})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-send-handler-thru-save-state.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-send-handler-to!-qfullp-test} \\  
\=\+{\rm{os-time-for-svc-send-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-qfullp-test} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-SEND-HANDLER-TO-QFULLP-TEST
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '0
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-MBUFFERS OS)
                          '499
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '2726
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '2747
    '0
    (PUTNTH '3310
            '1
            (PUTNTH (ARRAY-QFIRST (OS-READYQ OS))
                    '2
                    (PUTNTH (PLUS '499
                                  (PLUS (TIMES '8
                                               (REMAINDER (TM-R2 OS) '16))
                                        (TIMES '128
                                               (ARRAY-QFIRST (OS-READYQ OS)))))
                            '3
                            (PUTNTH (TIMES '8
                                           (REMAINDER (TM-R2 OS) '16))
                                    '4
                                    (PUTNTH (REMAINDER (TM-R2 OS) '16)
                                            '6
                                            (PUTNTH (TM-R3 OS)
                                                    '7
                                                    (TM-REGS OS))))))))
  (TM-CC-VALUE (TM-ALU-PLUS (PLUS (TIMES '8
                                         (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                    '16))
                                  (TIMES '128
                                         (ARRAY-QFIRST (OS-READYQ OS))))
                            '499))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-send-handler-to-qfullp-test \\ \index{trace-svc-send-handler-to-qfullp!-test}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-send-handler-thru-save-st!ate}, \\ 
{\rm{os-time-for-svc-send-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-qfullp-test})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-send-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-send-handler-to-qfullp-te!st})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-send-handler-to-qfullp-test.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-send-handler-to!-dispatcher} \\  
\=\+{\rm{os-time-for-svc-send-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-dispatcher} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-SEND-HANDLER-TO-DISPATCHER
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '0
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-DEQ (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (ARRAY-QFIRST (OS-READYQ OS))
                                    '2
                                    (OS-DESTID OS '16)
                                    OS)
                  '211
                  (PUTSEG (OS-MBUFFERS OS)
                          '499
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '2796
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3206
   '0
   (PUTNTH '3310
           '1
           (PUTNTH (ARRAY-QFIRST (OS-READYQ OS))
                   '2
                   (PUTNTH (PLUS '211
                                 (TIMES '2
                                        (ARRAY-QFIRST (OS-READYQ OS))))
                           '3
                           (PUTNTH (TIMES '8
                                          (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                     '16))
                                   '4
                                   (PUTNTH (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                      '16)
                                           '6
                                           (PUTNTH (GETNTH '3 (TM-REGS OS))
                                                   '7
                                                   (TM-REGS OS))))))))
  (TM-CC-VALUE (TM-ALU-PLUS (TIMES '2
                                   (ARRAY-QFIRST (OS-READYQ OS)))
                            '211))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-send-handler-to-dispatcher \\ \index{trace-svc-send-handler-to-dispat!cher}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-send-handler-to-qfullp-te!st}, \\ 
{\rm{os-time-for-svc-send-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-dispatcher})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-send-handler-to-dispatcher}}\,({\it{os\/}})\index{os-svc-send-handler-to-dispatche!r})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-send-handler-to-dispatcher.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-send-handler-to!-wait-state} \\  
\=\+{\rm{os-time-for-svc-send-handler-to-wait-state}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-wait-state} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-SEND-HANDLER-PATH1
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '0
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-DEQ (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (ARRAY-QFIRST (OS-READYQ OS))
                                    '2
                                    (OS-DESTID OS '16)
                                    OS)
                  '211
                  (PUTSEG (OS-MBUFFERS OS)
                          '499
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3211
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3222
   '0
   (PUTNTH '3310
           '1
           (PUTNTH (ARRAY-QFIRST (OS-READYQ OS))
                   '2
                   (PUTNTH '191
                           '3
                           (PUTNTH (TIMES '8
                                          (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                     '16))
                                   '4
                                   (PUTNTH (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                      '16)
                                           '6
                                           (PUTNTH (GETNTH '3 (TM-REGS OS))
                                                   '7
                                                   (TM-REGS OS))))))))
  '1
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '1
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-send-handler-to-wait-state \\ \index{trace-svc-send-handler-to-wait-!state}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-to-dispatcher}}\,({\it{os\/}})\index{os-svc-send-handler-to-dispatche!r}, \\ 
{\rm{os-time-for-svc-send-handler-to-wait-state}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-wait-state})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-send-handler-to-wait-state.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-send-handler-to!-lpsw} \\  
\=\+{\rm{os-time-for-svc-send-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-lpsw} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-SEND-HANDLER-PATH2
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS))))
           (OS-NEW-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))))
            (OS-NEW-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))))
             (OS-NEW-TASK-TABLE OS))
     '2
     (PUTNTH '0
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-DEQ (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (ARRAY-QFIRST (OS-READYQ OS))
                                    '2
                                    (OS-DESTID OS '16)
                                    OS)
                  '211
                  (PUTSEG (OS-MBUFFERS OS)
                          '499
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3217
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
               OS)
  (OS-NEW-CC (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
             OS)
  (OS-NEW-ERROR (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                OS)
  (OS-NEW-SVCFLAG (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                  OS)
  (OS-NEW-SVCID (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                OS)
  (OS-NEW-BASE (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
               OS)
  (OS-NEW-LIMIT (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                OS)
  (TM-SLIMIT OS)
  '0
  '0
  '1000
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-send-handler-to-lpsw \\ \index{trace-svc-send-handler-to-lpsw}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-to-dispatcher}}\,({\it{os\/}})\index{os-svc-send-handler-to-dispatche!r}, \\ 
{\rm{os-time-for-svc-send-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-lpsw})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-send-handler-to-lpsw.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-send-handler-th!ru-enqueue} \\  
\=\+{\rm{os-time-for-svc-send-handler-thru-enqueue}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-th!ru-enqueue} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-SEND-HANDLER-THRU-ENQUEUE
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '0
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-MBUFFERS-WITH-ENQUEUED-MESSAGE OS)
                          '499
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '2756
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '2756
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (TM-R3 OS)
     '2
     (PUTNTH
      (PLUS '499
            (PLUS (TIMES '8
                         (REMAINDER (GETNTH '2 (TM-REGS OS))
                                    '16))
                  (TIMES '128
                         (ARRAY-QFIRST (OS-READYQ OS)))))
      '3
      (PUTNTH
        (PLUS '503
              (PLUS (PLUS (TIMES '8
                                 (REMAINDER (GETNTH '2 (TM-REGS OS))
                                            '16))
                          (TIMES '128
                                 (ARRAY-QFIRST (OS-READYQ OS))))
                    (GETNTH '1
                            (GETNTH (PLUS (TIMES '16
                                                 (ARRAY-QFIRST (OS-READYQ OS)))
                                          (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                     '16))
                                    (TABLE '8 (OS-MBUFFERS OS))))))
        '4
        (PUTNTH (REMAINDER (TM-R2 OS) '16)
                '6
                (PUTNTH (TM-R3 OS)
                        '7
                        (TM-REGS OS))))))))
  (TM-CC-VALUE
   (TM-ALU-INCR-MOD (GETNTH '1
                            (GETNTH (PLUS (TIMES '16
                                                 (ARRAY-QFIRST (OS-READYQ OS)))
                                          (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                     '16))
                                    (TABLE '8 (OS-MBUFFERS OS))))
                    (GETNTH '3
                            (GETNTH (PLUS (TIMES '16
                                                 (ARRAY-QFIRST (OS-READYQ OS)))
                                          (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                     '16))
                                    (TABLE '8 (OS-MBUFFERS OS))))))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-send-handler-thru-enqueue \\ \index{trace-svc-send-handler-thru-enq!ueue}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp}))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-send-handler-to-qfullp-te!st}, \\ 
{\rm{os-time-for-svc-send-handler-thru-enqueue}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-th!ru-enqueue})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-send-handler-thru-enqueue}}\,({\it{os\/}})\index{os-svc-send-handler-thru-enqueue})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-send-handler-thru-enqueue.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-send-handler-to!-svc-resume-task1} \\  
\=\+{\rm{os-time-for-svc-send-handler-to-svc-resume-task1}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-svc-resume-task1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-SEND-HANDLER-TO-SVC-RESUME-TASK1
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '0
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-ENQ (OS-DESTID OS '16)
                       (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (OS-DESTID OS '16)
                                    '0
                                    '0
                                    OS)
                  '211
                  (PUTSEG (OS-MBUFFERS-WITH-ENQUEUED-MESSAGE OS)
                          '499
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '2789
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3222
   '0
   (PUTNTH '3310
           '1
           (PUTNTH (REMAINDER (GETNTH '2 (TM-REGS OS))
                              '16)
                   '2
                   (PUTNTH '191
                           '3
                           (PUTNTH (PLUS '195
                                         (GETNTH '1 (OS-READYQ OS)))
                                   '4
                                   (PUTNTH (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                      '16)
                                           '6
                                           (PUTNTH (GETNTH '3 (TM-REGS OS))
                                                   '7
                                                   (TM-REGS OS))))))))
  (TM-CC-VALUE (TM-ALU-INCR-MOD (GETNTH '1 (OS-READYQ OS))
                                '16))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-send-handler-to-svc-resume-task1 \\ \index{trace-svc-send-handler-to-svc-re!sume-task1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{3}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}} $+$ ({\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}), \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-thru-enqueue}}\,({\it{os\/}})\index{os-svc-send-handler-thru-enqueue}, \\ 
{\rm{os-time-for-svc-send-handler-to-svc-resume-task1}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-svc-resume-task1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-send-handler-to-svc-resume-task1}}\,({\it{os\/}})\index{os-svc-send-handler-to-svc-resu!me-task1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-send-handler-to-svc-resume-task1.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-send-handler-to!-svc-resume-task2} \\  
\=\+{\rm{os-time-for-svc-send-handler-to-svc-resume-task2}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-svc-resume-task2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-SEND-HANDLER-TO-SVC-RESUME-TASK2
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '0
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-MBUFFERS-WITH-ENQUEUED-MESSAGE OS)
                          '499
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '2756
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3222
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (TM-R3 OS)
     '2
     (PUTNTH
      (PLUS '211
            (TIMES '2 (OS-DESTID OS '16)))
      '3
      (PUTNTH
        (PLUS '503
              (PLUS (PLUS (TIMES '8
                                 (REMAINDER (GETNTH '2 (TM-REGS OS))
                                            '16))
                          (TIMES '128
                                 (ARRAY-QFIRST (OS-READYQ OS))))
                    (GETNTH '1
                            (GETNTH (PLUS (TIMES '16
                                                 (ARRAY-QFIRST (OS-READYQ OS)))
                                          (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                     '16))
                                    (TABLE '8 (OS-MBUFFERS OS))))))
        '4
        (PUTNTH (REMAINDER (GETNTH '2 (TM-REGS OS))
                           '16)
                '6
                (PUTNTH (GETNTH '3 (TM-REGS OS))
                        '7
                        (TM-REGS OS))))))))
  (TM-CC-VALUE
         (TM-ALU-DIFFERENCE (GETNTH (TIMES '2
                                           (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                      '16))
                                    (OS-STATUS-TABLE OS))
                            '3))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-send-handler-to-svc-resume-task2 \\ \index{trace-svc-send-handler-to-svc-re!sume-task2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{3}})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-thru-enqueue}}\,({\it{os\/}})\index{os-svc-send-handler-thru-enqueue}, \\ 
{\rm{os-time-for-svc-send-handler-to-svc-resume-task2}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-svc-resume-task2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-send-handler-to-svc-resume-task2}}\,({\it{os\/}})\index{os-svc-send-handler-to-svc-resu!me-task2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-send-handler-to-svc-resume-task2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-send-handler-to!-svc-resume-task3} \\  
\=\+{\rm{os-time-for-svc-send-handler-to-svc-resume-task3}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-svc-resume-task3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-SEND-HANDLER-TO-SVC-RESUME-TASK3
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '0
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-MBUFFERS-WITH-ENQUEUED-MESSAGE OS)
                          '499
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '2756
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3222
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (TM-R3 OS)
     '2
     (PUTNTH
      (PLUS '211
            (TIMES '2 (OS-DESTID OS '16)))
      '3
      (PUTNTH
        (PLUS '503
              (PLUS (PLUS (TIMES '8
                                 (REMAINDER (GETNTH '2 (TM-REGS OS))
                                            '16))
                          (TIMES '128
                                 (ARRAY-QFIRST (OS-READYQ OS))))
                    (GETNTH '1
                            (GETNTH (PLUS (TIMES '16
                                                 (ARRAY-QFIRST (OS-READYQ OS)))
                                          (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                     '16))
                                    (TABLE '8 (OS-MBUFFERS OS))))))
        '4
        (PUTNTH (REMAINDER (GETNTH '2 (TM-REGS OS))
                           '16)
                '6
                (PUTNTH (GETNTH '3 (TM-REGS OS))
                        '7
                        (TM-REGS OS))))))))
  (TM-CC-VALUE
   (TM-ALU-DIFFERENCE (GETNTH (PLUS '1
                                    (TIMES '2
                                           (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                      '16)))
                              (OS-STATUS-TABLE OS))
                      (ARRAY-QFIRST (OS-READYQ OS))))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-send-handler-to-svc-resume-task3 \\ \index{trace-svc-send-handler-to-svc-re!sume-task3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{3}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}} $+$ ({\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}), \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-thru-enqueue}}\,({\it{os\/}})\index{os-svc-send-handler-thru-enqueue}, \\ 
{\rm{os-time-for-svc-send-handler-to-svc-resume-task3}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-svc-resume-task3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-send-handler-to-svc-resume-task3}}\,({\it{os\/}})\index{os-svc-send-handler-to-svc-resu!me-task3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-send-handler-to-svc-resume-task3.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-send-handler-to!-svcr} \\  
\=\+{\rm{os-time-for-svc-send-handler-to-svcr}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-svcr} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-SEND-HANDLER-PATH3
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (OS-READYQ OS)))
           (OS-NEW-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (OS-READYQ OS))))
            (OS-NEW-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (OS-READYQ OS))))
             (OS-NEW-TASK-TABLE OS))
     '2
     (PUTNTH '0
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-ENQ (OS-DESTID OS '16)
                       (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (OS-DESTID OS '16)
                                    '0
                                    '0
                                    OS)
                  '211
                  (PUTSEG (OS-MBUFFERS-WITH-ENQUEUED-MESSAGE OS)
                          '499
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3229
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (TM-REGS OS)
  (TM-CC OS)
  (TM-ERROR OS)
  '0
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-send-handler-to-svcr1 \\ \index{trace-svc-send-handler-to-svcr1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{3}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}} $+$ ({\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}), \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-to-svc-resume-task1}}\,({\it{os\/}})\index{os-svc-send-handler-to-svc-resu!me-task1}, \\ 
{\rm{os-time-for-svc-send-handler-to-svcr}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-svcr})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-send-handler-to-svcr1.

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN
 OS-SVC-SEND-HANDLER-PATH4
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (OS-READYQ OS)))
           (OS-NEW-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (OS-READYQ OS))))
            (OS-NEW-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (OS-READYQ OS))))
             (OS-NEW-TASK-TABLE OS))
     '2
     (PUTNTH '0
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-MBUFFERS-WITH-ENQUEUED-MESSAGE OS)
                          '499
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3229
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (TM-REGS OS)
  (TM-CC OS)
  (TM-ERROR OS)
  '0
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-send-handler-to-svcr2 \\ \index{trace-svc-send-handler-to-svcr2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-to-svc-resume-task2}}\,({\it{os\/}})\index{os-svc-send-handler-to-svc-resu!me-task2}, \\ 
{\rm{os-time-for-svc-send-handler-to-svcr}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-svcr})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-send-handler-to-svcr2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-svc-send-handler-to-svcr3 \\ \index{trace-svc-send-handler-to-svcr3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-to-svc-resume-task3}}\,({\it{os\/}})\index{os-svc-send-handler-to-svc-resu!me-task3}, \\ 
{\rm{os-time-for-svc-send-handler-to-svcr}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-svcr})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-send-handler-to-svcr3.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-svc-send-time1} \\  
\=\+{\rm{os-svc-send-time1}}\,({\it{os\/}})\index{os-svc-send-time1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-send-time2} \\  
\=\+{\rm{os-svc-send-time2}}\,({\it{os\/}})\index{os-svc-send-time2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-send-handler-pat!h1} \\  
\=\+{\rm{os-time-for-svc-send-handler-path1}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-send-trace1 \\ \index{rewrite-svc-send-trace1}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-send-interrupt}}\,({\it{os\/}})\index{os-intended-svc-send-interrupt}, \\ 
{\rm{os-time-for-svc-send-handler-path1}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-send-interrupt}}\,({\it{os\/}})\index{os-intended-svc-send-interrupt}, \\ 
{\rm{os-time-for-svc-send-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-th!ru-save-state})\-\index{tm-processor}, \\ 
{\rm{os-svc-send-time1}}\,({\it{os\/}})\index{os-svc-send-time1})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-send-trace1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-send-trace2 \\ \index{rewrite-svc-send-trace2}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-send-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-send-handler-thru-save-st!ate}, {\rm{os-svc-send-time1}}\,({\it{os\/}})\index{os-svc-send-time1})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-send-handler-thru-save-st!ate}, \\ 
{\rm{os-time-for-svc-send-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-qfullp-test})\-\index{tm-processor}, \\ 
{\rm{os-svc-send-time2}}\,({\it{os\/}})\index{os-svc-send-time2})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-send-trace2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-send-trace3 \\ \index{rewrite-svc-send-trace3}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-send-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-send-handler-to-qfullp-te!st}, {\rm{os-svc-send-time2}}\,({\it{os\/}})\index{os-svc-send-time2})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-send-handler-to-qfullp-te!st}, \\ 
{\rm{os-time-for-svc-send-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-dispatcher})\-\index{tm-processor}, \\ 
{\rm{os-time-for-svc-send-handler-to-wait-state}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-wait-state})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-send-trace3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-svc-send-handler-path1 \\ \index{trace-svc-send-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-send-interrupt}}\,({\it{os\/}})\index{os-intended-svc-send-interrupt}, \\ 
{\rm{os-time-for-svc-send-handler-path1}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-svc-send-time3} \\  
\=\+{\rm{os-svc-send-time3}}\,({\it{os\/}})\index{os-svc-send-time3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-send-time4} \\  
\=\+{\rm{os-svc-send-time4}}\,({\it{os\/}})\index{os-svc-send-time4} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-send-handler-pat!h2} \\  
\=\+{\rm{os-time-for-svc-send-handler-path2}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-send-trace4 \\ \index{rewrite-svc-send-trace4}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-send-interrupt}}\,({\it{os\/}})\index{os-intended-svc-send-interrupt}, \\ 
{\rm{os-time-for-svc-send-handler-path2}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-send-interrupt}}\,({\it{os\/}})\index{os-intended-svc-send-interrupt}, \\ 
{\rm{os-time-for-svc-send-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-th!ru-save-state})\-\index{tm-processor}, \\ 
{\rm{os-svc-send-time3}}\,({\it{os\/}})\index{os-svc-send-time3})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-send-trace4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-send-trace5 \\ \index{rewrite-svc-send-trace5}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-send-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-send-handler-thru-save-st!ate}, {\rm{os-svc-send-time3}}\,({\it{os\/}})\index{os-svc-send-time3})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-send-handler-thru-save-st!ate}, \\ 
{\rm{os-time-for-svc-send-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-qfullp-test})\-\index{tm-processor}, \\ 
{\rm{os-svc-send-time4}}\,({\it{os\/}})\index{os-svc-send-time4})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-send-trace5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-send-trace6 \\ \index{rewrite-svc-send-trace6}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-send-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-send-handler-to-qfullp-te!st}, {\rm{os-svc-send-time4}}\,({\it{os\/}})\index{os-svc-send-time4})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-send-handler-to-qfullp-te!st}, \\ 
{\rm{os-time-for-svc-send-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-dispatcher})\-\index{tm-processor}, \\ 
{\rm{os-time-for-svc-send-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-lpsw})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-send-trace6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-svc-send-handler-path2 \\ \index{trace-svc-send-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-send-interrupt}}\,({\it{os\/}})\index{os-intended-svc-send-interrupt}, \\ 
{\rm{os-time-for-svc-send-handler-path2}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-svc-send-time5} \\  
\=\+{\rm{os-svc-send-time5}}\,({\it{os\/}})\index{os-svc-send-time5} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-send-time6} \\  
\=\+{\rm{os-svc-send-time6}}\,({\it{os\/}})\index{os-svc-send-time6} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-send-time7} \\  
\=\+{\rm{os-svc-send-time7}}\,({\it{os\/}})\index{os-svc-send-time7} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-send-handler-pat!h3} \\  
\=\+{\rm{os-time-for-svc-send-handler-path3}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-send-trace7 \\ \index{rewrite-svc-send-trace7}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-send-interrupt}}\,({\it{os\/}})\index{os-intended-svc-send-interrupt}, \\ 
{\rm{os-time-for-svc-send-handler-path3}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-send-interrupt}}\,({\it{os\/}})\index{os-intended-svc-send-interrupt}, \\ 
{\rm{os-time-for-svc-send-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-th!ru-save-state})\-\index{tm-processor}, \\ 
{\rm{os-svc-send-time5}}\,({\it{os\/}})\index{os-svc-send-time5})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-send-trace7.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-send-trace8 \\ \index{rewrite-svc-send-trace8}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-send-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-send-handler-thru-save-st!ate}, {\rm{os-svc-send-time5}}\,({\it{os\/}})\index{os-svc-send-time5})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-send-handler-thru-save-st!ate}, \\ 
{\rm{os-time-for-svc-send-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-qfullp-test})\-\index{tm-processor}, \\ 
{\rm{os-svc-send-time6}}\,({\it{os\/}})\index{os-svc-send-time6})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-send-trace8.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-send-trace9 \\ \index{rewrite-svc-send-trace9}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-send-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-send-handler-to-qfullp-te!st}, {\rm{os-svc-send-time6}}\,({\it{os\/}})\index{os-svc-send-time6})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-send-handler-to-qfullp-te!st}, \\ 
{\rm{os-time-for-svc-send-handler-thru-enqueue}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-th!ru-enqueue})\-\index{tm-processor}, \\ 
{\rm{os-svc-send-time7}}\,({\it{os\/}})\index{os-svc-send-time7})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-send-trace9.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-send-trace10 \\ \index{rewrite-svc-send-trace10}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-send-handler-thru-enqueue}}\,({\it{os\/}})\index{os-svc-send-handler-thru-enqueue}, {\rm{os-svc-send-time7}}\,({\it{os\/}})\index{os-svc-send-time7})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-thru-enqueue}}\,({\it{os\/}})\index{os-svc-send-handler-thru-enqueue}, \\ 
{\rm{os-time-for-svc-send-handler-to-svc-resume-task1}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-svc-resume-task1})\-\index{tm-processor}, \\ 
{\rm{os-time-for-svc-send-handler-to-svcr}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-svcr})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-send-trace10.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-svc-send-handler-path3 \\ \index{trace-svc-send-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{3}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{1}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid})\-\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-send-interrupt}}\,({\it{os\/}})\index{os-intended-svc-send-interrupt}, \\ 
{\rm{os-time-for-svc-send-handler-path3}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-svc-send-time8} \\  
\=\+{\rm{os-svc-send-time8}}\,({\it{os\/}})\index{os-svc-send-time8} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-send-time9} \\  
\=\+{\rm{os-svc-send-time9}}\,({\it{os\/}})\index{os-svc-send-time9} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-send-time10} \\  
\=\+{\rm{os-svc-send-time10}}\,({\it{os\/}})\index{os-svc-send-time10} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-send-handler-pat!h4a} \\  
\=\+{\rm{os-time-for-svc-send-handler-path4a}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h4a} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-send-trace11 \\ \index{rewrite-svc-send-trace11}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-send-interrupt}}\,({\it{os\/}})\index{os-intended-svc-send-interrupt}, \\ 
{\rm{os-time-for-svc-send-handler-path4a}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h4a})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-send-interrupt}}\,({\it{os\/}})\index{os-intended-svc-send-interrupt}, \\ 
{\rm{os-time-for-svc-send-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-th!ru-save-state})\-\index{tm-processor}, \\ 
{\rm{os-svc-send-time8}}\,({\it{os\/}})\index{os-svc-send-time8})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-send-trace11.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-send-trace12 \\ \index{rewrite-svc-send-trace12}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-send-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-send-handler-thru-save-st!ate}, {\rm{os-svc-send-time8}}\,({\it{os\/}})\index{os-svc-send-time8})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-send-handler-thru-save-st!ate}, \\ 
{\rm{os-time-for-svc-send-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-qfullp-test})\-\index{tm-processor}, \\ 
{\rm{os-svc-send-time9}}\,({\it{os\/}})\index{os-svc-send-time9})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-send-trace12.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-send-trace13 \\ \index{rewrite-svc-send-trace13}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-send-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-send-handler-to-qfullp-te!st}, {\rm{os-svc-send-time9}}\,({\it{os\/}})\index{os-svc-send-time9})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-send-handler-to-qfullp-te!st}, \\ 
{\rm{os-time-for-svc-send-handler-thru-enqueue}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-th!ru-enqueue})\-\index{tm-processor}, \\ 
{\rm{os-svc-send-time10}}\,({\it{os\/}})\index{os-svc-send-time10})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-send-trace13.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-send-trace14 \\ \index{rewrite-svc-send-trace14}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-send-handler-thru-enqueue}}\,({\it{os\/}})\index{os-svc-send-handler-thru-enqueue}, {\rm{os-svc-send-time10}}\,({\it{os\/}})\index{os-svc-send-time10})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-thru-enqueue}}\,({\it{os\/}})\index{os-svc-send-handler-thru-enqueue}, \\ 
{\rm{os-time-for-svc-send-handler-to-svc-resume-task2}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-svc-resume-task2})\-\index{tm-processor}, \\ 
{\rm{os-time-for-svc-send-handler-to-svcr}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-svcr})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-send-trace14.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-svc-send-handler-path4a \\ \index{trace-svc-send-handler-path4a}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{3}})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-send-interrupt}}\,({\it{os\/}})\index{os-intended-svc-send-interrupt}, \\ 
{\rm{os-time-for-svc-send-handler-path4a}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h4a})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-send-handler-path4a.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-svc-send-time11} \\  
\=\+{\rm{os-svc-send-time11}}\,({\it{os\/}})\index{os-svc-send-time11} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-send-time12} \\  
\=\+{\rm{os-svc-send-time12}}\,({\it{os\/}})\index{os-svc-send-time12} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-send-time13} \\  
\=\+{\rm{os-svc-send-time13}}\,({\it{os\/}})\index{os-svc-send-time13} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-send-handler-pat!h4b} \\  
\=\+{\rm{os-time-for-svc-send-handler-path4b}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h4b} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-send-trace15 \\ \index{rewrite-svc-send-trace15}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-send-interrupt}}\,({\it{os\/}})\index{os-intended-svc-send-interrupt}, \\ 
{\rm{os-time-for-svc-send-handler-path4b}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h4b})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-send-interrupt}}\,({\it{os\/}})\index{os-intended-svc-send-interrupt}, \\ 
{\rm{os-time-for-svc-send-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-th!ru-save-state})\-\index{tm-processor}, \\ 
{\rm{os-svc-send-time11}}\,({\it{os\/}})\index{os-svc-send-time11})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-send-trace15.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-send-trace16 \\ \index{rewrite-svc-send-trace16}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-send-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-send-handler-thru-save-st!ate}, {\rm{os-svc-send-time11}}\,({\it{os\/}})\index{os-svc-send-time11})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-send-handler-thru-save-st!ate}, \\ 
{\rm{os-time-for-svc-send-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-qfullp-test})\-\index{tm-processor}, \\ 
{\rm{os-svc-send-time12}}\,({\it{os\/}})\index{os-svc-send-time12})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-send-trace16.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-send-trace17 \\ \index{rewrite-svc-send-trace17}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-send-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-send-handler-to-qfullp-te!st}, {\rm{os-svc-send-time12}}\,({\it{os\/}})\index{os-svc-send-time12})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-send-handler-to-qfullp-te!st}, \\ 
{\rm{os-time-for-svc-send-handler-thru-enqueue}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-th!ru-enqueue})\-\index{tm-processor}, \\ 
{\rm{os-svc-send-time13}}\,({\it{os\/}})\index{os-svc-send-time13})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-send-trace17.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-send-trace18 \\ \index{rewrite-svc-send-trace18}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-send-handler-thru-enqueue}}\,({\it{os\/}})\index{os-svc-send-handler-thru-enqueue}, {\rm{os-svc-send-time13}}\,({\it{os\/}})\index{os-svc-send-time13})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-send-handler-thru-enqueue}}\,({\it{os\/}})\index{os-svc-send-handler-thru-enqueue}, \\ 
{\rm{os-time-for-svc-send-handler-to-svc-resume-task3}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-svc-resume-task3})\-\index{tm-processor}, \\ 
{\rm{os-time-for-svc-send-handler-to-svcr}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-to!-svcr})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-send-trace18.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-svc-send-handler-path4b \\ \index{trace-svc-send-handler-path4b}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{3}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{1}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid})\-\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-send-interrupt}}\,({\it{os\/}})\index{os-intended-svc-send-interrupt}, \\ 
{\rm{os-time-for-svc-send-handler-path4b}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h4b})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-send-handler-path4b.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-send-handler-pat!h4} \\  
\=\+{\rm{os-time-for-svc-send-handler-path4}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h4} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} $\not=$ {\tt{'}}{\tt{3}} \\ 
{\bf then }{\rm{os-time-for-svc-send-handler-path4a}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h4a} \\ 
{\bf else }{\rm{os-time-for-svc-send-handler-path4b}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h4b}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  trace-svc-send-handler-path4 \\ \index{trace-svc-send-handler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ (\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{3}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{1}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid})\-\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-send-interrupt}}\,({\it{os\/}})\index{os-intended-svc-send-interrupt}, \\ 
{\rm{os-time-for-svc-send-handler-path4}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h4})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-send-handler} \\  
\=\+{\rm{os-time-for-svc-send-handler}}\,({\it{os\/}})\index{os-time-for-svc-send-handler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp} \\ 
{\bf then }\=\+{\bf if }{\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp} \\ 
{\bf then }{\rm{os-time-for-svc-send-handler-path1}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h1} \\ 
{\bf else }{\rm{os-time-for-svc-send-handler-path2}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h2}$\;${\bf  endif}\- \\ 
{\bf elseif }\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{3}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}} $+$ ({\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}), \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-\- \\ 
{\bf then }{\rm{os-time-for-svc-send-handler-path3}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h3} \\ 
{\bf else }{\rm{os-time-for-svc-send-handler-path4}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-pat!h4}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-send-handler} \\  
\=\+{\rm{os-svc-send-handler}}\,({\it{os\/}})\index{os-svc-send-handler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp} \\ 
{\bf then }\=\+{\bf if }{\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp} \\ 
{\bf then }{\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1} \\ 
{\bf else }{\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2}$\;${\bf  endif}\- \\ 
{\bf elseif }\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{3}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}} $+$ ({\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}), \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-\- \\ 
{\bf then }{\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3} \\ 
{\bf else }{\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  trace-svc-send-handler \\ \index{trace-svc-send-handler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-send-interrupt}}\,({\it{os\/}})\index{os-intended-svc-send-interrupt}, \\ 
{\rm{os-time-for-svc-send-handler}}\,({\it{os\/}})\index{os-time-for-svc-send-handler})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-send-handler}}\,({\it{os\/}})\index{os-svc-send-handler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-send-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-intended-svc-receive-interrupt} \\  
\=\+{\rm{os-intended-svc-receive-interrupt}}\,({\it{tm\/}})\index{os-intended-svc-receive-interrupt} \\ 
$=$$\;\;\;\;${\rm{os-intended-svc-send-interrupt}}\,({\it{tm\/}})\index{os-intended-svc-send-interrupt}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equivalence-of-svc-receive-interrupt-expressions \\ \index{equivalence-of-svc-receive-inte!rrupt-expressions}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-execute-svc-interrupt}}\,({\it{os\/}})\index{tm-execute-svc-interrupt} \\ 
$=$$\;\;\;\;${\rm{os-intended-svc-receive-interrupt}}\,({\it{os\/}})\index{os-intended-svc-receive-interrupt})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable equivalence-of-svc-receive-interrupt-expressions.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-receive-handler!-thru-save-state} \\  
\=\+{\rm{os-time-for-svc-receive-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-thru-save-state} \\ 
$=$$\;\;\;\;${\rm{os-time-for-svc-send-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-send-handler-th!ru-save-state}\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-receive-handler-thru-save!-state} \\  
\=\+{\rm{os-svc-receive-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-save!-state} \\ 
$=$$\;\;\;\;${\rm{os-svc-send-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-send-handler-thru-save-st!ate}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  trace-svc-receive-handler-thru-save-state \\ \index{trace-svc-receive-handler-thru-!save-state}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-receive-interrupt}}\,({\it{os\/}})\index{os-intended-svc-receive-interrupt}, \\ 
{\rm{os-time-for-svc-receive-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-thru-save-state})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-receive-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-save!-state})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-receive-handler-thru-save-state.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-receive-handler!-to-qemptyp-test} \\  
\=\+{\rm{os-time-for-svc-receive-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-qemptyp-test} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-RECEIVE-HANDLER-TO-QEMPTYP-TEST
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '1
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-MBUFFERS OS)
                          '499
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '2824
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '2845
      '0
      (PUTNTH '3310
              '1
              (PUTNTH (ARRAY-QFIRST (OS-READYQ OS))
                      '2
                      (PUTNTH (PLUS '499
                                    (PLUS (TIMES '8
                                                 (ARRAY-QFIRST (OS-READYQ OS)))
                                          (TIMES '128
                                                 (REMAINDER (TM-R2 OS) '16))))
                              '3
                              (PUTNTH (TIMES '8
                                             (ARRAY-QFIRST (OS-READYQ OS)))
                                      '4
                                      (PUTNTH (REMAINDER (TM-R2 OS) '16)
                                              '6
                                              (TM-REGS OS)))))))
  (TM-CC-VALUE (TM-ALU-PLUS (PLUS (TIMES '8
                                         (ARRAY-QFIRST (OS-READYQ OS)))
                                  (TIMES '128
                                         (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                    '16)))
                            '499))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-receive-handler-to-qemptyp-test \\ \index{trace-svc-receive-handler-to-qe!mptyp-test}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-save!-state}, \\ 
{\rm{os-time-for-svc-receive-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-qemptyp-test})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-receive-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-receive-handler-to-qempt!yp-test})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-receive-handler-to-qemptyp-test.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-receive-handler!-to-dispatcher} \\  
\=\+{\rm{os-time-for-svc-receive-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-dispatcher} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-RECEIVE-HANDLER-TO-DISPATCHER
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '1
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-DEQ (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (ARRAY-QFIRST (OS-READYQ OS))
                                    '3
                                    (OS-SRCID OS '16)
                                    OS)
                  '211
                  (PUTSEG (OS-MBUFFERS OS)
                          '499
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '2905
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3206
   '0
   (PUTNTH '3310
           '1
           (PUTNTH (ARRAY-QFIRST (OS-READYQ OS))
                   '2
                   (PUTNTH (PLUS '211
                                 (TIMES '2
                                        (ARRAY-QFIRST (OS-READYQ OS))))
                           '3
                           (PUTNTH (TIMES '8
                                          (ARRAY-QFIRST (OS-READYQ OS)))
                                   '4
                                   (PUTNTH (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                      '16)
                                           '6
                                           (TM-REGS OS)))))))
  (TM-CC-VALUE (TM-ALU-PLUS (TIMES '2
                                   (ARRAY-QFIRST (OS-READYQ OS)))
                            '211))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-receive-handler-to-dispatcher \\ \index{trace-svc-receive-handler-to-di!spatcher}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-receive-handler-to-qempt!yp-test}, \\ 
{\rm{os-time-for-svc-receive-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-dispatcher})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-receive-handler-to-dispatcher}}\,({\it{os\/}})\index{os-svc-receive-handler-to-dispat!cher})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-receive-handler-to-dispatcher.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-receive-handler!-to-wait-state} \\  
\=\+{\rm{os-time-for-svc-receive-handler-to-wait-state}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-wait-state} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-RECEIVE-HANDLER-PATH1
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '1
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-DEQ (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (ARRAY-QFIRST (OS-READYQ OS))
                                    '3
                                    (OS-SRCID OS '16)
                                    OS)
                  '211
                  (PUTSEG (OS-MBUFFERS OS)
                          '499
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3211
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3222
   '0
   (PUTNTH '3310
           '1
           (PUTNTH (ARRAY-QFIRST (OS-READYQ OS))
                   '2
                   (PUTNTH '191
                           '3
                           (PUTNTH (TIMES '8
                                          (ARRAY-QFIRST (OS-READYQ OS)))
                                   '4
                                   (PUTNTH (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                      '16)
                                           '6
                                           (TM-REGS OS)))))))
  '1
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '1
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-receive-handler-to-wait-state \\ \index{trace-svc-receive-handler-to-wait!-state}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-to-dispatcher}}\,({\it{os\/}})\index{os-svc-receive-handler-to-dispat!cher}, \\ 
{\rm{os-time-for-svc-receive-handler-to-wait-state}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-wait-state})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-receive-handler-to-wait-state.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-receive-handler!-to-lpsw} \\  
\=\+{\rm{os-time-for-svc-receive-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-lpsw} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-RECEIVE-HANDLER-PATH2
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS))))
           (OS-NEW-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))))
            (OS-NEW-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))))
             (OS-NEW-TASK-TABLE OS))
     '2
     (PUTNTH '1
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-DEQ (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (ARRAY-QFIRST (OS-READYQ OS))
                                    '3
                                    (OS-SRCID OS '16)
                                    OS)
                  '211
                  (PUTSEG (OS-MBUFFERS OS)
                          '499
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3217
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
               OS)
  (OS-NEW-CC (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
             OS)
  (OS-NEW-ERROR (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                OS)
  (OS-NEW-SVCFLAG (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                  OS)
  (OS-NEW-SVCID (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                OS)
  (OS-NEW-BASE (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
               OS)
  (OS-NEW-LIMIT (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                OS)
  (TM-SLIMIT OS)
  '0
  '0
  '1000
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-receive-handler-to-lpsw \\ \index{trace-svc-receive-handler-to-lp!sw}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-to-dispatcher}}\,({\it{os\/}})\index{os-svc-receive-handler-to-dispat!cher}, \\ 
{\rm{os-time-for-svc-receive-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-lpsw})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-receive-handler-to-lpsw.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-receive-handler!-thru-delivery} \\  
\=\+{\rm{os-time-for-svc-receive-handler-thru-delivery}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-thru-delivery} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-RECEIVE-HANDLER-THRU-DELIVERY
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '1
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE-WITH-DELIVERED-MESSAGE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-MBUFFERS-WITH-DEQUEUED-MESSAGE OS)
                          '499
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '2853
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '2865
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
        (ARRAY-QFIRST (GETNTH (PLUS (ARRAY-QFIRST (OS-READYQ OS))
                                    (TIMES '16
                                           (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                      '16)))
                              (TABLE '8 (OS-MBUFFERS OS))))
        '2
        (PUTNTH (PLUS '15
                      (TIMES '9
                             (ARRAY-QFIRST (OS-READYQ OS))))
                '3
                (PUTNTH (TIMES '8
                               (ARRAY-QFIRST (OS-READYQ OS)))
                        '4
                        (PUTNTH (REMAINDER (GETNTH '2 (TM-REGS OS))
                                           '16)
                                '6
                                (TM-REGS OS)))))))
  (TM-CC-VALUE (TM-ALU-PLUS (TIMES '9
                                   (ARRAY-QFIRST (OS-READYQ OS)))
                            '15))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-receive-handler-thru-delivery \\ \index{trace-svc-receive-handler-thru-!delivery}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp}))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-receive-handler-to-qempt!yp-test}, \\ 
{\rm{os-time-for-svc-receive-handler-thru-delivery}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-thru-delivery})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-receive-handler-thru-delivery}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-delive!ry})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-receive-handler-thru-delivery.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-receive-handler!-to-svc-resume-task1} \\  
\=\+{\rm{os-time-for-svc-receive-handler-to-svc-resume-task1}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-svc-resume-task1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-RECEIVE-HANDLER-TO-SVC-RESUME-TASK1
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '1
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE-WITH-DELIVERED-MESSAGE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-ENQ (OS-SRCID OS '16)
                       (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (OS-SRCID OS '16)
                                    '0
                                    '0
                                    OS)
                  '211
                  (PUTSEG (OS-MBUFFERS-WITH-DEQUEUED-MESSAGE OS)
                          '499
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '2898
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3222
   '0
   (PUTNTH '3310
           '1
           (PUTNTH (REMAINDER (GETNTH '2 (TM-REGS OS))
                              '16)
                   '2
                   (PUTNTH '191
                           '3
                           (PUTNTH (PLUS '195
                                         (GETNTH '1 (OS-READYQ OS)))
                                   '4
                                   (PUTNTH (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                      '16)
                                           '6
                                           (TM-REGS OS)))))))
  (TM-CC-VALUE (TM-ALU-INCR-MOD (GETNTH '1 (OS-READYQ OS))
                                '16))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-receive-handler-to-svc-resume-task1 \\ \index{trace-svc-receive-handler-to-sv!c-resume-task1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{2}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}} $+$ ({\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}), \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-thru-delivery}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-delive!ry}, \\ 
{\rm{os-time-for-svc-receive-handler-to-svc-resume-task1}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-svc-resume-task1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-receive-handler-to-svc-resume-task1}}\,({\it{os\/}})\index{os-svc-receive-handler-to-svc-re!sume-task1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-receive-handler-to-svc-resume-task1.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-receive-handler!-to-svc-resume-task2} \\  
\=\+{\rm{os-time-for-svc-receive-handler-to-svc-resume-task2}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-svc-resume-task2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-RECEIVE-HANDLER-TO-SVC-RESUME-TASK2
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '1
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE-WITH-DELIVERED-MESSAGE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-MBUFFERS-WITH-DEQUEUED-MESSAGE OS)
                          '499
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '2853
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3222
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
        (ARRAY-QFIRST (GETNTH (PLUS (ARRAY-QFIRST (OS-READYQ OS))
                                    (TIMES '16
                                           (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                      '16)))
                              (TABLE '8 (OS-MBUFFERS OS))))
        '2
        (PUTNTH (PLUS '211
                      (TIMES '2
                             (REMAINDER (GETNTH '2 (TM-REGS OS))
                                        '16)))
                '3
                (PUTNTH (TIMES '8
                               (ARRAY-QFIRST (OS-READYQ OS)))
                        '4
                        (PUTNTH (REMAINDER (GETNTH '2 (TM-REGS OS))
                                           '16)
                                '6
                                (TM-REGS OS)))))))
  (TM-CC-VALUE
         (TM-ALU-DIFFERENCE (GETNTH (TIMES '2
                                           (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                      '16))
                                    (OS-STATUS-TABLE OS))
                            '2))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-receive-handler-to-svc-resume-task2 \\ \index{trace-svc-receive-handler-to-sv!c-resume-task2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{2}})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-thru-delivery}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-delive!ry}, \\ 
{\rm{os-time-for-svc-receive-handler-to-svc-resume-task2}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-svc-resume-task2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-receive-handler-to-svc-resume-task2}}\,({\it{os\/}})\index{os-svc-receive-handler-to-svc-re!sume-task2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-receive-handler-to-svc-resume-task2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-receive-handler!-to-svc-resume-task3} \\  
\=\+{\rm{os-time-for-svc-receive-handler-to-svc-resume-task3}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-svc-resume-task3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-RECEIVE-HANDLER-TO-SVC-RESUME-TASK3
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '1
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE-WITH-DELIVERED-MESSAGE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-MBUFFERS-WITH-DEQUEUED-MESSAGE OS)
                          '499
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '2853
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3222
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
        (ARRAY-QFIRST (GETNTH (PLUS (ARRAY-QFIRST (OS-READYQ OS))
                                    (TIMES '16
                                           (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                      '16)))
                              (TABLE '8 (OS-MBUFFERS OS))))
        '2
        (PUTNTH (PLUS '211
                      (TIMES '2
                             (REMAINDER (GETNTH '2 (TM-REGS OS))
                                        '16)))
                '3
                (PUTNTH (TIMES '8
                               (ARRAY-QFIRST (OS-READYQ OS)))
                        '4
                        (PUTNTH (REMAINDER (GETNTH '2 (TM-REGS OS))
                                           '16)
                                '6
                                (TM-REGS OS)))))))
  (TM-CC-VALUE
   (TM-ALU-DIFFERENCE (GETNTH (PLUS '1
                                    (TIMES '2
                                           (REMAINDER (GETNTH '2 (TM-REGS OS))
                                                      '16)))
                              (OS-STATUS-TABLE OS))
                      (ARRAY-QFIRST (OS-READYQ OS))))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-receive-handler-to-svc-resume-task3 \\ \index{trace-svc-receive-handler-to-sv!c-resume-task3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{2}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}} $+$ ({\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}), \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-thru-delivery}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-delive!ry}, \\ 
{\rm{os-time-for-svc-receive-handler-to-svc-resume-task3}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-svc-resume-task3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-receive-handler-to-svc-resume-task3}}\,({\it{os\/}})\index{os-svc-receive-handler-to-svc-re!sume-task3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-receive-handler-to-svc-resume-task3.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-receive-handler!-to-svcr} \\  
\=\+{\rm{os-time-for-svc-receive-handler-to-svcr}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-svcr} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-RECEIVE-HANDLER-PATH3
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (OS-READYQ OS)))
           (OS-TASK-TABLE-WITH-DELIVERED-MESSAGE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (OS-READYQ OS))))
            (OS-TASK-TABLE-WITH-DELIVERED-MESSAGE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (OS-READYQ OS))))
             (OS-TASK-TABLE-WITH-DELIVERED-MESSAGE OS))
     '2
     (PUTNTH '1
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE-WITH-DELIVERED-MESSAGE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-ENQ (OS-SRCID OS '16)
                       (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (OS-SRCID OS '16)
                                    '0
                                    '0
                                    OS)
                  '211
                  (PUTSEG (OS-MBUFFERS-WITH-DEQUEUED-MESSAGE OS)
                          '499
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3229
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH (ARRAY-QFIRST (OS-CURRENT-MBUFFER (OS-SRCID OS '16)
                                            (OS-CURRENT-TASKID OS)
                                            OS))
          '3
          (TM-REGS OS))
  (TM-CC OS)
  (TM-ERROR OS)
  '0
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-receive-handler-to-svcr1 \\ \index{trace-svc-receive-handler-to-sv!cr1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{2}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}} $+$ ({\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}), \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-to-svc-resume-task1}}\,({\it{os\/}})\index{os-svc-receive-handler-to-svc-re!sume-task1}, \\ 
{\rm{os-time-for-svc-receive-handler-to-svcr}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-svcr})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-receive-handler-to-svcr1.

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN
 OS-SVC-RECEIVE-HANDLER-PATH4
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (OS-READYQ OS)))
           (OS-TASK-TABLE-WITH-DELIVERED-MESSAGE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (OS-READYQ OS))))
            (OS-TASK-TABLE-WITH-DELIVERED-MESSAGE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (OS-READYQ OS))))
             (OS-TASK-TABLE-WITH-DELIVERED-MESSAGE OS))
     '2
     (PUTNTH '1
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE-WITH-DELIVERED-MESSAGE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-MBUFFERS-WITH-DEQUEUED-MESSAGE OS)
                          '499
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3229
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH (ARRAY-QFIRST (OS-CURRENT-MBUFFER (OS-SRCID OS '16)
                                            (OS-CURRENT-TASKID OS)
                                            OS))
          '3
          (TM-REGS OS))
  (TM-CC OS)
  (TM-ERROR OS)
  '0
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-receive-handler-to-svcr2 \\ \index{trace-svc-receive-handler-to-sv!cr2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-to-svc-resume-task2}}\,({\it{os\/}})\index{os-svc-receive-handler-to-svc-re!sume-task2}, \\ 
{\rm{os-time-for-svc-receive-handler-to-svcr}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-svcr})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-receive-handler-to-svcr2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-svc-receive-handler-to-svcr3 \\ \index{trace-svc-receive-handler-to-sv!cr3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-to-svc-resume-task3}}\,({\it{os\/}})\index{os-svc-receive-handler-to-svc-re!sume-task3}, \\ 
{\rm{os-time-for-svc-receive-handler-to-svcr}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-svcr})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-receive-handler-to-svcr3.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-svc-receive-time1} \\  
\=\+{\rm{os-svc-receive-time1}}\,({\it{os\/}})\index{os-svc-receive-time1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-receive-time2} \\  
\=\+{\rm{os-svc-receive-time2}}\,({\it{os\/}})\index{os-svc-receive-time2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-receive-handler!-path1} \\  
\=\+{\rm{os-time-for-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-receive-trace1 \\ \index{rewrite-svc-receive-trace1}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-receive-interrupt}}\,({\it{os\/}})\index{os-intended-svc-receive-interrupt}, \\ 
{\rm{os-time-for-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-receive-interrupt}}\,({\it{os\/}})\index{os-intended-svc-receive-interrupt}, \\ 
{\rm{os-time-for-svc-receive-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-thru-save-state})\-\index{tm-processor}, \\ 
{\rm{os-svc-receive-time1}}\,({\it{os\/}})\index{os-svc-receive-time1})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-receive-trace1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-receive-trace2 \\ \index{rewrite-svc-receive-trace2}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-save!-state}, \\ 
{\rm{os-svc-receive-time1}}\,({\it{os\/}})\index{os-svc-receive-time1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-save!-state}, \\ 
{\rm{os-time-for-svc-receive-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-qemptyp-test})\-\index{tm-processor}, \\ 
{\rm{os-svc-receive-time2}}\,({\it{os\/}})\index{os-svc-receive-time2})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-receive-trace2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-receive-trace3 \\ \index{rewrite-svc-receive-trace3}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-receive-handler-to-qempt!yp-test}, \\ 
{\rm{os-svc-receive-time2}}\,({\it{os\/}})\index{os-svc-receive-time2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-receive-handler-to-qempt!yp-test}, \\ 
{\rm{os-time-for-svc-receive-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-dispatcher})\-\index{tm-processor}, \\ 
{\rm{os-time-for-svc-receive-handler-to-wait-state}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-wait-state})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-receive-trace3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-svc-receive-handler-path1 \\ \index{trace-svc-receive-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-receive-interrupt}}\,({\it{os\/}})\index{os-intended-svc-receive-interrupt}, \\ 
{\rm{os-time-for-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-svc-receive-time3} \\  
\=\+{\rm{os-svc-receive-time3}}\,({\it{os\/}})\index{os-svc-receive-time3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-receive-time4} \\  
\=\+{\rm{os-svc-receive-time4}}\,({\it{os\/}})\index{os-svc-receive-time4} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-receive-handler!-path2} \\  
\=\+{\rm{os-time-for-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-receive-trace4 \\ \index{rewrite-svc-receive-trace4}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-receive-interrupt}}\,({\it{os\/}})\index{os-intended-svc-receive-interrupt}, \\ 
{\rm{os-time-for-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-receive-interrupt}}\,({\it{os\/}})\index{os-intended-svc-receive-interrupt}, \\ 
{\rm{os-time-for-svc-receive-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-thru-save-state})\-\index{tm-processor}, \\ 
{\rm{os-svc-receive-time3}}\,({\it{os\/}})\index{os-svc-receive-time3})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-receive-trace4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-receive-trace5 \\ \index{rewrite-svc-receive-trace5}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-save!-state}, \\ 
{\rm{os-svc-receive-time3}}\,({\it{os\/}})\index{os-svc-receive-time3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-save!-state}, \\ 
{\rm{os-time-for-svc-receive-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-qemptyp-test})\-\index{tm-processor}, \\ 
{\rm{os-svc-receive-time4}}\,({\it{os\/}})\index{os-svc-receive-time4})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-receive-trace5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-receive-trace6 \\ \index{rewrite-svc-receive-trace6}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-receive-handler-to-qempt!yp-test}, \\ 
{\rm{os-svc-receive-time4}}\,({\it{os\/}})\index{os-svc-receive-time4})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-receive-handler-to-qempt!yp-test}, \\ 
{\rm{os-time-for-svc-receive-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-dispatcher})\-\index{tm-processor}, \\ 
{\rm{os-time-for-svc-receive-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-lpsw})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-receive-trace6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-svc-receive-handler-path2 \\ \index{trace-svc-receive-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-receive-interrupt}}\,({\it{os\/}})\index{os-intended-svc-receive-interrupt}, \\ 
{\rm{os-time-for-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-svc-receive-time5} \\  
\=\+{\rm{os-svc-receive-time5}}\,({\it{os\/}})\index{os-svc-receive-time5} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-receive-time6} \\  
\=\+{\rm{os-svc-receive-time6}}\,({\it{os\/}})\index{os-svc-receive-time6} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-receive-time7} \\  
\=\+{\rm{os-svc-receive-time7}}\,({\it{os\/}})\index{os-svc-receive-time7} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-receive-handler!-path3} \\  
\=\+{\rm{os-time-for-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-receive-trace7 \\ \index{rewrite-svc-receive-trace7}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-receive-interrupt}}\,({\it{os\/}})\index{os-intended-svc-receive-interrupt}, \\ 
{\rm{os-time-for-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-receive-interrupt}}\,({\it{os\/}})\index{os-intended-svc-receive-interrupt}, \\ 
{\rm{os-time-for-svc-receive-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-thru-save-state})\-\index{tm-processor}, \\ 
{\rm{os-svc-receive-time5}}\,({\it{os\/}})\index{os-svc-receive-time5})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-receive-trace7.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-receive-trace8 \\ \index{rewrite-svc-receive-trace8}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-save!-state}, \\ 
{\rm{os-svc-receive-time5}}\,({\it{os\/}})\index{os-svc-receive-time5})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-save!-state}, \\ 
{\rm{os-time-for-svc-receive-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-qemptyp-test})\-\index{tm-processor}, \\ 
{\rm{os-svc-receive-time6}}\,({\it{os\/}})\index{os-svc-receive-time6})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-receive-trace8.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-receive-trace9 \\ \index{rewrite-svc-receive-trace9}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-receive-handler-to-qempt!yp-test}, \\ 
{\rm{os-svc-receive-time6}}\,({\it{os\/}})\index{os-svc-receive-time6})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-receive-handler-to-qempt!yp-test}, \\ 
{\rm{os-time-for-svc-receive-handler-thru-delivery}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-thru-delivery})\-\index{tm-processor}, \\ 
{\rm{os-svc-receive-time7}}\,({\it{os\/}})\index{os-svc-receive-time7})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-receive-trace9.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-receive-trace10 \\ \index{rewrite-svc-receive-trace10}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-thru-delivery}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-delive!ry}, \\ 
{\rm{os-svc-receive-time7}}\,({\it{os\/}})\index{os-svc-receive-time7})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-thru-delivery}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-delive!ry}, \\ 
{\rm{os-time-for-svc-receive-handler-to-svc-resume-task1}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-svc-resume-task1})\-\index{tm-processor}, \\ 
{\rm{os-time-for-svc-receive-handler-to-svcr}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-svcr})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-receive-trace10.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-svc-receive-handler-path3 \\ \index{trace-svc-receive-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{2}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{1}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid})\-\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-receive-interrupt}}\,({\it{os\/}})\index{os-intended-svc-receive-interrupt}, \\ 
{\rm{os-time-for-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-svc-receive-time8} \\  
\=\+{\rm{os-svc-receive-time8}}\,({\it{os\/}})\index{os-svc-receive-time8} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-receive-time9} \\  
\=\+{\rm{os-svc-receive-time9}}\,({\it{os\/}})\index{os-svc-receive-time9} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-receive-time10} \\  
\=\+{\rm{os-svc-receive-time10}}\,({\it{os\/}})\index{os-svc-receive-time10} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-receive-handler!-path4a} \\  
\=\+{\rm{os-time-for-svc-receive-handler-path4a}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path4a} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-receive-trace11 \\ \index{rewrite-svc-receive-trace11}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-receive-interrupt}}\,({\it{os\/}})\index{os-intended-svc-receive-interrupt}, \\ 
{\rm{os-time-for-svc-receive-handler-path4a}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path4a})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-receive-interrupt}}\,({\it{os\/}})\index{os-intended-svc-receive-interrupt}, \\ 
{\rm{os-time-for-svc-receive-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-thru-save-state})\-\index{tm-processor}, \\ 
{\rm{os-svc-receive-time8}}\,({\it{os\/}})\index{os-svc-receive-time8})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-receive-trace11.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-receive-trace12 \\ \index{rewrite-svc-receive-trace12}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-save!-state}, \\ 
{\rm{os-svc-receive-time8}}\,({\it{os\/}})\index{os-svc-receive-time8})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-save!-state}, \\ 
{\rm{os-time-for-svc-receive-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-qemptyp-test})\-\index{tm-processor}, \\ 
{\rm{os-svc-receive-time9}}\,({\it{os\/}})\index{os-svc-receive-time9})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-receive-trace12.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-receive-trace13 \\ \index{rewrite-svc-receive-trace13}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-receive-handler-to-qempt!yp-test}, \\ 
{\rm{os-svc-receive-time9}}\,({\it{os\/}})\index{os-svc-receive-time9})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-receive-handler-to-qempt!yp-test}, \\ 
{\rm{os-time-for-svc-receive-handler-thru-delivery}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-thru-delivery})\-\index{tm-processor}, \\ 
{\rm{os-svc-receive-time10}}\,({\it{os\/}})\index{os-svc-receive-time10})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-receive-trace13.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-receive-trace14 \\ \index{rewrite-svc-receive-trace14}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-thru-delivery}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-delive!ry}, \\ 
{\rm{os-svc-receive-time10}}\,({\it{os\/}})\index{os-svc-receive-time10})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-thru-delivery}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-delive!ry}, \\ 
{\rm{os-time-for-svc-receive-handler-to-svc-resume-task2}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-svc-resume-task2})\-\index{tm-processor}, \\ 
{\rm{os-time-for-svc-receive-handler-to-svcr}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-svcr})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-receive-trace14.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-svc-receive-handler-path4a \\ \index{trace-svc-receive-handler-path4!a}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{2}})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-receive-interrupt}}\,({\it{os\/}})\index{os-intended-svc-receive-interrupt}, \\ 
{\rm{os-time-for-svc-receive-handler-path4a}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path4a})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-receive-handler-path4a.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-svc-receive-time11} \\  
\=\+{\rm{os-svc-receive-time11}}\,({\it{os\/}})\index{os-svc-receive-time11} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-receive-time12} \\  
\=\+{\rm{os-svc-receive-time12}}\,({\it{os\/}})\index{os-svc-receive-time12} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-receive-time13} \\  
\=\+{\rm{os-svc-receive-time13}}\,({\it{os\/}})\index{os-svc-receive-time13} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-receive-handler!-path4b} \\  
\=\+{\rm{os-time-for-svc-receive-handler-path4b}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path4b} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-receive-trace15 \\ \index{rewrite-svc-receive-trace15}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-receive-interrupt}}\,({\it{os\/}})\index{os-intended-svc-receive-interrupt}, \\ 
{\rm{os-time-for-svc-receive-handler-path4b}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path4b})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-receive-interrupt}}\,({\it{os\/}})\index{os-intended-svc-receive-interrupt}, \\ 
{\rm{os-time-for-svc-receive-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-thru-save-state})\-\index{tm-processor}, \\ 
{\rm{os-svc-receive-time11}}\,({\it{os\/}})\index{os-svc-receive-time11})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-receive-trace15.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-receive-trace16 \\ \index{rewrite-svc-receive-trace16}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-save!-state}, \\ 
{\rm{os-svc-receive-time11}}\,({\it{os\/}})\index{os-svc-receive-time11})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-save!-state}, \\ 
{\rm{os-time-for-svc-receive-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-qemptyp-test})\-\index{tm-processor}, \\ 
{\rm{os-svc-receive-time12}}\,({\it{os\/}})\index{os-svc-receive-time12})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-receive-trace16.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-receive-trace17 \\ \index{rewrite-svc-receive-trace17}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-receive-handler-to-qempt!yp-test}, \\ 
{\rm{os-svc-receive-time12}}\,({\it{os\/}})\index{os-svc-receive-time12})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-receive-handler-to-qempt!yp-test}, \\ 
{\rm{os-time-for-svc-receive-handler-thru-delivery}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-thru-delivery})\-\index{tm-processor}, \\ 
{\rm{os-svc-receive-time13}}\,({\it{os\/}})\index{os-svc-receive-time13})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-receive-trace17.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-receive-trace18 \\ \index{rewrite-svc-receive-trace18}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-thru-delivery}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-delive!ry}, \\ 
{\rm{os-svc-receive-time13}}\,({\it{os\/}})\index{os-svc-receive-time13})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-receive-handler-thru-delivery}}\,({\it{os\/}})\index{os-svc-receive-handler-thru-delive!ry}, \\ 
{\rm{os-time-for-svc-receive-handler-to-svc-resume-task3}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-svc-resume-task3})\-\index{tm-processor}, \\ 
{\rm{os-time-for-svc-receive-handler-to-svcr}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-to-svcr})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-receive-trace18.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-svc-receive-handler-path4b \\ \index{trace-svc-receive-handler-path4!b}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{2}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{1}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid})\-\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-receive-interrupt}}\,({\it{os\/}})\index{os-intended-svc-receive-interrupt}, \\ 
{\rm{os-time-for-svc-receive-handler-path4b}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path4b})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-receive-handler-path4b.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-receive-handler!-path4} \\  
\=\+{\rm{os-time-for-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path4} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} $\not=$ {\tt{'}}{\tt{2}} \\ 
{\bf then }{\rm{os-time-for-svc-receive-handler-path4a}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path4a} \\ 
{\bf else }{\rm{os-time-for-svc-receive-handler-path4b}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path4b}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  trace-svc-receive-handler-path4 \\ \index{trace-svc-receive-handler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ (\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{2}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{1}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid})\-\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-receive-interrupt}}\,({\it{os\/}})\index{os-intended-svc-receive-interrupt}, \\ 
{\rm{os-time-for-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path4})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-receive-handler} \\  
\=\+{\rm{os-time-for-svc-receive-handler}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp} \\ 
{\bf then }\=\+{\bf if }{\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp} \\ 
{\bf then }{\rm{os-time-for-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path1} \\ 
{\bf else }{\rm{os-time-for-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path2}$\;${\bf  endif}\- \\ 
{\bf elseif }\=\+({\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}} $+$ ({\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}), \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-\- \\ 
{\bf then }{\rm{os-time-for-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path3} \\ 
{\bf else }{\rm{os-time-for-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler!-path4}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-receive-handler} \\  
\=\+{\rm{os-svc-receive-handler}}\,({\it{os\/}})\index{os-svc-receive-handler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp} \\ 
{\bf then }\=\+{\bf if }{\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp} \\ 
{\bf then }{\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1} \\ 
{\bf else }{\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2}$\;${\bf  endif}\- \\ 
{\bf elseif }\=\+({\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}} $+$ ({\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}), \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-\- \\ 
{\bf then }{\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3} \\ 
{\bf else }{\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  trace-svc-receive-handler \\ \index{trace-svc-receive-handler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-receive-interrupt}}\,({\it{os\/}})\index{os-intended-svc-receive-interrupt}, \\ 
{\rm{os-time-for-svc-receive-handler}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-receive-handler}}\,({\it{os\/}})\index{os-svc-receive-handler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-receive-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-intended-svc-tyi-interrupt} \\  
\=\+{\rm{os-intended-svc-tyi-interrupt}}\,({\it{tm\/}})\index{os-intended-svc-tyi-interrupt} \\ 
$=$$\;\;\;\;${\rm{tm-set-memory}}\,(\=\+{\rm{putnth}}\,(\=\+{\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp}, \\ 
{\tt{'}}{\tt{1}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{2}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-task-table}}\,({\it{tm\/}})\index{os-task-table}, \\ 
{\tt{'}}{\tt{15}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-segment-table}}\,({\it{tm\/}})\index{os-segment-table}, \\ 
{\tt{'}}{\tt{159}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-readyq}}\,({\it{tm\/}})\index{os-readyq}, \\ 
{\tt{'}}{\tt{191}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-status-table}}\,({\it{tm\/}})\index{os-status-table}, \\ 
{\tt{'}}{\tt{211}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-ibuffers}}\,({\it{tm\/}})\index{os-ibuffers}, \\ 
{\tt{'}}{\tt{243}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-code}}\,({\it{tm\/}})\index{os-code}, \\ 
{\tt{'}}{\tt{2547}}, \\ 
{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\-\index{putseg})\-\index{putseg})\-\index{putseg})\-\index{putseg})\-\index{putseg})\-\index{putseg})\-\index{putnth})\-\index{putnth})\-\index{putnth})\-\index{putnth}, \\ 
{\rm{tm-set-pc}}\,(\=\+{\tt{'}}{\tt{2690}}, \\ 
{\rm{tm-set-sp}}\,(\=\+{\tt{'}}{\tt{3310}}, \\ 
{\rm{tm-set-svmode}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{tm-set-error}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-set-rwstate}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\it{tm\/}})\-\index{tm-set-rwstate})\-\index{tm-set-error})\-\index{tm-set-svmode})\-\index{tm-set-sp})\-\index{tm-set-pc})\-\index{tm-set-memory}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equivalence-of-svc-tyi-interrupt-expressions \\ \index{equivalence-of-svc-tyi-interrupt!-expressions}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}))) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-execute-svc-interrupt}}\,({\it{os\/}})\index{tm-execute-svc-interrupt} $=$ {\rm{os-intended-svc-tyi-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyi-interrupt})\-
\end{tabbing}


\noindent{\sc Event}:   Disable equivalence-of-svc-tyi-interrupt-expressions.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyi-handler-thr!u-save-state} \\  
\=\+{\rm{os-time-for-svc-tyi-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-thr!u-save-state} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-TYI-HANDLER-THRU-SAVE-STATE
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-SVCID OS)
      '8
      (PUTNTH
       (TM-R2 OS)
       '13
       (PUTNTH
        (TM-R3 OS)
        '14
        (PUTSEG
         (OS-NEW-TASK-TABLE OS)
         '15
         (PUTSEG
          (OS-SEGMENT-TABLE OS)
          '159
          (PUTSEG
           (OS-READYQ OS)
           '191
           (PUTSEG (OS-STATUS-TABLE OS)
                   '211
                   (PUTSEG (OS-IBUFFERS OS)
                           '243
                           (PUTSEG (OS-CODE OS)
                                   '2547
                                   (PUTNTH '2558
                                           '3309
                                           (PUTNTH '2692
                                                   '3310
                                                   (TM-MEMORY OS)))))))))))))))
  (PUTNTH '2692
          '0
          (PUTNTH '3310
                  '1
                  (PUTNTH (TM-R2 OS)
                          '2
                          (PUTNTH (TM-R3 OS)
                                  '3
                                  (TM-REGS OS)))))
  (TM-CC-VALUE (TM-ALU-PLUS (PLUS '15
                                  (TIMES '9
                                         (ARRAY-QFIRST (OS-READYQ OS))))
                            '8))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-tyi-handler-thru-save-state \\ \index{trace-svc-tyi-handler-thru-save!-state}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyi-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyi-interrupt}, \\ 
{\rm{os-time-for-svc-tyi-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-thr!u-save-state})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyi-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-tyi-handler-thru-save-st!ate})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyi-handler-thru-save-state.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyi-handler-to-qe!mptyp-test} \\  
\=\+{\rm{os-time-for-svc-tyi-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-to-qe!mptyp-test} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-TYI-HANDLER-TO-QEMPTYP-TEST
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '3
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-IBUFFERS OS)
                          '243
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '2986
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '2998
          '0
          (PUTNTH '3310
                  '1
                  (PUTNTH (ARRAY-QFIRST (OS-READYQ OS))
                          '2
                          (PUTNTH (PLUS '243
                                        (TIMES '8
                                               (ARRAY-QFIRST (OS-READYQ OS))))
                                  '3
                                  (TM-REGS OS)))))
  (TM-CC-VALUE (TM-ALU-PLUS (TIMES '8
                                   (ARRAY-QFIRST (OS-READYQ OS)))
                            '243))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-tyi-handler-to-qemptyp-test \\ \index{trace-svc-tyi-handler-to-qemptyp!-test}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{3}}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyi-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-tyi-handler-thru-save-st!ate}, \\ 
{\rm{os-time-for-svc-tyi-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-to-qe!mptyp-test})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyi-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-tyi-handler-to-qemptyp-te!st})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyi-handler-to-qemptyp-test.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyi-handler-to-!dispatcher} \\  
\=\+{\rm{os-time-for-svc-tyi-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-to-!dispatcher} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-TYI-HANDLER-TO-DISPATCHER
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '3
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-DEQ (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (ARRAY-QFIRST (OS-READYQ OS))
                                    '5
                                    '0
                                    OS)
                  '211
                  (PUTSEG (OS-IBUFFERS OS)
                          '243
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3025
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3206
          '0
          (PUTNTH '3310
                  '1
                  (PUTNTH (ARRAY-QFIRST (OS-READYQ OS))
                          '2
                          (PUTNTH (PLUS '211
                                        (TIMES '2
                                               (ARRAY-QFIRST (OS-READYQ OS))))
                                  '3
                                  (TM-REGS OS)))))
  (TM-CC-VALUE (TM-ALU-PLUS (TIMES '2
                                   (ARRAY-QFIRST (OS-READYQ OS)))
                            '211))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-tyi-handler-to-dispatcher \\ \index{trace-svc-tyi-handler-to-dispat!cher}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-ibuffer}}\,({\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, {\it{os\/}})\index{os-current-ibuffer})\index{array-qemptyp})\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyi-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-tyi-handler-to-qemptyp-te!st}, \\ 
{\rm{os-time-for-svc-tyi-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-to-!dispatcher})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyi-handler-to-dispatcher}}\,({\it{os\/}})\index{os-svc-tyi-handler-to-dispatche!r})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyi-handler-to-dispatcher.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyi-handler-to-!wait-state} \\  
\=\+{\rm{os-time-for-svc-tyi-handler-to-wait-state}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-to-!wait-state} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-TYI-HANDLER-PATH1
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '3
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-DEQ (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (ARRAY-QFIRST (OS-READYQ OS))
                                    '5
                                    '0
                                    OS)
                  '211
                  (PUTSEG (OS-IBUFFERS OS)
                          '243
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3211
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3222
          '0
          (PUTNTH '3310
                  '1
                  (PUTNTH (ARRAY-QFIRST (OS-READYQ OS))
                          '2
                          (PUTNTH '191 '3 (TM-REGS OS)))))
  '1
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '1
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-tyi-handler-to-wait-state \\ \index{trace-svc-tyi-handler-to-wait-st!ate}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyi-handler-to-dispatcher}}\,({\it{os\/}})\index{os-svc-tyi-handler-to-dispatche!r}, \\ 
{\rm{os-time-for-svc-tyi-handler-to-wait-state}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-to-!wait-state})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyi-handler-to-wait-state.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyi-handler-to-!lpsw} \\  
\=\+{\rm{os-time-for-svc-tyi-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-to-!lpsw} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-TYI-HANDLER-PATH2
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS))))
           (OS-NEW-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))))
            (OS-NEW-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))))
             (OS-NEW-TASK-TABLE OS))
     '2
     (PUTNTH '3
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-DEQ (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (ARRAY-QFIRST (OS-READYQ OS))
                                    '5
                                    '0
                                    OS)
                  '211
                  (PUTSEG (OS-IBUFFERS OS)
                          '243
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3217
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
               OS)
  (OS-NEW-CC (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
             OS)
  (OS-NEW-ERROR (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                OS)
  (OS-NEW-SVCFLAG (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                  OS)
  (OS-NEW-SVCID (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                OS)
  (OS-NEW-BASE (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
               OS)
  (OS-NEW-LIMIT (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                OS)
  (TM-SLIMIT OS)
  '0
  '0
  '1000
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-tyi-handler-to-lpsw \\ \index{trace-svc-tyi-handler-to-lpsw}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyi-handler-to-dispatcher}}\,({\it{os\/}})\index{os-svc-tyi-handler-to-dispatche!r}, \\ 
{\rm{os-time-for-svc-tyi-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-to-!lpsw})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyi-handler-to-lpsw.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyi-handler-thr!u-delivery} \\  
\=\+{\rm{os-time-for-svc-tyi-handler-thru-delivery}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-thr!u-delivery} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-TYI-HANDLER-THRU-DELIVERY
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '3
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE-WITH-DELIVERED-CHARACTER OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-IBUFFERS-WITH-DEQUEUED-CHARACTER OS)
                          '243
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3006
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3222
          '0
          (PUTNTH '3310
                  '1
                  (PUTNTH (ARRAY-QFIRST (GETNTH (ARRAY-QFIRST (OS-READYQ OS))
                                                (TABLE '8 (OS-IBUFFERS OS))))
                          '2
                          (PUTNTH (PLUS '15
                                        (TIMES '9
                                               (ARRAY-QFIRST (OS-READYQ OS))))
                                  '3
                                  (TM-REGS OS)))))
  (TM-CC-VALUE (TM-ALU-PLUS (TIMES '9
                                   (ARRAY-QFIRST (OS-READYQ OS)))
                            '15))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-tyi-handler-thru-delivery \\ \index{trace-svc-tyi-handler-thru-delive!ry}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyi-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-tyi-handler-to-qemptyp-te!st}, \\ 
{\rm{os-time-for-svc-tyi-handler-thru-delivery}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-thr!u-delivery})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyi-handler-thru-delivery}}\,({\it{os\/}})\index{os-svc-tyi-handler-thru-deliver!y})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyi-handler-thru-delivery.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyi-handler-to-!svcr} \\  
\=\+{\rm{os-time-for-svc-tyi-handler-to-svcr}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-to-!svcr} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-TYI-HANDLER-PATH3
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (OS-READYQ OS)))
           (OS-TASK-TABLE-WITH-DELIVERED-CHARACTER OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (OS-READYQ OS))))
            (OS-TASK-TABLE-WITH-DELIVERED-CHARACTER OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (OS-READYQ OS))))
             (OS-TASK-TABLE-WITH-DELIVERED-CHARACTER OS))
     '2
     (PUTNTH '3
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE-WITH-DELIVERED-CHARACTER OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-IBUFFERS-WITH-DEQUEUED-CHARACTER OS)
                          '243
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3229
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH (ARRAY-QFIRST (GETNTH (OS-CURRENT-TASKID OS)
                                (TABLE '8 (OS-IBUFFERS OS))))
          '3
          (TM-REGS OS))
  (TM-CC OS)
  (TM-ERROR OS)
  '0
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-tyi-handler-to-svcr \\ \index{trace-svc-tyi-handler-to-svcr}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyi-handler-thru-delivery}}\,({\it{os\/}})\index{os-svc-tyi-handler-thru-deliver!y}, \\ 
{\rm{os-time-for-svc-tyi-handler-to-svcr}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-to-!svcr})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyi-handler-to-svcr.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-svc-tyi-time1} \\  
\=\+{\rm{os-svc-tyi-time1}}\,({\it{os\/}})\index{os-svc-tyi-time1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-tyi-time2} \\  
\=\+{\rm{os-svc-tyi-time2}}\,({\it{os\/}})\index{os-svc-tyi-time2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyi-handler-pat!h1} \\  
\=\+{\rm{os-time-for-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-pat!h1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-tyi-trace1 \\ \index{rewrite-svc-tyi-trace1}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyi-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyi-interrupt}, \\ 
{\rm{os-time-for-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-pat!h1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyi-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyi-interrupt}, \\ 
{\rm{os-time-for-svc-tyi-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-thr!u-save-state})\-\index{tm-processor}, \\ 
{\rm{os-svc-tyi-time1}}\,({\it{os\/}})\index{os-svc-tyi-time1})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-tyi-trace1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-tyi-trace2 \\ \index{rewrite-svc-tyi-trace2}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-tyi-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-tyi-handler-thru-save-st!ate}, {\rm{os-svc-tyi-time1}}\,({\it{os\/}})\index{os-svc-tyi-time1})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyi-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-tyi-handler-thru-save-st!ate}, \\ 
{\rm{os-time-for-svc-tyi-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-to-qe!mptyp-test})\-\index{tm-processor}, \\ 
{\rm{os-svc-tyi-time2}}\,({\it{os\/}})\index{os-svc-tyi-time2})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-tyi-trace2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-tyi-trace3 \\ \index{rewrite-svc-tyi-trace3}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-tyi-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-tyi-handler-to-qemptyp-te!st}, {\rm{os-svc-tyi-time2}}\,({\it{os\/}})\index{os-svc-tyi-time2})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyi-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-tyi-handler-to-qemptyp-te!st}, \\ 
{\rm{os-time-for-svc-tyi-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-to-!dispatcher})\-\index{tm-processor}, \\ 
{\rm{os-time-for-svc-tyi-handler-to-wait-state}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-to-!wait-state})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-tyi-trace3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-svc-tyi-handler-path1 \\ \index{trace-svc-tyi-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{3}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qemptyp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qemptyp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyi-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyi-interrupt}, \\ 
{\rm{os-time-for-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-pat!h1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-svc-tyi-time3} \\  
\=\+{\rm{os-svc-tyi-time3}}\,({\it{os\/}})\index{os-svc-tyi-time3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-tyi-time4} \\  
\=\+{\rm{os-svc-tyi-time4}}\,({\it{os\/}})\index{os-svc-tyi-time4} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyi-handler-pat!h2} \\  
\=\+{\rm{os-time-for-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-pat!h2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-tyi-trace4 \\ \index{rewrite-svc-tyi-trace4}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyi-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyi-interrupt}, \\ 
{\rm{os-time-for-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-pat!h2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyi-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyi-interrupt}, \\ 
{\rm{os-time-for-svc-tyi-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-thr!u-save-state})\-\index{tm-processor}, \\ 
{\rm{os-svc-tyi-time3}}\,({\it{os\/}})\index{os-svc-tyi-time3})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-tyi-trace4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-tyi-trace5 \\ \index{rewrite-svc-tyi-trace5}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-tyi-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-tyi-handler-thru-save-st!ate}, {\rm{os-svc-tyi-time3}}\,({\it{os\/}})\index{os-svc-tyi-time3})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyi-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-tyi-handler-thru-save-st!ate}, \\ 
{\rm{os-time-for-svc-tyi-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-to-qe!mptyp-test})\-\index{tm-processor}, \\ 
{\rm{os-svc-tyi-time4}}\,({\it{os\/}})\index{os-svc-tyi-time4})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-tyi-trace5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-tyi-trace6 \\ \index{rewrite-svc-tyi-trace6}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-tyi-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-tyi-handler-to-qemptyp-te!st}, {\rm{os-svc-tyi-time4}}\,({\it{os\/}})\index{os-svc-tyi-time4})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyi-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-tyi-handler-to-qemptyp-te!st}, \\ 
{\rm{os-time-for-svc-tyi-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-to-!dispatcher})\-\index{tm-processor}, \\ 
{\rm{os-time-for-svc-tyi-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-to-!lpsw})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-tyi-trace6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-svc-tyi-handler-path2 \\ \index{trace-svc-tyi-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{3}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qemptyp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qemptyp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyi-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyi-interrupt}, \\ 
{\rm{os-time-for-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-pat!h2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-svc-tyi-time5} \\  
\=\+{\rm{os-svc-tyi-time5}}\,({\it{os\/}})\index{os-svc-tyi-time5} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-tyi-time6} \\  
\=\+{\rm{os-svc-tyi-time6}}\,({\it{os\/}})\index{os-svc-tyi-time6} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyi-handler-pat!h3} \\  
\=\+{\rm{os-time-for-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-pat!h3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-tyi-trace7 \\ \index{rewrite-svc-tyi-trace7}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyi-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyi-interrupt}, \\ 
{\rm{os-time-for-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-pat!h3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyi-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyi-interrupt}, \\ 
{\rm{os-time-for-svc-tyi-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-thr!u-save-state})\-\index{tm-processor}, \\ 
{\rm{os-svc-tyi-time5}}\,({\it{os\/}})\index{os-svc-tyi-time5})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-tyi-trace7.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-tyi-trace8 \\ \index{rewrite-svc-tyi-trace8}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-tyi-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-tyi-handler-thru-save-st!ate}, {\rm{os-svc-tyi-time5}}\,({\it{os\/}})\index{os-svc-tyi-time5})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyi-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-tyi-handler-thru-save-st!ate}, \\ 
{\rm{os-time-for-svc-tyi-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-to-qe!mptyp-test})\-\index{tm-processor}, \\ 
{\rm{os-svc-tyi-time6}}\,({\it{os\/}})\index{os-svc-tyi-time6})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-tyi-trace8.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-tyi-trace9 \\ \index{rewrite-svc-tyi-trace9}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-tyi-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-tyi-handler-to-qemptyp-te!st}, {\rm{os-svc-tyi-time6}}\,({\it{os\/}})\index{os-svc-tyi-time6})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyi-handler-to-qemptyp-test}}\,({\it{os\/}})\index{os-svc-tyi-handler-to-qemptyp-te!st}, \\ 
{\rm{os-time-for-svc-tyi-handler-thru-delivery}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-thr!u-delivery})\-\index{tm-processor}, \\ 
{\rm{os-time-for-svc-tyi-handler-to-svcr}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-to-!svcr})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-tyi-trace9.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-svc-tyi-handler-path3 \\ \index{trace-svc-tyi-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{3}}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qemptyp}))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyi-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyi-interrupt}, \\ 
{\rm{os-time-for-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-pat!h3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyi-handler} \\  
\=\+{\rm{os-time-for-svc-tyi-handler}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{array-qemptyp}}\,({\rm{os-current-ibuffer}}\,({\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, {\it{os\/}})\index{os-current-ibuffer})\index{array-qemptyp} \\ 
{\bf then }\=\+{\bf if }{\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp} \\ 
{\bf then }{\rm{os-time-for-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-pat!h1} \\ 
{\bf else }{\rm{os-time-for-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-pat!h2}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{os-time-for-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler-pat!h3}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-tyi-handler} \\  
\=\+{\rm{os-svc-tyi-handler}}\,({\it{os\/}})\index{os-svc-tyi-handler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{array-qemptyp}}\,({\rm{os-current-ibuffer}}\,({\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, {\it{os\/}})\index{os-current-ibuffer})\index{array-qemptyp} \\ 
{\bf then }\=\+{\bf if }{\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp} \\ 
{\bf then }{\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1} \\ 
{\bf else }{\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2}$\;${\bf  endif}\- \\ 
{\bf else }{\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  trace-svc-tyi-handler \\ \index{trace-svc-tyi-handler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{3}}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyi-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyi-interrupt}, \\ 
{\rm{os-time-for-svc-tyi-handler}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyi-handler}}\,({\it{os\/}})\index{os-svc-tyi-handler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyi-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-intended-svc-tyo-interrupt} \\  
\=\+{\rm{os-intended-svc-tyo-interrupt}}\,({\it{tm\/}})\index{os-intended-svc-tyo-interrupt} \\ 
$=$$\;\;\;\;${\rm{tm-set-memory}}\,(\=\+{\rm{putnth}}\,(\=\+{\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp}, \\ 
{\tt{'}}{\tt{1}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{2}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-task-table}}\,({\it{tm\/}})\index{os-task-table}, \\ 
{\tt{'}}{\tt{15}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-segment-table}}\,({\it{tm\/}})\index{os-segment-table}, \\ 
{\tt{'}}{\tt{159}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-readyq}}\,({\it{tm\/}})\index{os-readyq}, \\ 
{\tt{'}}{\tt{191}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-status-table}}\,({\it{tm\/}})\index{os-status-table}, \\ 
{\tt{'}}{\tt{211}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-obuffers}}\,({\it{tm\/}})\index{os-obuffers}, \\ 
{\tt{'}}{\tt{371}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-code}}\,({\it{tm\/}})\index{os-code}, \\ 
{\tt{'}}{\tt{2547}}, \\ 
{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\-\index{putseg})\-\index{putseg})\-\index{putseg})\-\index{putseg})\-\index{putseg})\-\index{putseg})\-\index{putnth})\-\index{putnth})\-\index{putnth})\-\index{putnth}, \\ 
{\rm{tm-set-pc}}\,(\=\+{\tt{'}}{\tt{2690}}, \\ 
{\rm{tm-set-sp}}\,(\=\+{\tt{'}}{\tt{3310}}, \\ 
{\rm{tm-set-svmode}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{tm-set-error}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-set-rwstate}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\it{tm\/}})\-\index{tm-set-rwstate})\-\index{tm-set-error})\-\index{tm-set-svmode})\-\index{tm-set-sp})\-\index{tm-set-pc})\-\index{tm-set-memory}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equivalence-of-svc-tyo-interrupt-expressions \\ \index{equivalence-of-svc-tyo-interrupt!-expressions}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}))) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-execute-svc-interrupt}}\,({\it{os\/}})\index{tm-execute-svc-interrupt} $=$ {\rm{os-intended-svc-tyo-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyo-interrupt})\-
\end{tabbing}


\noindent{\sc Event}:   Disable equivalence-of-svc-tyo-interrupt-expressions.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyo-handler-thr!u-save-state} \\  
\=\+{\rm{os-time-for-svc-tyo-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-thr!u-save-state} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-TYO-HANDLER-THRU-SAVE-STATE
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-SVCID OS)
      '8
      (PUTNTH
       (TM-R2 OS)
       '13
       (PUTNTH
        (TM-R3 OS)
        '14
        (PUTSEG
         (OS-NEW-TASK-TABLE OS)
         '15
         (PUTSEG
          (OS-SEGMENT-TABLE OS)
          '159
          (PUTSEG
           (OS-READYQ OS)
           '191
           (PUTSEG (OS-STATUS-TABLE OS)
                   '211
                   (PUTSEG (OS-OBUFFERS OS)
                           '371
                           (PUTSEG (OS-CODE OS)
                                   '2547
                                   (PUTNTH '2558
                                           '3309
                                           (PUTNTH '2692
                                                   '3310
                                                   (TM-MEMORY OS)))))))))))))))
  (PUTNTH '2692
          '0
          (PUTNTH '3310
                  '1
                  (PUTNTH (TM-R2 OS)
                          '2
                          (PUTNTH (TM-R3 OS)
                                  '3
                                  (TM-REGS OS)))))
  (TM-CC-VALUE (TM-ALU-PLUS (PLUS '15
                                  (TIMES '9
                                         (ARRAY-QFIRST (OS-READYQ OS))))
                            '8))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-tyo-handler-thru-save-state \\ \index{trace-svc-tyo-handler-thru-save!-state}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyo-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyo-interrupt}, \\ 
{\rm{os-time-for-svc-tyo-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-thr!u-save-state})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyo-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-tyo-handler-thru-save-st!ate})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyo-handler-thru-save-state.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyo-handler-to-q!fullp-test} \\  
\=\+{\rm{os-time-for-svc-tyo-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-q!fullp-test} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-TYO-HANDLER-TO-QFULLP-TEST
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '2
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-OBUFFERS OS)
                          '371
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '2930
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '2942
          '0
          (PUTNTH '3310
                  '1
                  (PUTNTH (ARRAY-QFIRST (OS-READYQ OS))
                          '2
                          (PUTNTH (PLUS '371
                                        (TIMES '8
                                               (ARRAY-QFIRST (OS-READYQ OS))))
                                  '3
                                  (PUTNTH (GETNTH '3 (TM-REGS OS))
                                          '7
                                          (TM-REGS OS))))))
  (TM-CC-VALUE (TM-ALU-PLUS (TIMES '8
                                   (ARRAY-QFIRST (OS-READYQ OS)))
                            '371))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-tyo-handler-to-qfullp-test \\ \index{trace-svc-tyo-handler-to-qfullp!-test}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyo-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-tyo-handler-thru-save-st!ate}, \\ 
{\rm{os-time-for-svc-tyo-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-q!fullp-test})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyo-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-tyo-handler-to-qfullp-te!st})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyo-handler-to-qfullp-test.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyo-handler-to-!dispatcher} \\  
\=\+{\rm{os-time-for-svc-tyo-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-!dispatcher} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-TYO-HANDLER-TO-DISPATCHER
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '2
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-DEQ (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (ARRAY-QFIRST (OS-READYQ OS))
                                    '4
                                    '0
                                    OS)
                  '211
                  (PUTSEG (OS-OBUFFERS OS)
                          '371
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '2964
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3206
          '0
          (PUTNTH '3310
                  '1
                  (PUTNTH (ARRAY-QFIRST (OS-READYQ OS))
                          '2
                          (PUTNTH (PLUS '211
                                        (TIMES '2
                                               (ARRAY-QFIRST (OS-READYQ OS))))
                                  '3
                                  (PUTNTH (GETNTH '3 (TM-REGS OS))
                                          '7
                                          (TM-REGS OS))))))
  (TM-CC-VALUE (TM-ALU-PLUS (TIMES '2
                                   (ARRAY-QFIRST (OS-READYQ OS)))
                            '211))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-tyo-handler-to-dispatcher \\ \index{trace-svc-tyo-handler-to-dispat!cher}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qfullp})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyo-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-tyo-handler-to-qfullp-te!st}, \\ 
{\rm{os-time-for-svc-tyo-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-!dispatcher})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyo-handler-to-dispatcher}}\,({\it{os\/}})\index{os-svc-tyo-handler-to-dispatche!r})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyo-handler-to-dispatcher.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyo-handler-to-!wait-state} \\  
\=\+{\rm{os-time-for-svc-tyo-handler-to-wait-state}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-!wait-state} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-TYO-HANDLER-PATH1
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '2
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-DEQ (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (ARRAY-QFIRST (OS-READYQ OS))
                                    '4
                                    '0
                                    OS)
                  '211
                  (PUTSEG (OS-OBUFFERS OS)
                          '371
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3211
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3222
          '0
          (PUTNTH '3310
                  '1
                  (PUTNTH (ARRAY-QFIRST (OS-READYQ OS))
                          '2
                          (PUTNTH '191
                                  '3
                                  (PUTNTH (GETNTH '3 (TM-REGS OS))
                                          '7
                                          (TM-REGS OS))))))
  '1
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '1
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-tyo-handler-to-wait-state \\ \index{trace-svc-tyo-handler-to-wait-st!ate}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyo-handler-to-dispatcher}}\,({\it{os\/}})\index{os-svc-tyo-handler-to-dispatche!r}, \\ 
{\rm{os-time-for-svc-tyo-handler-to-wait-state}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-!wait-state})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyo-handler-to-wait-state.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyo-handler-to-!lpsw} \\  
\=\+{\rm{os-time-for-svc-tyo-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-!lpsw} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-TYO-HANDLER-PATH2
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS))))
           (OS-NEW-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))))
            (OS-NEW-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))))
             (OS-NEW-TASK-TABLE OS))
     '2
     (PUTNTH '2
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-DEQ (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (ARRAY-QFIRST (OS-READYQ OS))
                                    '4
                                    '0
                                    OS)
                  '211
                  (PUTSEG (OS-OBUFFERS OS)
                          '371
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3217
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
               OS)
  (OS-NEW-CC (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
             OS)
  (OS-NEW-ERROR (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                OS)
  (OS-NEW-SVCFLAG (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                  OS)
  (OS-NEW-SVCID (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                OS)
  (OS-NEW-BASE (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
               OS)
  (OS-NEW-LIMIT (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                OS)
  (TM-SLIMIT OS)
  '0
  '0
  '1000
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-tyo-handler-to-lpsw \\ \index{trace-svc-tyo-handler-to-lpsw}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyo-handler-to-dispatcher}}\,({\it{os\/}})\index{os-svc-tyo-handler-to-dispatche!r}, \\ 
{\rm{os-time-for-svc-tyo-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-!lpsw})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyo-handler-to-lpsw.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyo-handler-thr!u-enqueue} \\  
\=\+{\rm{os-time-for-svc-tyo-handler-thru-enqueue}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-thr!u-enqueue} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-TYO-HANDLER-THRU-ENQUEUE
 (OS)
 (TM
  (PUTNTH
   (TM-R0 OS)
   '0
   (PUTNTH
    (TM-R1 OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH '2
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-OBUFFERS-WITH-ENQUEUED-CHARACTER OS)
                          '371
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '2951
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '2951
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (GETNTH '3 (TM-REGS OS))
     '2
     (PUTNTH
           (PLUS '371
                 (TIMES '8
                        (ARRAY-QFIRST (OS-READYQ OS))))
           '3
           (PUTNTH (PLUS '375
                         (PLUS (TIMES '8
                                      (ARRAY-QFIRST (OS-READYQ OS)))
                               (GETNTH '1
                                       (GETNTH (ARRAY-QFIRST (OS-READYQ OS))
                                               (TABLE '8 (OS-OBUFFERS OS))))))
                   '4
                   (PUTNTH (GETNTH '3 (TM-REGS OS))
                           '7
                           (TM-REGS OS)))))))
  (TM-CC-VALUE
              (TM-ALU-INCR-MOD (GETNTH '1
                                       (GETNTH (ARRAY-QFIRST (OS-READYQ OS))
                                               (TABLE '8 (OS-OBUFFERS OS))))
                               (GETNTH '3
                                       (GETNTH (ARRAY-QFIRST (OS-READYQ OS))
                                               (TABLE '8 (OS-OBUFFERS OS))))))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-tyo-handler-thru-enqueue \\ \index{trace-svc-tyo-handler-thru-enque!ue}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qfullp}))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyo-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-tyo-handler-to-qfullp-te!st}, \\ 
{\rm{os-time-for-svc-tyo-handler-thru-enqueue}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-thr!u-enqueue})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyo-handler-thru-enqueue}}\,({\it{os\/}})\index{os-svc-tyo-handler-thru-enqueue})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyo-handler-thru-enqueue.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyo-handler-to-!svcr1} \\  
\=\+{\rm{os-time-for-svc-tyo-handler-to-svcr1}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-!svcr1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-TYO-HANDLER-PATH3
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (OS-READYQ OS)))
           (OS-NEW-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (OS-READYQ OS))))
            (OS-NEW-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (OS-READYQ OS))))
             (OS-NEW-TASK-TABLE OS))
     '2
     (PUTNTH '2
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-OBUFFERS-WITH-ENQUEUED-CHARACTER OS)
                          '371
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3229
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (TM-REGS OS)
  (TM-CC OS)
  (TM-ERROR OS)
  '0
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-POST-OUTPUT-INTERRUPT (ARRAY-QFIRST (OS-READYQ OS))
                            (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-tyo-handler-to-svcr1 \\ \index{trace-svc-tyo-handler-to-svcr1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-oport-idlep}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-oport-idlep})\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyo-handler-thru-enqueue}}\,({\it{os\/}})\index{os-svc-tyo-handler-thru-enqueue}, \\ 
{\rm{os-time-for-svc-tyo-handler-to-svcr1}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-!svcr1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyo-handler-to-svcr1.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyo-handler-to-!svcr2} \\  
\=\+{\rm{os-time-for-svc-tyo-handler-to-svcr2}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-!svcr2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-SVC-TYO-HANDLER-PATH4
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (OS-READYQ OS)))
           (OS-NEW-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (OS-READYQ OS))))
            (OS-NEW-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (OS-READYQ OS))))
             (OS-NEW-TASK-TABLE OS))
     '2
     (PUTNTH '2
      '8
      (PUTNTH
       (ARRAY-QFIRST (OS-READYQ OS))
       '12
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-OBUFFERS-WITH-ENQUEUED-CHARACTER OS)
                          '371
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3229
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (TM-REGS OS)
  (TM-CC OS)
  (TM-ERROR OS)
  '0
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-svc-tyo-handler-to-svcr2 \\ \index{trace-svc-tyo-handler-to-svcr2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-oport-idlep}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\-\index{tm-oport-idlep}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyo-handler-thru-enqueue}}\,({\it{os\/}})\index{os-svc-tyo-handler-thru-enqueue}, \\ 
{\rm{os-time-for-svc-tyo-handler-to-svcr2}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-!svcr2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyo-handler-to-svcr2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-svc-tyo-time1} \\  
\=\+{\rm{os-svc-tyo-time1}}\,({\it{os\/}})\index{os-svc-tyo-time1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-tyo-time2} \\  
\=\+{\rm{os-svc-tyo-time2}}\,({\it{os\/}})\index{os-svc-tyo-time2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyo-handler-pat!h1} \\  
\=\+{\rm{os-time-for-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-pat!h1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-tyo-trace1 \\ \index{rewrite-svc-tyo-trace1}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyo-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyo-interrupt}, \\ 
{\rm{os-time-for-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-pat!h1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyo-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyo-interrupt}, \\ 
{\rm{os-time-for-svc-tyo-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-thr!u-save-state})\-\index{tm-processor}, \\ 
{\rm{os-svc-tyo-time1}}\,({\it{os\/}})\index{os-svc-tyo-time1})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-tyo-trace1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-tyo-trace2 \\ \index{rewrite-svc-tyo-trace2}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-tyo-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-tyo-handler-thru-save-st!ate}, {\rm{os-svc-tyo-time1}}\,({\it{os\/}})\index{os-svc-tyo-time1})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyo-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-tyo-handler-thru-save-st!ate}, \\ 
{\rm{os-time-for-svc-tyo-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-q!fullp-test})\-\index{tm-processor}, \\ 
{\rm{os-svc-tyo-time2}}\,({\it{os\/}})\index{os-svc-tyo-time2})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-tyo-trace2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-tyo-trace3 \\ \index{rewrite-svc-tyo-trace3}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-tyo-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-tyo-handler-to-qfullp-te!st}, {\rm{os-svc-tyo-time2}}\,({\it{os\/}})\index{os-svc-tyo-time2})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyo-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-tyo-handler-to-qfullp-te!st}, \\ 
{\rm{os-time-for-svc-tyo-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-!dispatcher})\-\index{tm-processor}, \\ 
{\rm{os-time-for-svc-tyo-handler-to-wait-state}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-!wait-state})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-tyo-trace3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-svc-tyo-handler-path1 \\ \index{trace-svc-tyo-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qfullp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyo-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyo-interrupt}, \\ 
{\rm{os-time-for-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-pat!h1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-svc-tyo-time3} \\  
\=\+{\rm{os-svc-tyo-time3}}\,({\it{os\/}})\index{os-svc-tyo-time3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-tyo-time4} \\  
\=\+{\rm{os-svc-tyo-time4}}\,({\it{os\/}})\index{os-svc-tyo-time4} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyo-handler-pat!h2} \\  
\=\+{\rm{os-time-for-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-pat!h2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-tyo-trace4 \\ \index{rewrite-svc-tyo-trace4}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyo-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyo-interrupt}, \\ 
{\rm{os-time-for-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-pat!h2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyo-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyo-interrupt}, \\ 
{\rm{os-time-for-svc-tyo-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-thr!u-save-state})\-\index{tm-processor}, \\ 
{\rm{os-svc-tyo-time3}}\,({\it{os\/}})\index{os-svc-tyo-time3})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-tyo-trace4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-tyo-trace5 \\ \index{rewrite-svc-tyo-trace5}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-tyo-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-tyo-handler-thru-save-st!ate}, {\rm{os-svc-tyo-time3}}\,({\it{os\/}})\index{os-svc-tyo-time3})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyo-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-tyo-handler-thru-save-st!ate}, \\ 
{\rm{os-time-for-svc-tyo-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-q!fullp-test})\-\index{tm-processor}, \\ 
{\rm{os-svc-tyo-time4}}\,({\it{os\/}})\index{os-svc-tyo-time4})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-tyo-trace5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-tyo-trace6 \\ \index{rewrite-svc-tyo-trace6}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-tyo-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-tyo-handler-to-qfullp-te!st}, {\rm{os-svc-tyo-time4}}\,({\it{os\/}})\index{os-svc-tyo-time4})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyo-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-tyo-handler-to-qfullp-te!st}, \\ 
{\rm{os-time-for-svc-tyo-handler-to-dispatcher}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-!dispatcher})\-\index{tm-processor}, \\ 
{\rm{os-time-for-svc-tyo-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-!lpsw})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-tyo-trace6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-svc-tyo-handler-path2 \\ \index{trace-svc-tyo-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qfullp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyo-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyo-interrupt}, \\ 
{\rm{os-time-for-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-pat!h2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-svc-tyo-time5} \\  
\=\+{\rm{os-svc-tyo-time5}}\,({\it{os\/}})\index{os-svc-tyo-time5} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-tyo-time6} \\  
\=\+{\rm{os-svc-tyo-time6}}\,({\it{os\/}})\index{os-svc-tyo-time6} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyo-handler-pat!h3} \\  
\=\+{\rm{os-time-for-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-pat!h3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-tyo-trace7 \\ \index{rewrite-svc-tyo-trace7}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyo-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyo-interrupt}, \\ 
{\rm{os-time-for-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-pat!h3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyo-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyo-interrupt}, \\ 
{\rm{os-time-for-svc-tyo-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-thr!u-save-state})\-\index{tm-processor}, \\ 
{\rm{os-svc-tyo-time5}}\,({\it{os\/}})\index{os-svc-tyo-time5})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-tyo-trace7.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-tyo-trace8 \\ \index{rewrite-svc-tyo-trace8}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-tyo-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-tyo-handler-thru-save-st!ate}, {\rm{os-svc-tyo-time5}}\,({\it{os\/}})\index{os-svc-tyo-time5})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyo-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-tyo-handler-thru-save-st!ate}, \\ 
{\rm{os-time-for-svc-tyo-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-q!fullp-test})\-\index{tm-processor}, \\ 
{\rm{os-svc-tyo-time6}}\,({\it{os\/}})\index{os-svc-tyo-time6})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-tyo-trace8.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-tyo-trace9 \\ \index{rewrite-svc-tyo-trace9}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-tyo-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-tyo-handler-to-qfullp-te!st}, {\rm{os-svc-tyo-time6}}\,({\it{os\/}})\index{os-svc-tyo-time6})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyo-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-tyo-handler-to-qfullp-te!st}, \\ 
{\rm{os-time-for-svc-tyo-handler-thru-enqueue}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-thr!u-enqueue})\-\index{tm-processor}, \\ 
{\rm{os-time-for-svc-tyo-handler-to-svcr1}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-!svcr1})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-tyo-trace9.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-svc-tyo-handler-path3 \\ \index{trace-svc-tyo-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-oport-idlep}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\-\index{tm-oport-idlep})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyo-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyo-interrupt}, \\ 
{\rm{os-time-for-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-pat!h3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-svc-tyo-time7} \\  
\=\+{\rm{os-svc-tyo-time7}}\,({\it{os\/}})\index{os-svc-tyo-time7} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-tyo-time8} \\  
\=\+{\rm{os-svc-tyo-time8}}\,({\it{os\/}})\index{os-svc-tyo-time8} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyo-handler-pat!h4} \\  
\=\+{\rm{os-time-for-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-pat!h4} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-tyo-trace10 \\ \index{rewrite-svc-tyo-trace10}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyo-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyo-interrupt}, \\ 
{\rm{os-time-for-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-pat!h4})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyo-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyo-interrupt}, \\ 
{\rm{os-time-for-svc-tyo-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-thr!u-save-state})\-\index{tm-processor}, \\ 
{\rm{os-svc-tyo-time7}}\,({\it{os\/}})\index{os-svc-tyo-time7})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-tyo-trace10.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-tyo-trace11 \\ \index{rewrite-svc-tyo-trace11}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-tyo-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-tyo-handler-thru-save-st!ate}, {\rm{os-svc-tyo-time7}}\,({\it{os\/}})\index{os-svc-tyo-time7})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyo-handler-thru-save-state}}\,({\it{os\/}})\index{os-svc-tyo-handler-thru-save-st!ate}, \\ 
{\rm{os-time-for-svc-tyo-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-q!fullp-test})\-\index{tm-processor}, \\ 
{\rm{os-svc-tyo-time8}}\,({\it{os\/}})\index{os-svc-tyo-time8})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-tyo-trace11.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-svc-tyo-trace12 \\ \index{rewrite-svc-tyo-trace12}
\=\+{\rm{tm-processor}}\,({\rm{os-svc-tyo-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-tyo-handler-to-qfullp-te!st}, {\rm{os-svc-tyo-time8}}\,({\it{os\/}})\index{os-svc-tyo-time8})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-svc-tyo-handler-to-qfullp-test}}\,({\it{os\/}})\index{os-svc-tyo-handler-to-qfullp-te!st}, \\ 
{\rm{os-time-for-svc-tyo-handler-thru-enqueue}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-thr!u-enqueue})\-\index{tm-processor}, \\ 
{\rm{os-time-for-svc-tyo-handler-to-svcr2}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-to-!svcr2})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-svc-tyo-trace12.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-svc-tyo-handler-path4 \\ \index{trace-svc-tyo-handler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-oport-idlep}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\-\index{tm-oport-idlep}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyo-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyo-interrupt}, \\ 
{\rm{os-time-for-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-pat!h4})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-tyo-handler} \\  
\=\+{\rm{os-time-for-svc-tyo-handler}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,({\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, {\it{os\/}})\index{os-current-obuffer})\index{array-qfullp} \\ 
{\bf then }\=\+{\bf if }{\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp} \\ 
{\bf then }{\rm{os-time-for-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-pat!h1} \\ 
{\bf else }{\rm{os-time-for-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-pat!h2}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{tm-oport-idlep}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-oport-idlep} \\ 
{\bf then }{\rm{os-time-for-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-pat!h3} \\ 
{\bf else }{\rm{os-time-for-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler-pat!h4}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-svc-tyo-handler} \\  
\=\+{\rm{os-svc-tyo-handler}}\,({\it{os\/}})\index{os-svc-tyo-handler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,({\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, {\it{os\/}})\index{os-current-obuffer})\index{array-qfullp} \\ 
{\bf then }\=\+{\bf if }{\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp} \\ 
{\bf then }{\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1} \\ 
{\bf else }{\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{tm-oport-idlep}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-oport-idlep} \\ 
{\bf then }{\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3} \\ 
{\bf else }{\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  trace-svc-tyo-handler \\ \index{trace-svc-tyo-handler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-tyo-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyo-interrupt}, \\ 
{\rm{os-time-for-svc-tyo-handler}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-tyo-handler}}\,({\it{os\/}})\index{os-svc-tyo-handler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-tyo-handler.

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN
 OS-INTENDED-INPUT-INTERRUPT
 (TM)
 (TM-SET-MEMORY
  (PUTNTH
   (TM-PC TM)
   '0
   (PUTNTH
    (TM-SP TM)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC TM)
                  (TM-ERROR TM)
                  (TM-SVCFLAG TM)
                  (TM-SVCID TM))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS TM))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS TM))
                         (TM-IPORTS TM)))
       '9
       (PUTSEG
              (OS-TASK-TABLE TM)
              '15
              (PUTSEG (OS-SEGMENT-TABLE TM)
                      '159
                      (PUTSEG (OS-READYQ TM)
                              '191
                              (PUTSEG (OS-STATUS-TABLE TM)
                                      '211
                                      (PUTSEG (OS-IBUFFERS TM)
                                              '243
                                              (PUTSEG (OS-CODE TM)
                                                      '2547
                                                      (TM-MEMORY TM))))))))))))
  (TM-SET-PC '3042
   (TM-SET-SP '3310
    (TM-SET-SVMODE '1
     (TM-SET-ERROR '0
      (TM-SET-RWSTATE '0
       (TM-SET-IPORTS
          (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS TM))
                                    (TM-IPORTS TM))
          TM)))))))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  equivalence-of-input-interrupt-expressions \\ \index{equivalence-of-input-interrupt-e!xpressions}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-execute-input-interrupt}}\,({\it{os\/}})\index{tm-execute-input-interrupt} $=$ {\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt})\-
\end{tabbing}


\noindent{\sc Event}:   Disable equivalence-of-input-interrupt-expressions.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-input-handle!r-thru-readyq-empty-test} \\  
\=\+{\rm{os-time-for-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-thru-readyq-empty-test} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-WAITING-INPUT-HANDLER-THRU-READYQ-EMPTY-TEST
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3206
        '10
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG (OS-READYQ OS)
                   '191
                   (PUTSEG (OS-STATUS-TABLE OS)
                           '211
                           (PUTSEG (OS-IBUFFERS OS)
                                   '243
                                   (PUTSEG (OS-CODE OS)
                                           '2547
                                           (PUTNTH '3053
                                                   '3310
                                                   (TM-MEMORY OS)))))))))))))))
  (PUTNTH '3063
          '0
          (PUTNTH '3310
                  '1
                  (PUTNTH '191 '3 (TM-REGS OS))))
  '1
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler-thru-readyq-empty-test \\ \index{trace-waiting-input-handler-thr!u-readyq-empty-test}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-thru-readyq-empty-test})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-input-handler-thru-re!adyq-empty-test})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler-thru-readyq-empty-test.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-input-handle!r-to-ibuffer-full-test} \\  
\=\+{\rm{os-time-for-waiting-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-ibuffer-full-test} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-WAITING-INPUT-HANDLER-TO-IBUFFER-FULL-TEST
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3206
        '10
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-ENQ (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                       (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    '0
                                    '0
                                    OS)
                  '211
                  (PUTSEG (OS-IBUFFERS OS)
                          '243
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '3085
                                          '3310
                                          (TM-MEMORY OS)))))))))))))))
  (PUTNTH '3091
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
     '2
     (PUTNTH '191
      '3
      (PUTNTH
             (PLUS '195
                   (GETNTH '1 (OS-READYQ OS)))
             '4
             (PUTNTH (PLUS '211
                           (TIMES '2
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     '5
                     (TM-REGS OS)))))))
  (TM-CC-VALUE (TM-ALU-INCR-MOD (GETNTH '1 (OS-READYQ OS))
                                '16))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler-to-ibuffer-full-test \\ \index{trace-waiting-input-handler-to-i!buffer-full-test}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-input-handler-thru-re!adyq-empty-test}, \\ 
{\rm{os-time-for-waiting-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-ibuffer-full-test})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-waiting-input-handler-to-ibu!ffer-full-test})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler-to-ibuffer-full-test.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-input-handle!r-to-dispatcher1} \\  
\=\+{\rm{os-time-for-waiting-input-handler-to-dispatcher1}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-dispatcher1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-WAITING-INPUT-HANDLER-TO-DISPATCHER1
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3206
        '10
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-ENQ (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                       (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    '0
                                    '0
                                    OS)
                  '211
                  (PUTSEG (OS-IBUFFERS-WITH-QREPLACED-OVERFLOW-CHARACTER OS)
                          '243
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '3112
                                          '3310
                                          (TM-MEMORY OS)))))))))))))))
  (PUTNTH '3206
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (PLUS '256
           (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                             (TM-IPORTS OS))))
     '2
     (PUTNTH
      (PLUS '243
            (TIMES '8
                   (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
      '3
      (PUTNTH
       (PLUS '247
        (PLUS
          (TIMES '8
                 (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
          (DECR-MOD (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))
                    '4)))
       '4
       (PUTNTH (PLUS '211
                     (TIMES '2
                            (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
               '5
               (TM-REGS OS)))))))
  (TM-CC-VALUE
   (TM-ALU-PLUS
    (PLUS '243
     (PLUS
          (TIMES '8
                 (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
          (DECR-MOD (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))
                    '4)))
    '4))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler-to-dispatcher1 \\ \index{trace-waiting-input-handler-to-!dispatcher1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-waiting-input-handler-to-ibu!ffer-full-test}, \\ 
{\rm{os-time-for-waiting-input-handler-to-dispatcher1}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-dispatcher1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler-to-dispatcher1}}\,({\it{os\/}})\index{os-waiting-input-handler-to-disp!atcher1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler-to-dispatcher1.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-input-handle!r-to-dispatcher2} \\  
\=\+{\rm{os-time-for-waiting-input-handler-to-dispatcher2}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-dispatcher2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-WAITING-INPUT-HANDLER-TO-DISPATCHER2
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3206
        '10
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-ENQ (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                       (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    '0
                                    '0
                                    OS)
                  '211
                  (PUTSEG (OS-IBUFFERS-WITH-ENQUEUED-OVERFLOW-CHARACTER OS)
                          '243
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '3126
                                          '3310
                                          (TM-MEMORY OS)))))))))))))))
  (PUTNTH '3206
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (PLUS '256
           (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                             (TM-IPORTS OS))))
     '2
     (PUTNTH
      (PLUS '243
            (TIMES '8
                   (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
      '3
      (PUTNTH
        (PLUS '247
              (PLUS (TIMES '8
                           (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
                    (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))))
        '4
        (PUTNTH (PLUS '211
                      (TIMES '2
                             (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                '5
                (TM-REGS OS)))))))
  (TM-CC-VALUE
   (TM-ALU-INCR-MOD (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))
                    (GETNTH '3
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler-to-dispatcher2 \\ \index{trace-waiting-input-handler-to-!dispatcher2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-waiting-input-handler-to-ibu!ffer-full-test}, \\ 
{\rm{os-time-for-waiting-input-handler-to-dispatcher2}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-dispatcher2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler-to-dispatcher2}}\,({\it{os\/}})\index{os-waiting-input-handler-to-disp!atcher2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler-to-dispatcher2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-input-handle!r-to-dispatcher3} \\  
\=\+{\rm{os-time-for-waiting-input-handler-to-dispatcher3}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-dispatcher3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-WAITING-INPUT-HANDLER-TO-DISPATCHER3
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3206
        '10
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-ENQ (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                       (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    '0
                                    '0
                                    OS)
                  '211
                  (PUTSEG (OS-IBUFFERS-WITH-ENQUEUED-CHARACTER OS)
                          '243
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '3133
                                          '3310
                                          (TM-MEMORY OS)))))))))))))))
  (PUTNTH '3206
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                       (TM-IPORTS OS)))
     '2
     (PUTNTH
      (PLUS '243
            (TIMES '8
                   (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
      '3
      (PUTNTH
        (PLUS '247
              (PLUS (TIMES '8
                           (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
                    (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))))
        '4
        (PUTNTH (PLUS '211
                      (TIMES '2
                             (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                '5
                (TM-REGS OS)))))))
  (TM-CC-VALUE
   (TM-ALU-INCR-MOD (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))
                    (GETNTH '3
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler-to-dispatcher3 \\ \index{trace-waiting-input-handler-to-!dispatcher3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-waiting-input-handler-to-ibu!ffer-full-test}, \\ 
{\rm{os-time-for-waiting-input-handler-to-dispatcher3}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-dispatcher3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler-to-dispatcher3}}\,({\it{os\/}})\index{os-waiting-input-handler-to-disp!atcher3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler-to-dispatcher3.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-input-handle!r-to-lpsw} \\  
\=\+{\rm{os-time-for-waiting-input-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-lpsw} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-WAITING-INPUT-HANDLER-PATH1
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
           (OS-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
            (OS-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
             (OS-TASK-TABLE OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3206
        '10
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-ENQ (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                       (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    '0
                                    '0
                                    OS)
                  '211
                  (PUTSEG (OS-IBUFFERS-WITH-QREPLACED-OVERFLOW-CHARACTER OS)
                          '243
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '3217
                                          '3310
                                          (TM-MEMORY OS)))))))))))))))
  (GETSEG '0
          '8
          (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                  (TABLE '9 (OS-TASK-TABLE OS))))
  (REMAINDER (GETNTH (PLUS '8
                           (TIMES '9
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     (OS-TASK-TABLE OS))
             '4)
  (QUOTIENT
   (REMAINDER
             (GETNTH (PLUS '8
                           (TIMES '9
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     (OS-TASK-TABLE OS))
             '256)
   '4)
  (QUOTIENT
   (REMAINDER
             (GETNTH (PLUS '8
                           (TIMES '9
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     (OS-TASK-TABLE OS))
             '512)
   '256)
  (QUOTIENT (GETNTH (PLUS '8
                          (TIMES '9
                                 (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                    (OS-TASK-TABLE OS))
            '512)
  (BASE (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                (TABLE '2 (OS-SEGMENT-TABLE OS))))
  (LIMIT (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                 (TABLE '2 (OS-SEGMENT-TABLE OS))))
  (TM-SLIMIT OS)
  '0
  '0
  '1000
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler-to-lpsw1 \\ \index{trace-waiting-input-handler-to-!lpsw1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-dispatcher1}}\,({\it{os\/}})\index{os-waiting-input-handler-to-disp!atcher1}, \\ 
{\rm{os-time-for-waiting-input-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-lpsw})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler-to-lpsw1.

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN
 OS-WAITING-INPUT-HANDLER-PATH2
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
           (OS-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
            (OS-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
             (OS-TASK-TABLE OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3206
        '10
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-ENQ (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                       (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    '0
                                    '0
                                    OS)
                  '211
                  (PUTSEG (OS-IBUFFERS-WITH-ENQUEUED-OVERFLOW-CHARACTER OS)
                          '243
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '3217
                                          '3310
                                          (TM-MEMORY OS)))))))))))))))
  (GETSEG '0
          '8
          (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                  (TABLE '9 (OS-TASK-TABLE OS))))
  (REMAINDER (GETNTH (PLUS '8
                           (TIMES '9
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     (OS-TASK-TABLE OS))
             '4)
  (QUOTIENT
   (REMAINDER
             (GETNTH (PLUS '8
                           (TIMES '9
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     (OS-TASK-TABLE OS))
             '256)
   '4)
  (QUOTIENT
   (REMAINDER
             (GETNTH (PLUS '8
                           (TIMES '9
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     (OS-TASK-TABLE OS))
             '512)
   '256)
  (QUOTIENT (GETNTH (PLUS '8
                          (TIMES '9
                                 (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                    (OS-TASK-TABLE OS))
            '512)
  (BASE (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                (TABLE '2 (OS-SEGMENT-TABLE OS))))
  (LIMIT (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                 (TABLE '2 (OS-SEGMENT-TABLE OS))))
  (TM-SLIMIT OS)
  '0
  '0
  '1000
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler-to-lpsw2 \\ \index{trace-waiting-input-handler-to-!lpsw2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-dispatcher2}}\,({\it{os\/}})\index{os-waiting-input-handler-to-disp!atcher2}, \\ 
{\rm{os-time-for-waiting-input-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-lpsw})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler-to-lpsw2.

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN
 OS-WAITING-INPUT-HANDLER-PATH3
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
           (OS-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
            (OS-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
             (OS-TASK-TABLE OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3206
        '10
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-ENQ (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                       (OS-READYQ OS))
            '191
            (PUTSEG
                  (OS-UPDATE-STATUS (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    '0
                                    '0
                                    OS)
                  '211
                  (PUTSEG (OS-IBUFFERS-WITH-ENQUEUED-CHARACTER OS)
                          '243
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '3217
                                          '3310
                                          (TM-MEMORY OS)))))))))))))))
  (GETSEG '0
          '8
          (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                  (TABLE '9 (OS-TASK-TABLE OS))))
  (REMAINDER (GETNTH (PLUS '8
                           (TIMES '9
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     (OS-TASK-TABLE OS))
             '4)
  (QUOTIENT
   (REMAINDER
             (GETNTH (PLUS '8
                           (TIMES '9
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     (OS-TASK-TABLE OS))
             '256)
   '4)
  (QUOTIENT
   (REMAINDER
             (GETNTH (PLUS '8
                           (TIMES '9
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     (OS-TASK-TABLE OS))
             '512)
   '256)
  (QUOTIENT (GETNTH (PLUS '8
                          (TIMES '9
                                 (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                    (OS-TASK-TABLE OS))
            '512)
  (BASE (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                (TABLE '2 (OS-SEGMENT-TABLE OS))))
  (LIMIT (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                 (TABLE '2 (OS-SEGMENT-TABLE OS))))
  (TM-SLIMIT OS)
  '0
  '0
  '1000
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler-to-lpsw3 \\ \index{trace-waiting-input-handler-to-!lpsw3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-dispatcher3}}\,({\it{os\/}})\index{os-waiting-input-handler-to-disp!atcher3}, \\ 
{\rm{os-time-for-waiting-input-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-lpsw})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler-to-lpsw3.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-waiting-input-time1} \\  
\=\+{\rm{os-waiting-input-time1}}\,({\it{os\/}})\index{os-waiting-input-time1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-waiting-input-time2} \\  
\=\+{\rm{os-waiting-input-time2}}\,({\it{os\/}})\index{os-waiting-input-time2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-input-handle!r-path1} \\  
\=\+{\rm{os-time-for-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-input-trace1 \\ \index{rewrite-waiting-input-trace1}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-thru-readyq-empty-test})\-\index{tm-processor}, \\ 
{\rm{os-waiting-input-time1}}\,({\it{os\/}})\index{os-waiting-input-time1})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-input-trace1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-input-trace2 \\ \index{rewrite-waiting-input-trace2}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-input-handler-thru-re!adyq-empty-test}, \\ 
{\rm{os-waiting-input-time1}}\,({\it{os\/}})\index{os-waiting-input-time1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-input-handler-thru-re!adyq-empty-test}, \\ 
{\rm{os-time-for-waiting-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-ibuffer-full-test})\-\index{tm-processor}, \\ 
{\rm{os-waiting-input-time2}}\,({\it{os\/}})\index{os-waiting-input-time2})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-input-trace2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-input-trace3 \\ \index{rewrite-waiting-input-trace3}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-waiting-input-handler-to-ibu!ffer-full-test}, \\ 
{\rm{os-waiting-input-time2}}\,({\it{os\/}})\index{os-waiting-input-time2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-waiting-input-handler-to-ibu!ffer-full-test}, \\ 
{\rm{os-time-for-waiting-input-handler-to-dispatcher1}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-dispatcher1})\-\index{tm-processor}, \\ 
{\rm{os-time-for-waiting-input-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-lpsw})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-input-trace3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler-path1 \\ \index{trace-waiting-input-handler-pat!h1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-waiting-input-time3} \\  
\=\+{\rm{os-waiting-input-time3}}\,({\it{os\/}})\index{os-waiting-input-time3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-waiting-input-time4} \\  
\=\+{\rm{os-waiting-input-time4}}\,({\it{os\/}})\index{os-waiting-input-time4} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-input-handle!r-path2} \\  
\=\+{\rm{os-time-for-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-input-trace4 \\ \index{rewrite-waiting-input-trace4}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-thru-readyq-empty-test})\-\index{tm-processor}, \\ 
{\rm{os-waiting-input-time3}}\,({\it{os\/}})\index{os-waiting-input-time3})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-input-trace4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-input-trace5 \\ \index{rewrite-waiting-input-trace5}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-input-handler-thru-re!adyq-empty-test}, \\ 
{\rm{os-waiting-input-time3}}\,({\it{os\/}})\index{os-waiting-input-time3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-input-handler-thru-re!adyq-empty-test}, \\ 
{\rm{os-time-for-waiting-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-ibuffer-full-test})\-\index{tm-processor}, \\ 
{\rm{os-waiting-input-time4}}\,({\it{os\/}})\index{os-waiting-input-time4})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-input-trace5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-input-trace6 \\ \index{rewrite-waiting-input-trace6}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-waiting-input-handler-to-ibu!ffer-full-test}, \\ 
{\rm{os-waiting-input-time4}}\,({\it{os\/}})\index{os-waiting-input-time4})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-waiting-input-handler-to-ibu!ffer-full-test}, \\ 
{\rm{os-time-for-waiting-input-handler-to-dispatcher2}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-dispatcher2})\-\index{tm-processor}, \\ 
{\rm{os-time-for-waiting-input-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-lpsw})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-input-trace6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler-path2 \\ \index{trace-waiting-input-handler-pat!h2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-waiting-input-time5} \\  
\=\+{\rm{os-waiting-input-time5}}\,({\it{os\/}})\index{os-waiting-input-time5} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-waiting-input-time6} \\  
\=\+{\rm{os-waiting-input-time6}}\,({\it{os\/}})\index{os-waiting-input-time6} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-input-handle!r-path3} \\  
\=\+{\rm{os-time-for-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-input-trace7 \\ \index{rewrite-waiting-input-trace7}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-thru-readyq-empty-test})\-\index{tm-processor}, \\ 
{\rm{os-waiting-input-time5}}\,({\it{os\/}})\index{os-waiting-input-time5})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-input-trace7.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-input-trace8 \\ \index{rewrite-waiting-input-trace8}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-input-handler-thru-re!adyq-empty-test}, \\ 
{\rm{os-waiting-input-time5}}\,({\it{os\/}})\index{os-waiting-input-time5})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-input-handler-thru-re!adyq-empty-test}, \\ 
{\rm{os-time-for-waiting-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-ibuffer-full-test})\-\index{tm-processor}, \\ 
{\rm{os-waiting-input-time6}}\,({\it{os\/}})\index{os-waiting-input-time6})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-input-trace8.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-input-trace9 \\ \index{rewrite-waiting-input-trace9}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-waiting-input-handler-to-ibu!ffer-full-test}, \\ 
{\rm{os-waiting-input-time6}}\,({\it{os\/}})\index{os-waiting-input-time6})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-waiting-input-handler-to-ibu!ffer-full-test}, \\ 
{\rm{os-time-for-waiting-input-handler-to-dispatcher3}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-dispatcher3})\-\index{tm-processor}, \\ 
{\rm{os-time-for-waiting-input-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-lpsw})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-input-trace9.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler-path3 \\ \index{trace-waiting-input-handler-pat!h3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-input-handle!r-to-ibuffer-full-test2} \\  
\=\+{\rm{os-time-for-waiting-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-ibuffer-full-test2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-WAITING-INPUT-HANDLER-TO-IBUFFER-FULL-TEST2
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3206
        '10
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG (OS-READYQ OS)
                   '191
                   (PUTSEG (OS-STATUS-TABLE OS)
                           '211
                           (PUTSEG (OS-IBUFFERS OS)
                                   '243
                                   (PUTSEG (OS-CODE OS)
                                           '2547
                                           (PUTNTH '3053
                                                   '3310
                                                   (TM-MEMORY OS)))))))))))))))
  (PUTNTH '3091
   '0
   (PUTNTH '3310
     '1
     (PUTNTH '191
             '3
             (PUTNTH (PLUS '211
                           (TIMES '2
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     '5
                     (TM-REGS OS)))))
  (TM-CC-VALUE
   (TM-ALU-DIFFERENCE
                    (GETNTH (TIMES '2
                                   (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
                            (OS-STATUS-TABLE OS))
                    '5))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler-to-ibuffer-full-test2 \\ \index{trace-waiting-input-handler-to-i!buffer-full-test2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-input-handler-thru-re!adyq-empty-test}, \\ 
{\rm{os-time-for-waiting-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-ibuffer-full-test2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-waiting-input-handler-to-ibu!ffer-full-test2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler-to-ibuffer-full-test2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-input-handle!r-to-dispatcher4} \\  
\=\+{\rm{os-time-for-waiting-input-handler-to-dispatcher4}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-dispatcher4} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-WAITING-INPUT-HANDLER-TO-DISPATCHER4
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3206
        '10
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
             (OS-READYQ OS)
             '191
             (PUTSEG (OS-STATUS-TABLE OS)
                     '211
                     (PUTSEG (OS-IBUFFERS-WITH-QREPLACED-OVERFLOW-CHARACTER OS)
                             '243
                             (PUTSEG (OS-CODE OS)
                                     '2547
                                     (PUTNTH '3112
                                             '3310
                                             (TM-MEMORY OS)))))))))))))))
  (PUTNTH '3206
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (PLUS '256
           (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                             (TM-IPORTS OS))))
     '2
     (PUTNTH
      (PLUS '243
            (TIMES '8
                   (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
      '3
      (PUTNTH
       (PLUS '247
        (PLUS
          (TIMES '8
                 (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
          (DECR-MOD (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))
                    '4)))
       '4
       (PUTNTH (PLUS '211
                     (TIMES '2
                            (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
               '5
               (TM-REGS OS)))))))
  (TM-CC-VALUE
   (TM-ALU-PLUS
    (PLUS '243
     (PLUS
          (TIMES '8
                 (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
          (DECR-MOD (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))
                    '4)))
    '4))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler-to-dispatcher4 \\ \index{trace-waiting-input-handler-to-!dispatcher4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-waiting-input-handler-to-ibu!ffer-full-test2}, \\ 
{\rm{os-time-for-waiting-input-handler-to-dispatcher4}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-dispatcher4})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler-to-dispatcher4}}\,({\it{os\/}})\index{os-waiting-input-handler-to-disp!atcher4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler-to-dispatcher4.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-input-handle!r-to-dispatcher5} \\  
\=\+{\rm{os-time-for-waiting-input-handler-to-dispatcher5}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-dispatcher5} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-WAITING-INPUT-HANDLER-TO-DISPATCHER5
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3206
        '10
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
              (OS-READYQ OS)
              '191
              (PUTSEG (OS-STATUS-TABLE OS)
                      '211
                      (PUTSEG (OS-IBUFFERS-WITH-ENQUEUED-OVERFLOW-CHARACTER OS)
                              '243
                              (PUTSEG (OS-CODE OS)
                                      '2547
                                      (PUTNTH '3126
                                              '3310
                                              (TM-MEMORY OS)))))))))))))))
  (PUTNTH '3206
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (PLUS '256
           (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                             (TM-IPORTS OS))))
     '2
     (PUTNTH
      (PLUS '243
            (TIMES '8
                   (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
      '3
      (PUTNTH
        (PLUS '247
              (PLUS (TIMES '8
                           (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
                    (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))))
        '4
        (PUTNTH (PLUS '211
                      (TIMES '2
                             (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                '5
                (TM-REGS OS)))))))
  (TM-CC-VALUE
   (TM-ALU-INCR-MOD (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))
                    (GETNTH '3
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler-to-dispatcher5 \\ \index{trace-waiting-input-handler-to-!dispatcher5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-waiting-input-handler-to-ibu!ffer-full-test2}, \\ 
{\rm{os-time-for-waiting-input-handler-to-dispatcher5}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-dispatcher5})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler-to-dispatcher5}}\,({\it{os\/}})\index{os-waiting-input-handler-to-disp!atcher5})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler-to-dispatcher5.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-input-handle!r-to-dispatcher6} \\  
\=\+{\rm{os-time-for-waiting-input-handler-to-dispatcher6}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-dispatcher6} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-WAITING-INPUT-HANDLER-TO-DISPATCHER6
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3206
        '10
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG (OS-READYQ OS)
                   '191
                   (PUTSEG (OS-STATUS-TABLE OS)
                           '211
                           (PUTSEG (OS-IBUFFERS-WITH-ENQUEUED-CHARACTER OS)
                                   '243
                                   (PUTSEG (OS-CODE OS)
                                           '2547
                                           (PUTNTH '3133
                                                   '3310
                                                   (TM-MEMORY OS)))))))))))))))
  (PUTNTH '3206
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                       (TM-IPORTS OS)))
     '2
     (PUTNTH
      (PLUS '243
            (TIMES '8
                   (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
      '3
      (PUTNTH
        (PLUS '247
              (PLUS (TIMES '8
                           (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
                    (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))))
        '4
        (PUTNTH (PLUS '211
                      (TIMES '2
                             (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                '5
                (TM-REGS OS)))))))
  (TM-CC-VALUE
   (TM-ALU-INCR-MOD (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))
                    (GETNTH '3
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler-to-dispatcher6 \\ \index{trace-waiting-input-handler-to-!dispatcher6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-waiting-input-handler-to-ibu!ffer-full-test2}, \\ 
{\rm{os-time-for-waiting-input-handler-to-dispatcher6}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-dispatcher6})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler-to-dispatcher6}}\,({\it{os\/}})\index{os-waiting-input-handler-to-disp!atcher6})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler-to-dispatcher6.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-input-handle!r-to-wait} \\  
\=\+{\rm{os-time-for-waiting-input-handler-to-wait}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-wait} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-WAITING-INPUT-HANDLER-PATH4
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3206
        '10
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
             (OS-READYQ OS)
             '191
             (PUTSEG (OS-STATUS-TABLE OS)
                     '211
                     (PUTSEG (OS-IBUFFERS-WITH-QREPLACED-OVERFLOW-CHARACTER OS)
                             '243
                             (PUTSEG (OS-CODE OS)
                                     '2547
                                     (PUTNTH '3211
                                             '3310
                                             (TM-MEMORY OS)))))))))))))))
  (PUTNTH '3222
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (PLUS '256
           (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                             (TM-IPORTS OS))))
     '2
     (PUTNTH '191
      '3
      (PUTNTH
       (PLUS '247
        (PLUS
          (TIMES '8
                 (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
          (DECR-MOD (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))
                    '4)))
       '4
       (PUTNTH (PLUS '211
                     (TIMES '2
                            (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
               '5
               (TM-REGS OS)))))))
  '1
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '1
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler-to-wait1 \\ \index{trace-waiting-input-handler-to-!wait1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-dispatcher4}}\,({\it{os\/}})\index{os-waiting-input-handler-to-disp!atcher4}, \\ 
{\rm{os-time-for-waiting-input-handler-to-wait}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-wait})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler-to-wait1.

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN
 OS-WAITING-INPUT-HANDLER-PATH5
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3206
        '10
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
              (OS-READYQ OS)
              '191
              (PUTSEG (OS-STATUS-TABLE OS)
                      '211
                      (PUTSEG (OS-IBUFFERS-WITH-ENQUEUED-OVERFLOW-CHARACTER OS)
                              '243
                              (PUTSEG (OS-CODE OS)
                                      '2547
                                      (PUTNTH '3211
                                              '3310
                                              (TM-MEMORY OS)))))))))))))))
  (PUTNTH '3222
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (PLUS '256
           (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                             (TM-IPORTS OS))))
     '2
     (PUTNTH '191
      '3
      (PUTNTH
        (PLUS '247
              (PLUS (TIMES '8
                           (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
                    (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))))
        '4
        (PUTNTH (PLUS '211
                      (TIMES '2
                             (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                '5
                (TM-REGS OS)))))))
  '1
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '1
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler-to-wait2 \\ \index{trace-waiting-input-handler-to-!wait2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-dispatcher5}}\,({\it{os\/}})\index{os-waiting-input-handler-to-disp!atcher5}, \\ 
{\rm{os-time-for-waiting-input-handler-to-wait}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-wait})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler-to-wait2.

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN
 OS-WAITING-INPUT-HANDLER-PATH6
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3206
        '10
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG (OS-READYQ OS)
                   '191
                   (PUTSEG (OS-STATUS-TABLE OS)
                           '211
                           (PUTSEG (OS-IBUFFERS-WITH-ENQUEUED-CHARACTER OS)
                                   '243
                                   (PUTSEG (OS-CODE OS)
                                           '2547
                                           (PUTNTH '3211
                                                   '3310
                                                   (TM-MEMORY OS)))))))))))))))
  (PUTNTH '3222
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                       (TM-IPORTS OS)))
     '2
     (PUTNTH '191
      '3
      (PUTNTH
        (PLUS '247
              (PLUS (TIMES '8
                           (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
                    (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))))
        '4
        (PUTNTH (PLUS '211
                      (TIMES '2
                             (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                '5
                (TM-REGS OS)))))))
  '1
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '1
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler-to-wait3 \\ \index{trace-waiting-input-handler-to-!wait3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-dispatcher6}}\,({\it{os\/}})\index{os-waiting-input-handler-to-disp!atcher6}, \\ 
{\rm{os-time-for-waiting-input-handler-to-wait}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-wait})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler-to-wait3.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-waiting-input-time7} \\  
\=\+{\rm{os-waiting-input-time7}}\,({\it{os\/}})\index{os-waiting-input-time7} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-waiting-input-time8} \\  
\=\+{\rm{os-waiting-input-time8}}\,({\it{os\/}})\index{os-waiting-input-time8} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-input-handle!r-path4} \\  
\=\+{\rm{os-time-for-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path4} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-input-trace10 \\ \index{rewrite-waiting-input-trace10}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path4})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-thru-readyq-empty-test})\-\index{tm-processor}, \\ 
{\rm{os-waiting-input-time7}}\,({\it{os\/}})\index{os-waiting-input-time7})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-input-trace10.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-input-trace11 \\ \index{rewrite-waiting-input-trace11}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-input-handler-thru-re!adyq-empty-test}, \\ 
{\rm{os-waiting-input-time7}}\,({\it{os\/}})\index{os-waiting-input-time7})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-input-handler-thru-re!adyq-empty-test}, \\ 
{\rm{os-time-for-waiting-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-ibuffer-full-test2})\-\index{tm-processor}, \\ 
{\rm{os-waiting-input-time8}}\,({\it{os\/}})\index{os-waiting-input-time8})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-input-trace11.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-input-trace12 \\ \index{rewrite-waiting-input-trace12}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-waiting-input-handler-to-ibu!ffer-full-test2}, \\ 
{\rm{os-waiting-input-time8}}\,({\it{os\/}})\index{os-waiting-input-time8})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-waiting-input-handler-to-ibu!ffer-full-test2}, \\ 
{\rm{os-time-for-waiting-input-handler-to-dispatcher4}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-dispatcher4})\-\index{tm-processor}, \\ 
{\rm{os-time-for-waiting-input-handler-to-wait}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-wait})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-input-trace12.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler-path4 \\ \index{trace-waiting-input-handler-pat!h4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path4})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-waiting-input-time9} \\  
\=\+{\rm{os-waiting-input-time9}}\,({\it{os\/}})\index{os-waiting-input-time9} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-waiting-input-time10} \\  
\=\+{\rm{os-waiting-input-time10}}\,({\it{os\/}})\index{os-waiting-input-time10} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-input-handle!r-path5} \\  
\=\+{\rm{os-time-for-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path5} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-input-trace13 \\ \index{rewrite-waiting-input-trace13}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path5})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-thru-readyq-empty-test})\-\index{tm-processor}, \\ 
{\rm{os-waiting-input-time9}}\,({\it{os\/}})\index{os-waiting-input-time9})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-input-trace13.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-input-trace14 \\ \index{rewrite-waiting-input-trace14}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-input-handler-thru-re!adyq-empty-test}, \\ 
{\rm{os-waiting-input-time9}}\,({\it{os\/}})\index{os-waiting-input-time9})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-input-handler-thru-re!adyq-empty-test}, \\ 
{\rm{os-time-for-waiting-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-ibuffer-full-test2})\-\index{tm-processor}, \\ 
{\rm{os-waiting-input-time10}}\,({\it{os\/}})\index{os-waiting-input-time10})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-input-trace14.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-input-trace15 \\ \index{rewrite-waiting-input-trace15}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-waiting-input-handler-to-ibu!ffer-full-test2}, \\ 
{\rm{os-waiting-input-time10}}\,({\it{os\/}})\index{os-waiting-input-time10})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-waiting-input-handler-to-ibu!ffer-full-test2}, \\ 
{\rm{os-time-for-waiting-input-handler-to-dispatcher5}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-dispatcher5})\-\index{tm-processor}, \\ 
{\rm{os-time-for-waiting-input-handler-to-wait}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-wait})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-input-trace15.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler-path5 \\ \index{trace-waiting-input-handler-pat!h5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path5})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-waiting-input-time11} \\  
\=\+{\rm{os-waiting-input-time11}}\,({\it{os\/}})\index{os-waiting-input-time11} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-waiting-input-time12} \\  
\=\+{\rm{os-waiting-input-time12}}\,({\it{os\/}})\index{os-waiting-input-time12} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-input-handle!r-path6} \\  
\=\+{\rm{os-time-for-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path6} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-input-trace16 \\ \index{rewrite-waiting-input-trace16}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path6})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-thru-readyq-empty-test})\-\index{tm-processor}, \\ 
{\rm{os-waiting-input-time11}}\,({\it{os\/}})\index{os-waiting-input-time11})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-input-trace16.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-input-trace17 \\ \index{rewrite-waiting-input-trace17}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-input-handler-thru-re!adyq-empty-test}, \\ 
{\rm{os-waiting-input-time11}}\,({\it{os\/}})\index{os-waiting-input-time11})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-input-handler-thru-re!adyq-empty-test}, \\ 
{\rm{os-time-for-waiting-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-ibuffer-full-test2})\-\index{tm-processor}, \\ 
{\rm{os-waiting-input-time12}}\,({\it{os\/}})\index{os-waiting-input-time12})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-input-trace17.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-input-trace18 \\ \index{rewrite-waiting-input-trace18}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-waiting-input-handler-to-ibu!ffer-full-test2}, \\ 
{\rm{os-waiting-input-time12}}\,({\it{os\/}})\index{os-waiting-input-time12})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-waiting-input-handler-to-ibu!ffer-full-test2}, \\ 
{\rm{os-time-for-waiting-input-handler-to-dispatcher6}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-dispatcher6})\-\index{tm-processor}, \\ 
{\rm{os-time-for-waiting-input-handler-to-wait}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-to-wait})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-input-trace18.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler-path6 \\ \index{trace-waiting-input-handler-pat!h6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path6})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-input-handle!r} \\  
\=\+{\rm{os-time-for-waiting-input-handler}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}}\- \\ 
{\bf then }\=\+{\bf if }{\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp} \\ 
{\bf then }{\rm{os-time-for-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path1} \\ 
{\bf elseif }{\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp} \\ 
{\bf then }{\rm{os-time-for-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path2} \\ 
{\bf else }{\rm{os-time-for-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path3}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp} \\ 
{\bf then }{\rm{os-time-for-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path4} \\ 
{\bf elseif }{\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp} \\ 
{\bf then }{\rm{os-time-for-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path5} \\ 
{\bf else }{\rm{os-time-for-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r-path6}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-waiting-input-handler} \\  
\=\+{\rm{os-waiting-input-handler}}\,({\it{os\/}})\index{os-waiting-input-handler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}}\- \\ 
{\bf then }\=\+{\bf if }{\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp} \\ 
{\bf then }{\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1} \\ 
{\bf elseif }{\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp} \\ 
{\bf then }{\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2} \\ 
{\bf else }{\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp} \\ 
{\bf then }{\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4} \\ 
{\bf elseif }{\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp} \\ 
{\bf then }{\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5} \\ 
{\bf else }{\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  trace-waiting-input-handler \\ \index{trace-waiting-input-handler}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-waiting-input-handler}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-input-handler}}\,({\it{os\/}})\index{os-waiting-input-handler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-input-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-input-handle!r-thru-save-state} \\  
\=\+{\rm{os-time-for-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-thru-save-state} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-RUNNING-INPUT-HANDLER-THRU-SAVE-STATE
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3231
        '10
        (PUTNTH
         (TM-R2 OS)
         '13
         (PUTNTH
          (TM-R3 OS)
          '14
          (PUTSEG
           (OS-NEW-TASK-TABLE OS)
           '15
           (PUTSEG
            (OS-SEGMENT-TABLE OS)
            '159
            (PUTSEG
             (OS-READYQ OS)
             '191
             (PUTSEG
                 (OS-STATUS-TABLE OS)
                 '211
                 (PUTSEG (OS-IBUFFERS OS)
                         '243
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '2558
                                         '3309
                                         (PUTNTH '3063
                                                 '3310
                                                 (TM-MEMORY OS)))))))))))))))))
  (PUTNTH '3063
          '0
          (PUTNTH '3310
                  '1
                  (PUTNTH (GETNTH '2 (TM-REGS OS))
                          '2
                          (PUTNTH (GETNTH '3 (TM-REGS OS))
                                  '3
                                  (TM-REGS OS)))))
  (TM-CC-VALUE (TM-ALU-PLUS (PLUS '15
                                  (TIMES '9
                                         (ARRAY-QFIRST (OS-READYQ OS))))
                            '8))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-input-handler-thru-save-state \\ \index{trace-running-input-handler-thr!u-save-state}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-thru-save-state})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-input-handler-thru-s!ave-state})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler-thru-save-state.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-input-handle!r-to-ibuffer-full-test} \\  
\=\+{\rm{os-time-for-running-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-ibuffer-full-test} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-RUNNING-INPUT-HANDLER-TO-IBUFFER-FULL-TEST
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3231
        '10
        (PUTNTH
         (TM-R2 OS)
         '13
         (PUTNTH
          (TM-R3 OS)
          '14
          (PUTSEG
           (OS-NEW-TASK-TABLE OS)
           '15
           (PUTSEG
            (OS-SEGMENT-TABLE OS)
            '159
            (PUTSEG
             (ARRAY-ENQ (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                        (OS-READYQ OS))
             '191
             (PUTSEG
                 (OS-UPDATE-STATUS (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                   '0
                                   '0
                                   OS)
                 '211
                 (PUTSEG (OS-IBUFFERS OS)
                         '243
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '2558
                                         '3309
                                         (PUTNTH '3085
                                                 '3310
                                                 (TM-MEMORY OS)))))))))))))))))
  (PUTNTH '3091
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
     '2
     (PUTNTH '191
      '3
      (PUTNTH
             (PLUS '195
                   (GETNTH '1 (OS-READYQ OS)))
             '4
             (PUTNTH (PLUS '211
                           (TIMES '2
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     '5
                     (TM-REGS OS)))))))
  (TM-CC-VALUE (TM-ALU-INCR-MOD (GETNTH '1 (OS-READYQ OS))
                                '16))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-input-handler-to-ibuffer-full-test \\ \index{trace-running-input-handler-to-i!buffer-full-test}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-input-handler-thru-s!ave-state}, \\ 
{\rm{os-time-for-running-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-ibuffer-full-test})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-running-input-handler-to-ibu!ffer-full-test})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler-to-ibuffer-full-test.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-input-handle!r-to-resume-task1} \\  
\=\+{\rm{os-time-for-running-input-handler-to-resume-task1}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-resume-task1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-RUNNING-INPUT-HANDLER-TO-RESUME-TASK1
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3231
        '10
        (PUTNTH
         (TM-R2 OS)
         '13
         (PUTNTH
          (TM-R3 OS)
          '14
          (PUTSEG
           (OS-NEW-TASK-TABLE OS)
           '15
           (PUTSEG
            (OS-SEGMENT-TABLE OS)
            '159
            (PUTSEG
             (ARRAY-ENQ (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                        (OS-READYQ OS))
             '191
             (PUTSEG
                 (OS-UPDATE-STATUS (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                   '0
                                   '0
                                   OS)
                 '211
                 (PUTSEG (OS-IBUFFERS-WITH-QREPLACED-OVERFLOW-CHARACTER OS)
                         '243
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '2558
                                         '3309
                                         (PUTNTH '3112
                                                 '3310
                                                 (TM-MEMORY OS)))))))))))))))))
  (PUTNTH '3231
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (PLUS '256
           (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                             (TM-IPORTS OS))))
     '2
     (PUTNTH
      (PLUS '243
            (TIMES '8
                   (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
      '3
      (PUTNTH
       (PLUS '247
        (PLUS
          (TIMES '8
                 (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
          (DECR-MOD (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))
                    '4)))
       '4
       (PUTNTH (PLUS '211
                     (TIMES '2
                            (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
               '5
               (TM-REGS OS)))))))
  (TM-CC-VALUE
   (TM-ALU-PLUS
    (PLUS '243
     (PLUS
          (TIMES '8
                 (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
          (DECR-MOD (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))
                    '4)))
    '4))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-input-handler-to-resume-task1 \\ \index{trace-running-input-handler-to-!resume-task1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-running-input-handler-to-ibu!ffer-full-test}, \\ 
{\rm{os-time-for-running-input-handler-to-resume-task1}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-resume-task1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler-to-resume-task1}}\,({\it{os\/}})\index{os-running-input-handler-to-res!ume-task1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler-to-resume-task1.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-input-handle!r-to-resume-task2} \\  
\=\+{\rm{os-time-for-running-input-handler-to-resume-task2}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-resume-task2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-RUNNING-INPUT-HANDLER-TO-RESUME-TASK2
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3231
        '10
        (PUTNTH
         (TM-R2 OS)
         '13
         (PUTNTH
          (TM-R3 OS)
          '14
          (PUTSEG
           (OS-NEW-TASK-TABLE OS)
           '15
           (PUTSEG
            (OS-SEGMENT-TABLE OS)
            '159
            (PUTSEG
             (ARRAY-ENQ (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                        (OS-READYQ OS))
             '191
             (PUTSEG
                 (OS-UPDATE-STATUS (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                   '0
                                   '0
                                   OS)
                 '211
                 (PUTSEG (OS-IBUFFERS-WITH-ENQUEUED-OVERFLOW-CHARACTER OS)
                         '243
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '2558
                                         '3309
                                         (PUTNTH '3126
                                                 '3310
                                                 (TM-MEMORY OS)))))))))))))))))
  (PUTNTH '3231
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (PLUS '256
           (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                             (TM-IPORTS OS))))
     '2
     (PUTNTH
      (PLUS '243
            (TIMES '8
                   (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
      '3
      (PUTNTH
        (PLUS '247
              (PLUS (TIMES '8
                           (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
                    (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))))
        '4
        (PUTNTH (PLUS '211
                      (TIMES '2
                             (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                '5
                (TM-REGS OS)))))))
  (TM-CC-VALUE
   (TM-ALU-INCR-MOD (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))
                    (GETNTH '3
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-input-handler-to-resume-task2 \\ \index{trace-running-input-handler-to-!resume-task2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-running-input-handler-to-ibu!ffer-full-test}, \\ 
{\rm{os-time-for-running-input-handler-to-resume-task2}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-resume-task2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler-to-resume-task2}}\,({\it{os\/}})\index{os-running-input-handler-to-res!ume-task2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler-to-resume-task2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-input-handle!r-to-resume-task3} \\  
\=\+{\rm{os-time-for-running-input-handler-to-resume-task3}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-resume-task3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-RUNNING-INPUT-HANDLER-TO-RESUME-TASK3
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3231
        '10
        (PUTNTH
         (TM-R2 OS)
         '13
         (PUTNTH
          (TM-R3 OS)
          '14
          (PUTSEG
           (OS-NEW-TASK-TABLE OS)
           '15
           (PUTSEG
            (OS-SEGMENT-TABLE OS)
            '159
            (PUTSEG
             (ARRAY-ENQ (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                        (OS-READYQ OS))
             '191
             (PUTSEG
                 (OS-UPDATE-STATUS (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                   '0
                                   '0
                                   OS)
                 '211
                 (PUTSEG (OS-IBUFFERS-WITH-ENQUEUED-CHARACTER OS)
                         '243
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '2558
                                         '3309
                                         (PUTNTH '3133
                                                 '3310
                                                 (TM-MEMORY OS)))))))))))))))))
  (PUTNTH '3231
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                       (TM-IPORTS OS)))
     '2
     (PUTNTH
      (PLUS '243
            (TIMES '8
                   (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
      '3
      (PUTNTH
        (PLUS '247
              (PLUS (TIMES '8
                           (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
                    (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))))
        '4
        (PUTNTH (PLUS '211
                      (TIMES '2
                             (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                '5
                (TM-REGS OS)))))))
  (TM-CC-VALUE
   (TM-ALU-INCR-MOD (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))
                    (GETNTH '3
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-input-handler-to-resume-task3 \\ \index{trace-running-input-handler-to-!resume-task3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-running-input-handler-to-ibu!ffer-full-test}, \\ 
{\rm{os-time-for-running-input-handler-to-resume-task3}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-resume-task3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler-to-resume-task3}}\,({\it{os\/}})\index{os-running-input-handler-to-res!ume-task3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler-to-resume-task3.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-input-handle!r-to-lpsw} \\  
\=\+{\rm{os-time-for-running-input-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-lpsw} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-RUNNING-INPUT-HANDLER-PATH1
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (OS-READYQ OS)))
           (OS-NEW-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (OS-READYQ OS))))
            (OS-NEW-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (OS-READYQ OS))))
             (OS-NEW-TASK-TABLE OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3231
        '10
        (PUTNTH
         (TM-R2 OS)
         '13
         (PUTNTH
          (TM-R3 OS)
          '14
          (PUTSEG
           (OS-NEW-TASK-TABLE OS)
           '15
           (PUTSEG
            (OS-SEGMENT-TABLE OS)
            '159
            (PUTSEG
             (ARRAY-ENQ (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                        (OS-READYQ OS))
             '191
             (PUTSEG
                 (OS-UPDATE-STATUS (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                   '0
                                   '0
                                   OS)
                 '211
                 (PUTSEG (OS-IBUFFERS-WITH-QREPLACED-OVERFLOW-CHARACTER OS)
                         '243
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '2558
                                         '3309
                                         (PUTNTH '3238
                                                 '3310
                                                 (TM-MEMORY OS)))))))))))))))))
  (TM-REGS OS)
  (TM-CC OS)
  (TM-ERROR OS)
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-input-handler-to-lpsw1 \\ \index{trace-running-input-handler-to-!lpsw1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-resume-task1}}\,({\it{os\/}})\index{os-running-input-handler-to-res!ume-task1}, \\ 
{\rm{os-time-for-running-input-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-lpsw})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler-to-lpsw1.

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN
 OS-RUNNING-INPUT-HANDLER-PATH2
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (OS-READYQ OS)))
           (OS-NEW-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (OS-READYQ OS))))
            (OS-NEW-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (OS-READYQ OS))))
             (OS-NEW-TASK-TABLE OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3231
        '10
        (PUTNTH
         (TM-R2 OS)
         '13
         (PUTNTH
          (TM-R3 OS)
          '14
          (PUTSEG
           (OS-NEW-TASK-TABLE OS)
           '15
           (PUTSEG
            (OS-SEGMENT-TABLE OS)
            '159
            (PUTSEG
             (ARRAY-ENQ (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                        (OS-READYQ OS))
             '191
             (PUTSEG
                 (OS-UPDATE-STATUS (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                   '0
                                   '0
                                   OS)
                 '211
                 (PUTSEG (OS-IBUFFERS-WITH-ENQUEUED-OVERFLOW-CHARACTER OS)
                         '243
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '2558
                                         '3309
                                         (PUTNTH '3238
                                                 '3310
                                                 (TM-MEMORY OS)))))))))))))))))
  (TM-REGS OS)
  (TM-CC OS)
  (TM-ERROR OS)
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-input-handler-to-lpsw2 \\ \index{trace-running-input-handler-to-!lpsw2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-resume-task2}}\,({\it{os\/}})\index{os-running-input-handler-to-res!ume-task2}, \\ 
{\rm{os-time-for-running-input-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-lpsw})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler-to-lpsw2.

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN
 OS-RUNNING-INPUT-HANDLER-PATH3
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (OS-READYQ OS)))
           (OS-NEW-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (OS-READYQ OS))))
            (OS-NEW-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (OS-READYQ OS))))
             (OS-NEW-TASK-TABLE OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3231
        '10
        (PUTNTH
         (TM-R2 OS)
         '13
         (PUTNTH
          (TM-R3 OS)
          '14
          (PUTSEG
           (OS-NEW-TASK-TABLE OS)
           '15
           (PUTSEG
            (OS-SEGMENT-TABLE OS)
            '159
            (PUTSEG
             (ARRAY-ENQ (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                        (OS-READYQ OS))
             '191
             (PUTSEG
                 (OS-UPDATE-STATUS (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                   '0
                                   '0
                                   OS)
                 '211
                 (PUTSEG (OS-IBUFFERS-WITH-ENQUEUED-CHARACTER OS)
                         '243
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '2558
                                         '3309
                                         (PUTNTH '3238
                                                 '3310
                                                 (TM-MEMORY OS)))))))))))))))))
  (TM-REGS OS)
  (TM-CC OS)
  (TM-ERROR OS)
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-input-handler-to-lpsw3 \\ \index{trace-running-input-handler-to-!lpsw3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-resume-task3}}\,({\it{os\/}})\index{os-running-input-handler-to-res!ume-task3}, \\ 
{\rm{os-time-for-running-input-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-lpsw})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler-to-lpsw3.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-running-input-time1} \\  
\=\+{\rm{os-running-input-time1}}\,({\it{os\/}})\index{os-running-input-time1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-running-input-time2} \\  
\=\+{\rm{os-running-input-time2}}\,({\it{os\/}})\index{os-running-input-time2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-input-handle!r-path1} \\  
\=\+{\rm{os-time-for-running-input-handler-path1}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-running-input-trace1 \\ \index{rewrite-running-input-trace1}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-running-input-handler-path1}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-thru-save-state})\-\index{tm-processor}, \\ 
{\rm{os-running-input-time1}}\,({\it{os\/}})\index{os-running-input-time1})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-input-trace1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-running-input-trace2 \\ \index{rewrite-running-input-trace2}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-input-handler-thru-s!ave-state}, \\ 
{\rm{os-running-input-time1}}\,({\it{os\/}})\index{os-running-input-time1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-input-handler-thru-s!ave-state}, \\ 
{\rm{os-time-for-running-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-ibuffer-full-test})\-\index{tm-processor}, \\ 
{\rm{os-running-input-time2}}\,({\it{os\/}})\index{os-running-input-time2})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-input-trace2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-running-input-trace3 \\ \index{rewrite-running-input-trace3}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-running-input-handler-to-ibu!ffer-full-test}, \\ 
{\rm{os-running-input-time2}}\,({\it{os\/}})\index{os-running-input-time2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-running-input-handler-to-ibu!ffer-full-test}, \\ 
{\rm{os-time-for-running-input-handler-to-resume-task1}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-resume-task1})\-\index{tm-processor}, \\ 
{\rm{os-time-for-running-input-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-lpsw})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-input-trace3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-running-input-handler-path1 \\ \index{trace-running-input-handler-pat!h1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-running-input-handler-path1}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-running-input-time3} \\  
\=\+{\rm{os-running-input-time3}}\,({\it{os\/}})\index{os-running-input-time3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-running-input-time4} \\  
\=\+{\rm{os-running-input-time4}}\,({\it{os\/}})\index{os-running-input-time4} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-input-handle!r-path2} \\  
\=\+{\rm{os-time-for-running-input-handler-path2}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-running-input-trace4 \\ \index{rewrite-running-input-trace4}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-running-input-handler-path2}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-thru-save-state})\-\index{tm-processor}, \\ 
{\rm{os-running-input-time3}}\,({\it{os\/}})\index{os-running-input-time3})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-input-trace4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-running-input-trace5 \\ \index{rewrite-running-input-trace5}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-input-handler-thru-s!ave-state}, \\ 
{\rm{os-running-input-time3}}\,({\it{os\/}})\index{os-running-input-time3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-input-handler-thru-s!ave-state}, \\ 
{\rm{os-time-for-running-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-ibuffer-full-test})\-\index{tm-processor}, \\ 
{\rm{os-running-input-time4}}\,({\it{os\/}})\index{os-running-input-time4})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-input-trace5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-running-input-trace6 \\ \index{rewrite-running-input-trace6}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-running-input-handler-to-ibu!ffer-full-test}, \\ 
{\rm{os-running-input-time4}}\,({\it{os\/}})\index{os-running-input-time4})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-running-input-handler-to-ibu!ffer-full-test}, \\ 
{\rm{os-time-for-running-input-handler-to-resume-task2}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-resume-task2})\-\index{tm-processor}, \\ 
{\rm{os-time-for-running-input-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-lpsw})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-input-trace6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-running-input-handler-path2 \\ \index{trace-running-input-handler-pat!h2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-running-input-handler-path2}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-running-input-time5} \\  
\=\+{\rm{os-running-input-time5}}\,({\it{os\/}})\index{os-running-input-time5} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-running-input-time6} \\  
\=\+{\rm{os-running-input-time6}}\,({\it{os\/}})\index{os-running-input-time6} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-input-handle!r-path3} \\  
\=\+{\rm{os-time-for-running-input-handler-path3}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-running-input-trace7 \\ \index{rewrite-running-input-trace7}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-running-input-handler-path3}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-thru-save-state})\-\index{tm-processor}, \\ 
{\rm{os-running-input-time5}}\,({\it{os\/}})\index{os-running-input-time5})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-input-trace7.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-running-input-trace8 \\ \index{rewrite-running-input-trace8}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-input-handler-thru-s!ave-state}, \\ 
{\rm{os-running-input-time5}}\,({\it{os\/}})\index{os-running-input-time5})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-input-handler-thru-s!ave-state}, \\ 
{\rm{os-time-for-running-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-ibuffer-full-test})\-\index{tm-processor}, \\ 
{\rm{os-running-input-time6}}\,({\it{os\/}})\index{os-running-input-time6})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-input-trace8.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-running-input-trace9 \\ \index{rewrite-running-input-trace9}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-running-input-handler-to-ibu!ffer-full-test}, \\ 
{\rm{os-running-input-time6}}\,({\it{os\/}})\index{os-running-input-time6})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-ibuffer-full-test}}\,({\it{os\/}})\index{os-running-input-handler-to-ibu!ffer-full-test}, \\ 
{\rm{os-time-for-running-input-handler-to-resume-task3}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-resume-task3})\-\index{tm-processor}, \\ 
{\rm{os-time-for-running-input-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-lpsw})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-input-trace9.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-running-input-handler-path3 \\ \index{trace-running-input-handler-pat!h3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-running-input-handler-path3}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-input-handle!r-to-ibuffer-full-test2} \\  
\=\+{\rm{os-time-for-running-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-ibuffer-full-test2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-RUNNING-INPUT-HANDLER-TO-IBUFFER-FULL-TEST2
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3231
        '10
        (PUTNTH
         (TM-R2 OS)
         '13
         (PUTNTH
          (TM-R3 OS)
          '14
          (PUTSEG
           (OS-NEW-TASK-TABLE OS)
           '15
           (PUTSEG
            (OS-SEGMENT-TABLE OS)
            '159
            (PUTSEG
             (OS-READYQ OS)
             '191
             (PUTSEG
                 (OS-STATUS-TABLE OS)
                 '211
                 (PUTSEG (OS-IBUFFERS OS)
                         '243
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '2558
                                         '3309
                                         (PUTNTH '3063
                                                 '3310
                                                 (TM-MEMORY OS)))))))))))))))))
  (PUTNTH '3091
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (GETNTH '2 (TM-REGS OS))
     '2
     (PUTNTH (GETNTH '3 (TM-REGS OS))
             '3
             (PUTNTH (PLUS '211
                           (TIMES '2
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     '5
                     (TM-REGS OS))))))
  (TM-CC-VALUE
   (TM-ALU-DIFFERENCE
                    (GETNTH (TIMES '2
                                   (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
                            (OS-STATUS-TABLE OS))
                    '5))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-input-handler-to-ibuffer-full-test2 \\ \index{trace-running-input-handler-to-i!buffer-full-test2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-input-handler-thru-s!ave-state}, \\ 
{\rm{os-time-for-running-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-ibuffer-full-test2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-running-input-handler-to-ibu!ffer-full-test2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler-to-ibuffer-full-test2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-input-handle!r-to-resume-task4} \\  
\=\+{\rm{os-time-for-running-input-handler-to-resume-task4}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-resume-task4} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-RUNNING-INPUT-HANDLER-TO-RESUME-TASK4
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3231
        '10
        (PUTNTH
         (TM-R2 OS)
         '13
         (PUTNTH
          (TM-R3 OS)
          '14
          (PUTSEG
           (OS-NEW-TASK-TABLE OS)
           '15
           (PUTSEG
            (OS-SEGMENT-TABLE OS)
            '159
            (PUTSEG
             (OS-READYQ OS)
             '191
             (PUTSEG
                 (OS-STATUS-TABLE OS)
                 '211
                 (PUTSEG (OS-IBUFFERS-WITH-QREPLACED-OVERFLOW-CHARACTER OS)
                         '243
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '2558
                                         '3309
                                         (PUTNTH '3112
                                                 '3310
                                                 (TM-MEMORY OS)))))))))))))))))
  (PUTNTH '3231
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (PLUS '256
           (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                             (TM-IPORTS OS))))
     '2
     (PUTNTH
      (PLUS '243
            (TIMES '8
                   (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
      '3
      (PUTNTH
       (PLUS '247
        (PLUS
          (TIMES '8
                 (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
          (DECR-MOD (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))
                    '4)))
       '4
       (PUTNTH (PLUS '211
                     (TIMES '2
                            (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
               '5
               (TM-REGS OS)))))))
  (TM-CC-VALUE
   (TM-ALU-PLUS
    (PLUS '243
     (PLUS
          (TIMES '8
                 (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
          (DECR-MOD (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))
                    '4)))
    '4))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-input-handler-to-resume-task4 \\ \index{trace-running-input-handler-to-!resume-task4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-running-input-handler-to-ibu!ffer-full-test2}, \\ 
{\rm{os-time-for-running-input-handler-to-resume-task4}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-resume-task4})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler-to-resume-task4}}\,({\it{os\/}})\index{os-running-input-handler-to-res!ume-task4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler-to-resume-task4.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-input-handle!r-to-resume-task5} \\  
\=\+{\rm{os-time-for-running-input-handler-to-resume-task5}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-resume-task5} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-RUNNING-INPUT-HANDLER-TO-RESUME-TASK5
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3231
        '10
        (PUTNTH
         (TM-R2 OS)
         '13
         (PUTNTH
          (TM-R3 OS)
          '14
          (PUTSEG
           (OS-NEW-TASK-TABLE OS)
           '15
           (PUTSEG
            (OS-SEGMENT-TABLE OS)
            '159
            (PUTSEG
             (OS-READYQ OS)
             '191
             (PUTSEG
                 (OS-STATUS-TABLE OS)
                 '211
                 (PUTSEG (OS-IBUFFERS-WITH-ENQUEUED-OVERFLOW-CHARACTER OS)
                         '243
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '2558
                                         '3309
                                         (PUTNTH '3126
                                                 '3310
                                                 (TM-MEMORY OS)))))))))))))))))
  (PUTNTH '3231
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (PLUS '256
           (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                             (TM-IPORTS OS))))
     '2
     (PUTNTH
      (PLUS '243
            (TIMES '8
                   (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
      '3
      (PUTNTH
        (PLUS '247
              (PLUS (TIMES '8
                           (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
                    (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))))
        '4
        (PUTNTH (PLUS '211
                      (TIMES '2
                             (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                '5
                (TM-REGS OS)))))))
  (TM-CC-VALUE
   (TM-ALU-INCR-MOD (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))
                    (GETNTH '3
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-input-handler-to-resume-task5 \\ \index{trace-running-input-handler-to-!resume-task5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-running-input-handler-to-ibu!ffer-full-test2}, \\ 
{\rm{os-time-for-running-input-handler-to-resume-task5}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-resume-task5})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler-to-resume-task5}}\,({\it{os\/}})\index{os-running-input-handler-to-res!ume-task5})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler-to-resume-task5.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-input-handle!r-to-resume-task6} \\  
\=\+{\rm{os-time-for-running-input-handler-to-resume-task6}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-resume-task6} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-RUNNING-INPUT-HANDLER-TO-RESUME-TASK6
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3231
        '10
        (PUTNTH
         (TM-R2 OS)
         '13
         (PUTNTH
          (TM-R3 OS)
          '14
          (PUTSEG
           (OS-NEW-TASK-TABLE OS)
           '15
           (PUTSEG
            (OS-SEGMENT-TABLE OS)
            '159
            (PUTSEG
             (OS-READYQ OS)
             '191
             (PUTSEG
                 (OS-STATUS-TABLE OS)
                 '211
                 (PUTSEG (OS-IBUFFERS-WITH-ENQUEUED-CHARACTER OS)
                         '243
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '2558
                                         '3309
                                         (PUTNTH '3133
                                                 '3310
                                                 (TM-MEMORY OS)))))))))))))))))
  (PUTNTH '3231
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                       (TM-IPORTS OS)))
     '2
     (PUTNTH
      (PLUS '243
            (TIMES '8
                   (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
      '3
      (PUTNTH
        (PLUS '247
              (PLUS (TIMES '8
                           (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS)))
                    (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))))
        '4
        (PUTNTH (PLUS '211
                      (TIMES '2
                             (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                '5
                (TM-REGS OS)))))))
  (TM-CC-VALUE
   (TM-ALU-INCR-MOD (GETNTH '1
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))
                    (GETNTH '3
                            (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                    (TABLE '8 (OS-IBUFFERS OS))))))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-input-handler-to-resume-task6 \\ \index{trace-running-input-handler-to-!resume-task6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-running-input-handler-to-ibu!ffer-full-test2}, \\ 
{\rm{os-time-for-running-input-handler-to-resume-task6}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-resume-task6})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler-to-resume-task6}}\,({\it{os\/}})\index{os-running-input-handler-to-res!ume-task6})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler-to-resume-task6.

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN
 OS-RUNNING-INPUT-HANDLER-PATH4
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (OS-READYQ OS)))
           (OS-NEW-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (OS-READYQ OS))))
            (OS-NEW-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (OS-READYQ OS))))
             (OS-NEW-TASK-TABLE OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3231
        '10
        (PUTNTH
         (TM-R2 OS)
         '13
         (PUTNTH
          (TM-R3 OS)
          '14
          (PUTSEG
           (OS-NEW-TASK-TABLE OS)
           '15
           (PUTSEG
            (OS-SEGMENT-TABLE OS)
            '159
            (PUTSEG
             (OS-READYQ OS)
             '191
             (PUTSEG
                 (OS-STATUS-TABLE OS)
                 '211
                 (PUTSEG (OS-IBUFFERS-WITH-QREPLACED-OVERFLOW-CHARACTER OS)
                         '243
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '2558
                                         '3309
                                         (PUTNTH '3238
                                                 '3310
                                                 (TM-MEMORY OS)))))))))))))))))
  (TM-REGS OS)
  (TM-CC OS)
  (TM-ERROR OS)
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-input-handler-to-lpsw4 \\ \index{trace-running-input-handler-to-!lpsw4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-resume-task4}}\,({\it{os\/}})\index{os-running-input-handler-to-res!ume-task4}, \\ 
{\rm{os-time-for-running-input-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-lpsw})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler-to-lpsw4.

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN
 OS-RUNNING-INPUT-HANDLER-PATH5
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (OS-READYQ OS)))
           (OS-NEW-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (OS-READYQ OS))))
            (OS-NEW-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (OS-READYQ OS))))
             (OS-NEW-TASK-TABLE OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3231
        '10
        (PUTNTH
         (TM-R2 OS)
         '13
         (PUTNTH
          (TM-R3 OS)
          '14
          (PUTSEG
           (OS-NEW-TASK-TABLE OS)
           '15
           (PUTSEG
            (OS-SEGMENT-TABLE OS)
            '159
            (PUTSEG
             (OS-READYQ OS)
             '191
             (PUTSEG
                 (OS-STATUS-TABLE OS)
                 '211
                 (PUTSEG (OS-IBUFFERS-WITH-ENQUEUED-OVERFLOW-CHARACTER OS)
                         '243
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '2558
                                         '3309
                                         (PUTNTH '3238
                                                 '3310
                                                 (TM-MEMORY OS)))))))))))))))))
  (TM-REGS OS)
  (TM-CC OS)
  (TM-ERROR OS)
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-input-handler-to-lpsw5 \\ \index{trace-running-input-handler-to-!lpsw5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-resume-task5}}\,({\it{os\/}})\index{os-running-input-handler-to-res!ume-task5}, \\ 
{\rm{os-time-for-running-input-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-lpsw})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler-to-lpsw5.

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN
 OS-RUNNING-INPUT-HANDLER-PATH6
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (OS-READYQ OS)))
           (OS-NEW-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (OS-READYQ OS))))
            (OS-NEW-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (OS-READYQ OS))))
             (OS-NEW-TASK-TABLE OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
      '8
      (PUTNTH
       (TM-ICHAR (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                         (TM-IPORTS OS)))
       '9
       (PUTNTH '3231
        '10
        (PUTNTH
         (TM-R2 OS)
         '13
         (PUTNTH
          (TM-R3 OS)
          '14
          (PUTSEG
           (OS-NEW-TASK-TABLE OS)
           '15
           (PUTSEG
            (OS-SEGMENT-TABLE OS)
            '159
            (PUTSEG
             (OS-READYQ OS)
             '191
             (PUTSEG
                 (OS-STATUS-TABLE OS)
                 '211
                 (PUTSEG (OS-IBUFFERS-WITH-ENQUEUED-CHARACTER OS)
                         '243
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '2558
                                         '3309
                                         (PUTNTH '3238
                                                 '3310
                                                 (TM-MEMORY OS)))))))))))))))))
  (TM-REGS OS)
  (TM-CC OS)
  (TM-ERROR OS)
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '0
  (TM-CLOCK OS)
  (TM-CLEAR-INPUT-INTERRUPT (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TM-IPORTS OS))
  (TM-OPORTS OS))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-input-handler-to-lpsw6 \\ \index{trace-running-input-handler-to-!lpsw6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-resume-task6}}\,({\it{os\/}})\index{os-running-input-handler-to-res!ume-task6}, \\ 
{\rm{os-time-for-running-input-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-lpsw})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler-to-lpsw6.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-running-input-time7} \\  
\=\+{\rm{os-running-input-time7}}\,({\it{os\/}})\index{os-running-input-time7} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-running-input-time8} \\  
\=\+{\rm{os-running-input-time8}}\,({\it{os\/}})\index{os-running-input-time8} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-input-handle!r-path4} \\  
\=\+{\rm{os-time-for-running-input-handler-path4}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path4} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-running-input-trace10 \\ \index{rewrite-running-input-trace10}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-running-input-handler-path4}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path4})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-thru-save-state})\-\index{tm-processor}, \\ 
{\rm{os-running-input-time7}}\,({\it{os\/}})\index{os-running-input-time7})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-input-trace10.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-running-input-trace11 \\ \index{rewrite-running-input-trace11}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-input-handler-thru-s!ave-state}, \\ 
{\rm{os-running-input-time7}}\,({\it{os\/}})\index{os-running-input-time7})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-input-handler-thru-s!ave-state}, \\ 
{\rm{os-time-for-running-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-ibuffer-full-test2})\-\index{tm-processor}, \\ 
{\rm{os-running-input-time8}}\,({\it{os\/}})\index{os-running-input-time8})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-input-trace11.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-running-input-trace12 \\ \index{rewrite-running-input-trace12}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-running-input-handler-to-ibu!ffer-full-test2}, \\ 
{\rm{os-running-input-time8}}\,({\it{os\/}})\index{os-running-input-time8})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-running-input-handler-to-ibu!ffer-full-test2}, \\ 
{\rm{os-time-for-running-input-handler-to-resume-task4}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-resume-task4})\-\index{tm-processor}, \\ 
{\rm{os-time-for-running-input-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-lpsw})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-input-trace12.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-running-input-handler-path4 \\ \index{trace-running-input-handler-pat!h4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-running-input-handler-path4}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path4})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-running-input-time9} \\  
\=\+{\rm{os-running-input-time9}}\,({\it{os\/}})\index{os-running-input-time9} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-running-input-time10} \\  
\=\+{\rm{os-running-input-time10}}\,({\it{os\/}})\index{os-running-input-time10} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-input-handle!r-path5} \\  
\=\+{\rm{os-time-for-running-input-handler-path5}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path5} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-running-input-trace13 \\ \index{rewrite-running-input-trace13}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-running-input-handler-path5}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path5})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-thru-save-state})\-\index{tm-processor}, \\ 
{\rm{os-running-input-time9}}\,({\it{os\/}})\index{os-running-input-time9})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-input-trace13.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-running-input-trace14 \\ \index{rewrite-running-input-trace14}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-input-handler-thru-s!ave-state}, \\ 
{\rm{os-running-input-time9}}\,({\it{os\/}})\index{os-running-input-time9})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-input-handler-thru-s!ave-state}, \\ 
{\rm{os-time-for-running-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-ibuffer-full-test2})\-\index{tm-processor}, \\ 
{\rm{os-running-input-time10}}\,({\it{os\/}})\index{os-running-input-time10})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-input-trace14.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-running-input-trace15 \\ \index{rewrite-running-input-trace15}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-running-input-handler-to-ibu!ffer-full-test2}, \\ 
{\rm{os-running-input-time10}}\,({\it{os\/}})\index{os-running-input-time10})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-running-input-handler-to-ibu!ffer-full-test2}, \\ 
{\rm{os-time-for-running-input-handler-to-resume-task5}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-resume-task5})\-\index{tm-processor}, \\ 
{\rm{os-time-for-running-input-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-lpsw})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-input-trace15.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-running-input-handler-path5 \\ \index{trace-running-input-handler-pat!h5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-running-input-handler-path5}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path5})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-running-input-time11} \\  
\=\+{\rm{os-running-input-time11}}\,({\it{os\/}})\index{os-running-input-time11} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-running-input-time12} \\  
\=\+{\rm{os-running-input-time12}}\,({\it{os\/}})\index{os-running-input-time12} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-input-handle!r-path6} \\  
\=\+{\rm{os-time-for-running-input-handler-path6}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path6} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-running-input-trace16 \\ \index{rewrite-running-input-trace16}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-running-input-handler-path6}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path6})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-thru-save-state})\-\index{tm-processor}, \\ 
{\rm{os-running-input-time11}}\,({\it{os\/}})\index{os-running-input-time11})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-input-trace16.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-running-input-trace17 \\ \index{rewrite-running-input-trace17}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-input-handler-thru-s!ave-state}, \\ 
{\rm{os-running-input-time11}}\,({\it{os\/}})\index{os-running-input-time11})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-input-handler-thru-s!ave-state}, \\ 
{\rm{os-time-for-running-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-ibuffer-full-test2})\-\index{tm-processor}, \\ 
{\rm{os-running-input-time12}}\,({\it{os\/}})\index{os-running-input-time12})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-input-trace17.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-running-input-trace18 \\ \index{rewrite-running-input-trace18}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-running-input-handler-to-ibu!ffer-full-test2}, \\ 
{\rm{os-running-input-time12}}\,({\it{os\/}})\index{os-running-input-time12})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-input-handler-to-ibuffer-full-test2}}\,({\it{os\/}})\index{os-running-input-handler-to-ibu!ffer-full-test2}, \\ 
{\rm{os-time-for-running-input-handler-to-resume-task6}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-resume-task6})\-\index{tm-processor}, \\ 
{\rm{os-time-for-running-input-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-to-lpsw})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-input-trace18.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-running-input-handler-path6 \\ \index{trace-running-input-handler-pat!h6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-running-input-handler-path6}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path6})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-input-handle!r} \\  
\=\+{\rm{os-time-for-running-input-handler}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}}\- \\ 
{\bf then }\=\+{\bf if }{\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp} \\ 
{\bf then }{\rm{os-time-for-running-input-handler-path1}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path1} \\ 
{\bf elseif }{\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp} \\ 
{\bf then }{\rm{os-time-for-running-input-handler-path2}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path2} \\ 
{\bf else }{\rm{os-time-for-running-input-handler-path3}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path3}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp} \\ 
{\bf then }{\rm{os-time-for-running-input-handler-path4}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path4} \\ 
{\bf elseif }{\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp} \\ 
{\bf then }{\rm{os-time-for-running-input-handler-path5}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path5} \\ 
{\bf else }{\rm{os-time-for-running-input-handler-path6}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r-path6}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-running-input-handler} \\  
\=\+{\rm{os-running-input-handler}}\,({\it{os\/}})\index{os-running-input-handler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}}\- \\ 
{\bf then }\=\+{\bf if }{\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp} \\ 
{\bf then }{\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1} \\ 
{\bf elseif }{\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp} \\ 
{\bf then }{\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2} \\ 
{\bf else }{\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp} \\ 
{\bf then }{\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4} \\ 
{\bf elseif }{\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp} \\ 
{\bf then }{\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5} \\ 
{\bf else }{\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  trace-running-input-handler \\ \index{trace-running-input-handler}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-running-input-handler}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-input-handler}}\,({\it{os\/}})\index{os-running-input-handler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-input-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-intended-output-interrupt} \\  
\=\+{\rm{os-intended-output-interrupt}}\,({\it{tm\/}})\index{os-intended-output-interrupt} \\ 
$=$$\;\;\;\;${\rm{tm-set-memory}}\,(\=\+{\rm{putnth}}\,(\=\+{\rm{tm-pc}}\,({\it{tm\/}})\index{tm-pc}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-sp}}\,({\it{tm\/}})\index{tm-sp}, \\ 
{\tt{'}}{\tt{1}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{tm-cc}}\,({\it{tm\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{tm\/}})\index{tm-error}, \\ 
{\rm{tm-svcflag}}\,({\it{tm\/}})\index{tm-svcflag}, \\ 
{\rm{tm-svcid}}\,({\it{tm\/}})\index{tm-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{2}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\tt{'}}{\tt{9}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-task-table}}\,({\it{tm\/}})\index{os-task-table}, \\ 
{\tt{'}}{\tt{15}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-segment-table}}\,({\it{tm\/}})\index{os-segment-table}, \\ 
{\tt{'}}{\tt{159}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-readyq}}\,({\it{tm\/}})\index{os-readyq}, \\ 
{\tt{'}}{\tt{191}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-status-table}}\,({\it{tm\/}})\index{os-status-table}, \\ 
{\tt{'}}{\tt{211}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-obuffers}}\,({\it{tm\/}})\index{os-obuffers}, \\ 
{\tt{'}}{\tt{371}}, \\ 
{\rm{putseg}}\,(\=\+{\rm{os-code}}\,({\it{tm\/}})\index{os-code}, \\ 
{\tt{'}}{\tt{2547}}, \\ 
{\rm{tm-memory}}\,({\it{tm\/}})\index{tm-memory})\-\index{putseg})\-\index{putseg})\-\index{putseg})\-\index{putseg})\-\index{putseg})\-\index{putseg})\-\index{putnth})\-\index{putnth})\-\index{putnth})\-\index{putnth}, \\ 
{\rm{tm-set-pc}}\,(\=\+{\tt{'}}{\tt{3135}}, \\ 
{\rm{tm-set-sp}}\,(\=\+{\tt{'}}{\tt{3310}}, \\ 
{\rm{tm-set-svmode}}\,(\=\+{\tt{'}}{\tt{1}}, \\ 
{\rm{tm-set-error}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-set-rwstate}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-set-oports}}\,(\=\+{\rm{tm-clear-output-interrupt}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{tm-oports}}\,({\it{tm\/}})\index{tm-oports})\-\index{tm-clear-output-interrupt}, \\ 
{\it{tm\/}})\-\index{tm-set-oports})\-\index{tm-set-rwstate})\-\index{tm-set-error})\-\index{tm-set-svmode})\-\index{tm-set-sp})\-\index{tm-set-pc})\-\index{tm-set-memory}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equivalence-of-output-interrupt-expressions \\ \index{equivalence-of-output-interrupt!-expressions}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-execute-output-interrupt}}\,({\it{os\/}})\index{tm-execute-output-interrupt} $=$ {\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt})\-
\end{tabbing}


\noindent{\sc Event}:   Disable equivalence-of-output-interrupt-expressions.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-output-hand!ler-thru-readyq-empty-test} \\  
\=\+{\rm{os-time-for-waiting-output-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-thru-readyq-empty-test} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-WAITING-OUTPUT-HANDLER-THRU-READYQ-EMPTY-TEST
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3206
       '10
       (PUTNTH
        (TM-R3 OS)
        '14
        (PUTSEG
         (OS-TASK-TABLE OS)
         '15
         (PUTSEG
            (OS-SEGMENT-TABLE OS)
            '159
            (PUTSEG (OS-READYQ OS)
                    '191
                    (PUTSEG (OS-STATUS-TABLE OS)
                            '211
                            (PUTSEG (OS-OBUFFERS OS)
                                    '371
                                    (PUTSEG (OS-CODE OS)
                                            '2547
                                            (PUTNTH '3146
                                                    '3310
                                                    (TM-MEMORY OS))))))))))))))
  (PUTNTH '3156
          '0
          (PUTNTH '3310
                  '1
                  (PUTNTH '191 '3 (TM-REGS OS))))
  '1
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-CLEAR-OUTPUT-INTERRUPT (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-output-handler-thru-readyq-empty-test \\ \index{trace-waiting-output-handler-th!ru-readyq-empty-test}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-waiting-output-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-thru-readyq-empty-test})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-output-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-output-handler-thru-!readyq-empty-test})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-output-handler-thru-readyq-empty-test.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-output-hand!ler-to-obuffer-empty-test} \\  
\=\+{\rm{os-time-for-waiting-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-obuffer-empty-test} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-WAITING-OUTPUT-HANDLER-TO-OBUFFER-EMPTY-TEST
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3206
       '10
       (PUTNTH
        (TM-R3 OS)
        '14
        (PUTSEG
         (OS-TASK-TABLE OS)
         '15
         (PUTSEG
          (OS-SEGMENT-TABLE OS)
          '159
          (PUTSEG
           (ARRAY-ENQ (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                      (OS-READYQ OS))
           '191
           (PUTSEG
                 (OS-UPDATE-STATUS (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   '0
                                   '0
                                   OS)
                 '211
                 (PUTSEG (OS-OBUFFERS OS)
                         '371
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '3178
                                         '3310
                                         (TM-MEMORY OS))))))))))))))
  (PUTNTH '3184
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
     '2
     (PUTNTH '191
      '3
      (PUTNTH
            (PLUS '195
                  (GETNTH '1 (OS-READYQ OS)))
            '4
            (PUTNTH (PLUS '211
                          (TIMES '2
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    '5
                    (TM-REGS OS)))))))
  (TM-CC-VALUE (TM-ALU-INCR-MOD (GETNTH '1 (OS-READYQ OS))
                                '16))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-CLEAR-OUTPUT-INTERRUPT (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-output-handler-to-obuffer-empty-test \\ \index{trace-waiting-output-handler-to!-obuffer-empty-test}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-output-handler-thru-!readyq-empty-test}, \\ 
{\rm{os-time-for-waiting-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-obuffer-empty-test})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-waiting-output-handler-to-ob!uffer-empty-test})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-output-handler-to-obuffer-empty-test.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-output-hand!ler-to-dispatcher1} \\  
\=\+{\rm{os-time-for-waiting-output-handler-to-dispatcher1}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-dispatcher1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-WAITING-OUTPUT-HANDLER-TO-DISPATCHER1
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3206
       '10
       (PUTNTH
        (TM-R3 OS)
        '14
        (PUTSEG
         (OS-TASK-TABLE OS)
         '15
         (PUTSEG
          (OS-SEGMENT-TABLE OS)
          '159
          (PUTSEG
           (ARRAY-ENQ (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                      (OS-READYQ OS))
           '191
           (PUTSEG
                 (OS-UPDATE-STATUS (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   '0
                                   '0
                                   OS)
                 '211
                 (PUTSEG (OS-OBUFFERS OS)
                         '371
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '3195
                                         '3310
                                         (TM-MEMORY OS))))))))))))))
  (PUTNTH '3206
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
     '2
     (PUTNTH
      (PLUS '371
            (TIMES '8
                   (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
      '3
      (PUTNTH
            (PLUS '195
                  (GETNTH '1 (OS-READYQ OS)))
            '4
            (PUTNTH (PLUS '211
                          (TIMES '2
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    '5
                    (TM-REGS OS)))))))
  '1
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-CLEAR-OUTPUT-INTERRUPT (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-output-handler-to-dispatcher1 \\ \index{trace-waiting-output-handler-to!-dispatcher1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-waiting-output-handler-to-ob!uffer-empty-test}, \\ 
{\rm{os-time-for-waiting-output-handler-to-dispatcher1}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-dispatcher1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-output-handler-to-dispatcher1}}\,({\it{os\/}})\index{os-waiting-output-handler-to-di!spatcher1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-output-handler-to-dispatcher1.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-output-hand!ler-to-dispatcher2} \\  
\=\+{\rm{os-time-for-waiting-output-handler-to-dispatcher2}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-dispatcher2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-WAITING-OUTPUT-HANDLER-TO-DISPATCHER2
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3206
       '10
       (PUTNTH
        (TM-R3 OS)
        '14
        (PUTSEG
         (OS-TASK-TABLE OS)
         '15
         (PUTSEG
          (OS-SEGMENT-TABLE OS)
          '159
          (PUTSEG
           (ARRAY-ENQ (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                      (OS-READYQ OS))
           '191
           (PUTSEG
                 (OS-UPDATE-STATUS (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   '0
                                   '0
                                   OS)
                 '211
                 (PUTSEG (OS-OBUFFERS-WITH-DEQUEUED-CHARACTER OS)
                         '371
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '3204
                                         '3310
                                         (TM-MEMORY OS))))))))))))))
  (PUTNTH '3206
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (ARRAY-QFIRST (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                           (TABLE '8 (OS-OBUFFERS OS))))
     '2
     (PUTNTH
      (PLUS '371
            (TIMES '8
                   (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
      '3
      (PUTNTH
            (PLUS '195
                  (GETNTH '1 (OS-READYQ OS)))
            '4
            (PUTNTH (PLUS '211
                          (TIMES '2
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    '5
                    (TM-REGS OS)))))))
  (TM-CC-VALUE
   (TM-ALU-INCR-MOD
                   (GETNTH '0
                           (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   (TABLE '8 (OS-OBUFFERS OS))))
                   (GETNTH '3
                           (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   (TABLE '8 (OS-OBUFFERS OS))))))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-START-OUTPUT
             (ARRAY-QFIRST (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   (TABLE '8 (OS-OBUFFERS OS))))
             (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-output-handler-to-dispatcher2 \\ \index{trace-waiting-output-handler-to!-dispatcher2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-waiting-output-handler-to-ob!uffer-empty-test}, \\ 
{\rm{os-time-for-waiting-output-handler-to-dispatcher2}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-dispatcher2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-output-handler-to-dispatcher2}}\,({\it{os\/}})\index{os-waiting-output-handler-to-di!spatcher2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-output-handler-to-dispatcher2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-output-hand!ler-to-lpsw} \\  
\=\+{\rm{os-time-for-waiting-output-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-lpsw} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-WAITING-OUTPUT-HANDLER-PATH1
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS)))
           (OS-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
            (OS-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
             (OS-TASK-TABLE OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3206
       '10
       (PUTNTH
        (TM-R3 OS)
        '14
        (PUTSEG
         (OS-TASK-TABLE OS)
         '15
         (PUTSEG
          (OS-SEGMENT-TABLE OS)
          '159
          (PUTSEG
           (ARRAY-ENQ (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                      (OS-READYQ OS))
           '191
           (PUTSEG
                 (OS-UPDATE-STATUS (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   '0
                                   '0
                                   OS)
                 '211
                 (PUTSEG (OS-OBUFFERS OS)
                         '371
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '3217
                                         '3310
                                         (TM-MEMORY OS))))))))))))))
  (GETSEG '0
          '8
          (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                  (TABLE '9 (OS-TASK-TABLE OS))))
  (REMAINDER
            (GETNTH (PLUS '8
                          (TIMES '9
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    (OS-TASK-TABLE OS))
            '4)
  (QUOTIENT
   (REMAINDER
            (GETNTH (PLUS '8
                          (TIMES '9
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    (OS-TASK-TABLE OS))
            '256)
   '4)
  (QUOTIENT
   (REMAINDER
            (GETNTH (PLUS '8
                          (TIMES '9
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    (OS-TASK-TABLE OS))
            '512)
   '256)
  (QUOTIENT (GETNTH (PLUS '8
                          (TIMES '9
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    (OS-TASK-TABLE OS))
            '512)
  (BASE (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                (TABLE '2 (OS-SEGMENT-TABLE OS))))
  (LIMIT (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                 (TABLE '2 (OS-SEGMENT-TABLE OS))))
  (TM-SLIMIT OS)
  '0
  '0
  '1000
  (TM-IPORTS OS)
  (TM-CLEAR-OUTPUT-INTERRUPT (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-output-handler-to-lpsw1 \\ \index{trace-waiting-output-handler-to!-lpsw1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-to-dispatcher1}}\,({\it{os\/}})\index{os-waiting-output-handler-to-di!spatcher1}, \\ 
{\rm{os-time-for-waiting-output-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-lpsw})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-output-handler-to-lpsw1.

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN
 OS-WAITING-OUTPUT-HANDLER-PATH2
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS)))
           (OS-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
            (OS-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
             (OS-TASK-TABLE OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3206
       '10
       (PUTNTH
        (TM-R3 OS)
        '14
        (PUTSEG
         (OS-TASK-TABLE OS)
         '15
         (PUTSEG
          (OS-SEGMENT-TABLE OS)
          '159
          (PUTSEG
           (ARRAY-ENQ (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                      (OS-READYQ OS))
           '191
           (PUTSEG
                 (OS-UPDATE-STATUS (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   '0
                                   '0
                                   OS)
                 '211
                 (PUTSEG (OS-OBUFFERS-WITH-DEQUEUED-CHARACTER OS)
                         '371
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '3217
                                         '3310
                                         (TM-MEMORY OS))))))))))))))
  (GETSEG '0
          '8
          (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                  (TABLE '9 (OS-TASK-TABLE OS))))
  (REMAINDER
            (GETNTH (PLUS '8
                          (TIMES '9
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    (OS-TASK-TABLE OS))
            '4)
  (QUOTIENT
   (REMAINDER
            (GETNTH (PLUS '8
                          (TIMES '9
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    (OS-TASK-TABLE OS))
            '256)
   '4)
  (QUOTIENT
   (REMAINDER
            (GETNTH (PLUS '8
                          (TIMES '9
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    (OS-TASK-TABLE OS))
            '512)
   '256)
  (QUOTIENT (GETNTH (PLUS '8
                          (TIMES '9
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    (OS-TASK-TABLE OS))
            '512)
  (BASE (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                (TABLE '2 (OS-SEGMENT-TABLE OS))))
  (LIMIT (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                 (TABLE '2 (OS-SEGMENT-TABLE OS))))
  (TM-SLIMIT OS)
  '0
  '0
  '1000
  (TM-IPORTS OS)
  (TM-START-OUTPUT
             (ARRAY-QFIRST (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   (TABLE '8 (OS-OBUFFERS OS))))
             (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-output-handler-to-lpsw2 \\ \index{trace-waiting-output-handler-to!-lpsw2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-to-dispatcher2}}\,({\it{os\/}})\index{os-waiting-output-handler-to-di!spatcher2}, \\ 
{\rm{os-time-for-waiting-output-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-lpsw})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-output-handler-to-lpsw2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-output-hand!ler-to-obuffer-empty-test2} \\  
\=\+{\rm{os-time-for-waiting-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-obuffer-empty-test2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-WAITING-OUTPUT-HANDLER-TO-OBUFFER-EMPTY-TEST2
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3206
       '10
       (PUTNTH
        (TM-R3 OS)
        '14
        (PUTSEG
         (OS-TASK-TABLE OS)
         '15
         (PUTSEG
            (OS-SEGMENT-TABLE OS)
            '159
            (PUTSEG (OS-READYQ OS)
                    '191
                    (PUTSEG (OS-STATUS-TABLE OS)
                            '211
                            (PUTSEG (OS-OBUFFERS OS)
                                    '371
                                    (PUTSEG (OS-CODE OS)
                                            '2547
                                            (PUTNTH '3146
                                                    '3310
                                                    (TM-MEMORY OS))))))))))))))
  (PUTNTH '3184
   '0
   (PUTNTH '3310
    '1
    (PUTNTH '191
            '3
            (PUTNTH (PLUS '211
                          (TIMES '2
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    '5
                    (TM-REGS OS)))))
  (TM-CC-VALUE
   (TM-ALU-DIFFERENCE
                   (GETNTH (TIMES '2
                                  (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS)))
                           (OS-STATUS-TABLE OS))
                   '4))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-CLEAR-OUTPUT-INTERRUPT (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-output-handler-to-obuffer-empty-test2 \\ \index{trace-waiting-output-handler-to!-obuffer-empty-test2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{4}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-output-handler-thru-!readyq-empty-test}, \\ 
{\rm{os-time-for-waiting-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-obuffer-empty-test2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-waiting-output-handler-to-ob!uffer-empty-test2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-output-handler-to-obuffer-empty-test2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-output-hand!ler-to-dispatcher3} \\  
\=\+{\rm{os-time-for-waiting-output-handler-to-dispatcher3}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-dispatcher3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-WAITING-OUTPUT-HANDLER-TO-DISPATCHER3
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3206
       '10
       (PUTNTH
        (TM-R3 OS)
        '14
        (PUTSEG
         (OS-TASK-TABLE OS)
         '15
         (PUTSEG
            (OS-SEGMENT-TABLE OS)
            '159
            (PUTSEG (OS-READYQ OS)
                    '191
                    (PUTSEG (OS-STATUS-TABLE OS)
                            '211
                            (PUTSEG (OS-OBUFFERS OS)
                                    '371
                                    (PUTSEG (OS-CODE OS)
                                            '2547
                                            (PUTNTH '3195
                                                    '3310
                                                    (TM-MEMORY OS))))))))))))))
  (PUTNTH '3206
   '0
   (PUTNTH '3310
    '1
    (PUTNTH (PLUS '371
                  (TIMES '8
                         (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
            '3
            (PUTNTH (PLUS '211
                          (TIMES '2
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    '5
                    (TM-REGS OS)))))
  '1
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-CLEAR-OUTPUT-INTERRUPT (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-output-handler-to-dispatcher3 \\ \index{trace-waiting-output-handler-to!-dispatcher3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-waiting-output-handler-to-ob!uffer-empty-test2}, \\ 
{\rm{os-time-for-waiting-output-handler-to-dispatcher3}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-dispatcher3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-output-handler-to-dispatcher3}}\,({\it{os\/}})\index{os-waiting-output-handler-to-di!spatcher3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-output-handler-to-dispatcher3.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-output-hand!ler-to-dispatcher4} \\  
\=\+{\rm{os-time-for-waiting-output-handler-to-dispatcher4}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-dispatcher4} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-WAITING-OUTPUT-HANDLER-TO-DISPATCHER4
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3206
       '10
       (PUTNTH
        (TM-R3 OS)
        '14
        (PUTSEG
         (OS-TASK-TABLE OS)
         '15
         (PUTSEG
            (OS-SEGMENT-TABLE OS)
            '159
            (PUTSEG (OS-READYQ OS)
                    '191
                    (PUTSEG (OS-STATUS-TABLE OS)
                            '211
                            (PUTSEG (OS-OBUFFERS-WITH-DEQUEUED-CHARACTER OS)
                                    '371
                                    (PUTSEG (OS-CODE OS)
                                            '2547
                                            (PUTNTH '3204
                                                    '3310
                                                    (TM-MEMORY OS))))))))))))))
  (PUTNTH '3206
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (ARRAY-QFIRST (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                           (TABLE '8 (OS-OBUFFERS OS))))
     '2
     (PUTNTH
            (PLUS '371
                  (TIMES '8
                         (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
            '3
            (PUTNTH (PLUS '211
                          (TIMES '2
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    '5
                    (TM-REGS OS))))))
  (TM-CC-VALUE
   (TM-ALU-INCR-MOD
                   (GETNTH '0
                           (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   (TABLE '8 (OS-OBUFFERS OS))))
                   (GETNTH '3
                           (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   (TABLE '8 (OS-OBUFFERS OS))))))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-START-OUTPUT
             (ARRAY-QFIRST (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   (TABLE '8 (OS-OBUFFERS OS))))
             (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-output-handler-to-dispatcher4 \\ \index{trace-waiting-output-handler-to!-dispatcher4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-waiting-output-handler-to-ob!uffer-empty-test2}, \\ 
{\rm{os-time-for-waiting-output-handler-to-dispatcher4}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-dispatcher4})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-output-handler-to-dispatcher4}}\,({\it{os\/}})\index{os-waiting-output-handler-to-di!spatcher4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-output-handler-to-dispatcher4.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-output-hand!ler-to-wait} \\  
\=\+{\rm{os-time-for-waiting-output-handler-to-wait}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-wait} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-WAITING-OUTPUT-HANDLER-PATH3
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3206
       '10
       (PUTNTH
        (TM-R3 OS)
        '14
        (PUTSEG
         (OS-TASK-TABLE OS)
         '15
         (PUTSEG
            (OS-SEGMENT-TABLE OS)
            '159
            (PUTSEG (OS-READYQ OS)
                    '191
                    (PUTSEG (OS-STATUS-TABLE OS)
                            '211
                            (PUTSEG (OS-OBUFFERS OS)
                                    '371
                                    (PUTSEG (OS-CODE OS)
                                            '2547
                                            (PUTNTH '3211
                                                    '3310
                                                    (TM-MEMORY OS))))))))))))))
  (PUTNTH '3222
   '0
   (PUTNTH '3310
    '1
    (PUTNTH '191
            '3
            (PUTNTH (PLUS '211
                          (TIMES '2
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    '5
                    (TM-REGS OS)))))
  '1
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '1
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-CLEAR-OUTPUT-INTERRUPT (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-output-handler-to-wait1 \\ \index{trace-waiting-output-handler-to!-wait1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-to-dispatcher3}}\,({\it{os\/}})\index{os-waiting-output-handler-to-di!spatcher3}, \\ 
{\rm{os-time-for-waiting-output-handler-to-wait}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-wait})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-output-handler-to-wait1.

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN
 OS-WAITING-OUTPUT-HANDLER-PATH4
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3206
       '10
       (PUTNTH
        (TM-R3 OS)
        '14
        (PUTSEG
         (OS-TASK-TABLE OS)
         '15
         (PUTSEG
            (OS-SEGMENT-TABLE OS)
            '159
            (PUTSEG (OS-READYQ OS)
                    '191
                    (PUTSEG (OS-STATUS-TABLE OS)
                            '211
                            (PUTSEG (OS-OBUFFERS-WITH-DEQUEUED-CHARACTER OS)
                                    '371
                                    (PUTSEG (OS-CODE OS)
                                            '2547
                                            (PUTNTH '3211
                                                    '3310
                                                    (TM-MEMORY OS))))))))))))))
  (PUTNTH '3222
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (ARRAY-QFIRST (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                           (TABLE '8 (OS-OBUFFERS OS))))
     '2
     (PUTNTH '191
            '3
            (PUTNTH (PLUS '211
                          (TIMES '2
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    '5
                    (TM-REGS OS))))))
  '1
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '1
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-START-OUTPUT
             (ARRAY-QFIRST (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   (TABLE '8 (OS-OBUFFERS OS))))
             (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-waiting-output-handler-to-wait2 \\ \index{trace-waiting-output-handler-to!-wait2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-to-dispatcher4}}\,({\it{os\/}})\index{os-waiting-output-handler-to-di!spatcher4}, \\ 
{\rm{os-time-for-waiting-output-handler-to-wait}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-wait})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-output-handler-to-wait2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-waiting-output-time1} \\  
\=\+{\rm{os-waiting-output-time1}}\,({\it{os\/}})\index{os-waiting-output-time1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-waiting-output-time2} \\  
\=\+{\rm{os-waiting-output-time2}}\,({\it{os\/}})\index{os-waiting-output-time2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-output-hand!ler-path1} \\  
\=\+{\rm{os-time-for-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-path1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-output-trace1 \\ \index{rewrite-waiting-output-trace1}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-path1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-waiting-output-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-thru-readyq-empty-test})\-\index{tm-processor}, \\ 
{\rm{os-waiting-output-time1}}\,({\it{os\/}})\index{os-waiting-output-time1})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-output-trace1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-output-trace2 \\ \index{rewrite-waiting-output-trace2}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-output-handler-thru-!readyq-empty-test}, \\ 
{\rm{os-waiting-output-time1}}\,({\it{os\/}})\index{os-waiting-output-time1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-output-handler-thru-!readyq-empty-test}, \\ 
{\rm{os-time-for-waiting-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-obuffer-empty-test})\-\index{tm-processor}, \\ 
{\rm{os-waiting-output-time2}}\,({\it{os\/}})\index{os-waiting-output-time2})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-output-trace2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-output-trace3 \\ \index{rewrite-waiting-output-trace3}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-waiting-output-handler-to-ob!uffer-empty-test}, \\ 
{\rm{os-waiting-output-time2}}\,({\it{os\/}})\index{os-waiting-output-time2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-waiting-output-handler-to-ob!uffer-empty-test}, \\ 
{\rm{os-time-for-waiting-output-handler-to-dispatcher1}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-dispatcher1})\-\index{tm-processor}, \\ 
{\rm{os-time-for-waiting-output-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-lpsw})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-output-trace3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-waiting-output-handler-path1 \\ \index{trace-waiting-output-handler-pat!h1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-path1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-waiting-output-time3} \\  
\=\+{\rm{os-waiting-output-time3}}\,({\it{os\/}})\index{os-waiting-output-time3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-waiting-output-time4} \\  
\=\+{\rm{os-waiting-output-time4}}\,({\it{os\/}})\index{os-waiting-output-time4} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-output-hand!ler-path2} \\  
\=\+{\rm{os-time-for-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-path2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-output-trace4 \\ \index{rewrite-waiting-output-trace4}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-path2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-waiting-output-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-thru-readyq-empty-test})\-\index{tm-processor}, \\ 
{\rm{os-waiting-output-time3}}\,({\it{os\/}})\index{os-waiting-output-time3})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-output-trace4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-output-trace5 \\ \index{rewrite-waiting-output-trace5}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-output-handler-thru-!readyq-empty-test}, \\ 
{\rm{os-waiting-output-time3}}\,({\it{os\/}})\index{os-waiting-output-time3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-output-handler-thru-!readyq-empty-test}, \\ 
{\rm{os-time-for-waiting-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-obuffer-empty-test})\-\index{tm-processor}, \\ 
{\rm{os-waiting-output-time4}}\,({\it{os\/}})\index{os-waiting-output-time4})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-output-trace5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-output-trace6 \\ \index{rewrite-waiting-output-trace6}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-waiting-output-handler-to-ob!uffer-empty-test}, \\ 
{\rm{os-waiting-output-time4}}\,({\it{os\/}})\index{os-waiting-output-time4})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-waiting-output-handler-to-ob!uffer-empty-test}, \\ 
{\rm{os-time-for-waiting-output-handler-to-dispatcher2}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-dispatcher2})\-\index{tm-processor}, \\ 
{\rm{os-time-for-waiting-output-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-lpsw})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-output-trace6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-waiting-output-handler-path2 \\ \index{trace-waiting-output-handler-pat!h2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-path2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-waiting-output-time5} \\  
\=\+{\rm{os-waiting-output-time5}}\,({\it{os\/}})\index{os-waiting-output-time5} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-waiting-output-time6} \\  
\=\+{\rm{os-waiting-output-time6}}\,({\it{os\/}})\index{os-waiting-output-time6} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-output-hand!ler-path3} \\  
\=\+{\rm{os-time-for-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-path3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-output-trace7 \\ \index{rewrite-waiting-output-trace7}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-path3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-waiting-output-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-thru-readyq-empty-test})\-\index{tm-processor}, \\ 
{\rm{os-waiting-output-time5}}\,({\it{os\/}})\index{os-waiting-output-time5})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-output-trace7.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-output-trace8 \\ \index{rewrite-waiting-output-trace8}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-output-handler-thru-!readyq-empty-test}, \\ 
{\rm{os-waiting-output-time5}}\,({\it{os\/}})\index{os-waiting-output-time5})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-output-handler-thru-!readyq-empty-test}, \\ 
{\rm{os-time-for-waiting-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-obuffer-empty-test2})\-\index{tm-processor}, \\ 
{\rm{os-waiting-output-time6}}\,({\it{os\/}})\index{os-waiting-output-time6})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-output-trace8.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-output-trace9 \\ \index{rewrite-waiting-output-trace9}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-waiting-output-handler-to-ob!uffer-empty-test2}, \\ 
{\rm{os-waiting-output-time6}}\,({\it{os\/}})\index{os-waiting-output-time6})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-waiting-output-handler-to-ob!uffer-empty-test2}, \\ 
{\rm{os-time-for-waiting-output-handler-to-dispatcher3}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-dispatcher3})\-\index{tm-processor}, \\ 
{\rm{os-time-for-waiting-output-handler-to-wait}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-wait})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-output-trace9.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-waiting-output-handler-path3 \\ \index{trace-waiting-output-handler-pat!h3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-path3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-waiting-output-time7} \\  
\=\+{\rm{os-waiting-output-time7}}\,({\it{os\/}})\index{os-waiting-output-time7} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-waiting-output-time8} \\  
\=\+{\rm{os-waiting-output-time8}}\,({\it{os\/}})\index{os-waiting-output-time8} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-output-hand!ler-path4} \\  
\=\+{\rm{os-time-for-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-path4} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-output-trace10 \\ \index{rewrite-waiting-output-trace10}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-path4})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-waiting-output-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-thru-readyq-empty-test})\-\index{tm-processor}, \\ 
{\rm{os-waiting-output-time7}}\,({\it{os\/}})\index{os-waiting-output-time7})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-output-trace10.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-output-trace11 \\ \index{rewrite-waiting-output-trace11}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-output-handler-thru-!readyq-empty-test}, \\ 
{\rm{os-waiting-output-time7}}\,({\it{os\/}})\index{os-waiting-output-time7})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-thru-readyq-empty-test}}\,({\it{os\/}})\index{os-waiting-output-handler-thru-!readyq-empty-test}, \\ 
{\rm{os-time-for-waiting-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-obuffer-empty-test2})\-\index{tm-processor}, \\ 
{\rm{os-waiting-output-time8}}\,({\it{os\/}})\index{os-waiting-output-time8})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-output-trace11.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-waiting-output-trace12 \\ \index{rewrite-waiting-output-trace12}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-waiting-output-handler-to-ob!uffer-empty-test2}, \\ 
{\rm{os-waiting-output-time8}}\,({\it{os\/}})\index{os-waiting-output-time8})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-waiting-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-waiting-output-handler-to-ob!uffer-empty-test2}, \\ 
{\rm{os-time-for-waiting-output-handler-to-dispatcher4}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-dispatcher4})\-\index{tm-processor}, \\ 
{\rm{os-time-for-waiting-output-handler-to-wait}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-to-wait})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-waiting-output-trace12.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-waiting-output-handler-path4 \\ \index{trace-waiting-output-handler-pat!h4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-path4})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-waiting-output-hand!ler} \\  
\=\+{\rm{os-time-for-waiting-output-handler}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}}\- \\ 
{\bf then }\=\+{\bf if }{\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp} \\ 
{\bf then }{\rm{os-time-for-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-path1} \\ 
{\bf else }{\rm{os-time-for-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-path2}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp} \\ 
{\bf then }{\rm{os-time-for-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-path3} \\ 
{\bf else }{\rm{os-time-for-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler-path4}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-waiting-output-handler} \\  
\=\+{\rm{os-waiting-output-handler}}\,({\it{os\/}})\index{os-waiting-output-handler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}}\- \\ 
{\bf then }\=\+{\bf if }{\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp} \\ 
{\bf then }{\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1} \\ 
{\bf else }{\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp} \\ 
{\bf then }{\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3} \\ 
{\bf else }{\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  trace-waiting-output-handler \\ \index{trace-waiting-output-handler}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-waiting-output-handler}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-waiting-output-handler}}\,({\it{os\/}})\index{os-waiting-output-handler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-waiting-output-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-output-hand!ler-thru-save-state} \\  
\=\+{\rm{os-time-for-running-output-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-thru-save-state} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-RUNNING-OUTPUT-HANDLER-THRU-SAVE-STATE
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3231
       '10
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-OBUFFERS OS)
                          '371
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3156
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3156
          '0
          (PUTNTH '3310
                  '1
                  (PUTNTH (GETNTH '2 (TM-REGS OS))
                          '2
                          (PUTNTH (GETNTH '3 (TM-REGS OS))
                                  '3
                                  (TM-REGS OS)))))
  (TM-CC-VALUE (TM-ALU-PLUS (PLUS '15
                                  (TIMES '9
                                         (ARRAY-QFIRST (OS-READYQ OS))))
                            '8))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-CLEAR-OUTPUT-INTERRUPT (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-output-handler-thru-save-state \\ \index{trace-running-output-handler-th!ru-save-state}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-running-output-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-thru-save-state})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-output-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-output-handler-thru-!save-state})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-output-handler-thru-save-state.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-output-hand!ler-to-obuffer-empty-test} \\  
\=\+{\rm{os-time-for-running-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-obuffer-empty-test} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-RUNNING-OUTPUT-HANDLER-TO-OBUFFER-EMPTY-TEST
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3231
       '10
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-ENQ (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                       (OS-READYQ OS))
            '191
            (PUTSEG
                 (OS-UPDATE-STATUS (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   '0
                                   '0
                                   OS)
                 '211
                 (PUTSEG (OS-OBUFFERS OS)
                         '371
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '2558
                                         '3309
                                         (PUTNTH '3178
                                                 '3310
                                                 (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3184
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
     '2
     (PUTNTH '191
      '3
      (PUTNTH
            (PLUS '195
                  (GETNTH '1 (OS-READYQ OS)))
            '4
            (PUTNTH (PLUS '211
                          (TIMES '2
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    '5
                    (TM-REGS OS)))))))
  (TM-CC-VALUE (TM-ALU-INCR-MOD (GETNTH '1 (OS-READYQ OS))
                                '16))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-CLEAR-OUTPUT-INTERRUPT (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-output-handler-to-obuffer-empty-test \\ \index{trace-running-output-handler-to!-obuffer-empty-test}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-output-handler-thru-!save-state}, \\ 
{\rm{os-time-for-running-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-obuffer-empty-test})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-running-output-handler-to-ob!uffer-empty-test})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-output-handler-to-obuffer-empty-test.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-output-hand!ler-to-resume-task1} \\  
\=\+{\rm{os-time-for-running-output-handler-to-resume-task1}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-resume-task1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-RUNNING-OUTPUT-HANDLER-TO-RESUME-TASK1
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3231
       '10
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-ENQ (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                       (OS-READYQ OS))
            '191
            (PUTSEG
                 (OS-UPDATE-STATUS (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   '0
                                   '0
                                   OS)
                 '211
                 (PUTSEG (OS-OBUFFERS OS)
                         '371
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '2558
                                         '3309
                                         (PUTNTH '3195
                                                 '3310
                                                 (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3231
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
     '2
     (PUTNTH
      (PLUS '371
            (TIMES '8
                   (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
      '3
      (PUTNTH
            (PLUS '195
                  (GETNTH '1 (OS-READYQ OS)))
            '4
            (PUTNTH (PLUS '211
                          (TIMES '2
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    '5
                    (TM-REGS OS)))))))
  '1
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-CLEAR-OUTPUT-INTERRUPT (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-output-handler-to-resume-task1 \\ \index{trace-running-output-handler-to!-resume-task1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-running-output-handler-to-ob!uffer-empty-test}, \\ 
{\rm{os-time-for-running-output-handler-to-resume-task1}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-resume-task1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-output-handler-to-resume-task1}}\,({\it{os\/}})\index{os-running-output-handler-to-re!sume-task1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-output-handler-to-resume-task1.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-output-hand!ler-to-resume-task2} \\  
\=\+{\rm{os-time-for-running-output-handler-to-resume-task2}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-resume-task2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-RUNNING-OUTPUT-HANDLER-TO-RESUME-TASK2
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3231
       '10
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-ENQ (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                       (OS-READYQ OS))
            '191
            (PUTSEG
                 (OS-UPDATE-STATUS (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   '0
                                   '0
                                   OS)
                 '211
                 (PUTSEG (OS-OBUFFERS-WITH-DEQUEUED-CHARACTER OS)
                         '371
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '2558
                                         '3309
                                         (PUTNTH '3204
                                                 '3310
                                                 (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3231
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (ARRAY-QFIRST (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                           (TABLE '8 (OS-OBUFFERS OS))))
     '2
     (PUTNTH
      (PLUS '371
            (TIMES '8
                   (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
      '3
      (PUTNTH
            (PLUS '195
                  (GETNTH '1 (OS-READYQ OS)))
            '4
            (PUTNTH (PLUS '211
                          (TIMES '2
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    '5
                    (TM-REGS OS)))))))
  (TM-CC-VALUE
   (TM-ALU-INCR-MOD
                   (GETNTH '0
                           (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   (TABLE '8 (OS-OBUFFERS OS))))
                   (GETNTH '3
                           (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   (TABLE '8 (OS-OBUFFERS OS))))))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-START-OUTPUT
             (ARRAY-QFIRST (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   (TABLE '8 (OS-OBUFFERS OS))))
             (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-output-handler-to-resume-task2 \\ \index{trace-running-output-handler-to!-resume-task2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-running-output-handler-to-ob!uffer-empty-test}, \\ 
{\rm{os-time-for-running-output-handler-to-resume-task2}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-resume-task2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-output-handler-to-resume-task2}}\,({\it{os\/}})\index{os-running-output-handler-to-re!sume-task2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-output-handler-to-resume-task2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-output-hand!ler-to-lpsw} \\  
\=\+{\rm{os-time-for-running-output-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-lpsw} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-RUNNING-OUTPUT-HANDLER-PATH1
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (OS-READYQ OS)))
           (OS-NEW-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (OS-READYQ OS))))
            (OS-NEW-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (OS-READYQ OS))))
             (OS-NEW-TASK-TABLE OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3231
       '10
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-ENQ (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                       (OS-READYQ OS))
            '191
            (PUTSEG
                 (OS-UPDATE-STATUS (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   '0
                                   '0
                                   OS)
                 '211
                 (PUTSEG (OS-OBUFFERS OS)
                         '371
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '2558
                                         '3309
                                         (PUTNTH '3238
                                                 '3310
                                                 (TM-MEMORY OS))))))))))))))))
  (TM-REGS OS)
  (TM-CC OS)
  (TM-ERROR OS)
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-CLEAR-OUTPUT-INTERRUPT (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-output-handler-to-lpsw1 \\ \index{trace-running-output-handler-to!-lpsw1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-to-resume-task1}}\,({\it{os\/}})\index{os-running-output-handler-to-re!sume-task1}, \\ 
{\rm{os-time-for-running-output-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-lpsw})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-output-handler-to-lpsw1.

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN
 OS-RUNNING-OUTPUT-HANDLER-PATH2
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (OS-READYQ OS)))
           (OS-NEW-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (OS-READYQ OS))))
            (OS-NEW-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (OS-READYQ OS))))
             (OS-NEW-TASK-TABLE OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3231
       '10
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (ARRAY-ENQ (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                       (OS-READYQ OS))
            '191
            (PUTSEG
                 (OS-UPDATE-STATUS (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   '0
                                   '0
                                   OS)
                 '211
                 (PUTSEG (OS-OBUFFERS-WITH-DEQUEUED-CHARACTER OS)
                         '371
                         (PUTSEG (OS-CODE OS)
                                 '2547
                                 (PUTNTH '2558
                                         '3309
                                         (PUTNTH '3238
                                                 '3310
                                                 (TM-MEMORY OS))))))))))))))))
  (TM-REGS OS)
  (TM-CC OS)
  (TM-ERROR OS)
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-START-OUTPUT
             (ARRAY-QFIRST (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   (TABLE '8 (OS-OBUFFERS OS))))
             (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-output-handler-to-lpsw2 \\ \index{trace-running-output-handler-to!-lpsw2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-to-resume-task2}}\,({\it{os\/}})\index{os-running-output-handler-to-re!sume-task2}, \\ 
{\rm{os-time-for-running-output-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-lpsw})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-output-handler-to-lpsw2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-output-hand!ler-to-obuffer-empty-test2} \\  
\=\+{\rm{os-time-for-running-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-obuffer-empty-test2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-RUNNING-OUTPUT-HANDLER-TO-OBUFFER-EMPTY-TEST2
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3231
       '10
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-OBUFFERS OS)
                          '371
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3156
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3184
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (GETNTH '2 (TM-REGS OS))
     '2
     (PUTNTH
            (GETNTH '3 (TM-REGS OS))
            '3
            (PUTNTH (PLUS '211
                          (TIMES '2
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    '5
                    (TM-REGS OS))))))
  (TM-CC-VALUE
   (TM-ALU-DIFFERENCE
                   (GETNTH (TIMES '2
                                  (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS)))
                           (OS-STATUS-TABLE OS))
                   '4))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-CLEAR-OUTPUT-INTERRUPT (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-output-handler-to-obuffer-empty-test2 \\ \index{trace-running-output-handler-to!-obuffer-empty-test2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{4}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-output-handler-thru-!save-state}, \\ 
{\rm{os-time-for-running-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-obuffer-empty-test2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-running-output-handler-to-ob!uffer-empty-test2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-output-handler-to-obuffer-empty-test2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-output-hand!ler-to-resume-task3} \\  
\=\+{\rm{os-time-for-running-output-handler-to-resume-task3}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-resume-task3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-RUNNING-OUTPUT-HANDLER-TO-RESUME-TASK3
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3231
       '10
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-OBUFFERS OS)
                          '371
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3195
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3231
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (GETNTH '2 (TM-REGS OS))
     '2
     (PUTNTH
            (PLUS '371
                  (TIMES '8
                         (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
            '3
            (PUTNTH (PLUS '211
                          (TIMES '2
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    '5
                    (TM-REGS OS))))))
  '1
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-CLEAR-OUTPUT-INTERRUPT (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-output-handler-to-resume-task3 \\ \index{trace-running-output-handler-to!-resume-task3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-running-output-handler-to-ob!uffer-empty-test2}, \\ 
{\rm{os-time-for-running-output-handler-to-resume-task3}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-resume-task3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-output-handler-to-resume-task3}}\,({\it{os\/}})\index{os-running-output-handler-to-re!sume-task3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-output-handler-to-resume-task3.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-output-hand!ler-to-resume-task4} \\  
\=\+{\rm{os-time-for-running-output-handler-to-resume-task4}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-resume-task4} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

%\item 
\begin{verbatim}


(DEFN OS-RUNNING-OUTPUT-HANDLER-TO-RESUME-TASK4
 (OS)
 (TM
  (PUTNTH
   (TM-PC OS)
   '0
   (PUTNTH
    (TM-SP OS)
    '1
    (PUTNTH
     (TM-PACK-PSW (TM-CC OS)
                  (TM-ERROR OS)
                  (TM-SVCFLAG OS)
                  (TM-SVCID OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3231
       '10
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-OBUFFERS-WITH-DEQUEUED-CHARACTER OS)
                          '371
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3204
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (PUTNTH '3231
   '0
   (PUTNTH '3310
    '1
    (PUTNTH
     (ARRAY-QFIRST (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                           (TABLE '8 (OS-OBUFFERS OS))))
     '2
     (PUTNTH
            (PLUS '371
                  (TIMES '8
                         (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
            '3
            (PUTNTH (PLUS '211
                          (TIMES '2
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    '5
                    (TM-REGS OS))))))
  (TM-CC-VALUE
   (TM-ALU-INCR-MOD
                   (GETNTH '0
                           (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   (TABLE '8 (OS-OBUFFERS OS))))
                   (GETNTH '3
                           (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   (TABLE '8 (OS-OBUFFERS OS))))))
  '0
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '1
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-START-OUTPUT
             (ARRAY-QFIRST (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   (TABLE '8 (OS-OBUFFERS OS))))
             (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-output-handler-to-resume-task4 \\ \index{trace-running-output-handler-to!-resume-task4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-running-output-handler-to-ob!uffer-empty-test2}, \\ 
{\rm{os-time-for-running-output-handler-to-resume-task4}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-resume-task4})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-output-handler-to-resume-task4}}\,({\it{os\/}})\index{os-running-output-handler-to-re!sume-task4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-output-handler-to-resume-task4.

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN
 OS-RUNNING-OUTPUT-HANDLER-PATH3
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (OS-READYQ OS)))
           (OS-NEW-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (OS-READYQ OS))))
            (OS-NEW-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (OS-READYQ OS))))
             (OS-NEW-TASK-TABLE OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3231
       '10
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-OBUFFERS OS)
                          '371
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3238
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (TM-REGS OS)
  (TM-CC OS)
  (TM-ERROR OS)
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-CLEAR-OUTPUT-INTERRUPT (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-output-handler-to-lpsw3 \\ \index{trace-running-output-handler-to!-lpsw3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-to-resume-task3}}\,({\it{os\/}})\index{os-running-output-handler-to-re!sume-task3}, \\ 
{\rm{os-time-for-running-output-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-lpsw})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-output-handler-to-lpsw3.

\addvspace{18pt}

%\item 
\begin{verbatim}


(DEFN
 OS-RUNNING-OUTPUT-HANDLER-PATH4
 (OS)
 (TM
  (PUTNTH
   (GETNTH (TIMES '9
                  (ARRAY-QFIRST (OS-READYQ OS)))
           (OS-NEW-TASK-TABLE OS))
   '0
   (PUTNTH
    (GETNTH (PLUS '1
                  (TIMES '9
                         (ARRAY-QFIRST (OS-READYQ OS))))
            (OS-NEW-TASK-TABLE OS))
    '1
    (PUTNTH
     (GETNTH (PLUS '8
                   (TIMES '9
                          (ARRAY-QFIRST (OS-READYQ OS))))
             (OS-NEW-TASK-TABLE OS))
     '2
     (PUTNTH
      (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
      '9
      (PUTNTH '3231
       '10
       (PUTNTH
        (TM-R2 OS)
        '13
        (PUTNTH
         (TM-R3 OS)
         '14
         (PUTSEG
          (OS-NEW-TASK-TABLE OS)
          '15
          (PUTSEG
           (OS-SEGMENT-TABLE OS)
           '159
           (PUTSEG
            (OS-READYQ OS)
            '191
            (PUTSEG
                  (OS-STATUS-TABLE OS)
                  '211
                  (PUTSEG (OS-OBUFFERS-WITH-DEQUEUED-CHARACTER OS)
                          '371
                          (PUTSEG (OS-CODE OS)
                                  '2547
                                  (PUTNTH '2558
                                          '3309
                                          (PUTNTH '3238
                                                  '3310
                                                  (TM-MEMORY OS))))))))))))))))
  (TM-REGS OS)
  (TM-CC OS)
  (TM-ERROR OS)
  (TM-SVCFLAG OS)
  (TM-SVCID OS)
  (TM-BASE OS)
  (TM-LIMIT OS)
  (TM-SLIMIT OS)
  '0
  '0
  (TM-CLOCK OS)
  (TM-IPORTS OS)
  (TM-START-OUTPUT
             (ARRAY-QFIRST (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                   (TABLE '8 (OS-OBUFFERS OS))))
             (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
             (TM-OPORTS OS)))
 NIL)
\end{verbatim}


\begin{tabbing}{\sc Theorem}:  trace-running-output-handler-to-lpsw4 \\ \index{trace-running-output-handler-to!-lpsw4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-to-resume-task4}}\,({\it{os\/}})\index{os-running-output-handler-to-re!sume-task4}, \\ 
{\rm{os-time-for-running-output-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-lpsw})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-output-handler-to-lpsw4.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-running-output-time1} \\  
\=\+{\rm{os-running-output-time1}}\,({\it{os\/}})\index{os-running-output-time1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-running-output-time2} \\  
\=\+{\rm{os-running-output-time2}}\,({\it{os\/}})\index{os-running-output-time2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-output-hand!ler-path1} \\  
\=\+{\rm{os-time-for-running-output-handler-path1}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-path1} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-running-output-trace1 \\ \index{rewrite-running-output-trace1}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-running-output-handler-path1}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-path1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-running-output-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-thru-save-state})\-\index{tm-processor}, \\ 
{\rm{os-running-output-time1}}\,({\it{os\/}})\index{os-running-output-time1})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-output-trace1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-running-output-trace2 \\ \index{rewrite-running-output-trace2}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-output-handler-thru-!save-state}, \\ 
{\rm{os-running-output-time1}}\,({\it{os\/}})\index{os-running-output-time1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-output-handler-thru-!save-state}, \\ 
{\rm{os-time-for-running-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-obuffer-empty-test})\-\index{tm-processor}, \\ 
{\rm{os-running-output-time2}}\,({\it{os\/}})\index{os-running-output-time2})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-output-trace2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-running-output-trace3 \\ \index{rewrite-running-output-trace3}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-running-output-handler-to-ob!uffer-empty-test}, \\ 
{\rm{os-running-output-time2}}\,({\it{os\/}})\index{os-running-output-time2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-running-output-handler-to-ob!uffer-empty-test}, \\ 
{\rm{os-time-for-running-output-handler-to-resume-task1}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-resume-task1})\-\index{tm-processor}, \\ 
{\rm{os-time-for-running-output-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-lpsw})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-output-trace3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-running-output-handler-path1 \\ \index{trace-running-output-handler-pat!h1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-running-output-handler-path1}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-path1})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-running-output-time3} \\  
\=\+{\rm{os-running-output-time3}}\,({\it{os\/}})\index{os-running-output-time3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-running-output-time4} \\  
\=\+{\rm{os-running-output-time4}}\,({\it{os\/}})\index{os-running-output-time4} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-output-hand!ler-path2} \\  
\=\+{\rm{os-time-for-running-output-handler-path2}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-path2} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-running-output-trace4 \\ \index{rewrite-running-output-trace4}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-running-output-handler-path2}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-path2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-running-output-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-thru-save-state})\-\index{tm-processor}, \\ 
{\rm{os-running-output-time3}}\,({\it{os\/}})\index{os-running-output-time3})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-output-trace4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-running-output-trace5 \\ \index{rewrite-running-output-trace5}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-output-handler-thru-!save-state}, \\ 
{\rm{os-running-output-time3}}\,({\it{os\/}})\index{os-running-output-time3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-output-handler-thru-!save-state}, \\ 
{\rm{os-time-for-running-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-obuffer-empty-test})\-\index{tm-processor}, \\ 
{\rm{os-running-output-time4}}\,({\it{os\/}})\index{os-running-output-time4})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-output-trace5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-running-output-trace6 \\ \index{rewrite-running-output-trace6}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-running-output-handler-to-ob!uffer-empty-test}, \\ 
{\rm{os-running-output-time4}}\,({\it{os\/}})\index{os-running-output-time4})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-to-obuffer-empty-test}}\,({\it{os\/}})\index{os-running-output-handler-to-ob!uffer-empty-test}, \\ 
{\rm{os-time-for-running-output-handler-to-resume-task2}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-resume-task2})\-\index{tm-processor}, \\ 
{\rm{os-time-for-running-output-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-lpsw})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-output-trace6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-running-output-handler-path2 \\ \index{trace-running-output-handler-pat!h2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-running-output-handler-path2}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-path2})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-running-output-time5} \\  
\=\+{\rm{os-running-output-time5}}\,({\it{os\/}})\index{os-running-output-time5} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-running-output-time6} \\  
\=\+{\rm{os-running-output-time6}}\,({\it{os\/}})\index{os-running-output-time6} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-output-hand!ler-path3} \\  
\=\+{\rm{os-time-for-running-output-handler-path3}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-path3} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-running-output-trace7 \\ \index{rewrite-running-output-trace7}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-running-output-handler-path3}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-path3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-running-output-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-thru-save-state})\-\index{tm-processor}, \\ 
{\rm{os-running-output-time5}}\,({\it{os\/}})\index{os-running-output-time5})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-output-trace7.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-running-output-trace8 \\ \index{rewrite-running-output-trace8}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-output-handler-thru-!save-state}, \\ 
{\rm{os-running-output-time5}}\,({\it{os\/}})\index{os-running-output-time5})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-output-handler-thru-!save-state}, \\ 
{\rm{os-time-for-running-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-obuffer-empty-test2})\-\index{tm-processor}, \\ 
{\rm{os-running-output-time6}}\,({\it{os\/}})\index{os-running-output-time6})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-output-trace8.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-running-output-trace9 \\ \index{rewrite-running-output-trace9}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-running-output-handler-to-ob!uffer-empty-test2}, \\ 
{\rm{os-running-output-time6}}\,({\it{os\/}})\index{os-running-output-time6})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-running-output-handler-to-ob!uffer-empty-test2}, \\ 
{\rm{os-time-for-running-output-handler-to-resume-task3}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-resume-task3})\-\index{tm-processor}, \\ 
{\rm{os-time-for-running-output-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-lpsw})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-output-trace9.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-running-output-handler-path3 \\ \index{trace-running-output-handler-pat!h3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-running-output-handler-path3}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-path3})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-running-output-time7} \\  
\=\+{\rm{os-running-output-time7}}\,({\it{os\/}})\index{os-running-output-time7} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-running-output-time8} \\  
\=\+{\rm{os-running-output-time8}}\,({\it{os\/}})\index{os-running-output-time8} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-output-hand!ler-path4} \\  
\=\+{\rm{os-time-for-running-output-handler-path4}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-path4} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}} \\ 
{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{ }}{\tt{tick}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  rewrite-running-output-trace10 \\ \index{rewrite-running-output-trace10}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-running-output-handler-path4}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-path4})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-running-output-handler-thru-save-state}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-thru-save-state})\-\index{tm-processor}, \\ 
{\rm{os-running-output-time7}}\,({\it{os\/}})\index{os-running-output-time7})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-output-trace10.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-running-output-trace11 \\ \index{rewrite-running-output-trace11}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-output-handler-thru-!save-state}, \\ 
{\rm{os-running-output-time7}}\,({\it{os\/}})\index{os-running-output-time7})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-thru-save-state}}\,({\it{os\/}})\index{os-running-output-handler-thru-!save-state}, \\ 
{\rm{os-time-for-running-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-obuffer-empty-test2})\-\index{tm-processor}, \\ 
{\rm{os-running-output-time8}}\,({\it{os\/}})\index{os-running-output-time8})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-output-trace11.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  rewrite-running-output-trace12 \\ \index{rewrite-running-output-trace12}
\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-running-output-handler-to-ob!uffer-empty-test2}, \\ 
{\rm{os-running-output-time8}}\,({\it{os\/}})\index{os-running-output-time8})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{tm-processor}}\,(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-running-output-handler-to-obuffer-empty-test2}}\,({\it{os\/}})\index{os-running-output-handler-to-ob!uffer-empty-test2}, \\ 
{\rm{os-time-for-running-output-handler-to-resume-task4}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-resume-task4})\-\index{tm-processor}, \\ 
{\rm{os-time-for-running-output-handler-to-lpsw}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-to-lpsw})\-\index{tm-processor}\-
\end{tabbing}


\noindent{\sc Event}:   Disable rewrite-running-output-trace12.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-running-output-handler-path4 \\ \index{trace-running-output-handler-pat!h4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-running-output-handler-path4}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-path4})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-time-for-running-output-hand!ler} \\  
\=\+{\rm{os-time-for-running-output-handler}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}}\- \\ 
{\bf then }\=\+{\bf if }{\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp} \\ 
{\bf then }{\rm{os-time-for-running-output-handler-path1}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-path1} \\ 
{\bf else }{\rm{os-time-for-running-output-handler-path2}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-path2}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp} \\ 
{\bf then }{\rm{os-time-for-running-output-handler-path3}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-path3} \\ 
{\bf else }{\rm{os-time-for-running-output-handler-path4}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler-path4}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-running-output-handler} \\  
\=\+{\rm{os-running-output-handler}}\,({\it{os\/}})\index{os-running-output-handler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}}\- \\ 
{\bf then }\=\+{\bf if }{\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp} \\ 
{\bf then }{\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1} \\ 
{\bf else }{\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2}$\;${\bf  endif}\- \\ 
{\bf elseif }{\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp} \\ 
{\bf then }{\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3} \\ 
{\bf else }{\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  trace-running-output-handler \\ \index{trace-running-output-handler}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-running-output-handler}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-running-output-handler}}\,({\it{os\/}})\index{os-running-output-handler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-running-output-handler.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{access-os-memory}} to consist of the following events: getnth-before-putseg,
getnth-putnth-non-interference,
getseg-after-putnth,
getseg-after-putseg,
getseg-before-putnth,
getseg-before-putseg,
getseg-for-length,
getseg-getseg,
getseg-within-putseg,
length-array-deq,
length-array-enq,
length-getseg,
length-putnth,
length-putseg,
plistp-array-deq,
plistp-array-enq,
plistp-getseg,
plistp-putnth,
plistp-putseg.\index{access-os-memory}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-intended-clock-interrupt \\ \index{good-tm-os-intended-clock-inter!rupt}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}))) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-intended-clock-interrupt}}\,({\it{os\/}})\index{os-intended-clock-interrupt})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-intended-clock-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-clock-interrupt-handler \\ \index{good-tm-os-clock-interrupt-hand!ler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}))) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-clock-interrupt-handler \\ \index{tm-slimit-os-clock-interrupt-ha!ndler}
{\rm{tm-slimit}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-clock-interrupt-handler \\ \index{os-code-os-clock-interrupt-hand!ler}
{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\rightarrow$ ({\rm{os-code}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-clock-interrupt-handler \\ \index{tm-interrupt-addresses-os-clock!-interrupt-handler}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-clock-interrupt-handler \\ \index{not-tm-in-supervisor-mode-os-cl!ock-interrupt-handler}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-clock-interrupt-handler \\ \index{os-task-table-os-clock-interrupt!-handler}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-clock-interrupt-handler \\ \index{os-segment-table-os-clock-inter!rupt-handler}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-clock-interrupt-handler \\ \index{os-readyq-os-clock-interrupt-ha!ndler}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-readyq}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{os-readyq} \\ 
$=$$\;\;\;\;${\rm{os-clock-new-readyq}}\,({\it{os\/}})\index{os-clock-new-readyq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-os-clock-new-readyq \\ \index{finite-number-queuep-os-clock-ne!w-readyq}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,({\rm{os-clock-new-readyq}}\,({\it{os\/}})\index{os-clock-new-readyq}, {\tt{'}}{\tt{16}}, {\tt{'}}{\tt{16}})\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-os-clock-new-readyq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-array-qemptyp-os-clock-new-readyq \\ \index{not-array-qemptyp-os-clock-new-!readyq}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-clock-new-readyq}}\,({\it{os\/}})\index{os-clock-new-readyq})\index{array-qemptyp})\-
\end{tabbing}


\noindent{\sc Event}:   Disable not-array-qemptyp-os-clock-new-readyq.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-clock-interrupt-handler \\ \index{os-ibuffers-os-clock-interrupt-!handler}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-clock-interrupt-handler \\ \index{os-obuffers-os-clock-interrupt-!handler}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-clock-interrupt-handler \\ \index{os-mbuffers-os-clock-interrupt-!handler}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-clock-interrupt-handler \\ \index{os-status-table-os-clock-interr!upt-handler}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-clock-interrupt-handler \\ \index{os-ready-set-os-clock-interrupt!-handler}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ready-set}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{os-ready-set} $=$ {\rm{os-ready-set}}\,({\it{os\/}})\index{os-ready-set})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-clock-new-readyq-os-ready-set \\ \index{permutation-os-clock-new-readyq!-os-ready-set}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{os-clock-new-readyq}}\,({\it{os\/}})\index{os-clock-new-readyq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-clock-new-readyq-os-ready-set.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-clock-interrupt-handler \\ \index{tm-base-os-clock-interrupt-hand!ler}
\=\+{\rm{tm-base}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{os-new-base}}\,({\rm{array-qfirst}}\,({\rm{os-clock-new-readyq}}\,({\it{os\/}})\index{os-clock-new-readyq})\index{array-qfirst}, {\it{os\/}})\index{os-new-base}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-clock-interrupt-handler \\ \index{tm-limit-os-clock-interrupt-han!dler}
\=\+{\rm{tm-limit}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{os-new-limit}}\,({\rm{array-qfirst}}\,({\rm{os-clock-new-readyq}}\,({\it{os\/}})\index{os-clock-new-readyq})\index{array-qfirst}, {\it{os\/}})\index{os-new-limit}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-clock-interrupt-handler \\ \index{tm-base-tm-limit-os-clock-inter!rupt-handler}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-clock-interrupt-handler \\ \index{not-tm-waiting-os-clock-interrupt!-handler}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-clock-interrupt-handler \\ \index{good-os-os-clock-interrupt-hand!ler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}))) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-intended-error-interrupt \\ \index{good-tm-os-intended-error-inter!rupt}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-intended-error-interrupt}}\,({\it{os\/}})\index{os-intended-error-interrupt})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-intended-error-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-error-handler-path1 \\ \index{good-tm-os-error-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-error-handler-path1 \\ \index{tm-slimit-os-error-handler-path!1}
{\rm{tm-slimit}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-error-handler-path1 \\ \index{os-code-os-error-handler-path1}
{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\rightarrow$ ({\rm{os-code}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-error-handler-path1 \\ \index{tm-interrupt-addresses-os-error!-handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-error-handler-path1 \\ \index{not-tm-in-supervisor-mode-os-er!ror-handler-path1}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-error-handler-path1 \\ \index{os-task-table-os-error-handler-p!ath1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-task-table}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{os-task-table} $=$ {\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-error-handler-path1 \\ \index{os-segment-table-os-error-handle!r-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-error-handler-path1 \\ \index{os-readyq-os-error-handler-path!1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-readyq}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{os-readyq} $=$ {\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-error-handler-path1 \\ \index{os-ibuffers-os-error-handler-pat!h1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-error-handler-path1 \\ \index{os-obuffers-os-error-handler-pat!h1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-error-handler-path1 \\ \index{os-mbuffers-os-error-handler-pat!h1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-error-handler-path1 \\ \index{os-status-table-os-error-handle!r-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-update-status}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\tt{'}}{\tt{1}}, {\tt{'}}{\tt{0}}, {\it{os\/}})\index{os-update-status})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-error-handler-path1.

\addvspace{18pt}


\noindent{\sc Event}:   Let us define the theory {\it{executable-theory}} to consist of the following events: *1*greaterp,
*1*leq,
*1*geq,
*1*member,
*1*iff,
*1*ord-lessp,
*1*ordinalp,
*1*assoc,
*1*pairlist,
*1*subrp,
*1*apply-subr,
*1*formals,
*1*body,
*1*fix-cost,
*1*strip-cars,
*1*sum-cdrs,
*1*v\&c\$,
*1*v\&c-apply\$,
*1*eval\$,
*1*quantifier-initial-value,
*1*add-to-set,
*1*append,
*1*max,
*1*union,
*1*quantifier-operation,
*1*for,
*1*exp,
*1*divides,
*1*min,
*1*length,
*1*insert,
*1*occurrences,
*1*remove,
*1*permutation,
*1*plistp,
*1*setp,
*1*sorted,
*1*getnth,
*1*putnth,
*1*getseg,
*1*putseg,
*1*fixlength,
*1*firstn,
*1*nthcdr,
*1*nested-intervals,
*1*getnth2,
*1*putnth2,
*1*reverse,
*1*finite-numberp,
*1*number-listp,
*1*finite-number-listp,
*1*non-zero-listp,
*1*tablep,
*1*table,
*1*flatten,
*1*finite-number-tablep,
*1*nonlast,
*1*incr-mod,
*1*decr-mod,
*1*qfirst,
*1*enq,
*1*deq,
*1*qemptyp,
*1*qfullp,
*1*qreplace,
*1*qhead-field,
*1*qtail-field,
*1*qcurrlength-field,
*1*qmaxlength-field,
*1*qarray-field,
*1*delta,
*1*array-qindex-relation,
*1*array-queuep,
*1*array-enq,
*1*array-deq,
*1*array-qfirst,
*1*array-qfullp,
*1*array-qemptyp,
*1*array-nonlast,
*1*array-qreplace,
*1*delta-segment,
*1*mapup-queue,
*1*qfirst2,
*1*enq2,
*1*deq2,
*1*qfullp2,
*1*qemptyp2.\index{executable-theory}

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-status-list-os-status-table-os-error-handler-path1 \\ \index{good-status-list-os-status-table!-os-error-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-status-list}}\,({\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-status-table}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{os-status-table})\-\index{table})\index{good-status-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-status-list-os-status-table-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-error-handler-path1 \\ \index{os-ready-set-os-error-handler-p!ath1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-update-status}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{1}}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\it{os\/}})\-\index{os-update-status})\-\index{table})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-error-handler-path1 \\ \index{permutation-os-readyq-os-ready-!set-for-os-error-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-waiting-os-error-handler-path1 \\ \index{tm-waiting-os-error-handler-pat!h1}
{\rm{tm-waiting}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-waiting-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-error-handler-path1 \\ \index{good-os-os-error-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-error-handler-path2 \\ \index{good-tm-os-error-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-error-handler-path2 \\ \index{tm-slimit-os-error-handler-path!2}
{\rm{tm-slimit}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-error-handler-path2 \\ \index{os-code-os-error-handler-path2}
{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\rightarrow$ ({\rm{os-code}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-error-handler-path2 \\ \index{tm-interrupt-addresses-os-error!-handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-error-handler-path2 \\ \index{not-tm-in-supervisor-mode-os-er!ror-handler-path2}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-error-handler-path2 \\ \index{os-task-table-os-error-handler-p!ath2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-task-table}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{os-task-table} $=$ {\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-error-handler-path2 \\ \index{os-segment-table-os-error-handle!r-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-error-handler-path2 \\ \index{os-readyq-os-error-handler-path!2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-readyq}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{os-readyq} $=$ {\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-error-handler-path2 \\ \index{os-ibuffers-os-error-handler-pat!h2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-error-handler-path2 \\ \index{os-obuffers-os-error-handler-pat!h2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-error-handler-path2 \\ \index{os-mbuffers-os-error-handler-pat!h2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-error-handler-path2 \\ \index{os-status-table-os-error-handle!r-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-update-status}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\tt{'}}{\tt{1}}, {\tt{'}}{\tt{0}}, {\it{os\/}})\index{os-update-status})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-status-list-os-status-table-os-error-handler-path2 \\ \index{good-status-list-os-status-table!-os-error-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-status-list}}\,({\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-status-table}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{os-status-table})\-\index{table})\index{good-status-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-status-list-os-status-table-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-error-handler-path2 \\ \index{os-ready-set-os-error-handler-p!ath2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-update-status}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{1}}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\it{os\/}})\-\index{os-update-status})\-\index{table})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-error-handler-path2 \\ \index{permutation-os-readyq-os-ready-!set-for-os-error-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-error-handler-path2 \\ \index{tm-base-os-error-handler-path2}
\=\+{\rm{tm-base}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{os-new-base}}\,({\rm{array-qfirst}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qfirst}, {\it{os\/}})\index{os-new-base}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-error-handler-path2 \\ \index{tm-limit-os-error-handler-path2}
\=\+{\rm{tm-limit}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{os-new-limit}}\,({\rm{array-qfirst}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qfirst}, {\it{os\/}})\index{os-new-limit}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-error-handler-path2 \\ \index{tm-base-tm-limit-os-error-handle!r-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-error-handler-path2 \\ \index{not-tm-waiting-os-error-handler!-path2}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-error-handler-path2 \\ \index{good-os-os-error-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-error-handler \\ \index{good-os-os-error-handler}
({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) $\rightarrow$ {\rm{good-os}}\,({\rm{os-error-handler}}\,({\it{os\/}})\index{os-error-handler})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-error-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-intended-svc-send-interrupt \\ \index{good-tm-os-intended-svc-send-inte!rrupt}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}))) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-intended-svc-send-interrupt}}\,({\it{os\/}})\index{os-intended-svc-send-interrupt})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-intended-svc-send-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-svc-send-handler-path1 \\ \index{good-tm-os-svc-send-handler-pat!h1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-svc-send-handler-path1 \\ \index{tm-slimit-os-svc-send-handler-p!ath1}
{\rm{tm-slimit}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-svc-send-handler-path1 \\ \index{os-code-os-svc-send-handler-pat!h1}
{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\rightarrow$ ({\rm{os-code}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-svc-send-handler-path1 \\ \index{tm-interrupt-addresses-os-svc-se!nd-handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-svc-send-handler-path1 \\ \index{not-tm-in-supervisor-mode-os-sv!c-send-handler-path1}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-svc-send-handler-path1 \\ \index{os-task-table-os-svc-send-handle!r-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-svc-send-handler-path1 \\ \index{os-segment-table-os-svc-send-ha!ndler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-svc-send-handler-path1 \\ \index{os-readyq-os-svc-send-handler-p!ath1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-readyq}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{os-readyq} \\ 
$=$$\;\;\;\;${\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-svc-send-handler-path1 \\ \index{os-ibuffers-os-svc-send-handler!-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-svc-send-handler-path1 \\ \index{os-obuffers-os-svc-send-handler!-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-svc-send-handler-path1 \\ \index{os-mbuffers-os-svc-send-handler!-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-svc-send-handler-path1 \\ \index{os-status-table-os-svc-send-han!dler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-update-status}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{2}}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-update-status})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-svc-send-handler-path1 \\ \index{os-ready-set-os-svc-send-handle!r-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{cons}}\,({\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, {\tt{'}}{\tt{nil}}))\-, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-svc-send-handler-path1 \\ \index{permutation-os-readyq-os-ready-!set-for-os-svc-send-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-waiting-os-svc-send-handler-path1 \\ \index{tm-waiting-os-svc-send-handler-p!ath1}
{\rm{tm-waiting}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-waiting-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-svc-send-handler-path1 \\ \index{good-os-os-svc-send-handler-pat!h1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-svc-send-handler-path2 \\ \index{good-tm-os-svc-send-handler-pat!h2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-svc-send-handler-path2 \\ \index{tm-slimit-os-svc-send-handler-p!ath2}
{\rm{tm-slimit}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-svc-send-handler-path2 \\ \index{os-code-os-svc-send-handler-pat!h2}
{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\rightarrow$ ({\rm{os-code}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-svc-send-handler-path2 \\ \index{tm-interrupt-addresses-os-svc-se!nd-handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-svc-send-handler-path2 \\ \index{not-tm-in-supervisor-mode-os-sv!c-send-handler-path2}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-svc-send-handler-path2 \\ \index{os-task-table-os-svc-send-handle!r-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-svc-send-handler-path2 \\ \index{os-segment-table-os-svc-send-ha!ndler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-svc-send-handler-path2 \\ \index{os-readyq-os-svc-send-handler-p!ath2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-readyq}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{os-readyq} \\ 
$=$$\;\;\;\;${\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-svc-send-handler-path2 \\ \index{os-ibuffers-os-svc-send-handler!-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-svc-send-handler-path2 \\ \index{os-obuffers-os-svc-send-handler!-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-svc-send-handler-path2 \\ \index{os-mbuffers-os-svc-send-handler!-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-svc-send-handler-path2 \\ \index{os-status-table-os-svc-send-han!dler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-update-status}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{2}}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-update-status})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-svc-send-handler-path2 \\ \index{os-ready-set-os-svc-send-handle!r-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{cons}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{cons}}\,({\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, {\tt{'}}{\tt{nil}}))\-, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-svc-send-handler-path2 \\ \index{permutation-os-readyq-os-ready-!set-for-os-svc-send-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-svc-send-handler-path2 \\ \index{tm-base-os-svc-send-handler-pat!h2}
\=\+{\rm{tm-base}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{os-new-base}}\,({\rm{array-qfirst}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qfirst}, {\it{os\/}})\index{os-new-base}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-svc-send-handler-path2 \\ \index{tm-limit-os-svc-send-handler-pat!h2}
\=\+{\rm{tm-limit}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{os-new-limit}}\,({\rm{array-qfirst}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qfirst}, {\it{os\/}})\index{os-new-limit}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-svc-send-handler-path2 \\ \index{tm-base-tm-limit-os-svc-send-ha!ndler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-svc-send-handler-path2 \\ \index{not-tm-waiting-os-svc-send-hand!ler-path2}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-svc-send-handler-path2 \\ \index{good-os-os-svc-send-handler-pat!h2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-svc-send-handler-path3 \\ \index{good-tm-os-svc-send-handler-pat!h3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{3}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{1}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid})\-\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-)\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-svc-send-handler-path3 \\ \index{tm-slimit-os-svc-send-handler-p!ath3}
{\rm{tm-slimit}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-svc-send-handler-path3 \\ \index{os-code-os-svc-send-handler-pat!h3}
{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\rightarrow$ ({\rm{os-code}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-svc-send-handler-path3 \\ \index{tm-interrupt-addresses-os-svc-se!nd-handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-svc-send-handler-path3 \\ \index{not-tm-in-supervisor-mode-os-sv!c-send-handler-path3}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-svc-send-handler-path3 \\ \index{os-task-table-os-svc-send-handle!r-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-svc-send-handler-path3 \\ \index{os-segment-table-os-svc-send-ha!ndler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-svc-send-handler-path3 \\ \index{os-readyq-os-svc-send-handler-p!ath3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-readyq}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{os-readyq} \\ 
$=$$\;\;\;\;${\rm{array-enq}}\,({\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-svc-send-handler-path3 \\ \index{os-ibuffers-os-svc-send-handler!-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-svc-send-handler-path3 \\ \index{os-obuffers-os-svc-send-handler!-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-svc-send-handler-path3 \\ \index{os-mbuffers-os-svc-send-handler!-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-mbuffers}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{os-mbuffers-with-enqueued-message}}\,({\it{os\/}})\index{os-mbuffers-with-enqueued-messa!ge})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-mbuffers-with-enqueued-message \\ \index{finite-number-queue-listp-os-mb!uffers-with-enqueued-message}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,(\=\+{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-mbuffers-with-enqueued-message}}\,({\it{os\/}})\index{os-mbuffers-with-enqueued-messa!ge})\-\index{table}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-mbuffers-with-enqueued-message.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-svc-send-handler-path3 \\ \index{os-status-table-os-svc-send-han!dler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{putseg}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{putseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-svc-send-handler-path3 \\ \index{os-ready-set-os-svc-send-handle!r-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-svc-send-handler-path3 \\ \index{permutation-os-readyq-os-ready-!set-for-os-svc-send-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{3}})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-enq}}\,({\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-enq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-svc-send-handler-path3 \\ \index{not-tm-waiting-os-svc-send-hand!ler-path3}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-svc-send-handler-path3 \\ \index{tm-base-os-svc-send-handler-pat!h3}
{\rm{tm-base}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{os\/}})\index{tm-base}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-svc-send-handler-path3 \\ \index{tm-limit-os-svc-send-handler-pat!h3}
{\rm{tm-limit}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{os\/}})\index{tm-limit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-svc-send-handler-path3 \\ \index{tm-base-tm-limit-os-svc-send-ha!ndler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{3}})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-os-destid \\ \index{finite-numberp-os-destid}
\=\+({\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid} $<$ {\tt{'}}{\tt{16}}) \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, {\tt{'}}{\tt{16}})\index{finite-numberp})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-os-destid.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-svc-send-handler-path3 \\ \index{good-os-os-svc-send-handler-pat!h3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{3}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{1}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid})\-\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-)\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-svc-send-handler-path4 \\ \index{good-tm-os-svc-send-handler-pat!h4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ (\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{3}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{1}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid})\-\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-svc-send-handler-path4 \\ \index{tm-slimit-os-svc-send-handler-p!ath4}
{\rm{tm-slimit}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-svc-send-handler-path4 \\ \index{os-code-os-svc-send-handler-pat!h4}
{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\rightarrow$ ({\rm{os-code}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-svc-send-handler-path4 \\ \index{tm-interrupt-addresses-os-svc-se!nd-handler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-svc-send-handler-path4 \\ \index{not-tm-in-supervisor-mode-os-sv!c-send-handler-path4}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-svc-send-handler-path4 \\ \index{os-task-table-os-svc-send-handle!r-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-svc-send-handler-path4 \\ \index{os-segment-table-os-svc-send-ha!ndler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-svc-send-handler-path4 \\ \index{os-readyq-os-svc-send-handler-p!ath4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-readyq}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{os-readyq} $=$ {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-svc-send-handler-path4 \\ \index{os-ibuffers-os-svc-send-handler!-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-svc-send-handler-path4 \\ \index{os-obuffers-os-svc-send-handler!-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-svc-send-handler-path4 \\ \index{os-mbuffers-os-svc-send-handler!-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-mbuffers}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{os-mbuffers-with-enqueued-message}}\,({\it{os\/}})\index{os-mbuffers-with-enqueued-messa!ge})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-svc-send-handler-path4 \\ \index{os-status-table-os-svc-send-han!dler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-svc-send-handler-path4 \\ \index{os-ready-set-os-svc-send-handle!r-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ready-set}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{os-ready-set} $=$ {\rm{os-ready-set}}\,({\it{os\/}})\index{os-ready-set})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-svc-send-handler-path4 \\ \index{not-tm-waiting-os-svc-send-hand!ler-path4}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-svc-send-handler-path4 \\ \index{tm-base-os-svc-send-handler-pat!h4}
{\rm{tm-base}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{os\/}})\index{tm-base}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-svc-send-handler-path4 \\ \index{tm-limit-os-svc-send-handler-pat!h4}
{\rm{tm-limit}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{os\/}})\index{tm-limit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-svc-send-handler-path4 \\ \index{tm-base-tm-limit-os-svc-send-ha!ndler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-svc-send-handler-path4 \\ \index{good-os-os-svc-send-handler-pat!h4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ (\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{3}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{1}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid})\-\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-svc-send-handler \\ \index{good-os-os-svc-send-handler}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) $\wedge$ (({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}})))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-svc-send-handler}}\,({\it{os\/}})\index{os-svc-send-handler})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-svc-send-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-intended-svc-receive-interrupt \\ \index{good-tm-os-intended-svc-receive!-interrupt}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}))) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-intended-svc-receive-interrupt}}\,({\it{os\/}})\index{os-intended-svc-receive-interrupt})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-intended-svc-receive-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-svc-receive-handler-path1 \\ \index{good-tm-os-svc-receive-handler-p!ath1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-svc-receive-handler-path1 \\ \index{tm-slimit-os-svc-receive-handle!r-path1}
{\rm{tm-slimit}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-svc-receive-handler-path1 \\ \index{os-code-os-svc-receive-handler-p!ath1}
{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\rightarrow$ ({\rm{os-code}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-svc-receive-handler-path1 \\ \index{tm-interrupt-addresses-os-svc-re!ceive-handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-svc-receive-handler-path1 \\ \index{not-tm-in-supervisor-mode-os-sv!c-receive-handler-path1}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-svc-receive-handler-path1 \\ \index{os-task-table-os-svc-receive-ha!ndler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-svc-receive-handler-path1 \\ \index{os-segment-table-os-svc-receive!-handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-svc-receive-handler-path1 \\ \index{os-readyq-os-svc-receive-handle!r-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-readyq}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{os-readyq} \\ 
$=$$\;\;\;\;${\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-svc-receive-handler-path1 \\ \index{os-ibuffers-os-svc-receive-hand!ler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-svc-receive-handler-path1 \\ \index{os-obuffers-os-svc-receive-hand!ler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-svc-receive-handler-path1 \\ \index{os-mbuffers-os-svc-receive-hand!ler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-svc-receive-handler-path1 \\ \index{os-status-table-os-svc-receive-!handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-update-status}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{3}}, \\ 
{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\it{os\/}})\-\index{os-update-status})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-svc-receive-handler-path1 \\ \index{os-ready-set-os-svc-receive-han!dler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{cons}}\,({\tt{'}}{\tt{3}}, {\rm{cons}}\,({\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, {\tt{'}}{\tt{nil}})), \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-svc-receive-handler-path1 \\ \index{permutation-os-readyq-os-ready-!set-for-os-svc-receive-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-waiting-os-svc-receive-handler-path1 \\ \index{tm-waiting-os-svc-receive-handle!r-path1}
{\rm{tm-waiting}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-waiting-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-svc-receive-handler-path1 \\ \index{good-os-os-svc-receive-handler-p!ath1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-svc-receive-handler-path2 \\ \index{good-tm-os-svc-receive-handler-p!ath2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-svc-receive-handler-path2 \\ \index{tm-slimit-os-svc-receive-handle!r-path2}
{\rm{tm-slimit}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-svc-receive-handler-path2 \\ \index{os-code-os-svc-receive-handler-p!ath2}
{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\rightarrow$ ({\rm{os-code}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-svc-receive-handler-path2 \\ \index{tm-interrupt-addresses-os-svc-re!ceive-handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-svc-receive-handler-path2 \\ \index{not-tm-in-supervisor-mode-os-sv!c-receive-handler-path2}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-svc-receive-handler-path2 \\ \index{os-task-table-os-svc-receive-ha!ndler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-svc-receive-handler-path2 \\ \index{os-segment-table-os-svc-receive!-handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-svc-receive-handler-path2 \\ \index{os-readyq-os-svc-receive-handle!r-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-readyq}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{os-readyq} \\ 
$=$$\;\;\;\;${\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-svc-receive-handler-path2 \\ \index{os-ibuffers-os-svc-receive-hand!ler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-svc-receive-handler-path2 \\ \index{os-obuffers-os-svc-receive-hand!ler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-svc-receive-handler-path2 \\ \index{os-mbuffers-os-svc-receive-hand!ler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-svc-receive-handler-path2 \\ \index{os-status-table-os-svc-receive-!handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-update-status}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{3}}, \\ 
{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\it{os\/}})\-\index{os-update-status})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-svc-receive-handler-path2 \\ \index{os-ready-set-os-svc-receive-han!dler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{cons}}\,({\tt{'}}{\tt{3}}, {\rm{cons}}\,({\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, {\tt{'}}{\tt{nil}})), \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-svc-receive-handler-path2 \\ \index{permutation-os-readyq-os-ready-!set-for-os-svc-receive-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-svc-receive-handler-path2 \\ \index{tm-base-os-svc-receive-handler-p!ath2}
\=\+{\rm{tm-base}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{os-new-base}}\,({\rm{array-qfirst}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qfirst}, {\it{os\/}})\index{os-new-base}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-svc-receive-handler-path2 \\ \index{tm-limit-os-svc-receive-handler!-path2}
\=\+{\rm{tm-limit}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{os-new-limit}}\,({\rm{array-qfirst}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qfirst}, {\it{os\/}})\index{os-new-limit}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-svc-receive-handler-path2 \\ \index{tm-base-tm-limit-os-svc-receive!-handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-svc-receive-handler-path2 \\ \index{not-tm-waiting-os-svc-receive-h!andler-path2}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-svc-receive-handler-path2 \\ \index{good-os-os-svc-receive-handler-p!ath2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-svc-receive-handler-path3 \\ \index{good-tm-os-svc-receive-handler-p!ath3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{2}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{1}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid})\-\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-)\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-svc-receive-handler-path3 \\ \index{tm-slimit-os-svc-receive-handle!r-path3}
{\rm{tm-slimit}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-svc-receive-handler-path3 \\ \index{os-code-os-svc-receive-handler-p!ath3}
{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\rightarrow$ ({\rm{os-code}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-svc-receive-handler-path3 \\ \index{tm-interrupt-addresses-os-svc-re!ceive-handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-svc-receive-handler-path3 \\ \index{not-tm-in-supervisor-mode-os-sv!c-receive-handler-path3}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-svc-receive-handler-path3 \\ \index{os-task-table-os-svc-receive-ha!ndler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-task-table-with-delivered-message}}\,({\it{os\/}})\index{os-task-table-with-delivered-me!ssage})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-crock-for-good-cpu-list-os-task-table-with-delivered-message \\ \index{lessp-crock-for-good-cpu-list-o!s-task-table-with-delivered-message}
({\it{n\/}} $<$ {\tt{'}}{\tt{16}}) $\rightarrow$ (({\tt{'}}{\tt{144}} $<$ ({\tt{'}}{\tt{9}} $+$ ({\tt{'}}{\tt{9}} $*$ {\it{n\/}}))) $=$ {\tt{'}}{\tt{*1*false}})
\end{tabbing}


\noindent{\sc Event}:   Disable lessp-crock-for-good-cpu-list-os-task-table-with-delivered-message.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-cpu-list-os-task-table-with-delivered-message \\ \index{good-cpu-list-os-task-table-wit!h-delivered-message}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-cpu-list}}\,({\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-task-table-with-delivered-message}}\,({\it{os\/}})\index{os-task-table-with-delivered-me!ssage})\index{table})\index{good-cpu-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-cpu-list-os-task-table-with-delivered-message.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-svc-receive-handler-path3 \\ \index{os-segment-table-os-svc-receive!-handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-svc-receive-handler-path3 \\ \index{os-readyq-os-svc-receive-handle!r-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-readyq}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{os-readyq} \\ 
$=$$\;\;\;\;${\rm{array-enq}}\,({\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-svc-receive-handler-path3 \\ \index{os-ibuffers-os-svc-receive-hand!ler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-svc-receive-handler-path3 \\ \index{os-obuffers-os-svc-receive-hand!ler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-svc-receive-handler-path3 \\ \index{os-mbuffers-os-svc-receive-hand!ler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-mbuffers}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{os-mbuffers-with-dequeued-message}}\,({\it{os\/}})\index{os-mbuffers-with-dequeued-messa!ge})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-mbuffers-with-dequeued-message \\ \index{finite-number-queue-listp-os-mb!uffers-with-dequeued-message}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,(\=\+{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-mbuffers-with-dequeued-message}}\,({\it{os\/}})\index{os-mbuffers-with-dequeued-messa!ge})\-\index{table}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-mbuffers-with-dequeued-message.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-svc-receive-handler-path3 \\ \index{os-status-table-os-svc-receive-!handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-update-status}}\,({\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, {\tt{'}}{\tt{0}}, {\tt{'}}{\tt{0}}, {\it{os\/}})\index{os-update-status})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-svc-receive-handler-path3 \\ \index{os-ready-set-os-svc-receive-han!dler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-svc-receive-handler-path3 \\ \index{permutation-os-readyq-os-ready-!set-for-os-svc-receive-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{2}})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-enq}}\,({\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-enq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-svc-receive-handler-path3 \\ \index{not-tm-waiting-os-svc-receive-h!andler-path3}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-svc-receive-handler-path3 \\ \index{tm-base-os-svc-receive-handler-p!ath3}
{\rm{tm-base}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{os\/}})\index{tm-base}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-svc-receive-handler-path3 \\ \index{tm-limit-os-svc-receive-handler!-path3}
{\rm{tm-limit}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{os\/}})\index{tm-limit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-svc-receive-handler-path3 \\ \index{tm-base-tm-limit-os-svc-receive!-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{2}})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-numberp-os-srcid \\ \index{finite-numberp-os-srcid}
\=\+({\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid} $<$ {\tt{'}}{\tt{16}}) \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, {\tt{'}}{\tt{16}})\index{finite-numberp})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-numberp-os-srcid.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-svc-receive-handler-path3 \\ \index{good-os-os-svc-receive-handler-p!ath3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{2}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{1}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid})\-\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-)\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-svc-receive-handler-path4 \\ \index{good-tm-os-svc-receive-handler-p!ath4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ (\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{2}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{1}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid})\-\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-svc-receive-handler-path4 \\ \index{tm-slimit-os-svc-receive-handle!r-path4}
{\rm{tm-slimit}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-svc-receive-handler-path4 \\ \index{os-code-os-svc-receive-handler-p!ath4}
{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\rightarrow$ ({\rm{os-code}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-svc-receive-handler-path4 \\ \index{tm-interrupt-addresses-os-svc-re!ceive-handler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-svc-receive-handler-path4 \\ \index{not-tm-in-supervisor-mode-os-sv!c-receive-handler-path4}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-svc-receive-handler-path4 \\ \index{os-task-table-os-svc-receive-ha!ndler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-task-table-with-delivered-message}}\,({\it{os\/}})\index{os-task-table-with-delivered-me!ssage})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-svc-receive-handler-path4 \\ \index{os-segment-table-os-svc-receive!-handler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-svc-receive-handler-path4 \\ \index{os-readyq-os-svc-receive-handle!r-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-readyq}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{os-readyq} $=$ {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-svc-receive-handler-path4 \\ \index{os-ibuffers-os-svc-receive-hand!ler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-svc-receive-handler-path4 \\ \index{os-obuffers-os-svc-receive-hand!ler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-svc-receive-handler-path4 \\ \index{os-mbuffers-os-svc-receive-hand!ler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-mbuffers}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{os-mbuffers-with-dequeued-message}}\,({\it{os\/}})\index{os-mbuffers-with-dequeued-messa!ge})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-svc-receive-handler-path4 \\ \index{os-status-table-os-svc-receive-!handler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-svc-receive-handler-path4 \\ \index{os-ready-set-os-svc-receive-han!dler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ready-set}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{os-ready-set} $=$ {\rm{os-ready-set}}\,({\it{os\/}})\index{os-ready-set})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-svc-receive-handler-path4 \\ \index{not-tm-waiting-os-svc-receive-h!andler-path4}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-svc-receive-handler-path4 \\ \index{tm-base-os-svc-receive-handler-p!ath4}
{\rm{tm-base}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{os\/}})\index{tm-base}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-svc-receive-handler-path4 \\ \index{tm-limit-os-svc-receive-handler!-path4}
{\rm{tm-limit}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{os\/}})\index{tm-limit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-svc-receive-handler-path4 \\ \index{tm-base-tm-limit-os-svc-receive!-handler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-svc-receive-handler-path4 \\ \index{good-os-os-svc-receive-handler-p!ath4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ (\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{2}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{1}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid})\-\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-svc-receive-handler \\ \index{good-os-os-svc-receive-handler}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) $\wedge$ (({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}})))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-svc-receive-handler}}\,({\it{os\/}})\index{os-svc-receive-handler})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-svc-receive-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-intended-svc-tyi-interrupt \\ \index{good-tm-os-intended-svc-tyi-inte!rrupt}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}))) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-intended-svc-tyi-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyi-interrupt})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-intended-svc-tyi-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-svc-tyi-handler-path1 \\ \index{good-tm-os-svc-tyi-handler-path!1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{3}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qemptyp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qemptyp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-svc-tyi-handler-path1 \\ \index{tm-slimit-os-svc-tyi-handler-pat!h1}
{\rm{tm-slimit}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-svc-tyi-handler-path1 \\ \index{os-code-os-svc-tyi-handler-path!1}
{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\rightarrow$ ({\rm{os-code}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-svc-tyi-handler-path1 \\ \index{tm-interrupt-addresses-os-svc-t!yi-handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-svc-tyi-handler-path1 \\ \index{not-tm-in-supervisor-mode-os-sv!c-tyi-handler-path1}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-svc-tyi-handler-path1 \\ \index{os-task-table-os-svc-tyi-handle!r-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-svc-tyi-handler-path1 \\ \index{os-segment-table-os-svc-tyi-han!dler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-svc-tyi-handler-path1 \\ \index{os-readyq-os-svc-tyi-handler-pat!h1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-readyq}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{os-readyq} $=$ {\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-svc-tyi-handler-path1 \\ \index{os-ibuffers-os-svc-tyi-handler-p!ath1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-svc-tyi-handler-path1 \\ \index{os-obuffers-os-svc-tyi-handler-p!ath1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-svc-tyi-handler-path1 \\ \index{os-mbuffers-os-svc-tyi-handler-p!ath1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-svc-tyi-handler-path1 \\ \index{os-status-table-os-svc-tyi-hand!ler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-update-status}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\tt{'}}{\tt{5}}, {\tt{'}}{\tt{0}}, {\it{os\/}})\index{os-update-status})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-svc-tyi-handler-path1 \\ \index{os-ready-set-os-svc-tyi-handler!-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{5}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-svc-tyi-handler-path1 \\ \index{permutation-os-readyq-os-ready-!set-for-os-svc-tyi-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-waiting-os-svc-tyi-handler-path1 \\ \index{tm-waiting-os-svc-tyi-handler-p!ath1}
{\rm{tm-waiting}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-waiting-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-svc-tyi-handler-path1 \\ \index{good-os-os-svc-tyi-handler-path!1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{3}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qemptyp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qemptyp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-svc-tyi-handler-path2 \\ \index{good-tm-os-svc-tyi-handler-path!2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{3}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qemptyp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qemptyp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-svc-tyi-handler-path2 \\ \index{tm-slimit-os-svc-tyi-handler-pat!h2}
{\rm{tm-slimit}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-svc-tyi-handler-path2 \\ \index{os-code-os-svc-tyi-handler-path!2}
{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\rightarrow$ ({\rm{os-code}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-svc-tyi-handler-path2 \\ \index{tm-interrupt-addresses-os-svc-t!yi-handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-svc-tyi-handler-path2 \\ \index{not-tm-in-supervisor-mode-os-sv!c-tyi-handler-path2}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-svc-tyi-handler-path2 \\ \index{os-task-table-os-svc-tyi-handle!r-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-svc-tyi-handler-path2 \\ \index{os-segment-table-os-svc-tyi-han!dler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-svc-tyi-handler-path2 \\ \index{os-readyq-os-svc-tyi-handler-pat!h2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-readyq}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{os-readyq} $=$ {\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-svc-tyi-handler-path2 \\ \index{os-ibuffers-os-svc-tyi-handler-p!ath2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-svc-tyi-handler-path2 \\ \index{os-obuffers-os-svc-tyi-handler-p!ath2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-svc-tyi-handler-path2 \\ \index{os-mbuffers-os-svc-tyi-handler-p!ath2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-svc-tyi-handler-path2 \\ \index{os-status-table-os-svc-tyi-hand!ler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-update-status}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\tt{'}}{\tt{5}}, {\tt{'}}{\tt{0}}, {\it{os\/}})\index{os-update-status})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-svc-tyi-handler-path2 \\ \index{os-ready-set-os-svc-tyi-handler!-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{5}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-svc-tyi-handler-path2 \\ \index{permutation-os-readyq-os-ready-!set-for-os-svc-tyi-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-svc-tyi-handler-path2 \\ \index{tm-base-os-svc-tyi-handler-path!2}
\=\+{\rm{tm-base}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{os-new-base}}\,({\rm{array-qfirst}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qfirst}, {\it{os\/}})\index{os-new-base}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-svc-tyi-handler-path2 \\ \index{tm-limit-os-svc-tyi-handler-pat!h2}
\=\+{\rm{tm-limit}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{os-new-limit}}\,({\rm{array-qfirst}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qfirst}, {\it{os\/}})\index{os-new-limit}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-svc-tyi-handler-path2 \\ \index{tm-base-tm-limit-os-svc-tyi-han!dler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-svc-tyi-handler-path2 \\ \index{not-tm-waiting-os-svc-tyi-handle!r-path2}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-svc-tyi-handler-path2 \\ \index{good-os-os-svc-tyi-handler-path!2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{3}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qemptyp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qemptyp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-svc-tyi-handler-path3 \\ \index{good-tm-os-svc-tyi-handler-path!3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{3}}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-svc-tyi-handler-path3 \\ \index{tm-slimit-os-svc-tyi-handler-pat!h3}
{\rm{tm-slimit}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-svc-tyi-handler-path3 \\ \index{os-code-os-svc-tyi-handler-path!3}
{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\rightarrow$ ({\rm{os-code}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-svc-tyi-handler-path3 \\ \index{tm-interrupt-addresses-os-svc-t!yi-handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-svc-tyi-handler-path3 \\ \index{not-tm-in-supervisor-mode-os-sv!c-tyi-handler-path3}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-svc-tyi-handler-path3 \\ \index{os-task-table-os-svc-tyi-handle!r-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-task-table-with-delivered-character}}\,({\it{os\/}})\index{os-task-table-with-delivered-ch!aracter})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-cpu-list-os-task-table-with-delivered-character \\ \index{good-cpu-list-os-task-table-wit!h-delivered-character}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-cpu-list}}\,({\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-task-table-with-delivered-character}}\,({\it{os\/}})\index{os-task-table-with-delivered-ch!aracter})\index{table})\index{good-cpu-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-cpu-list-os-task-table-with-delivered-character.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-svc-tyi-handler-path3 \\ \index{os-segment-table-os-svc-tyi-han!dler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-svc-tyi-handler-path3 \\ \index{os-readyq-os-svc-tyi-handler-pat!h3}
{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\rightarrow$ ({\rm{os-readyq}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{os-readyq} $=$ {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-svc-tyi-handler-path3 \\ \index{os-ibuffers-os-svc-tyi-handler-p!ath3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ibuffers}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{os-ibuffers-with-dequeued-character}}\,({\it{os\/}})\index{os-ibuffers-with-dequeued-chara!cter})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-ibuffers-with-dequeued-character \\ \index{finite-number-queue-listp-os-ib!uffers-with-dequeued-character}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,(\=\+{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-ibuffers-with-dequeued-character}}\,({\it{os\/}})\index{os-ibuffers-with-dequeued-chara!cter})\-\index{table}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-ibuffers-with-dequeued-character.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-svc-tyi-handler-path3 \\ \index{os-obuffers-os-svc-tyi-handler-p!ath3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-svc-tyi-handler-path3 \\ \index{os-mbuffers-os-svc-tyi-handler-p!ath3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-svc-tyi-handler-path3 \\ \index{os-status-table-os-svc-tyi-hand!ler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-svc-tyi-handler-path3 \\ \index{not-tm-waiting-os-svc-tyi-handle!r-path3}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-svc-tyi-handler-path3 \\ \index{tm-base-os-svc-tyi-handler-path!3}
{\rm{tm-base}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{os\/}})\index{tm-base}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-svc-tyi-handler-path3 \\ \index{tm-limit-os-svc-tyi-handler-pat!h3}
{\rm{tm-limit}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{os\/}})\index{tm-limit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-svc-tyi-handler-path3 \\ \index{tm-base-tm-limit-os-svc-tyi-han!dler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-svc-tyi-handler-path3 \\ \index{good-os-os-svc-tyi-handler-path!3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{3}}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-svc-tyi-handler \\ \index{good-os-os-svc-tyi-handler}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) $\wedge$ (({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{3}})))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-svc-tyi-handler}}\,({\it{os\/}})\index{os-svc-tyi-handler})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-svc-tyi-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-intended-svc-tyo-interrupt \\ \index{good-tm-os-intended-svc-tyo-inte!rrupt}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}))) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-intended-svc-tyo-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyo-interrupt})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-intended-svc-tyo-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-svc-tyo-handler-path1 \\ \index{good-tm-os-svc-tyo-handler-path!1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qfullp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-svc-tyo-handler-path1 \\ \index{tm-slimit-os-svc-tyo-handler-pat!h1}
{\rm{tm-slimit}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-svc-tyo-handler-path1 \\ \index{os-code-os-svc-tyo-handler-path!1}
{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\rightarrow$ ({\rm{os-code}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-svc-tyo-handler-path1 \\ \index{tm-interrupt-addresses-os-svc-t!yo-handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-svc-tyo-handler-path1 \\ \index{not-tm-in-supervisor-mode-os-sv!c-tyo-handler-path1}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-svc-tyo-handler-path1 \\ \index{os-task-table-os-svc-tyo-handle!r-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-svc-tyo-handler-path1 \\ \index{os-segment-table-os-svc-tyo-han!dler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-svc-tyo-handler-path1 \\ \index{os-readyq-os-svc-tyo-handler-pat!h1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-readyq}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{os-readyq} $=$ {\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-svc-tyo-handler-path1 \\ \index{os-ibuffers-os-svc-tyo-handler-p!ath1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-svc-tyo-handler-path1 \\ \index{os-obuffers-os-svc-tyo-handler-p!ath1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-svc-tyo-handler-path1 \\ \index{os-mbuffers-os-svc-tyo-handler-p!ath1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-svc-tyo-handler-path1 \\ \index{os-status-table-os-svc-tyo-hand!ler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-update-status}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{0}}, {\it{os\/}})\index{os-update-status})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-svc-tyo-handler-path1 \\ \index{os-ready-set-os-svc-tyo-handler!-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{4}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-svc-tyo-handler-path1 \\ \index{permutation-os-readyq-os-ready-!set-for-os-svc-tyo-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-waiting-os-svc-tyo-handler-path1 \\ \index{tm-waiting-os-svc-tyo-handler-p!ath1}
{\rm{tm-waiting}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-waiting-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-svc-tyo-handler-path1 \\ \index{good-os-os-svc-tyo-handler-path!1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qfullp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-svc-tyo-handler-path2 \\ \index{good-tm-os-svc-tyo-handler-path!2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qfullp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-svc-tyo-handler-path2 \\ \index{tm-slimit-os-svc-tyo-handler-pat!h2}
{\rm{tm-slimit}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-svc-tyo-handler-path2 \\ \index{os-code-os-svc-tyo-handler-path!2}
{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\rightarrow$ ({\rm{os-code}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-svc-tyo-handler-path2 \\ \index{tm-interrupt-addresses-os-svc-t!yo-handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-svc-tyo-handler-path2 \\ \index{not-tm-in-supervisor-mode-os-sv!c-tyo-handler-path2}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-svc-tyo-handler-path2 \\ \index{os-task-table-os-svc-tyo-handle!r-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-svc-tyo-handler-path2 \\ \index{os-segment-table-os-svc-tyo-han!dler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-svc-tyo-handler-path2 \\ \index{os-readyq-os-svc-tyo-handler-pat!h2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-readyq}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{os-readyq} $=$ {\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-svc-tyo-handler-path2 \\ \index{os-ibuffers-os-svc-tyo-handler-p!ath2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-svc-tyo-handler-path2 \\ \index{os-obuffers-os-svc-tyo-handler-p!ath2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-svc-tyo-handler-path2 \\ \index{os-mbuffers-os-svc-tyo-handler-p!ath2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-svc-tyo-handler-path2 \\ \index{os-status-table-os-svc-tyo-hand!ler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-update-status}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\tt{'}}{\tt{4}}, {\tt{'}}{\tt{0}}, {\it{os\/}})\index{os-update-status})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-svc-tyo-handler-path2 \\ \index{os-ready-set-os-svc-tyo-handler!-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{4}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-svc-tyo-handler-path2 \\ \index{permutation-os-readyq-os-ready-!set-for-os-svc-tyo-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-svc-tyo-handler-path2 \\ \index{tm-base-os-svc-tyo-handler-path!2}
\=\+{\rm{tm-base}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{os-new-base}}\,({\rm{array-qfirst}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qfirst}, {\it{os\/}})\index{os-new-base}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-svc-tyo-handler-path2 \\ \index{tm-limit-os-svc-tyo-handler-pat!h2}
\=\+{\rm{tm-limit}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{os-new-limit}}\,({\rm{array-qfirst}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qfirst}, {\it{os\/}})\index{os-new-limit}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-svc-tyo-handler-path2 \\ \index{tm-base-tm-limit-os-svc-tyo-han!dler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-svc-tyo-handler-path2 \\ \index{not-tm-waiting-os-svc-tyo-handle!r-path2}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-svc-tyo-handler-path2 \\ \index{good-os-os-svc-tyo-handler-path!2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qfullp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-svc-tyo-handler-path3 \\ \index{good-tm-os-svc-tyo-handler-path!3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-oport-idlep}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\-\index{tm-oport-idlep})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-svc-tyo-handler-path3 \\ \index{tm-slimit-os-svc-tyo-handler-pat!h3}
{\rm{tm-slimit}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-svc-tyo-handler-path3 \\ \index{os-code-os-svc-tyo-handler-path!3}
{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\rightarrow$ ({\rm{os-code}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-svc-tyo-handler-path3 \\ \index{tm-interrupt-addresses-os-svc-t!yo-handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-svc-tyo-handler-path3 \\ \index{not-tm-in-supervisor-mode-os-sv!c-tyo-handler-path3}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-svc-tyo-handler-path3 \\ \index{os-task-table-os-svc-tyo-handle!r-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-svc-tyo-handler-path3 \\ \index{os-segment-table-os-svc-tyo-han!dler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-svc-tyo-handler-path3 \\ \index{os-readyq-os-svc-tyo-handler-pat!h3}
{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\rightarrow$ ({\rm{os-readyq}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{os-readyq} $=$ {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-svc-tyo-handler-path3 \\ \index{os-ibuffers-os-svc-tyo-handler-p!ath3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-svc-tyo-handler-path3 \\ \index{os-obuffers-os-svc-tyo-handler-p!ath3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-obuffers}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{os-obuffers} \\ 
$=$$\;\;\;\;${\rm{os-obuffers-with-enqueued-character}}\,({\it{os\/}})\index{os-obuffers-with-enqueued-chara!cter})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-obuffers-with-enqueued-character \\ \index{finite-number-queue-listp-os-ob!uffers-with-enqueued-character}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,(\=\+{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-obuffers-with-enqueued-character}}\,({\it{os\/}})\index{os-obuffers-with-enqueued-chara!cter})\-\index{table}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-obuffers-with-enqueued-character.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-svc-tyo-handler-path3 \\ \index{os-mbuffers-os-svc-tyo-handler-p!ath3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-svc-tyo-handler-path3 \\ \index{os-status-table-os-svc-tyo-hand!ler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-svc-tyo-handler-path3 \\ \index{not-tm-waiting-os-svc-tyo-handle!r-path3}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-svc-tyo-handler-path3 \\ \index{tm-base-os-svc-tyo-handler-path!3}
{\rm{tm-base}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{os\/}})\index{tm-base}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-svc-tyo-handler-path3 \\ \index{tm-limit-os-svc-tyo-handler-pat!h3}
{\rm{tm-limit}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{os\/}})\index{tm-limit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-svc-tyo-handler-path3 \\ \index{tm-base-tm-limit-os-svc-tyo-han!dler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-svc-tyo-handler-path3 \\ \index{good-os-os-svc-tyo-handler-path!3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-oport-idlep}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\-\index{tm-oport-idlep})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-svc-tyo-handler-path4 \\ \index{good-tm-os-svc-tyo-handler-path!4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-oport-idlep}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\-\index{tm-oport-idlep}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-svc-tyo-handler-path4 \\ \index{tm-slimit-os-svc-tyo-handler-pat!h4}
{\rm{tm-slimit}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-svc-tyo-handler-path4 \\ \index{os-code-os-svc-tyo-handler-path!4}
{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\rightarrow$ ({\rm{os-code}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-svc-tyo-handler-path4 \\ \index{tm-interrupt-addresses-os-svc-t!yo-handler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-svc-tyo-handler-path4 \\ \index{not-tm-in-supervisor-mode-os-sv!c-tyo-handler-path4}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-svc-tyo-handler-path4 \\ \index{os-task-table-os-svc-tyo-handle!r-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-svc-tyo-handler-path4 \\ \index{os-segment-table-os-svc-tyo-han!dler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-svc-tyo-handler-path4 \\ \index{os-readyq-os-svc-tyo-handler-pat!h4}
{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\rightarrow$ ({\rm{os-readyq}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{os-readyq} $=$ {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-svc-tyo-handler-path4 \\ \index{os-ibuffers-os-svc-tyo-handler-p!ath4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-svc-tyo-handler-path4 \\ \index{os-obuffers-os-svc-tyo-handler-p!ath4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-obuffers}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{os-obuffers} \\ 
$=$$\;\;\;\;${\rm{os-obuffers-with-enqueued-character}}\,({\it{os\/}})\index{os-obuffers-with-enqueued-chara!cter})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-svc-tyo-handler-path4 \\ \index{os-mbuffers-os-svc-tyo-handler-p!ath4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-svc-tyo-handler-path4 \\ \index{os-status-table-os-svc-tyo-hand!ler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-svc-tyo-handler-path4 \\ \index{not-tm-waiting-os-svc-tyo-handle!r-path4}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-svc-tyo-handler-path4 \\ \index{tm-base-os-svc-tyo-handler-path!4}
{\rm{tm-base}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{os\/}})\index{tm-base}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-svc-tyo-handler-path4 \\ \index{tm-limit-os-svc-tyo-handler-pat!h4}
{\rm{tm-limit}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{os\/}})\index{tm-limit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-svc-tyo-handler-path4 \\ \index{tm-base-tm-limit-os-svc-tyo-han!dler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-svc-tyo-handler-path4 \\ \index{good-os-os-svc-tyo-handler-path!4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-oport-idlep}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\-\index{tm-oport-idlep}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-svc-tyo-handler \\ \index{good-os-os-svc-tyo-handler}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) $\wedge$ (({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}})))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-svc-tyo-handler}}\,({\it{os\/}})\index{os-svc-tyo-handler})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-svc-tyo-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-intended-input-interrupt \\ \index{good-tm-os-intended-input-inter!rupt}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-intended-input-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-array-enq-interrupting-input-port \\ \index{finite-number-queuep-array-enq-i!nterrupting-input-port}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,(\=\+{\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq}, \\ 
{\tt{'}}{\tt{16}}, \\ 
{\tt{'}}{\tt{16}})\-\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-array-enq-interrupting-input-port.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-waiting-input-handler-path1 \\ \index{good-tm-os-waiting-input-handle!r-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-waiting-input-handler-path1 \\ \index{tm-slimit-os-waiting-input-hand!ler-path1}
{\rm{tm-slimit}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-waiting-input-handler-path1 \\ \index{os-code-os-waiting-input-handle!r-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-code}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-waiting-input-handler-path1 \\ \index{tm-interrupt-addresses-os-waiti!ng-input-handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-waiting-input-handler-path1 \\ \index{not-tm-in-supervisor-mode-os-waiti!ng-input-handler-path1}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-waiting-input-handler-path1 \\ \index{os-task-table-os-waiting-input-!handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-waiting-input-handler-path1 \\ \index{os-segment-table-os-waiting-inp!ut-handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-waiting-input-handler-path1 \\ \index{os-readyq-os-waiting-input-hand!ler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-readyq}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{os-readyq} \\ 
$=$$\;\;\;\;${\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-waiting-input-handler-path1 \\ \index{os-ibuffers-os-waiting-input-ha!ndler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ibuffers}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{os-ibuffers-with-qreplaced-overflow-character}}\,({\it{os\/}})\index{os-ibuffers-with-qreplaced-over!flow-character})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-ibuffers-os-waiting-input-handler-path1 \\ \index{finite-number-queue-listp-os-ib!uffers-os-waiting-input-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,(\=\+{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-ibuffers}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{os-ibuffers})\-\index{table}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-ibuffers-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-waiting-input-handler-path1 \\ \index{os-obuffers-os-waiting-input-ha!ndler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-waiting-input-handler-path1 \\ \index{os-mbuffers-os-waiting-input-ha!ndler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-waiting-input-handler-path1 \\ \index{os-status-table-os-waiting-input!-handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-update-status}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\it{os\/}})\-\index{os-update-status})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-status-list-os-status-table-os-waiting-input-handler-path1 \\ \index{good-status-list-os-status-table!-os-waiting-input-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-status-list}}\,({\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-status-table}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{os-status-table})\-\index{table})\index{good-status-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-status-list-os-status-table-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-waiting-input-handler-path1 \\ \index{os-ready-set-os-waiting-input-h!andler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-waiting-input-handler-path1 \\ \index{permutation-os-readyq-os-ready-!set-for-os-waiting-input-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-waiting-input-handler-path1 \\ \index{not-tm-waiting-os-waiting-input!-handler-path1}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-waiting-input-handler-path1 \\ \index{tm-base-os-waiting-input-handle!r-path1}
\=\+{\rm{tm-base}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-waiting-input-handler-path1 \\ \index{tm-limit-os-waiting-input-handle!r-path1}
\=\+{\rm{tm-limit}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-waiting-input-handler-path1 \\ \index{tm-base-tm-limit-os-waiting-inp!ut-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-waiting-input-handler-path1 \\ \index{good-os-os-waiting-input-handle!r-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-waiting-input-handler-path2 \\ \index{good-tm-os-waiting-input-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-waiting-input-handler-path2 \\ \index{tm-slimit-os-waiting-input-hand!ler-path2}
{\rm{tm-slimit}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-waiting-input-handler-path2 \\ \index{os-code-os-waiting-input-handle!r-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-code}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-waiting-input-handler-path2 \\ \index{tm-interrupt-addresses-os-waiti!ng-input-handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-waiting-input-handler-path2 \\ \index{not-tm-in-supervisor-mode-os-waiti!ng-input-handler-path2}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-waiting-input-handler-path2 \\ \index{os-task-table-os-waiting-input-!handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-waiting-input-handler-path2 \\ \index{os-segment-table-os-waiting-inp!ut-handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-waiting-input-handler-path2 \\ \index{os-readyq-os-waiting-input-hand!ler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-readyq}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{os-readyq} \\ 
$=$$\;\;\;\;${\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-waiting-input-handler-path2 \\ \index{os-ibuffers-os-waiting-input-ha!ndler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ibuffers}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{os-ibuffers-with-enqueued-overflow-character}}\,({\it{os\/}})\index{os-ibuffers-with-enqueued-overf!low-character})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-ibuffers-os-waiting-input-handler-path2 \\ \index{finite-number-queue-listp-os-ib!uffers-os-waiting-input-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,(\=\+{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-ibuffers}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{os-ibuffers})\-\index{table}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-ibuffers-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-waiting-input-handler-path2 \\ \index{os-obuffers-os-waiting-input-ha!ndler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-waiting-input-handler-path2 \\ \index{os-mbuffers-os-waiting-input-ha!ndler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-waiting-input-handler-path2 \\ \index{os-status-table-os-waiting-input!-handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-update-status}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\it{os\/}})\-\index{os-update-status})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-status-list-os-status-table-os-waiting-input-handler-path2 \\ \index{good-status-list-os-status-table!-os-waiting-input-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-status-list}}\,({\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-status-table}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{os-status-table})\-\index{table})\index{good-status-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-status-list-os-status-table-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-waiting-input-handler-path2 \\ \index{os-ready-set-os-waiting-input-h!andler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-waiting-input-handler-path2 \\ \index{permutation-os-readyq-os-ready-!set-for-os-waiting-input-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-waiting-input-handler-path2 \\ \index{not-tm-waiting-os-waiting-input!-handler-path2}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-waiting-input-handler-path2 \\ \index{tm-base-os-waiting-input-handle!r-path2}
\=\+{\rm{tm-base}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-waiting-input-handler-path2 \\ \index{tm-limit-os-waiting-input-handle!r-path2}
\=\+{\rm{tm-limit}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-waiting-input-handler-path2 \\ \index{tm-base-tm-limit-os-waiting-inp!ut-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-waiting-input-handler-path2 \\ \index{good-os-os-waiting-input-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-waiting-input-handler-path3 \\ \index{good-tm-os-waiting-input-handle!r-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-waiting-input-handler-path3 \\ \index{tm-slimit-os-waiting-input-hand!ler-path3}
{\rm{tm-slimit}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-waiting-input-handler-path3 \\ \index{os-code-os-waiting-input-handle!r-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-code}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-waiting-input-handler-path3 \\ \index{tm-interrupt-addresses-os-waiti!ng-input-handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-waiting-input-handler-path3 \\ \index{not-tm-in-supervisor-mode-os-waiti!ng-input-handler-path3}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-waiting-input-handler-path3 \\ \index{os-task-table-os-waiting-input-!handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-waiting-input-handler-path3 \\ \index{os-segment-table-os-waiting-inp!ut-handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-waiting-input-handler-path3 \\ \index{os-readyq-os-waiting-input-hand!ler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-readyq}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{os-readyq} \\ 
$=$$\;\;\;\;${\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-waiting-input-handler-path3 \\ \index{os-ibuffers-os-waiting-input-ha!ndler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ibuffers}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{os-ibuffers-with-enqueued-character}}\,({\it{os\/}})\index{os-ibuffers-with-enqueued-chara!cter})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-ibuffers-os-waiting-input-handler-path3 \\ \index{finite-number-queue-listp-os-ib!uffers-os-waiting-input-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,(\=\+{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-ibuffers}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{os-ibuffers})\-\index{table}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-ibuffers-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-waiting-input-handler-path3 \\ \index{os-obuffers-os-waiting-input-ha!ndler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-waiting-input-handler-path3 \\ \index{os-mbuffers-os-waiting-input-ha!ndler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-waiting-input-handler-path3 \\ \index{os-status-table-os-waiting-input!-handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-update-status}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\it{os\/}})\-\index{os-update-status})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-status-list-os-status-table-os-waiting-input-handler-path3 \\ \index{good-status-list-os-status-table!-os-waiting-input-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-status-list}}\,({\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-status-table}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{os-status-table})\-\index{table})\index{good-status-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-status-list-os-status-table-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-waiting-input-handler-path3 \\ \index{os-ready-set-os-waiting-input-h!andler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-waiting-input-handler-path3 \\ \index{permutation-os-readyq-os-ready-!set-for-os-waiting-input-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-waiting-input-handler-path3 \\ \index{not-tm-waiting-os-waiting-input!-handler-path3}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-waiting-input-handler-path3 \\ \index{tm-base-os-waiting-input-handle!r-path3}
\=\+{\rm{tm-base}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-waiting-input-handler-path3 \\ \index{tm-limit-os-waiting-input-handle!r-path3}
\=\+{\rm{tm-limit}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-waiting-input-handler-path3 \\ \index{tm-base-tm-limit-os-waiting-inp!ut-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-waiting-input-handler-path3 \\ \index{good-os-os-waiting-input-handle!r-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-waiting-input-handler-path4 \\ \index{good-tm-os-waiting-input-handle!r-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-waiting-input-handler-path4 \\ \index{tm-slimit-os-waiting-input-hand!ler-path4}
{\rm{tm-slimit}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-waiting-input-handler-path4 \\ \index{os-code-os-waiting-input-handle!r-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-code}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-waiting-input-handler-path4 \\ \index{tm-interrupt-addresses-os-waiti!ng-input-handler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-waiting-input-handler-path4 \\ \index{not-tm-in-supervisor-mode-os-waiti!ng-input-handler-path4}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-waiting-input-handler-path4 \\ \index{os-task-table-os-waiting-input-!handler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-waiting-input-handler-path4 \\ \index{os-segment-table-os-waiting-inp!ut-handler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-waiting-input-handler-path4 \\ \index{os-readyq-os-waiting-input-hand!ler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-readyq}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{os-readyq} $=$ {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-waiting-input-handler-path4 \\ \index{os-ibuffers-os-waiting-input-ha!ndler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ibuffers}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{os-ibuffers-with-qreplaced-overflow-character}}\,({\it{os\/}})\index{os-ibuffers-with-qreplaced-over!flow-character})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-ibuffers-os-waiting-input-handler-path4 \\ \index{finite-number-queue-listp-os-ib!uffers-os-waiting-input-handler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,(\=\+{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-ibuffers}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{os-ibuffers})\-\index{table}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-ibuffers-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-waiting-input-handler-path4 \\ \index{os-obuffers-os-waiting-input-ha!ndler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-waiting-input-handler-path4 \\ \index{os-mbuffers-os-waiting-input-ha!ndler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-waiting-input-handler-path4 \\ \index{os-status-table-os-waiting-input!-handler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-waiting-os-waiting-input-handler-path4 \\ \index{tm-waiting-os-waiting-input-han!dler-path4}
{\rm{tm-waiting}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-waiting-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-waiting-input-handler-path4 \\ \index{good-os-os-waiting-input-handle!r-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-waiting-input-handler-path5 \\ \index{good-tm-os-waiting-input-handle!r-path5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-waiting-input-handler-path5 \\ \index{tm-slimit-os-waiting-input-hand!ler-path5}
{\rm{tm-slimit}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-waiting-input-handler-path5 \\ \index{os-code-os-waiting-input-handle!r-path5}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-code}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-waiting-input-handler-path5 \\ \index{tm-interrupt-addresses-os-waiti!ng-input-handler-path5}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-waiting-input-handler-path5 \\ \index{not-tm-in-supervisor-mode-os-waiti!ng-input-handler-path5}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-waiting-input-handler-path5 \\ \index{os-task-table-os-waiting-input-!handler-path5}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-waiting-input-handler-path5 \\ \index{os-segment-table-os-waiting-inp!ut-handler-path5}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-waiting-input-handler-path5 \\ \index{os-readyq-os-waiting-input-hand!ler-path5}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-readyq}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{os-readyq} $=$ {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-waiting-input-handler-path5 \\ \index{os-ibuffers-os-waiting-input-ha!ndler-path5}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ibuffers}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{os-ibuffers-with-enqueued-overflow-character}}\,({\it{os\/}})\index{os-ibuffers-with-enqueued-overf!low-character})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-ibuffers-os-waiting-input-handler-path5 \\ \index{finite-number-queue-listp-os-ib!uffers-os-waiting-input-handler-path5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,(\=\+{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-ibuffers}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{os-ibuffers})\-\index{table}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-ibuffers-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-waiting-input-handler-path5 \\ \index{os-obuffers-os-waiting-input-ha!ndler-path5}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-waiting-input-handler-path5 \\ \index{os-mbuffers-os-waiting-input-ha!ndler-path5}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-waiting-input-handler-path5 \\ \index{os-status-table-os-waiting-input!-handler-path5}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-waiting-os-waiting-input-handler-path5 \\ \index{tm-waiting-os-waiting-input-han!dler-path5}
{\rm{tm-waiting}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-waiting-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-waiting-input-handler-path5 \\ \index{good-os-os-waiting-input-handle!r-path5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-waiting-input-handler-path6 \\ \index{good-tm-os-waiting-input-handle!r-path6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-waiting-input-handler-path6 \\ \index{tm-slimit-os-waiting-input-hand!ler-path6}
{\rm{tm-slimit}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-waiting-input-handler-path6 \\ \index{os-code-os-waiting-input-handle!r-path6}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-code}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-waiting-input-handler-path6 \\ \index{tm-interrupt-addresses-os-waiti!ng-input-handler-path6}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-waiting-input-handler-path6 \\ \index{not-tm-in-supervisor-mode-os-waiti!ng-input-handler-path6}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-waiting-input-handler-path6 \\ \index{os-task-table-os-waiting-input-!handler-path6}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-waiting-input-handler-path6 \\ \index{os-segment-table-os-waiting-inp!ut-handler-path6}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-waiting-input-handler-path6 \\ \index{os-readyq-os-waiting-input-hand!ler-path6}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-readyq}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{os-readyq} $=$ {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-waiting-input-handler-path6 \\ \index{os-ibuffers-os-waiting-input-ha!ndler-path6}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ibuffers}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{os-ibuffers-with-enqueued-character}}\,({\it{os\/}})\index{os-ibuffers-with-enqueued-chara!cter})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-ibuffers-os-waiting-input-handler-path6 \\ \index{finite-number-queue-listp-os-ib!uffers-os-waiting-input-handler-path6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,(\=\+{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-ibuffers}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{os-ibuffers})\-\index{table}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-ibuffers-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-waiting-input-handler-path6 \\ \index{os-obuffers-os-waiting-input-ha!ndler-path6}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-waiting-input-handler-path6 \\ \index{os-mbuffers-os-waiting-input-ha!ndler-path6}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-waiting-input-handler-path6 \\ \index{os-status-table-os-waiting-input!-handler-path6}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-waiting-os-waiting-input-handler-path6 \\ \index{tm-waiting-os-waiting-input-han!dler-path6}
{\rm{tm-waiting}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-waiting-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-waiting-input-handler-path6 \\ \index{good-os-os-waiting-input-handle!r-path6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-waiting-input-handler \\ \index{good-os-os-waiting-input-handle!r}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-waiting-input-handler}}\,({\it{os\/}})\index{os-waiting-input-handler})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-waiting-input-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-array-enq-interrupting-input-port2 \\ \index{finite-number-queuep-array-enq-i!nterrupting-input-port2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,(\=\+{\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq}, \\ 
{\tt{'}}{\tt{16}}, \\ 
{\tt{'}}{\tt{16}})\-\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-array-enq-interrupting-input-port2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-running-input-handler-path1 \\ \index{good-tm-os-running-input-handle!r-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-running-input-handler-path1 \\ \index{tm-slimit-os-running-input-hand!ler-path1}
{\rm{tm-slimit}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-running-input-handler-path1 \\ \index{os-code-os-running-input-handle!r-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-code}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-running-input-handler-path1 \\ \index{tm-interrupt-addresses-os-runni!ng-input-handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-running-input-handler-path1 \\ \index{not-tm-in-supervisor-mode-os-ru!nning-input-handler-path1}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-running-input-handler-path1 \\ \index{os-task-table-os-running-input-!handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-running-input-handler-path1 \\ \index{os-segment-table-os-running-inp!ut-handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-running-input-handler-path1 \\ \index{os-readyq-os-running-input-hand!ler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-readyq}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{os-readyq} \\ 
$=$$\;\;\;\;${\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-running-input-handler-path1 \\ \index{os-ibuffers-os-running-input-ha!ndler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ibuffers}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{os-ibuffers-with-qreplaced-overflow-character}}\,({\it{os\/}})\index{os-ibuffers-with-qreplaced-over!flow-character})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-ibuffers-os-running-input-handler-path1 \\ \index{finite-number-queue-listp-os-ib!uffers-os-running-input-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,(\=\+{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-ibuffers}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{os-ibuffers})\-\index{table}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-ibuffers-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-running-input-handler-path1 \\ \index{os-obuffers-os-running-input-ha!ndler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-running-input-handler-path1 \\ \index{os-mbuffers-os-running-input-ha!ndler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-running-input-handler-path1 \\ \index{os-status-table-os-running-input!-handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-update-status}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\it{os\/}})\-\index{os-update-status})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-status-list-os-status-table-os-running-input-handler-path1 \\ \index{good-status-list-os-status-table!-os-running-input-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-status-list}}\,({\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-status-table}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{os-status-table})\-\index{table})\index{good-status-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-status-list-os-status-table-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-running-input-handler-path1 \\ \index{os-ready-set-os-running-input-h!andler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-running-input-handler-path1 \\ \index{permutation-os-readyq-os-ready-!set-for-os-running-input-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-running-input-handler-path1 \\ \index{not-tm-waiting-os-running-input!-handler-path1}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-running-input-handler-path1 \\ \index{tm-base-os-running-input-handle!r-path1}
{\rm{tm-base}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{os\/}})\index{tm-base}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-running-input-handler-path1 \\ \index{tm-limit-os-running-input-handle!r-path1}
{\rm{tm-limit}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{os\/}})\index{tm-limit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-running-input-handler-path1 \\ \index{tm-base-tm-limit-os-running-inp!ut-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-running-input-handler-path1 \\ \index{good-os-os-running-input-handle!r-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-running-input-handler-path2 \\ \index{good-tm-os-running-input-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-running-input-handler-path2 \\ \index{tm-slimit-os-running-input-hand!ler-path2}
{\rm{tm-slimit}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-running-input-handler-path2 \\ \index{os-code-os-running-input-handle!r-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-code}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-running-input-handler-path2 \\ \index{tm-interrupt-addresses-os-runni!ng-input-handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-running-input-handler-path2 \\ \index{not-tm-in-supervisor-mode-os-ru!nning-input-handler-path2}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-running-input-handler-path2 \\ \index{os-task-table-os-running-input-!handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-running-input-handler-path2 \\ \index{os-segment-table-os-running-inp!ut-handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-running-input-handler-path2 \\ \index{os-readyq-os-running-input-hand!ler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-readyq}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{os-readyq} \\ 
$=$$\;\;\;\;${\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-running-input-handler-path2 \\ \index{os-ibuffers-os-running-input-ha!ndler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ibuffers}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{os-ibuffers-with-enqueued-overflow-character}}\,({\it{os\/}})\index{os-ibuffers-with-enqueued-overf!low-character})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-ibuffers-os-running-input-handler-path2 \\ \index{finite-number-queue-listp-os-ib!uffers-os-running-input-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,(\=\+{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-ibuffers}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{os-ibuffers})\-\index{table}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-ibuffers-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-running-input-handler-path2 \\ \index{os-obuffers-os-running-input-ha!ndler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-running-input-handler-path2 \\ \index{os-mbuffers-os-running-input-ha!ndler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-running-input-handler-path2 \\ \index{os-status-table-os-running-input!-handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-update-status}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\it{os\/}})\-\index{os-update-status})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-status-list-os-status-table-os-running-input-handler-path2 \\ \index{good-status-list-os-status-table!-os-running-input-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-status-list}}\,({\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-status-table}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{os-status-table})\-\index{table})\index{good-status-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-status-list-os-status-table-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-running-input-handler-path2 \\ \index{os-ready-set-os-running-input-h!andler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-running-input-handler-path2 \\ \index{permutation-os-readyq-os-ready-!set-for-os-running-input-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-running-input-handler-path2 \\ \index{not-tm-waiting-os-running-input!-handler-path2}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-running-input-handler-path2 \\ \index{tm-base-os-running-input-handle!r-path2}
{\rm{tm-base}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{os\/}})\index{tm-base}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-running-input-handler-path2 \\ \index{tm-limit-os-running-input-handle!r-path2}
{\rm{tm-limit}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{os\/}})\index{tm-limit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-running-input-handler-path2 \\ \index{tm-base-tm-limit-os-running-inp!ut-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-running-input-handler-path2 \\ \index{good-os-os-running-input-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-running-input-handler-path3 \\ \index{good-tm-os-running-input-handle!r-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-running-input-handler-path3 \\ \index{tm-slimit-os-running-input-hand!ler-path3}
{\rm{tm-slimit}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-running-input-handler-path3 \\ \index{os-code-os-running-input-handle!r-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-code}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-running-input-handler-path3 \\ \index{tm-interrupt-addresses-os-runni!ng-input-handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-running-input-handler-path3 \\ \index{not-tm-in-supervisor-mode-os-ru!nning-input-handler-path3}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-running-input-handler-path3 \\ \index{os-task-table-os-running-input-!handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-running-input-handler-path3 \\ \index{os-segment-table-os-running-inp!ut-handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-running-input-handler-path3 \\ \index{os-readyq-os-running-input-hand!ler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-readyq}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{os-readyq} \\ 
$=$$\;\;\;\;${\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-running-input-handler-path3 \\ \index{os-ibuffers-os-running-input-ha!ndler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ibuffers}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{os-ibuffers-with-enqueued-character}}\,({\it{os\/}})\index{os-ibuffers-with-enqueued-chara!cter})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-ibuffers-os-running-input-handler-path3 \\ \index{finite-number-queue-listp-os-ib!uffers-os-running-input-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,(\=\+{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-ibuffers}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{os-ibuffers})\-\index{table}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-ibuffers-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-running-input-handler-path3 \\ \index{os-obuffers-os-running-input-ha!ndler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-running-input-handler-path3 \\ \index{os-mbuffers-os-running-input-ha!ndler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-running-input-handler-path3 \\ \index{os-status-table-os-running-input!-handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-update-status}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\it{os\/}})\-\index{os-update-status})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-status-list-os-status-table-os-running-input-handler-path3 \\ \index{good-status-list-os-status-table!-os-running-input-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-status-list}}\,({\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-status-table}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{os-status-table})\-\index{table})\index{good-status-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-status-list-os-status-table-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-running-input-handler-path3 \\ \index{os-ready-set-os-running-input-h!andler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-running-input-handler-path3 \\ \index{permutation-os-readyq-os-ready-!set-for-os-running-input-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-running-input-handler-path3 \\ \index{not-tm-waiting-os-running-input!-handler-path3}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-running-input-handler-path3 \\ \index{tm-base-os-running-input-handle!r-path3}
{\rm{tm-base}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{os\/}})\index{tm-base}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-running-input-handler-path3 \\ \index{tm-limit-os-running-input-handle!r-path3}
{\rm{tm-limit}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{os\/}})\index{tm-limit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-running-input-handler-path3 \\ \index{tm-base-tm-limit-os-running-inp!ut-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-running-input-handler-path3 \\ \index{good-os-os-running-input-handle!r-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-running-input-handler-path4 \\ \index{good-tm-os-running-input-handle!r-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-running-input-handler-path4 \\ \index{tm-slimit-os-running-input-hand!ler-path4}
{\rm{tm-slimit}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-running-input-handler-path4 \\ \index{os-code-os-running-input-handle!r-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-code}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-running-input-handler-path4 \\ \index{tm-interrupt-addresses-os-runni!ng-input-handler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-running-input-handler-path4 \\ \index{not-tm-in-supervisor-mode-os-ru!nning-input-handler-path4}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-running-input-handler-path4 \\ \index{os-task-table-os-running-input-!handler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-running-input-handler-path4 \\ \index{os-segment-table-os-running-inp!ut-handler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-running-input-handler-path4 \\ \index{os-readyq-os-running-input-hand!ler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-readyq}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{os-readyq} $=$ {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-running-input-handler-path4 \\ \index{os-ibuffers-os-running-input-ha!ndler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ibuffers}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{os-ibuffers-with-qreplaced-overflow-character}}\,({\it{os\/}})\index{os-ibuffers-with-qreplaced-over!flow-character})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-ibuffers-os-running-input-handler-path4 \\ \index{finite-number-queue-listp-os-ib!uffers-os-running-input-handler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,(\=\+{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-ibuffers}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{os-ibuffers})\-\index{table}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-ibuffers-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-running-input-handler-path4 \\ \index{os-obuffers-os-running-input-ha!ndler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-running-input-handler-path4 \\ \index{os-mbuffers-os-running-input-ha!ndler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-running-input-handler-path4 \\ \index{os-status-table-os-running-input!-handler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-running-input-handler-path4 \\ \index{not-tm-waiting-os-running-input!-handler-path4}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-running-input-handler-path4 \\ \index{tm-base-os-running-input-handle!r-path4}
{\rm{tm-base}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{os\/}})\index{tm-base}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-running-input-handler-path4 \\ \index{tm-limit-os-running-input-handle!r-path4}
{\rm{tm-limit}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{os\/}})\index{tm-limit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-running-input-handler-path4 \\ \index{tm-base-tm-limit-os-running-inp!ut-handler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-running-input-handler-path4 \\ \index{good-os-os-running-input-handle!r-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-running-input-handler-path5 \\ \index{good-tm-os-running-input-handle!r-path5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-running-input-handler-path5 \\ \index{tm-slimit-os-running-input-hand!ler-path5}
{\rm{tm-slimit}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-running-input-handler-path5 \\ \index{os-code-os-running-input-handle!r-path5}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-code}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-running-input-handler-path5 \\ \index{tm-interrupt-addresses-os-runni!ng-input-handler-path5}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-running-input-handler-path5 \\ \index{not-tm-in-supervisor-mode-os-ru!nning-input-handler-path5}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-running-input-handler-path5 \\ \index{os-task-table-os-running-input-!handler-path5}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-running-input-handler-path5 \\ \index{os-segment-table-os-running-inp!ut-handler-path5}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-running-input-handler-path5 \\ \index{os-readyq-os-running-input-hand!ler-path5}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-readyq}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{os-readyq} $=$ {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-running-input-handler-path5 \\ \index{os-ibuffers-os-running-input-ha!ndler-path5}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ibuffers}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{os-ibuffers-with-enqueued-overflow-character}}\,({\it{os\/}})\index{os-ibuffers-with-enqueued-overf!low-character})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-ibuffers-os-running-input-handler-path5 \\ \index{finite-number-queue-listp-os-ib!uffers-os-running-input-handler-path5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,(\=\+{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-ibuffers}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{os-ibuffers})\-\index{table}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-ibuffers-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-running-input-handler-path5 \\ \index{os-obuffers-os-running-input-ha!ndler-path5}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-running-input-handler-path5 \\ \index{os-mbuffers-os-running-input-ha!ndler-path5}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-running-input-handler-path5 \\ \index{os-status-table-os-running-input!-handler-path5}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-running-input-handler-path5 \\ \index{not-tm-waiting-os-running-input!-handler-path5}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-running-input-handler-path5 \\ \index{tm-base-os-running-input-handle!r-path5}
{\rm{tm-base}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{os\/}})\index{tm-base}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-running-input-handler-path5 \\ \index{tm-limit-os-running-input-handle!r-path5}
{\rm{tm-limit}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{os\/}})\index{tm-limit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-running-input-handler-path5 \\ \index{tm-base-tm-limit-os-running-inp!ut-handler-path5}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-running-input-handler-path5 \\ \index{good-os-os-running-input-handle!r-path5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-running-input-handler-path6 \\ \index{good-tm-os-running-input-handle!r-path6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-running-input-handler-path6 \\ \index{tm-slimit-os-running-input-hand!ler-path6}
{\rm{tm-slimit}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-running-input-handler-path6 \\ \index{os-code-os-running-input-handle!r-path6}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-code}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-running-input-handler-path6 \\ \index{tm-interrupt-addresses-os-runni!ng-input-handler-path6}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-running-input-handler-path6 \\ \index{not-tm-in-supervisor-mode-os-ru!nning-input-handler-path6}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-running-input-handler-path6 \\ \index{os-task-table-os-running-input-!handler-path6}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-running-input-handler-path6 \\ \index{os-segment-table-os-running-inp!ut-handler-path6}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-running-input-handler-path6 \\ \index{os-readyq-os-running-input-hand!ler-path6}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-readyq}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{os-readyq} $=$ {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-running-input-handler-path6 \\ \index{os-ibuffers-os-running-input-ha!ndler-path6}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ibuffers}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{os-ibuffers-with-enqueued-character}}\,({\it{os\/}})\index{os-ibuffers-with-enqueued-chara!cter})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-ibuffers-os-running-input-handler-path6 \\ \index{finite-number-queue-listp-os-ib!uffers-os-running-input-handler-path6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,(\=\+{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-ibuffers}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{os-ibuffers})\-\index{table}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-ibuffers-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-running-input-handler-path6 \\ \index{os-obuffers-os-running-input-ha!ndler-path6}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-running-input-handler-path6 \\ \index{os-mbuffers-os-running-input-ha!ndler-path6}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-running-input-handler-path6 \\ \index{os-status-table-os-running-input!-handler-path6}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-running-input-handler-path6 \\ \index{not-tm-waiting-os-running-input!-handler-path6}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-running-input-handler-path6 \\ \index{tm-base-os-running-input-handle!r-path6}
{\rm{tm-base}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{os\/}})\index{tm-base}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-running-input-handler-path6 \\ \index{tm-limit-os-running-input-handle!r-path6}
{\rm{tm-limit}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{os\/}})\index{tm-limit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-running-input-handler-path6 \\ \index{tm-base-tm-limit-os-running-inp!ut-handler-path6}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-running-input-handler-path6 \\ \index{good-os-os-running-input-handle!r-path6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-running-input-handler \\ \index{good-os-os-running-input-handle!r}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-running-input-handler}}\,({\it{os\/}})\index{os-running-input-handler})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-running-input-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-intended-output-interrupt \\ \index{good-tm-os-intended-output-inte!rrupt}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-intended-output-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-array-enq-interrupting-output-port \\ \index{finite-number-queuep-array-enq-i!nterrupting-output-port}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,(\=\+{\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq}, \\ 
{\tt{'}}{\tt{16}}, \\ 
{\tt{'}}{\tt{16}})\-\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-array-enq-interrupting-output-port.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-waiting-output-handler-path1 \\ \index{good-tm-os-waiting-output-handle!r-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-waiting-output-handler-path1 \\ \index{tm-slimit-os-waiting-output-han!dler-path1}
{\rm{tm-slimit}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-waiting-output-handler-path1 \\ \index{os-code-os-waiting-output-handle!r-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-code}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-waiting-output-handler-path1 \\ \index{tm-interrupt-addresses-os-waiti!ng-output-handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-waiting-output-handler-path1 \\ \index{not-tm-in-supervisor-mode-os-waiti!ng-output-handler-path1}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-waiting-output-handler-path1 \\ \index{os-task-table-os-waiting-output!-handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-waiting-output-handler-path1 \\ \index{os-segment-table-os-waiting-outp!ut-handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-waiting-output-handler-path1 \\ \index{os-readyq-os-waiting-output-han!dler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-readyq}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{os-readyq} \\ 
$=$$\;\;\;\;${\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-waiting-output-handler-path1 \\ \index{os-ibuffers-os-waiting-output-h!andler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-waiting-output-handler-path1 \\ \index{os-obuffers-os-waiting-output-h!andler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-waiting-output-handler-path1 \\ \index{os-mbuffers-os-waiting-output-h!andler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-waiting-output-handler-path1 \\ \index{os-status-table-os-waiting-outp!ut-handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-update-status}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\it{os\/}})\-\index{os-update-status})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-status-list-os-status-table-os-waiting-output-handler-path1 \\ \index{good-status-list-os-status-table!-os-waiting-output-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-status-list}}\,({\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-status-table}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{os-status-table})\-\index{table})\index{good-status-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-status-list-os-status-table-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-waiting-output-handler-path1 \\ \index{os-ready-set-os-waiting-output-!handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-waiting-output-handler-path1 \\ \index{permutation-os-readyq-os-ready-!set-for-os-waiting-output-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-waiting-output-handler-path1 \\ \index{not-tm-waiting-os-waiting-output!-handler-path1}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-waiting-output-handler-path1 \\ \index{tm-base-os-waiting-output-handle!r-path1}
\=\+{\rm{tm-base}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-waiting-output-handler-path1 \\ \index{tm-limit-os-waiting-output-hand!ler-path1}
\=\+{\rm{tm-limit}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-waiting-output-handler-path1 \\ \index{tm-base-tm-limit-os-waiting-outp!ut-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-waiting-output-handler-path1 \\ \index{good-os-os-waiting-output-handle!r-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-waiting-output-handler-path2 \\ \index{good-tm-os-waiting-output-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-waiting-output-handler-path2 \\ \index{tm-slimit-os-waiting-output-han!dler-path2}
{\rm{tm-slimit}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-waiting-output-handler-path2 \\ \index{os-code-os-waiting-output-handle!r-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-code}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-waiting-output-handler-path2 \\ \index{tm-interrupt-addresses-os-waiti!ng-output-handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-waiting-output-handler-path2 \\ \index{not-tm-in-supervisor-mode-os-waiti!ng-output-handler-path2}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-waiting-output-handler-path2 \\ \index{os-task-table-os-waiting-output!-handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-waiting-output-handler-path2 \\ \index{os-segment-table-os-waiting-outp!ut-handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-waiting-output-handler-path2 \\ \index{os-readyq-os-waiting-output-han!dler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-readyq}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{os-readyq} \\ 
$=$$\;\;\;\;${\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-waiting-output-handler-path2 \\ \index{os-ibuffers-os-waiting-output-h!andler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-waiting-output-handler-path2 \\ \index{os-obuffers-os-waiting-output-h!andler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-obuffers}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{os-obuffers} \\ 
$=$$\;\;\;\;${\rm{os-obuffers-with-dequeued-character}}\,({\it{os\/}})\index{os-obuffers-with-dequeued-chara!cter})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-obuffers-os-waiting-output-handler-path2 \\ \index{finite-number-queue-listp-os-ob!uffers-os-waiting-output-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,(\=\+{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-obuffers}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{os-obuffers})\-\index{table}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-obuffers-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-waiting-output-handler-path2 \\ \index{os-mbuffers-os-waiting-output-h!andler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-waiting-output-handler-path2 \\ \index{os-status-table-os-waiting-outp!ut-handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-update-status}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\it{os\/}})\-\index{os-update-status})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-status-list-os-status-table-os-waiting-output-handler-path2 \\ \index{good-status-list-os-status-table!-os-waiting-output-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-status-list}}\,({\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-status-table}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{os-status-table})\-\index{table})\index{good-status-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-status-list-os-status-table-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-waiting-output-handler-path2 \\ \index{os-ready-set-os-waiting-output-!handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-waiting-output-handler-path2 \\ \index{permutation-os-readyq-os-ready-!set-for-os-waiting-output-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-waiting-output-handler-path2 \\ \index{not-tm-waiting-os-waiting-output!-handler-path2}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-waiting-output-handler-path2 \\ \index{tm-base-os-waiting-output-handle!r-path2}
\=\+{\rm{tm-base}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-waiting-output-handler-path2 \\ \index{tm-limit-os-waiting-output-hand!ler-path2}
\=\+{\rm{tm-limit}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-waiting-output-handler-path2 \\ \index{tm-base-tm-limit-os-waiting-outp!ut-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-waiting-output-handler-path2 \\ \index{good-os-os-waiting-output-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-waiting-output-handler-path3 \\ \index{good-tm-os-waiting-output-handle!r-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-waiting-output-handler-path3 \\ \index{tm-slimit-os-waiting-output-han!dler-path3}
{\rm{tm-slimit}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-waiting-output-handler-path3 \\ \index{os-code-os-waiting-output-handle!r-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-code}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-waiting-output-handler-path3 \\ \index{tm-interrupt-addresses-os-waiti!ng-output-handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-waiting-output-handler-path3 \\ \index{not-tm-in-supervisor-mode-os-waiti!ng-output-handler-path3}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-waiting-output-handler-path3 \\ \index{os-task-table-os-waiting-output!-handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-waiting-output-handler-path3 \\ \index{os-segment-table-os-waiting-outp!ut-handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-waiting-output-handler-path3 \\ \index{os-readyq-os-waiting-output-han!dler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-readyq}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{os-readyq} $=$ {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-waiting-output-handler-path3 \\ \index{os-ibuffers-os-waiting-output-h!andler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-waiting-output-handler-path3 \\ \index{os-obuffers-os-waiting-output-h!andler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-waiting-output-handler-path3 \\ \index{os-mbuffers-os-waiting-output-h!andler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-waiting-output-handler-path3 \\ \index{os-status-table-os-waiting-outp!ut-handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-waiting-os-waiting-output-handler-path3 \\ \index{tm-waiting-os-waiting-output-ha!ndler-path3}
{\rm{tm-waiting}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-waiting-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-waiting-output-handler-path3 \\ \index{good-os-os-waiting-output-handle!r-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-waiting-output-handler-path4 \\ \index{good-tm-os-waiting-output-handle!r-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-waiting-output-handler-path4 \\ \index{tm-slimit-os-waiting-output-han!dler-path4}
{\rm{tm-slimit}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-waiting-output-handler-path4 \\ \index{os-code-os-waiting-output-handle!r-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-code}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-waiting-output-handler-path4 \\ \index{tm-interrupt-addresses-os-waiti!ng-output-handler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-waiting-output-handler-path4 \\ \index{not-tm-in-supervisor-mode-os-waiti!ng-output-handler-path4}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-waiting-output-handler-path4 \\ \index{os-task-table-os-waiting-output!-handler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-task-table}}\,({\it{os\/}})\index{os-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-waiting-output-handler-path4 \\ \index{os-segment-table-os-waiting-outp!ut-handler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-waiting-output-handler-path4 \\ \index{os-readyq-os-waiting-output-han!dler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-readyq}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{os-readyq} $=$ {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-waiting-output-handler-path4 \\ \index{os-ibuffers-os-waiting-output-h!andler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-waiting-output-handler-path4 \\ \index{os-obuffers-os-waiting-output-h!andler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-obuffers}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{os-obuffers} \\ 
$=$$\;\;\;\;${\rm{os-obuffers-with-dequeued-character}}\,({\it{os\/}})\index{os-obuffers-with-dequeued-chara!cter})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-obuffers-os-waiting-output-handler-path4 \\ \index{finite-number-queue-listp-os-ob!uffers-os-waiting-output-handler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,(\=\+{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-obuffers}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{os-obuffers})\-\index{table}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-obuffers-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-waiting-output-handler-path4 \\ \index{os-mbuffers-os-waiting-output-h!andler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-waiting-output-handler-path4 \\ \index{os-status-table-os-waiting-outp!ut-handler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-waiting-os-waiting-output-handler-path4 \\ \index{tm-waiting-os-waiting-output-ha!ndler-path4}
{\rm{tm-waiting}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-waiting-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-waiting-output-handler-path4 \\ \index{good-os-os-waiting-output-handle!r-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-waiting-output-handler \\ \index{good-os-os-waiting-output-handle!r}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-waiting-output-handler}}\,({\it{os\/}})\index{os-waiting-output-handler})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-waiting-output-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queuep-array-enq-interrupting-output-port2 \\ \index{finite-number-queuep-array-enq-i!nterrupting-output-port2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queuep}}\,(\=\+{\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq}, \\ 
{\tt{'}}{\tt{16}}, \\ 
{\tt{'}}{\tt{16}})\-\index{finite-number-queuep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queuep-array-enq-interrupting-output-port2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-running-output-handler-path1 \\ \index{good-tm-os-running-output-handle!r-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-running-output-handler-path1 \\ \index{tm-slimit-os-running-output-han!dler-path1}
{\rm{tm-slimit}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-running-output-handler-path1 \\ \index{os-code-os-running-output-handle!r-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-code}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-running-output-handler-path1 \\ \index{tm-interrupt-addresses-os-runni!ng-output-handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-running-output-handler-path1 \\ \index{not-tm-in-supervisor-mode-os-ru!nning-output-handler-path1}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-running-output-handler-path1 \\ \index{os-task-table-os-running-output!-handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-running-output-handler-path1 \\ \index{os-segment-table-os-running-outp!ut-handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-running-output-handler-path1 \\ \index{os-readyq-os-running-output-han!dler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-readyq}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{os-readyq} \\ 
$=$$\;\;\;\;${\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-running-output-handler-path1 \\ \index{os-ibuffers-os-running-output-h!andler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-running-output-handler-path1 \\ \index{os-obuffers-os-running-output-h!andler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-running-output-handler-path1 \\ \index{os-mbuffers-os-running-output-h!andler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-running-output-handler-path1 \\ \index{os-status-table-os-running-outp!ut-handler-path1}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-update-status}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\it{os\/}})\-\index{os-update-status})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-status-list-os-status-table-os-running-output-handler-path1 \\ \index{good-status-list-os-status-table!-os-running-output-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-status-list}}\,({\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-status-table}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{os-status-table})\-\index{table})\index{good-status-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-status-list-os-status-table-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-running-output-handler-path1 \\ \index{os-ready-set-os-running-output-!handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-running-output-handler-path1 \\ \index{permutation-os-readyq-os-ready-!set-for-os-running-output-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-running-output-handler-path1 \\ \index{not-tm-waiting-os-running-output!-handler-path1}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-running-output-handler-path1 \\ \index{tm-base-os-running-output-handle!r-path1}
{\rm{tm-base}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{os\/}})\index{tm-base}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-running-output-handler-path1 \\ \index{tm-limit-os-running-output-hand!ler-path1}
{\rm{tm-limit}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{os\/}})\index{tm-limit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-running-output-handler-path1 \\ \index{tm-base-tm-limit-os-running-outp!ut-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-running-output-handler-path1 \\ \index{good-os-os-running-output-handle!r-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-running-output-handler-path2 \\ \index{good-tm-os-running-output-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-running-output-handler-path2 \\ \index{tm-slimit-os-running-output-han!dler-path2}
{\rm{tm-slimit}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-running-output-handler-path2 \\ \index{os-code-os-running-output-handle!r-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-code}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-running-output-handler-path2 \\ \index{tm-interrupt-addresses-os-runni!ng-output-handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-running-output-handler-path2 \\ \index{not-tm-in-supervisor-mode-os-ru!nning-output-handler-path2}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-running-output-handler-path2 \\ \index{os-task-table-os-running-output!-handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-running-output-handler-path2 \\ \index{os-segment-table-os-running-outp!ut-handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-running-output-handler-path2 \\ \index{os-readyq-os-running-output-han!dler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-readyq}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{os-readyq} \\ 
$=$$\;\;\;\;${\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-running-output-handler-path2 \\ \index{os-ibuffers-os-running-output-h!andler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-running-output-handler-path2 \\ \index{os-obuffers-os-running-output-h!andler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-obuffers}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{os-obuffers} \\ 
$=$$\;\;\;\;${\rm{os-obuffers-with-dequeued-character}}\,({\it{os\/}})\index{os-obuffers-with-dequeued-chara!cter})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-obuffers-os-running-output-handler-path2 \\ \index{finite-number-queue-listp-os-ob!uffers-os-running-output-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,(\=\+{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-obuffers}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{os-obuffers})\-\index{table}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-obuffers-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-running-output-handler-path2 \\ \index{os-mbuffers-os-running-output-h!andler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-running-output-handler-path2 \\ \index{os-status-table-os-running-outp!ut-handler-path2}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-update-status}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\it{os\/}})\-\index{os-update-status})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-status-list-os-status-table-os-running-output-handler-path2 \\ \index{good-status-list-os-status-table!-os-running-output-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-status-list}}\,({\rm{table}}\,(\=\+{\tt{'}}{\tt{2}}, \\ 
{\rm{os-status-table}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{os-status-table})\-\index{table})\index{good-status-list}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-status-list-os-status-table-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ready-set-os-running-output-handler-path2 \\ \index{os-ready-set-os-running-output-!handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-ready-set}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{os-ready-set} \\ 
$=$$\;\;\;\;${\rm{index-ready-set}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\index{index-ready-set})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ready-set-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  permutation-os-readyq-os-ready-set-for-os-running-output-handler-path2 \\ \index{permutation-os-readyq-os-ready-!set-for-os-running-output-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{permutation}}\,(\=\+{\rm{mapup-queue}}\,({\rm{array-enq}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-\index{array-enq})\index{mapup-queue}, \\ 
{\rm{os-ready-set}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{os-ready-set})\-\index{permutation}\-
\end{tabbing}


\noindent{\sc Event}:   Disable permutation-os-readyq-os-ready-set-for-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-running-output-handler-path2 \\ \index{not-tm-waiting-os-running-output!-handler-path2}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-running-output-handler-path2 \\ \index{tm-base-os-running-output-handle!r-path2}
{\rm{tm-base}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{os\/}})\index{tm-base}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-running-output-handler-path2 \\ \index{tm-limit-os-running-output-hand!ler-path2}
{\rm{tm-limit}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{os\/}})\index{tm-limit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-running-output-handler-path2 \\ \index{tm-base-tm-limit-os-running-outp!ut-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-running-output-handler-path2 \\ \index{good-os-os-running-output-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-running-output-handler-path3 \\ \index{good-tm-os-running-output-handle!r-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-running-output-handler-path3 \\ \index{tm-slimit-os-running-output-han!dler-path3}
{\rm{tm-slimit}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-running-output-handler-path3 \\ \index{os-code-os-running-output-handle!r-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-code}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-running-output-handler-path3 \\ \index{tm-interrupt-addresses-os-runni!ng-output-handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-running-output-handler-path3 \\ \index{not-tm-in-supervisor-mode-os-ru!nning-output-handler-path3}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-running-output-handler-path3 \\ \index{os-task-table-os-running-output!-handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-running-output-handler-path3 \\ \index{os-segment-table-os-running-outp!ut-handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-running-output-handler-path3 \\ \index{os-readyq-os-running-output-han!dler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-readyq}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{os-readyq} $=$ {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-running-output-handler-path3 \\ \index{os-ibuffers-os-running-output-h!andler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-running-output-handler-path3 \\ \index{os-obuffers-os-running-output-h!andler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-obuffers}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{os-obuffers} $=$ {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-running-output-handler-path3 \\ \index{os-mbuffers-os-running-output-h!andler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-running-output-handler-path3 \\ \index{os-status-table-os-running-outp!ut-handler-path3}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-running-output-handler-path3 \\ \index{not-tm-waiting-os-running-output!-handler-path3}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-running-output-handler-path3 \\ \index{tm-base-os-running-output-handle!r-path3}
{\rm{tm-base}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{os\/}})\index{tm-base}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-running-output-handler-path3 \\ \index{tm-limit-os-running-output-hand!ler-path3}
{\rm{tm-limit}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{os\/}})\index{tm-limit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-running-output-handler-path3 \\ \index{tm-base-tm-limit-os-running-outp!ut-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-running-output-handler-path3 \\ \index{good-os-os-running-output-handle!r-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-tm-os-running-output-handler-path4 \\ \index{good-tm-os-running-output-handle!r-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-tm}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{good-tm}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-tm-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-slimit-os-running-output-handler-path4 \\ \index{tm-slimit-os-running-output-han!dler-path4}
{\rm{tm-slimit}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{tm-slimit} $=$ {\rm{tm-slimit}}\,({\it{os\/}})\index{tm-slimit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-slimit-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-code-os-running-output-handler-path4 \\ \index{os-code-os-running-output-handle!r-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-code}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{os-code} $=$ {\rm{os-code}}\,({\it{os\/}})\index{os-code})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-code-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-interrupt-addresses-os-running-output-handler-path4 \\ \index{tm-interrupt-addresses-os-runni!ng-output-handler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{tm-memory})\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{4}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{5}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{5}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{6}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{6}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{7}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\tt{'}}{\tt{7}}, {\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\index{getnth})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{tm-memory})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\tt{'}}{\tt{11}}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getnth})\-)\-)\-)\-)\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-interrupt-addresses-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-os-running-output-handler-path4 \\ \index{not-tm-in-supervisor-mode-os-ru!nning-output-handler-path4}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-task-table-os-running-output-handler-path4 \\ \index{os-task-table-os-running-output!-handler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-task-table}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{os-task-table} \\ 
$=$$\;\;\;\;${\rm{os-new-task-table}}\,({\it{os\/}})\index{os-new-task-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-task-table-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-segment-table-os-running-output-handler-path4 \\ \index{os-segment-table-os-running-outp!ut-handler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-segment-table}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{os-segment-table} \\ 
$=$$\;\;\;\;${\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-segment-table-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-readyq-os-running-output-handler-path4 \\ \index{os-readyq-os-running-output-han!dler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-readyq}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{os-readyq} $=$ {\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-readyq-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-ibuffers-os-running-output-handler-path4 \\ \index{os-ibuffers-os-running-output-h!andler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-ibuffers}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{os-ibuffers} $=$ {\rm{os-ibuffers}}\,({\it{os\/}})\index{os-ibuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-ibuffers-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-obuffers-os-running-output-handler-path4 \\ \index{os-obuffers-os-running-output-h!andler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-obuffers}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{os-obuffers} \\ 
$=$$\;\;\;\;${\rm{os-obuffers-with-dequeued-character}}\,({\it{os\/}})\index{os-obuffers-with-dequeued-chara!cter})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-obuffers-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  finite-number-queue-listp-os-obuffers-os-running-output-handler-path4 \\ \index{finite-number-queue-listp-os-ob!uffers-os-running-output-handler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{finite-number-queue-listp}}\,(\=\+{\rm{table}}\,(\=\+{\tt{'}}{\tt{8}}, \\ 
{\rm{os-obuffers}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{os-obuffers})\-\index{table}, \\ 
{\tt{'}}{\tt{4}}, \\ 
{\tt{'}}{\tt{65536}})\-\index{finite-number-queue-listp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable finite-number-queue-listp-os-obuffers-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-mbuffers-os-running-output-handler-path4 \\ \index{os-mbuffers-os-running-output-h!andler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$({\rm{os-mbuffers}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{os-mbuffers} $=$ {\rm{os-mbuffers}}\,({\it{os\/}})\index{os-mbuffers})\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-mbuffers-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-status-table-os-running-output-handler-path4 \\ \index{os-status-table-os-running-outp!ut-handler-path4}
\=\+{\rm{good-tm}}\,({\it{os\/}})\index{good-tm} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{os-status-table}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{os-status-table} \\ 
$=$$\;\;\;\;${\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-status-table-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-waiting-os-running-output-handler-path4 \\ \index{not-tm-waiting-os-running-output!-handler-path4}
$\neg$ {\rm{tm-waiting}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{tm-waiting}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-waiting-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-os-running-output-handler-path4 \\ \index{tm-base-os-running-output-handle!r-path4}
{\rm{tm-base}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{tm-base} $=$ {\rm{tm-base}}\,({\it{os\/}})\index{tm-base}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-limit-os-running-output-handler-path4 \\ \index{tm-limit-os-running-output-hand!ler-path4}
{\rm{tm-limit}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{tm-limit} $=$ {\rm{tm-limit}}\,({\it{os\/}})\index{tm-limit}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-limit-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-base-tm-limit-os-running-output-handler-path4 \\ \index{tm-base-tm-limit-os-running-outp!ut-handler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-base}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{tm-base} \\ 
$=$$\;\;\;\;${\rm{base}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{base})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-limit}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{tm-limit} \\ 
$=$$\;\;\;\;${\rm{limit}}\,({\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-segment-table}}\,({\it{os\/}})\index{os-segment-table})\index{table})\-\index{getnth})\index{limit})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-base-tm-limit-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-running-output-handler-path4 \\ \index{good-os-os-running-output-handle!r-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-running-output-handler \\ \index{good-os-os-running-output-handle!r}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})))\- \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-running-output-handler}}\,({\it{os\/}})\index{os-running-output-handler})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-running-output-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-svc-handler} \\  
\=\+{\rm{os-svc-handler}}\,({\it{os\/}})\index{os-svc-handler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}$\;\;${\bf then }{\rm{os-svc-send-handler}}\,({\it{os\/}})\index{os-svc-send-handler} \\ 
{\bf elseif }({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}$\;\;${\bf then }{\rm{os-svc-receive-handler}}\,({\it{os\/}})\index{os-svc-receive-handler} \\ 
{\bf elseif }({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}}$\;\;${\bf then }{\rm{os-svc-tyo-handler}}\,({\it{os\/}})\index{os-svc-tyo-handler} \\ 
{\bf else }{\rm{os-svc-tyi-handler}}\,({\it{os\/}})\index{os-svc-tyi-handler}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-svc-handler} \\  
\=\+{\rm{os-time-for-svc-handler}}\,({\it{os\/}})\index{os-time-for-svc-handler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}} \\ 
{\bf then }{\rm{os-time-for-svc-send-handler}}\,({\it{os\/}})\index{os-time-for-svc-send-handler} \\ 
{\bf elseif }({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}} \\ 
{\bf then }{\rm{os-time-for-svc-receive-handler}}\,({\it{os\/}})\index{os-time-for-svc-receive-handler} \\ 
{\bf elseif }({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}} \\ 
{\bf then }{\rm{os-time-for-svc-tyo-handler}}\,({\it{os\/}})\index{os-time-for-svc-tyo-handler} \\ 
{\bf else }{\rm{os-time-for-svc-tyi-handler}}\,({\it{os\/}})\index{os-time-for-svc-tyi-handler}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-intended-svc-interrupt} \\  
\=\+{\rm{os-intended-svc-interrupt}}\,({\it{os\/}})\index{os-intended-svc-interrupt} \\ 
$=$$\;\;\;\;$\=\+{\bf if }({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}} \\ 
{\bf then }{\rm{os-intended-svc-send-interrupt}}\,({\it{os\/}})\index{os-intended-svc-send-interrupt} \\ 
{\bf elseif }({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}} \\ 
{\bf then }{\rm{os-intended-svc-receive-interrupt}}\,({\it{os\/}})\index{os-intended-svc-receive-interrupt} \\ 
{\bf elseif }({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}} \\ 
{\bf then }{\rm{os-intended-svc-tyo-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyo-interrupt} \\ 
{\bf else }{\rm{os-intended-svc-tyi-interrupt}}\,({\it{os\/}})\index{os-intended-svc-tyi-interrupt}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  equivalence-of-svc-interrupt-expressions \\ \index{equivalence-of-svc-interrupt-exp!ressions}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}))) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-execute-svc-interrupt}}\,({\it{os\/}})\index{tm-execute-svc-interrupt} $=$ {\rm{os-intended-svc-interrupt}}\,({\it{os\/}})\index{os-intended-svc-interrupt})\-
\end{tabbing}


\noindent{\sc Event}:   Disable equivalence-of-svc-interrupt-expressions.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  lessp-4-crock \\ \index{lessp-4-crock}
\=\+(\=\+({\it{a\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(({\it{a\/}} $<$ {\tt{'}}{\tt{4}}) $\wedge$ (({\it{a\/}} $\not=$ {\tt{'}}{\tt{0}}) $\wedge$ (({\it{a\/}} $\not=$ {\tt{'}}{\tt{1}}) $\wedge$ ({\it{a\/}} $\not=$ {\tt{'}}{\tt{2}})))))\- \\ 
$\rightarrow$$\;\;\;\;$({\it{a\/}} $=$ {\tt{'}}{\tt{3}})\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  remainder-4-equals-3 \\ \index{remainder-4-equals-3}
\=\+((({\it{n\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $\not=$ {\tt{'}}{\tt{0}}) $\wedge$ ((({\it{n\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $\not=$ {\tt{'}}{\tt{1}}) $\wedge$ (({\it{n\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $\not=$ {\tt{'}}{\tt{2}}))) \\ 
$\rightarrow$$\;\;\;\;$(({\it{n\/}} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{3}})\-
\end{tabbing}


\noindent{\sc Event}:   Disable remainder-4-equals-3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  trace-svc-interrupt-handler \\ \index{trace-svc-interrupt-handler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-svc-interrupt}}\,({\it{os\/}})\index{os-intended-svc-interrupt}, \\ 
{\rm{os-time-for-svc-handler}}\,({\it{os\/}})\index{os-time-for-svc-handler})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-svc-handler}}\,({\it{os\/}})\index{os-svc-handler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-svc-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-svc-handler \\ \index{good-os-os-svc-handler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}))) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-svc-handler}}\,({\it{os\/}})\index{os-svc-handler})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-svc-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-input-interrupt-handler} \\  
\=\+{\rm{os-input-interrupt-handler}}\,({\it{os\/}})\index{os-input-interrupt-handler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}$\;\;${\bf then }{\rm{os-waiting-input-handler}}\,({\it{os\/}})\index{os-waiting-input-handler} \\ 
{\bf else }{\rm{os-running-input-handler}}\,({\it{os\/}})\index{os-running-input-handler}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-input-interrupt-han!dler} \\  
\=\+{\rm{os-time-for-input-interrupt-handler}}\,({\it{os\/}})\index{os-time-for-input-interrupt-han!dler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}$\;\;${\bf then }{\rm{os-time-for-waiting-input-handler}}\,({\it{os\/}})\index{os-time-for-waiting-input-handle!r} \\ 
{\bf else }{\rm{os-time-for-running-input-handler}}\,({\it{os\/}})\index{os-time-for-running-input-handle!r}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  trace-input-interrupt-handler \\ \index{trace-input-interrupt-handler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-input-interrupt}}\,({\it{os\/}})\index{os-intended-input-interrupt}, \\ 
{\rm{os-time-for-input-interrupt-handler}}\,({\it{os\/}})\index{os-time-for-input-interrupt-han!dler})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-input-interrupt-handler}}\,({\it{os\/}})\index{os-input-interrupt-handler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-input-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-input-interrupt-handler \\ \index{good-os-os-input-interrupt-hand!ler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-input-interrupt-handler}}\,({\it{os\/}})\index{os-input-interrupt-handler})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-input-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-output-interrupt-handler} \\  
\=\+{\rm{os-output-interrupt-handler}}\,({\it{os\/}})\index{os-output-interrupt-handler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}$\;\;${\bf then }{\rm{os-waiting-output-handler}}\,({\it{os\/}})\index{os-waiting-output-handler} \\ 
{\bf else }{\rm{os-running-output-handler}}\,({\it{os\/}})\index{os-running-output-handler}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-time-for-output-interrupt-ha!ndler} \\  
\=\+{\rm{os-time-for-output-interrupt-handler}}\,({\it{os\/}})\index{os-time-for-output-interrupt-ha!ndler} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}$\;\;${\bf then }{\rm{os-time-for-waiting-output-handler}}\,({\it{os\/}})\index{os-time-for-waiting-output-hand!ler} \\ 
{\bf else }{\rm{os-time-for-running-output-handler}}\,({\it{os\/}})\index{os-time-for-running-output-hand!ler}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  trace-output-interrupt-handler \\ \index{trace-output-interrupt-handler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-processor}}\,(\=\+{\rm{os-intended-output-interrupt}}\,({\it{os\/}})\index{os-intended-output-interrupt}, \\ 
{\rm{os-time-for-output-interrupt-handler}}\,({\it{os\/}})\index{os-time-for-output-interrupt-ha!ndler})\-\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{os-output-interrupt-handler}}\,({\it{os\/}})\index{os-output-interrupt-handler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable trace-output-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-output-interrupt-handler \\ \index{good-os-os-output-interrupt-han!dler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;${\rm{good-os}}\,({\rm{os-output-interrupt-handler}}\,({\it{os\/}})\index{os-output-interrupt-handler})\index{good-os}\-
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-output-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{os-step} \\  
\=\+{\rm{os-step}}\,({\it{os\/}})\index{os-step} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-input-interruptp}}\,({\it{os\/}})\index{tm-input-interruptp}$\;\;${\bf then }{\rm{os-input-interrupt-handler}}\,({\it{os\/}})\index{os-input-interrupt-handler} \\ 
{\bf elseif }{\rm{tm-output-interruptp}}\,({\it{os\/}})\index{tm-output-interruptp}$\;\;${\bf then }{\rm{os-output-interrupt-handler}}\,({\it{os\/}})\index{os-output-interrupt-handler} \\ 
{\bf elseif }{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}$\;\;${\bf then }{\it{os\/}} \\ 
{\bf elseif }{\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}$\;\;${\bf then }{\rm{os-error-handler}}\,({\it{os\/}})\index{os-error-handler} \\ 
{\bf elseif }{\rm{tm-clock-interruptp}}\,({\it{os\/}})\index{tm-clock-interruptp}$\;\;${\bf then }{\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler} \\ 
{\bf elseif }{\rm{tm-svc-interruptp}}\,({\it{os\/}})\index{tm-svc-interruptp}$\;\;${\bf then }{\rm{os-svc-handler}}\,({\it{os\/}})\index{os-svc-handler} \\ 
{\bf else }{\rm{tm-fetch-execute}}\,({\it{os\/}})\index{tm-fetch-execute}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-processor} \\  
\=\+{\rm{os-processor}}\,({\it{os\/}}, {\it{oracle\/}})\index{os-processor} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{oracle\/}}) \\ 
{\bf then }{\rm{os-processor}}\,(\=\+{\rm{os-step}}\,({\rm{tm-post-interrupt}}\,({\rm{car}}\,({\it{oracle\/}}), {\it{os\/}})\index{tm-post-interrupt})\index{os-step}, \\ 
{\rm{cdr}}\,({\it{oracle\/}}))\-\index{os-processor} \\ 
{\bf else }{\it{os\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  good-os-os-step \\ \index{good-os-os-step}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-os}}\,({\rm{os-step}}\,({\it{os\/}})\index{os-step})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-step.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-os-processor \\ \index{good-os-os-processor}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-os}}\,({\rm{os-processor}}\,({\it{os\/}}, {\it{oracle\/}})\index{os-processor})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-os-processor.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{timed-tm-step} \\  
\=\+{\rm{timed-tm-step}}\,({\it{tm\/}})\index{timed-tm-step} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-input-interruptp}}\,({\it{tm\/}})\index{tm-input-interruptp} \\ 
{\bf then }{\rm{tm-processor}}\,(\=\+{\rm{tm-execute-input-interrupt}}\,({\it{tm\/}})\index{tm-execute-input-interrupt}, \\ 
{\rm{os-time-for-input-interrupt-handler}}\,({\it{tm\/}})\index{os-time-for-input-interrupt-han!dler})\-\index{tm-processor} \\ 
{\bf elseif }{\rm{tm-output-interruptp}}\,({\it{tm\/}})\index{tm-output-interruptp} \\ 
{\bf then }{\rm{tm-processor}}\,(\=\+{\rm{tm-execute-output-interrupt}}\,({\it{tm\/}})\index{tm-execute-output-interrupt}, \\ 
{\rm{os-time-for-output-interrupt-handler}}\,({\it{tm\/}})\index{os-time-for-output-interrupt-ha!ndler})\-\index{tm-processor} \\ 
{\bf elseif }{\rm{tm-waiting}}\,({\it{tm\/}})\index{tm-waiting}$\;\;${\bf then }{\it{tm\/}} \\ 
{\bf elseif }{\rm{tm-errorp}}\,({\it{tm\/}})\index{tm-errorp} \\ 
{\bf then }{\rm{tm-processor}}\,(\=\+{\rm{tm-execute-error-interrupt}}\,({\it{tm\/}})\index{tm-execute-error-interrupt}, \\ 
{\rm{os-time-for-error-handler}}\,({\it{tm\/}})\index{os-time-for-error-handler})\-\index{tm-processor} \\ 
{\bf elseif }{\rm{tm-clock-interruptp}}\,({\it{tm\/}})\index{tm-clock-interruptp} \\ 
{\bf then }{\rm{tm-processor}}\,(\=\+{\rm{tm-execute-clock-interrupt}}\,({\it{tm\/}})\index{tm-execute-clock-interrupt}, \\ 
{\rm{os-time-for-clock-interrupt-handler}}\,({\it{tm\/}})\index{os-time-for-clock-interrupt-han!dler})\-\index{tm-processor} \\ 
{\bf elseif }{\rm{tm-svc-interruptp}}\,({\it{tm\/}})\index{tm-svc-interruptp} \\ 
{\bf then }{\rm{tm-processor}}\,(\=\+{\rm{tm-execute-svc-interrupt}}\,({\it{tm\/}})\index{tm-execute-svc-interrupt}, \\ 
{\rm{os-time-for-svc-handler}}\,({\it{tm\/}})\index{os-time-for-svc-handler})\-\index{tm-processor} \\ 
{\bf else }{\rm{tm-fetch-execute}}\,({\it{tm\/}})\index{tm-fetch-execute}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{timed-tm-processor} \\  
\=\+{\rm{timed-tm-processor}}\,({\it{tm\/}}, {\it{oracle\/}})\index{timed-tm-processor} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{oracle\/}}) \\ 
{\bf then }{\rm{timed-tm-processor}}\,(\=\+{\rm{timed-tm-step}}\,({\rm{tm-post-interrupt}}\,(\=\+{\rm{car}}\,({\it{oracle\/}}), \\ 
{\it{tm\/}})\-\index{tm-post-interrupt})\index{timed-tm-step}, \\ 
{\rm{cdr}}\,({\it{oracle\/}}))\-\index{timed-tm-processor} \\ 
{\bf else }{\it{tm\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-oracle-step} \\  
\=\+{\rm{os-oracle-step}}\,({\it{event\/}}, {\it{os\/}})\index{os-oracle-step} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{tm-input-interruptp}}\,({\it{os\/}})\index{tm-input-interruptp} \\ 
{\bf then }{\rm{cons}}\,({\it{event\/}}, {\rm{os-time-for-input-interrupt-handler}}\,({\it{os\/}})\index{os-time-for-input-interrupt-han!dler}) \\ 
{\bf elseif }{\rm{tm-output-interruptp}}\,({\it{os\/}})\index{tm-output-interruptp} \\ 
{\bf then }{\rm{cons}}\,({\it{event\/}}, {\rm{os-time-for-output-interrupt-handler}}\,({\it{os\/}})\index{os-time-for-output-interrupt-ha!ndler}) \\ 
{\bf elseif }{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}$\;\;${\bf then }{\rm{cons}}\,({\it{event\/}}, {\tt{'}}{\tt{nil}}) \\ 
{\bf elseif }{\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}$\;\;${\bf then }{\rm{cons}}\,({\it{event\/}}, {\rm{os-time-for-error-handler}}\,({\it{os\/}})\index{os-time-for-error-handler}) \\ 
{\bf elseif }{\rm{tm-clock-interruptp}}\,({\it{os\/}})\index{tm-clock-interruptp} \\ 
{\bf then }{\rm{cons}}\,({\it{event\/}}, {\rm{os-time-for-clock-interrupt-handler}}\,({\it{os\/}})\index{os-time-for-clock-interrupt-han!dler}) \\ 
{\bf elseif }{\rm{tm-svc-interruptp}}\,({\it{os\/}})\index{tm-svc-interruptp} \\ 
{\bf then }{\rm{cons}}\,({\it{event\/}}, {\rm{os-time-for-svc-handler}}\,({\it{os\/}})\index{os-time-for-svc-handler}) \\ 
{\bf else }{\rm{cons}}\,({\it{event\/}}, {\tt{'}}{\tt{nil}})$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{os-oracle} \\  
\=\+{\rm{os-oracle}}\,({\it{os\/}}, {\it{oracle\/}})\index{os-oracle} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{oracle\/}}) \\ 
{\bf then }{\rm{append}}\,(\=\+{\rm{os-oracle-step}}\,(\=\+{\rm{car}}\,({\it{oracle\/}}), \\ 
{\rm{tm-post-interrupt}}\,({\rm{car}}\,({\it{oracle\/}}), {\it{os\/}})\index{tm-post-interrupt})\-\index{os-oracle-step}, \\ 
{\rm{os-oracle}}\,(\=\+{\rm{timed-tm-step}}\,({\rm{tm-post-interrupt}}\,({\rm{car}}\,({\it{oracle\/}}), {\it{os\/}})\index{tm-post-interrupt})\index{timed-tm-step}, \\ 
{\rm{cdr}}\,({\it{oracle\/}}))\-\index{os-oracle})\- \\ 
{\bf else }{\it{oracle\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tm-processor-oracle-distributes \\ \index{tm-processor-oracle-distributes}
{\rm{tm-processor}}\,({\it{tm\/}}, {\rm{append}}\,({\it{a\/}}, {\it{b\/}}))\index{tm-processor} $=$ {\rm{tm-processor}}\,({\rm{tm-processor}}\,({\it{tm\/}}, {\it{a\/}})\index{tm-processor}, {\it{b\/}})\index{tm-processor}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-processor-oracle-distributes.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-processor-implements-timed-tm-step \\ \index{tm-processor-implements-timed-t!m-step}
\=\+{\rm{tm-processor}}\,({\it{tm\/}}, {\rm{os-oracle-step}}\,({\it{x\/}}, {\rm{tm-post-interrupt}}\,({\it{x\/}}, {\it{tm\/}})\index{tm-post-interrupt})\index{os-oracle-step})\index{tm-processor} \\ 
$=$$\;\;\;\;${\rm{timed-tm-step}}\,({\rm{tm-post-interrupt}}\,({\it{x\/}}, {\it{tm\/}})\index{tm-post-interrupt})\index{timed-tm-step}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-processor-implements-timed-tm-step.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-implements-timed-tm \\ \index{tm-implements-timed-tm}
{\rm{tm-processor}}\,({\it{tm\/}}, {\rm{os-oracle}}\,({\it{tm\/}}, {\it{oracle\/}})\index{os-oracle})\index{tm-processor} $=$ {\rm{timed-tm-processor}}\,({\it{tm\/}}, {\it{oracle\/}})\index{timed-tm-processor}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-implements-timed-tm.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{btimed-tm-processor} \\  
\=\+{\rm{btimed-tm-processor}}\,({\it{tm\/}}, {\it{oracle\/}})\index{btimed-tm-processor} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{oracle\/}}) \\ 
{\bf then }{\rm{timed-tm-step}}\,({\rm{tm-post-interrupt}}\,(\=\+{\rm{car}}\,({\it{oracle\/}}), \\ 
{\rm{btimed-tm-processor}}\,(\=\+{\it{tm\/}}, \\ 
{\rm{cdr}}\,({\it{oracle\/}}))\-\index{btimed-tm-processor})\-\index{tm-post-interrupt})\index{timed-tm-step} \\ 
{\bf else }{\it{tm\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  timed-tm-implements-btimed-tm \\ \index{timed-tm-implements-btimed-tm}
{\rm{timed-tm-processor}}\,({\it{tm\/}}, {\it{oracle\/}})\index{timed-tm-processor} $=$ {\rm{btimed-tm-processor}}\,({\it{tm\/}}, {\rm{reverse}}\,({\it{oracle\/}})\index{reverse})\index{btimed-tm-processor}
\end{tabbing}


\noindent{\sc Event}:   Disable timed-tm-implements-btimed-tm.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{bos-processor} \\  
\=\+{\rm{bos-processor}}\,({\it{os\/}}, {\it{oracle\/}})\index{bos-processor} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{oracle\/}}) \\ 
{\bf then }{\rm{os-step}}\,({\rm{tm-post-interrupt}}\,(\=\+{\rm{car}}\,({\it{oracle\/}}), \\ 
{\rm{bos-processor}}\,({\it{os\/}}, {\rm{cdr}}\,({\it{oracle\/}}))\index{bos-processor})\-\index{tm-post-interrupt})\index{os-step} \\ 
{\bf else }{\it{os\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bos-implements-os \\ \index{bos-implements-os}
{\rm{bos-processor}}\,({\it{os\/}}, {\rm{reverse}}\,({\it{oracle\/}})\index{reverse})\index{bos-processor} $=$ {\rm{os-processor}}\,({\it{os\/}}, {\it{oracle\/}})\index{os-processor}
\end{tabbing}


\noindent{\sc Event}:   Disable bos-implements-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  timed-tm-step-implements-os-step \\ \index{timed-tm-step-implements-os-step}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ ({\rm{timed-tm-step}}\,({\it{os\/}})\index{timed-tm-step} $=$ {\rm{os-step}}\,({\it{os\/}})\index{os-step})
\end{tabbing}


\noindent{\sc Event}:   Disable timed-tm-step-implements-os-step.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-bos-processor \\ \index{good-os-bos-processor}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-os}}\,({\rm{bos-processor}}\,({\it{os\/}}, {\it{oracle\/}})\index{bos-processor})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-bos-processor.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-timed-tm-step \\ \index{good-os-timed-tm-step}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-os}}\,({\rm{timed-tm-step}}\,({\it{os\/}})\index{timed-tm-step})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-timed-tm-step.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  good-os-btimed-tm-processor \\ \index{good-os-btimed-tm-processor}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ {\rm{good-os}}\,({\rm{btimed-tm-processor}}\,({\it{os\/}}, {\it{oracle\/}})\index{btimed-tm-processor})\index{good-os}
\end{tabbing}


\noindent{\sc Event}:   Disable good-os-btimed-tm-processor.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  btimed-tm-implements-bos \\ \index{btimed-tm-implements-bos}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$({\rm{btimed-tm-processor}}\,({\it{os\/}}, {\it{oracle\/}})\index{btimed-tm-processor} $=$ {\rm{bos-processor}}\,({\it{os\/}}, {\it{oracle\/}})\index{bos-processor})\-
\end{tabbing}


\noindent{\sc Event}:   Disable btimed-tm-implements-bos.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-implements-os \\ \index{tm-implements-os}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-processor}}\,({\it{os\/}}, {\rm{os-oracle}}\,({\it{os\/}}, {\it{oracle\/}})\index{os-oracle})\index{tm-processor} $=$ {\rm{os-processor}}\,({\it{os\/}}, {\it{oracle\/}})\index{os-processor})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-implements-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-clock-interrupt-handler \\ \index{mapup-base-os-clock-interrupt-h!andler}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-clock-interrupt-handler \\ \index{mapup-limit-os-clock-interrupt-!handler}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-clock-interrupt-handler \\ \index{getseg-tm-memory-os-clock-inter!rupt-handler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-clock-interrupt-handler.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 TM-CPU-OS-CLOCK-INTERRUPT-HANDLER-CROCK
 (REWRITE)
 (IMPLIES
  (AND (GOOD-OS OS)
       (NOT (TM-WAITING OS)))
  (EQUAL
   (TM-CPU (OS-CLOCK-INTERRUPT-HANDLER OS))
   (CONS
    (GETNTH '0
            (OS-NEW-REGS (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS))
                         OS))
    (CONS
     (GETNTH '1
             (OS-NEW-REGS (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS))
                          OS))
     (CONS
      (GETNTH '2
              (OS-NEW-REGS (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS))
                           OS))
      (CONS
       (GETNTH '3
               (OS-NEW-REGS (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS))
                            OS))
       (CONS
        (GETNTH '4
                (OS-NEW-REGS (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS))
                             OS))
        (CONS
         (GETNTH '5
                 (OS-NEW-REGS (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS))
                              OS))
         (CONS
          (GETNTH '6
                  (OS-NEW-REGS (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS))
                               OS))
          (CONS
           (GETNTH '7
                   (OS-NEW-REGS (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS))
                                OS))
           (CONS
            (TM-PACK-PSW
                        (OS-NEW-CC (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS))
                                   OS)
                        (OS-NEW-ERROR (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS))
                                      OS)
                        (OS-NEW-SVCFLAG (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS))
                                        OS)
                        (OS-NEW-SVCID (ARRAY-QFIRST (OS-CLOCK-NEW-READYQ OS))
                                      OS))
            'NIL)))))))))))
 ((ENABLE OS-CLOCK-INTERRUPT-HANDLER TM-CPU TM-R0 TM-R1 TM-R2 TM-R3 TM-R4
          TM-R5 TM-R6 TM-R7)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable tm-cpu-os-clock-interrupt-handler-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-clock-interrupt-handler-case1 \\ \index{tm-cpu-os-clock-interrupt-handle!r-case1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfirst}}\,({\rm{os-clock-new-readyq}}\,({\it{os\/}})\index{os-clock-new-readyq})\index{array-qfirst} \\ 
$=$$\;\;\;\;${\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{os-current-taskid}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{os-task-table}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{os-task-table})\-\index{table})\-\index{getnth})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-clock-interrupt-handler-case2 \\ \index{tm-cpu-os-clock-interrupt-handle!r-case2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfirst}}\,({\rm{os-clock-new-readyq}}\,({\it{os\/}})\index{os-clock-new-readyq})\index{array-qfirst} \\ 
$\not=$$\;\;\;\;${\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{os-current-taskid}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{os-task-table}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{os-task-table})\-\index{table})\-\index{getnth})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-clock-interrupt-handler \\ \index{tm-cpu-os-clock-interrupt-handle!r}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{os-current-taskid}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{os-task-table}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{os-task-table})\-\index{table})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-clock-interrupt-handler \\ \index{mapup-cpu-os-clock-interrupt-ha!ndler}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-clock-interrupt-handler \\ \index{mapup-regs-os-clock-interrupt-h!andler}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-clock-interrupt-handler \\ \index{mapup-cc-os-clock-interrupt-han!dler}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-clock-interrupt-handler \\ \index{mapup-error-os-clock-interrupt-!handler}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-clock-interrupt-handler \\ \index{mapup-svcflag-os-clock-interrupt!-handler}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-clock-interrupt-handler \\ \index{mapup-svcid-os-clock-interrupt-!handler}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-clock-interrupt-handler \\ \index{mapup-task-os-clock-interrupt-h!andler}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-clock-interrupt-handler \\ \index{mapup-tasks-os-clock-interrupt-!handler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ({\it{taskid\/}} $\in\;${\bf{N}}${}$))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-clock-interrupt-handler \\ \index{mapup-os-tasks-os-clock-interrupt!-handler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-clock-interrupt-handler \\ \index{mapup-os-ibuffers-os-clock-inte!rrupt-handler}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-clock-interrupt-handler \\ \index{mapup-os-obuffers-os-clock-inte!rrupt-handler}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-clock-interrupt-handler \\ \index{mapup-os-mbuffers-os-clock-inte!rrupt-handler}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-clock-interrupt-handler \\ \index{mapup-queue-os-readyq-os-clock-i!nterrupt-handler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{enq}}\,(\=\+{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{deq}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{deq})\-\index{enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-clock-interrupt-handler \\ \index{mapup-os-status-table-os-clock-i!nterrupt-handler}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-clock-interrupt-handler \\ \index{tm-rwstate-os-clock-interrupt-h!andler}
{\rm{tm-rwstate}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{tm-rwstate} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-clock-interrupt-handler \\ \index{tm-clock-os-clock-interrupt-han!dler}
{\rm{tm-clock}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{tm-clock} $=$ {\tt{'}}{\tt{1000}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-clock-interrupt-handler \\ \index{tm-iports-os-clock-interrupt-ha!ndler}
{\rm{tm-iports}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-clock-interrupt-handler \\ \index{tm-oports-os-clock-interrupt-ha!ndler}
{\rm{tm-oports}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-clock-interrupt-handler \\ \index{correctness-of-clock-interrupt-!handler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-clock-interrupt-handler}}\,({\it{os\/}})\index{os-clock-interrupt-handler})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-clock-interrupt-handler}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-clock-interrupt-handler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-clock-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-error-handler-path1 \\ \index{mapup-base-os-error-handler-pat!h1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-error-handler-path1 \\ \index{mapup-limit-os-error-handler-pat!h1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-error-handler-path1 \\ \index{getseg-tm-memory-os-error-handle!r-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-error-handler-path1 \\ \index{mapup-cpu-os-error-handler-path!1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-error-handler-path1 \\ \index{mapup-regs-os-error-handler-pat!h1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-error-handler-path1 \\ \index{mapup-cc-os-error-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{mapup-cc} $=$ {\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-error-handler-path1 \\ \index{mapup-error-os-error-handler-pat!h1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-error-handler-path1 \\ \index{mapup-svcflag-os-error-handler-p!ath1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-error-handler-path1 \\ \index{mapup-svcid-os-error-handler-pat!h1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-error-handler-path1 \\ \index{mapup-task-os-error-handler-pat!h1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-error-handler-path1 \\ \index{mapup-tasks-os-error-handler-pat!h1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ({\it{taskid\/}} $\in\;${\bf{N}}${}$))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-error-handler-path1 \\ \index{mapup-os-tasks-os-error-handler!-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{mapup-os-tasks}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{mapup-os-tasks} $=$ {\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-error-handler-path1 \\ \index{mapup-os-ibuffers-os-error-hand!ler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-error-handler-path1 \\ \index{mapup-os-obuffers-os-error-hand!ler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-error-handler-path1 \\ \index{mapup-os-mbuffers-os-error-hand!ler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-error-handler-path1 \\ \index{mapup-queue-os-readyq-os-error-!handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{deq}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{deq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-error-handler-path1 \\ \index{mapup-os-status-table-os-error-!handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-error-handler-path1 \\ \index{tm-rwstate-os-error-handler-pat!h1}
{\rm{tm-rwstate}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{tm-rwstate} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-error-handler-path1 \\ \index{tm-clock-os-error-handler-path1}
{\rm{tm-clock}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-error-handler-path1 \\ \index{tm-iports-os-error-handler-path!1}
{\rm{tm-iports}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-error-handler-path1 \\ \index{tm-oports-os-error-handler-path!1}
{\rm{tm-oports}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-error-handler-path1 \\ \index{correctness-of-os-error-handler!-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-error-handler-path1}}\,({\it{os\/}})\index{os-error-handler-path1})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-error-handler}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-error-handler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-error-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-error-handler-path2 \\ \index{mapup-base-os-error-handler-pat!h2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-error-handler-path2 \\ \index{mapup-limit-os-error-handler-pat!h2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-error-handler-path2 \\ \index{getseg-tm-memory-os-error-handle!r-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-error-handler-path2.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 TM-CPU-OS-ERROR-HANDLER-PATH2-CROCK
 (REWRITE)
 (IMPLIES
  (AND (GOOD-OS OS)
       (NOT (TM-WAITING OS)))
  (EQUAL
   (TM-CPU (OS-ERROR-HANDLER-PATH2 OS))
   (CONS
    (GETNTH '0
            (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                         OS))
    (CONS
     (GETNTH '1
             (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                          OS))
     (CONS
      (GETNTH '2
              (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                           OS))
      (CONS
       (GETNTH '3
               (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                            OS))
       (CONS
        (GETNTH '4
                (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                             OS))
        (CONS
         (GETNTH '5
                 (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                              OS))
         (CONS
          (GETNTH '6
                  (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                               OS))
          (CONS
           (GETNTH '7
                   (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                OS))
           (CONS
            (TM-PACK-PSW
                      (OS-NEW-CC (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                 OS)
                      (OS-NEW-ERROR (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                    OS)
                      (OS-NEW-SVCFLAG (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                      OS)
                      (OS-NEW-SVCID (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                    OS))
            'NIL)))))))))))
 ((ENABLE OS-ERROR-HANDLER-PATH2 TM-CPU TM-R0 TM-R1 TM-R2 TM-R3 TM-R4 TM-R5
          TM-R6 TM-R7)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable tm-cpu-os-error-handler-path2-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-error-handler-path2-case1 \\ \index{tm-cpu-os-error-handler-path2-c!ase1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfirst}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qfirst} \\ 
$=$$\;\;\;\;${\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-task-table}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{os-task-table})\index{table})\-\index{getnth})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-error-handler-path2-case2 \\ \index{tm-cpu-os-error-handler-path2-c!ase2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfirst}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qfirst} \\ 
$\not=$$\;\;\;\;${\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-task-table}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{os-task-table})\index{table})\-\index{getnth})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-error-handler-path2 \\ \index{tm-cpu-os-error-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-task-table}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{os-task-table})\index{table})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-error-handler-path2 \\ \index{mapup-cpu-os-error-handler-path!2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-error-handler-path2 \\ \index{mapup-regs-os-error-handler-pat!h2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-error-handler-path2 \\ \index{mapup-cc-os-error-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{mapup-cc} $=$ {\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-error-handler-path2 \\ \index{mapup-error-os-error-handler-pat!h2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-error-handler-path2 \\ \index{mapup-svcflag-os-error-handler-p!ath2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-error-handler-path2 \\ \index{mapup-svcid-os-error-handler-pat!h2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-error-handler-path2 \\ \index{mapup-task-os-error-handler-pat!h2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-error-handler-path2 \\ \index{mapup-tasks-os-error-handler-pat!h2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$({\it{taskid\/}} $\in\;${\bf{N}}${}$))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-error-handler-path2 \\ \index{mapup-os-tasks-os-error-handler!-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{mapup-os-tasks}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{mapup-os-tasks} $=$ {\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-error-handler-path2 \\ \index{mapup-os-ibuffers-os-error-hand!ler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-error-handler-path2 \\ \index{mapup-os-obuffers-os-error-hand!ler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-error-handler-path2 \\ \index{mapup-os-mbuffers-os-error-hand!ler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-error-handler-path2 \\ \index{mapup-queue-os-readyq-os-error-!handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{deq}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{deq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-error-handler-path2 \\ \index{mapup-os-status-table-os-error-!handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{1}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-error-handler-path2 \\ \index{tm-clock-os-error-handler-path2}
{\rm{tm-clock}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{tm-clock} $=$ {\tt{'}}{\tt{1000}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-error-handler-path2 \\ \index{tm-iports-os-error-handler-path!2}
{\rm{tm-iports}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-error-handler-path2 \\ \index{tm-oports-os-error-handler-path!2}
{\rm{tm-oports}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-error-handler-path2 \\ \index{tm-rwstate-os-error-handler-pat!h2}
{\rm{tm-rwstate}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{tm-rwstate} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-error-handler-path2 \\ \index{correctness-of-os-error-handler!-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-error-handler-path2}}\,({\it{os\/}})\index{os-error-handler-path2})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-error-handler}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-error-handler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-error-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-error-handler \\ \index{correctness-of-os-error-handler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{mapup-os}}\,({\rm{os-error-handler}}\,({\it{os\/}})\index{os-error-handler})\index{mapup-os} $=$ {\rm{ak-error-handler}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-error-handler})\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-error-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-svc-send-handler-path1 \\ \index{mapup-base-os-svc-send-handler-p!ath1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-svc-send-handler-path1 \\ \index{mapup-limit-os-svc-send-handler!-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-svc-send-handler-path1 \\ \index{getseg-tm-memory-os-svc-send-ha!ndler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-send-handler-path1 \\ \index{mapup-cpu-os-svc-send-handler-p!ath1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-svc-send-handler-path1 \\ \index{mapup-regs-os-svc-send-handler-p!ath1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-svc-send-handler-path1 \\ \index{mapup-cc-os-svc-send-handler-pat!h1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-svc-send-handler-path1 \\ \index{mapup-error-os-svc-send-handler!-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-svc-send-handler-path1 \\ \index{mapup-svcflag-os-svc-send-handle!r-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-svc-send-handler-path1 \\ \index{mapup-svcid-os-svc-send-handler!-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-svc-send-handler-path1 \\ \index{mapup-task-os-svc-send-handler-p!ath1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-send-handler-path1 \\ \index{mapup-tasks-os-svc-send-handler!-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ({\it{taskid\/}} $\in\;${\bf{N}}${}$))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-send-handler-path1 \\ \index{mapup-os-tasks-os-svc-send-hand!ler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{mapup-os-tasks}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{mapup-os-tasks} $=$ {\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-svc-send-handler-path1 \\ \index{mapup-os-ibuffers-os-svc-send-h!andler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-svc-send-handler-path1 \\ \index{mapup-os-obuffers-os-svc-send-h!andler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-svc-send-handler-path1 \\ \index{mapup-os-mbuffers-os-svc-send-h!andler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-svc-send-handler-path1 \\ \index{mapup-queue-os-readyq-os-svc-se!nd-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{deq}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{deq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-svc-send-handler-path1 \\ \index{mapup-os-status-table-os-svc-se!nd-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{cons}}\,({\tt{'}}{\tt{2}}, {\rm{cons}}\,({\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, {\tt{'}}{\tt{nil}})), \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-svc-send-handler-path1 \\ \index{tm-rwstate-os-svc-send-handler-p!ath1}
{\rm{tm-rwstate}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{tm-rwstate} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-svc-send-handler-path1 \\ \index{tm-clock-os-svc-send-handler-pat!h1}
{\rm{tm-clock}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-svc-send-handler-path1 \\ \index{tm-iports-os-svc-send-handler-p!ath1}
{\rm{tm-iports}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-svc-send-handler-path1 \\ \index{tm-oports-os-svc-send-handler-p!ath1}
{\rm{tm-oports}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-svc-send-handler-path1 \\ \index{correctness-of-os-svc-send-hand!ler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-svc-send-handler-path1}}\,({\it{os\/}})\index{os-svc-send-handler-path1})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-execute-send}}\,(\=\+{\rm{os-message}}\,({\it{os\/}})\index{os-message}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-execute-send})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-svc-send-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-svc-send-handler-path2 \\ \index{mapup-base-os-svc-send-handler-p!ath2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-svc-send-handler-path2 \\ \index{mapup-limit-os-svc-send-handler!-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-svc-send-handler-path2 \\ \index{getseg-tm-memory-os-svc-send-ha!ndler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-svc-send-handler-path2.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 TM-CPU-OS-SVC-SEND-HANDLER-PATH2-CROCK
 (REWRITE)
 (IMPLIES
  (AND (GOOD-OS OS)
       (NOT (TM-WAITING OS)))
  (EQUAL
   (TM-CPU (OS-SVC-SEND-HANDLER-PATH2 OS))
   (CONS
    (GETNTH '0
            (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                         OS))
    (CONS
     (GETNTH '1
             (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                          OS))
     (CONS
      (GETNTH '2
              (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                           OS))
      (CONS
       (GETNTH '3
               (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                            OS))
       (CONS
        (GETNTH '4
                (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                             OS))
        (CONS
         (GETNTH '5
                 (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                              OS))
         (CONS
          (GETNTH '6
                  (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                               OS))
          (CONS
           (GETNTH '7
                   (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                OS))
           (CONS
            (TM-PACK-PSW
                      (OS-NEW-CC (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                 OS)
                      (OS-NEW-ERROR (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                    OS)
                      (OS-NEW-SVCFLAG (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                      OS)
                      (OS-NEW-SVCID (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                    OS))
            'NIL)))))))))))
 ((ENABLE OS-SVC-SEND-HANDLER-PATH2 TM-CPU TM-R0 TM-R1 TM-R2 TM-R3 TM-R4 TM-R5
          TM-R6 TM-R7)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable tm-cpu-os-svc-send-handler-path2-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-svc-send-handler-path2-case1 \\ \index{tm-cpu-os-svc-send-handler-path!2-case1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfirst}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qfirst} \\ 
$=$$\;\;\;\;${\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-task-table}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{os-task-table})\index{table})\-\index{getnth})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-svc-send-handler-path2-case2 \\ \index{tm-cpu-os-svc-send-handler-path!2-case2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfirst}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qfirst} \\ 
$\not=$$\;\;\;\;${\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-task-table}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{os-task-table})\index{table})\-\index{getnth})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-svc-send-handler-path2 \\ \index{tm-cpu-os-svc-send-handler-path!2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-task-table}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{os-task-table})\index{table})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-send-handler-path2 \\ \index{mapup-cpu-os-svc-send-handler-p!ath2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-svc-send-handler-path2 \\ \index{mapup-regs-os-svc-send-handler-p!ath2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-svc-send-handler-path2 \\ \index{mapup-cc-os-svc-send-handler-pat!h2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-svc-send-handler-path2 \\ \index{mapup-error-os-svc-send-handler!-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-svc-send-handler-path2 \\ \index{mapup-svcflag-os-svc-send-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-svc-send-handler-path2 \\ \index{mapup-svcid-os-svc-send-handler!-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-svc-send-handler-path2 \\ \index{mapup-task-os-svc-send-handler-p!ath2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-send-handler-path2 \\ \index{mapup-tasks-os-svc-send-handler!-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$({\it{taskid\/}} $\in\;${\bf{N}}${}$))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-send-handler-path2 \\ \index{mapup-os-tasks-os-svc-send-hand!ler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{mapup-os-tasks}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{mapup-os-tasks} $=$ {\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-svc-send-handler-path2 \\ \index{mapup-os-ibuffers-os-svc-send-h!andler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-svc-send-handler-path2 \\ \index{mapup-os-obuffers-os-svc-send-h!andler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-svc-send-handler-path2 \\ \index{mapup-os-mbuffers-os-svc-send-h!andler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-svc-send-handler-path2 \\ \index{mapup-queue-os-readyq-os-svc-se!nd-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{deq}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{deq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-svc-send-handler-path2 \\ \index{mapup-os-status-table-os-svc-se!nd-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{cons}}\,({\tt{'}}{\tt{2}}, {\rm{cons}}\,({\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, {\tt{'}}{\tt{nil}})), \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-svc-send-handler-path2 \\ \index{tm-clock-os-svc-send-handler-pat!h2}
{\rm{tm-clock}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{tm-clock} $=$ {\tt{'}}{\tt{1000}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-svc-send-handler-path2 \\ \index{tm-iports-os-svc-send-handler-p!ath2}
{\rm{tm-iports}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-svc-send-handler-path2 \\ \index{tm-oports-os-svc-send-handler-p!ath2}
{\rm{tm-oports}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-svc-send-handler-path2 \\ \index{tm-rwstate-os-svc-send-handler-p!ath2}
{\rm{tm-rwstate}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{tm-rwstate} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-svc-send-handler-path2 \\ \index{correctness-of-os-svc-send-hand!ler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-svc-send-handler-path2}}\,({\it{os\/}})\index{os-svc-send-handler-path2})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-execute-send}}\,(\=\+{\rm{os-message}}\,({\it{os\/}})\index{os-message}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-execute-send})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-svc-send-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-svc-send-handler-path3 \\ \index{mapup-base-os-svc-send-handler-p!ath3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-svc-send-handler-path3 \\ \index{mapup-limit-os-svc-send-handler!-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-svc-send-handler-path3 \\ \index{getseg-tm-memory-os-svc-send-ha!ndler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-svc-send-handler-path3 \\ \index{tm-cpu-os-svc-send-handler-path!3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,({\rm{tm-cc}}\,({\it{os\/}})\index{tm-cc}, {\rm{tm-error}}\,({\it{os\/}})\index{tm-error}, {\tt{'}}{\tt{0}}, {\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid})\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qfirst-os-readyq-os-svc-send-handler-path3 \\ \index{array-qfirst-os-readyq-os-svc-se!nd-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{os-readyq})\index{array-qfirst} \\ 
$=$$\;\;\;\;${\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qfirst-os-readyq-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-send-handler-path3-case1 \\ \index{mapup-cpu-os-svc-send-handler-p!ath3-case1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{mapup-cc}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\it{os\/}})\index{mapup-cc}, \\ 
{\rm{mapup-error}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\it{os\/}})\index{mapup-error}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{mapup-svcid}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\it{os\/}})\index{mapup-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{mapup-cpu}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\it{os\/}})\index{mapup-cpu})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-send-handler-path3-case1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-send-handler-path3-case2 \\ \index{mapup-cpu-os-svc-send-handler-p!ath3-case2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}) \\ 
$\wedge$$\;\;\;\;$({\it{taskid\/}} $\not=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-send-handler-path3-case2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-send-handler-path3 \\ \index{mapup-cpu-os-svc-send-handler-p!ath3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{mapup-cpu} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
{\bf then }{\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc}, \\ 
{\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\index{putnth} \\ 
{\bf else }{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-svc-send-handler-path3 \\ \index{mapup-regs-os-svc-send-handler-p!ath3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-svc-send-handler-path3 \\ \index{mapup-cc-os-svc-send-handler-pat!h3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-svc-send-handler-path3 \\ \index{mapup-error-os-svc-send-handler!-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-svc-send-handler-path3 \\ \index{mapup-svcflag-os-svc-send-handle!r-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf else }{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-svc-send-handler-path3 \\ \index{mapup-svcid-os-svc-send-handler!-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-svc-send-handler-path3 \\ \index{mapup-task-os-svc-send-handler-p!ath3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{mapup-task} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
{\bf then }{\rm{tm-set-svcflag}}\,({\tt{'}}{\tt{0}}, {\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\index{tm-set-svcflag} \\ 
{\bf else }{\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-send-handler-path3-case1 \\ \index{mapup-tasks-os-svc-send-handler!-path3-case1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} $<$ {\it{taskid\/}}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-send-handler-path3-case1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-send-handler-path3-case2 \\ \index{mapup-tasks-os-svc-send-handler!-path3-case2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} $<$ {\it{taskid\/}} \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
$-$$\;\;\;\;${\it{taskid\/}}\-, \\ 
{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\index{getnth})\-\index{tm-set-svcflag}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} $-$ {\it{taskid\/}}, \\ 
{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-send-handler-path3-case2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-send-handler-path3-support \\ \index{mapup-os-tasks-os-svc-send-hand!ler-path3-support}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{getnth})\-\index{tm-set-svcflag}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-send-handler-path3-support.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-send-handler-path3 \\ \index{mapup-os-tasks-os-svc-send-hand!ler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{3}})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{getnth})\-\index{tm-set-svcflag}, \\ 
{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-svc-send-handler-path3 \\ \index{mapup-os-ibuffers-os-svc-send-h!andler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-svc-send-handler-path3 \\ \index{mapup-os-obuffers-os-svc-send-h!andler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-svc-send-handler-path3-support \\ \index{mapup-os-mbuffers-os-svc-send-h!andler-path3-support}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{enq2}}\,(\=\+{\rm{tm-r3}}\,({\it{os\/}})\index{tm-r3}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\index{enq2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-svc-send-handler-path3-support.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-svc-send-handler-path3 \\ \index{mapup-os-mbuffers-os-svc-send-h!andler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{enq2}}\,(\=\+{\rm{tm-r3}}\,({\it{os\/}})\index{tm-r3}, \\ 
{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\index{enq2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-svc-send-handler-path3 \\ \index{mapup-queue-os-readyq-os-svc-se!nd-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{3}})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{enq}}\,({\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, {\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-svc-send-handler-path3 \\ \index{mapup-os-status-table-os-svc-se!nd-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-svc-send-handler-path3 \\ \index{tm-clock-os-svc-send-handler-pat!h3}
{\rm{tm-clock}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-svc-send-handler-path3 \\ \index{tm-iports-os-svc-send-handler-p!ath3}
{\rm{tm-iports}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-svc-send-handler-path3 \\ \index{tm-oports-os-svc-send-handler-p!ath3}
{\rm{tm-oports}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-svc-send-handler-path3 \\ \index{tm-rwstate-os-svc-send-handler-p!ath3}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-rwstate}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{tm-rwstate} $=$ {\rm{tm-rwstate}}\,({\it{os\/}})\index{tm-rwstate})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-waiting-to-receivep-mapup-os \\ \index{ak-waiting-to-receivep-mapup-os}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{3}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{1}} \\ 
$+$$\;\;\;\;$({\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid})\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{ak-waiting-to-receivep}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-waiting-to-receivep}\-
\end{tabbing}


\noindent{\sc Event}:   Disable ak-waiting-to-receivep-mapup-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-svc-send-handler-path3 \\ \index{correctness-of-os-svc-send-hand!ler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{3}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{1}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid})\-\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-)\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-svc-send-handler-path3}}\,({\it{os\/}})\index{os-svc-send-handler-path3})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-execute-send}}\,(\=\+{\rm{os-message}}\,({\it{os\/}})\index{os-message}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-execute-send})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-svc-send-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-svc-send-handler-path4 \\ \index{mapup-base-os-svc-send-handler-p!ath4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-svc-send-handler-path4 \\ \index{mapup-limit-os-svc-send-handler!-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-svc-send-handler-path4 \\ \index{getseg-tm-memory-os-svc-send-ha!ndler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-svc-send-handler-path4 \\ \index{tm-cpu-os-svc-send-handler-path!4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,({\rm{tm-cc}}\,({\it{os\/}})\index{tm-cc}, {\rm{tm-error}}\,({\it{os\/}})\index{tm-error}, {\tt{'}}{\tt{0}}, {\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid})\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-send-handler-path4-case1 \\ \index{mapup-cpu-os-svc-send-handler-p!ath4-case1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{mapup-cc}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\it{os\/}})\index{mapup-cc}, \\ 
{\rm{mapup-error}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\it{os\/}})\index{mapup-error}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{mapup-svcid}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\it{os\/}})\index{mapup-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{mapup-cpu}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\it{os\/}})\index{mapup-cpu})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-send-handler-path4-case1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-send-handler-path4-case2 \\ \index{mapup-cpu-os-svc-send-handler-p!ath4-case2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}) \\ 
$\wedge$$\;\;\;\;$({\it{taskid\/}} $\not=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-send-handler-path4-case2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-send-handler-path4 \\ \index{mapup-cpu-os-svc-send-handler-p!ath4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{mapup-cpu} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
{\bf then }{\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc}, \\ 
{\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\index{putnth} \\ 
{\bf else }{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-svc-send-handler-path4 \\ \index{mapup-regs-os-svc-send-handler-p!ath4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-svc-send-handler-path4 \\ \index{mapup-cc-os-svc-send-handler-pat!h4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-svc-send-handler-path4 \\ \index{mapup-error-os-svc-send-handler!-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-svc-send-handler-path4 \\ \index{mapup-svcflag-os-svc-send-handle!r-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf else }{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-svc-send-handler-path4 \\ \index{mapup-svcid-os-svc-send-handler!-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-svc-send-handler-path4 \\ \index{mapup-task-os-svc-send-handler-p!ath4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{mapup-task} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
{\bf then }{\rm{tm-set-svcflag}}\,({\tt{'}}{\tt{0}}, {\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\index{tm-set-svcflag} \\ 
{\bf else }{\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-send-handler-path4-case1 \\ \index{mapup-tasks-os-svc-send-handler!-path4-case1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} $<$ {\it{taskid\/}})))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-send-handler-path4-case1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-send-handler-path4-case2 \\ \index{mapup-tasks-os-svc-send-handler!-path4-case2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} $<$ {\it{taskid\/}} \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
$-$$\;\;\;\;${\it{taskid\/}}\-, \\ 
{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\index{getnth})\-\index{tm-set-svcflag}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} $-$ {\it{taskid\/}}, \\ 
{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-send-handler-path4-case2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-send-handler-path4-support \\ \index{mapup-os-tasks-os-svc-send-hand!ler-path4-support}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{getnth})\-\index{tm-set-svcflag}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-send-handler-path4-support.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-send-handler-path4 \\ \index{mapup-os-tasks-os-svc-send-hand!ler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{getnth})\-\index{tm-set-svcflag}, \\ 
{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-svc-send-handler-path4 \\ \index{mapup-os-ibuffers-os-svc-send-h!andler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-svc-send-handler-path4 \\ \index{mapup-os-obuffers-os-svc-send-h!andler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-svc-send-handler-path4-support \\ \index{mapup-os-mbuffers-os-svc-send-h!andler-path4-support}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{enq2}}\,(\=\+{\rm{tm-r3}}\,({\it{os\/}})\index{tm-r3}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\index{enq2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-svc-send-handler-path4-support.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-svc-send-handler-path4 \\ \index{mapup-os-mbuffers-os-svc-send-h!andler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{enq2}}\,(\=\+{\rm{tm-r3}}\,({\it{os\/}})\index{tm-r3}, \\ 
{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\index{enq2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-svc-send-handler-path4 \\ \index{mapup-queue-os-readyq-os-svc-se!nd-handler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-svc-send-handler-path4 \\ \index{mapup-os-status-table-os-svc-se!nd-handler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-svc-send-handler-path4 \\ \index{tm-clock-os-svc-send-handler-pat!h4}
{\rm{tm-clock}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-svc-send-handler-path4 \\ \index{tm-iports-os-svc-send-handler-p!ath4}
{\rm{tm-iports}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-svc-send-handler-path4 \\ \index{tm-oports-os-svc-send-handler-p!ath4}
{\rm{tm-oports}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-svc-send-handler-path4 \\ \index{tm-rwstate-os-svc-send-handler-p!ath4}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-rwstate}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{tm-rwstate} $=$ {\rm{tm-rwstate}}\,({\it{os\/}})\index{tm-rwstate})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-ak-waiting-to-receivep-mapup-os \\ \index{not-ak-waiting-to-receivep-mapup!-os}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ (\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{3}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{1}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid})\-\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{ak-waiting-to-receivep}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-waiting-to-receivep})\-
\end{tabbing}


\noindent{\sc Event}:   Disable not-ak-waiting-to-receivep-mapup-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-svc-send-handler-path4 \\ \index{correctness-of-os-svc-send-hand!ler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ (\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{3}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{1}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-destid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-destid})\-\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-svc-send-handler-path4}}\,({\it{os\/}})\index{os-svc-send-handler-path4})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-execute-send}}\,(\=\+{\rm{os-message}}\,({\it{os\/}})\index{os-message}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-execute-send})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-svc-send-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-svc-send-handler \\ \index{correctness-of-os-svc-send-hand!ler}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) $\wedge$ (({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{0}})))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-svc-send-handler}}\,({\it{os\/}})\index{os-svc-send-handler})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-execute-send}}\,(\=\+{\rm{os-message}}\,({\it{os\/}})\index{os-message}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{os-destid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-destid}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-execute-send})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-svc-send-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-svc-receive-handler-path1 \\ \index{mapup-base-os-svc-receive-handle!r-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-svc-receive-handler-path1 \\ \index{mapup-limit-os-svc-receive-hand!ler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-svc-receive-handler-path1 \\ \index{getseg-tm-memory-os-svc-receive!-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-receive-handler-path1 \\ \index{mapup-cpu-os-svc-receive-handle!r-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-svc-receive-handler-path1 \\ \index{mapup-regs-os-svc-receive-handle!r-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-svc-receive-handler-path1 \\ \index{mapup-cc-os-svc-receive-handler!-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-svc-receive-handler-path1 \\ \index{mapup-error-os-svc-receive-hand!ler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-svc-receive-handler-path1 \\ \index{mapup-svcflag-os-svc-receive-ha!ndler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-svc-receive-handler-path1 \\ \index{mapup-svcid-os-svc-receive-hand!ler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-svc-receive-handler-path1 \\ \index{mapup-task-os-svc-receive-handle!r-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-receive-handler-path1 \\ \index{mapup-tasks-os-svc-receive-hand!ler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ({\it{taskid\/}} $\in\;${\bf{N}}${}$))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-receive-handler-path1 \\ \index{mapup-os-tasks-os-svc-receive-h!andler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-svc-receive-handler-path1 \\ \index{mapup-os-ibuffers-os-svc-receive!-handler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-svc-receive-handler-path1 \\ \index{mapup-os-obuffers-os-svc-receive!-handler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-svc-receive-handler-path1 \\ \index{mapup-os-mbuffers-os-svc-receive!-handler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-svc-receive-handler-path1 \\ \index{mapup-queue-os-readyq-os-svc-re!ceive-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{deq}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{deq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-svc-receive-handler-path1 \\ \index{mapup-os-status-table-os-svc-re!ceive-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{cons}}\,({\tt{'}}{\tt{3}}, {\rm{cons}}\,({\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, {\tt{'}}{\tt{nil}})), \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-svc-receive-handler-path1 \\ \index{tm-rwstate-os-svc-receive-handle!r-path1}
{\rm{tm-rwstate}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{tm-rwstate} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-svc-receive-handler-path1 \\ \index{tm-clock-os-svc-receive-handler!-path1}
{\rm{tm-clock}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-svc-receive-handler-path1 \\ \index{tm-iports-os-svc-receive-handle!r-path1}
{\rm{tm-iports}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-svc-receive-handler-path1 \\ \index{tm-oports-os-svc-receive-handle!r-path1}
{\rm{tm-oports}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-svc-receive-handler-path1 \\ \index{correctness-of-os-svc-receive-h!andler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-svc-receive-handler-path1}}\,({\it{os\/}})\index{os-svc-receive-handler-path1})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-execute-receive}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-execute-receive})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-svc-receive-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-svc-receive-handler-path2 \\ \index{mapup-base-os-svc-receive-handle!r-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-svc-receive-handler-path2 \\ \index{mapup-limit-os-svc-receive-hand!ler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-svc-receive-handler-path2 \\ \index{getseg-tm-memory-os-svc-receive!-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-svc-receive-handler-path2.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 TM-CPU-OS-SVC-RECEIVE-HANDLER-PATH2-CROCK
 (REWRITE)
 (IMPLIES
  (AND (GOOD-OS OS)
       (NOT (TM-WAITING OS)))
  (EQUAL
   (TM-CPU (OS-SVC-RECEIVE-HANDLER-PATH2 OS))
   (CONS
    (GETNTH '0
            (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                         OS))
    (CONS
     (GETNTH '1
             (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                          OS))
     (CONS
      (GETNTH '2
              (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                           OS))
      (CONS
       (GETNTH '3
               (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                            OS))
       (CONS
        (GETNTH '4
                (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                             OS))
        (CONS
         (GETNTH '5
                 (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                              OS))
         (CONS
          (GETNTH '6
                  (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                               OS))
          (CONS
           (GETNTH '7
                   (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                OS))
           (CONS
            (TM-PACK-PSW
                      (OS-NEW-CC (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                 OS)
                      (OS-NEW-ERROR (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                    OS)
                      (OS-NEW-SVCFLAG (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                      OS)
                      (OS-NEW-SVCID (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                    OS))
            'NIL)))))))))))
 ((ENABLE OS-SVC-RECEIVE-HANDLER-PATH2 TM-CPU TM-R0 TM-R1 TM-R2 TM-R3 TM-R4
          TM-R5 TM-R6 TM-R7)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable tm-cpu-os-svc-receive-handler-path2-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-svc-receive-handler-path2-case1 \\ \index{tm-cpu-os-svc-receive-handler-p!ath2-case1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfirst}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qfirst} \\ 
$=$$\;\;\;\;${\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{os-task-table}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{os-task-table})\-\index{table})\-\index{getnth})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-svc-receive-handler-path2-case2 \\ \index{tm-cpu-os-svc-receive-handler-p!ath2-case2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfirst}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qfirst} \\ 
$\not=$$\;\;\;\;${\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{os-task-table}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{os-task-table})\-\index{table})\-\index{getnth})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-svc-receive-handler-path2 \\ \index{tm-cpu-os-svc-receive-handler-p!ath2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{os-task-table}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{os-task-table})\-\index{table})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-receive-handler-path2 \\ \index{mapup-cpu-os-svc-receive-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-svc-receive-handler-path2 \\ \index{mapup-regs-os-svc-receive-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-svc-receive-handler-path2 \\ \index{mapup-cc-os-svc-receive-handler!-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-svc-receive-handler-path2 \\ \index{mapup-error-os-svc-receive-hand!ler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-svc-receive-handler-path2 \\ \index{mapup-svcflag-os-svc-receive-ha!ndler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-svc-receive-handler-path2 \\ \index{mapup-svcid-os-svc-receive-hand!ler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-svc-receive-handler-path2 \\ \index{mapup-task-os-svc-receive-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-receive-handler-path2 \\ \index{mapup-tasks-os-svc-receive-hand!ler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$({\it{taskid\/}} $\in\;${\bf{N}}${}$))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-receive-handler-path2 \\ \index{mapup-os-tasks-os-svc-receive-h!andler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-svc-receive-handler-path2 \\ \index{mapup-os-ibuffers-os-svc-receive!-handler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-svc-receive-handler-path2 \\ \index{mapup-os-obuffers-os-svc-receive!-handler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-svc-receive-handler-path2 \\ \index{mapup-os-mbuffers-os-svc-receive!-handler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-svc-receive-handler-path2 \\ \index{mapup-queue-os-readyq-os-svc-re!ceive-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{deq}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{deq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-svc-receive-handler-path2 \\ \index{mapup-os-status-table-os-svc-re!ceive-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{cons}}\,({\tt{'}}{\tt{3}}, {\rm{cons}}\,({\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, {\tt{'}}{\tt{nil}})), \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-svc-receive-handler-path2 \\ \index{tm-clock-os-svc-receive-handler!-path2}
{\rm{tm-clock}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{tm-clock} $=$ {\tt{'}}{\tt{1000}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-svc-receive-handler-path2 \\ \index{tm-iports-os-svc-receive-handle!r-path2}
{\rm{tm-iports}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-svc-receive-handler-path2 \\ \index{tm-oports-os-svc-receive-handle!r-path2}
{\rm{tm-oports}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-svc-receive-handler-path2 \\ \index{tm-rwstate-os-svc-receive-handle!r-path2}
{\rm{tm-rwstate}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{tm-rwstate} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-svc-receive-handler-path2 \\ \index{correctness-of-os-svc-receive-h!andler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-svc-receive-handler-path2}}\,({\it{os\/}})\index{os-svc-receive-handler-path2})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-execute-receive}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-execute-receive})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-svc-receive-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-svc-receive-handler-path3 \\ \index{mapup-base-os-svc-receive-handle!r-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-svc-receive-handler-path3 \\ \index{mapup-limit-os-svc-receive-hand!ler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-svc-receive-handler-path3 \\ \index{getseg-tm-memory-os-svc-receive!-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-svc-receive-handler-path3 \\ \index{tm-cpu-os-svc-receive-handler-p!ath3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{3}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{tm-cc}}\,({\it{os\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{os\/}})\index{tm-error}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu})\-\index{putnth})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  array-qfirst-os-readyq-os-svc-receive-handler-path3 \\ \index{array-qfirst-os-readyq-os-svc-re!ceive-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{os-readyq})\index{array-qfirst} \\ 
$=$$\;\;\;\;${\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable array-qfirst-os-readyq-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-receive-handler-path3-case1 \\ \index{mapup-cpu-os-svc-receive-handle!r-path3-case1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\-\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{3}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{mapup-cc}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\it{os\/}})\-\index{mapup-cc}, \\ 
{\rm{mapup-error}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\it{os\/}})\-\index{mapup-error}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{mapup-svcid}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\it{os\/}})\-\index{mapup-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{mapup-cpu}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\it{os\/}})\index{mapup-cpu})\-\index{putnth})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-receive-handler-path3-case1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-receive-handler-path3-case2 \\ \index{mapup-cpu-os-svc-receive-handle!r-path3-case2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}) \\ 
$\wedge$$\;\;\;\;$({\it{taskid\/}} $\not=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-receive-handler-path3-case2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-receive-handler-path3 \\ \index{mapup-cpu-os-svc-receive-handle!r-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{mapup-cpu} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
{\bf then }{\rm{putnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{3}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc}, \\ 
{\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\index{putnth})\-\index{putnth} \\ 
{\bf else }{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-svc-receive-handler-path3 \\ \index{mapup-regs-os-svc-receive-handle!r-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{mapup-regs} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
{\bf then }{\rm{putnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{3}}, \\ 
{\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\index{putnth} \\ 
{\bf else }{\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-svc-receive-handler-path3 \\ \index{mapup-cc-os-svc-receive-handler!-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-svc-receive-handler-path3 \\ \index{mapup-error-os-svc-receive-hand!ler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-svc-receive-handler-path3 \\ \index{mapup-svcflag-os-svc-receive-ha!ndler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf else }{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-svc-receive-handler-path3 \\ \index{mapup-svcid-os-svc-receive-hand!ler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-svc-receive-handler-path3 \\ \index{mapup-task-os-svc-receive-handle!r-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{mapup-task} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
{\bf then }{\rm{os-store-message}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfirst}, \\ 
{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\index{tm-set-svcflag})\-\index{os-store-message} \\ 
{\bf else }{\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-receive-handler-path3-case1 \\ \index{mapup-tasks-os-svc-receive-hand!ler-path3-case1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} $<$ {\it{taskid\/}}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-receive-handler-path3-case1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-receive-handler-path3-case2 \\ \index{mapup-tasks-os-svc-receive-hand!ler-path3-case2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} $<$ {\it{taskid\/}} \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{os-store-message}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfirst}, \\ 
{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
$-$$\;\;\;\;${\it{taskid\/}}\-, \\ 
{\rm{mapup-tasks}}\,(\=\+{\it{taskid\/}}, \\ 
{\it{os\/}})\-\index{mapup-tasks})\-\index{getnth})\-\index{tm-set-svcflag})\-\index{os-store-message}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} $-$ {\it{taskid\/}}, \\ 
{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-receive-handler-path3-case2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-receive-handler-path3-support \\ \index{mapup-os-tasks-os-svc-receive-h!andler-path3-support}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{array-qfullp}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfullp})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{os-store-message}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfirst}, \\ 
{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{getnth})\-\index{tm-set-svcflag})\-\index{os-store-message}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-receive-handler-path3-support.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-receive-handler-path3 \\ \index{mapup-os-tasks-os-svc-receive-h!andler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{2}})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{os-store-message}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfirst}, \\ 
{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{getnth})\-\index{tm-set-svcflag})\-\index{os-store-message}, \\ 
{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-svc-receive-handler-path3 \\ \index{mapup-os-ibuffers-os-svc-receive!-handler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-svc-receive-handler-path3 \\ \index{mapup-os-obuffers-os-svc-receive!-handler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-svc-receive-handler-path3-support \\ \index{mapup-os-mbuffers-os-svc-receive!-handler-path3-support}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{deq2}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\index{deq2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-svc-receive-handler-path3-support.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-svc-receive-handler-path3 \\ \index{mapup-os-mbuffers-os-svc-receive!-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{deq2}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\index{deq2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-svc-receive-handler-path3 \\ \index{mapup-queue-os-readyq-os-svc-re!ceive-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,({\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{2}})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{enq}}\,({\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, {\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-svc-receive-handler-path3 \\ \index{mapup-os-status-table-os-svc-re!ceive-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-svc-receive-handler-path3 \\ \index{tm-clock-os-svc-receive-handler!-path3}
{\rm{tm-clock}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-svc-receive-handler-path3 \\ \index{tm-iports-os-svc-receive-handle!r-path3}
{\rm{tm-iports}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-svc-receive-handler-path3 \\ \index{tm-oports-os-svc-receive-handle!r-path3}
{\rm{tm-oports}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-svc-receive-handler-path3 \\ \index{tm-rwstate-os-svc-receive-handle!r-path3}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-rwstate}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{tm-rwstate} $=$ {\rm{tm-rwstate}}\,({\it{os\/}})\index{tm-rwstate})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-waiting-to-sendp-mapup-os \\ \index{ak-waiting-to-sendp-mapup-os}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{2}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{1}} $+$ ({\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}), \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{ak-waiting-to-sendp}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-waiting-to-sendp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable ak-waiting-to-sendp-mapup-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-set-svcflag-commutes-with-os-store-message \\ \index{tm-set-svcflag-commutes-with-os!-store-message}
\=\+{\rm{os-store-message}}\,({\it{msg\/}}, {\rm{tm-set-svcflag}}\,({\it{flag\/}}, {\it{tm\/}})\index{tm-set-svcflag})\index{os-store-message} \\ 
$=$$\;\;\;\;${\rm{tm-set-svcflag}}\,({\it{flag\/}}, {\rm{os-store-message}}\,({\it{msg\/}}, {\it{tm\/}})\index{os-store-message})\index{tm-set-svcflag}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-set-svcflag-commutes-with-os-store-message.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-svc-receive-handler-path3 \\ \index{correctness-of-os-svc-receive-h!andler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{2}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{1}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid})\-\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-)\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-svc-receive-handler-path3}}\,({\it{os\/}})\index{os-svc-receive-handler-path3})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-execute-receive}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-execute-receive})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-svc-receive-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-svc-receive-handler-path4 \\ \index{mapup-base-os-svc-receive-handle!r-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-svc-receive-handler-path4 \\ \index{mapup-limit-os-svc-receive-hand!ler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-svc-receive-handler-path4 \\ \index{getseg-tm-memory-os-svc-receive!-handler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-svc-receive-handler-path4 \\ \index{tm-cpu-os-svc-receive-handler-p!ath4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{3}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{tm-cc}}\,({\it{os\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{os\/}})\index{tm-error}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu})\-\index{putnth})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-receive-handler-path4-case1 \\ \index{mapup-cpu-os-svc-receive-handle!r-path4-case1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\-\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{3}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{mapup-cc}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\it{os\/}})\-\index{mapup-cc}, \\ 
{\rm{mapup-error}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\it{os\/}})\-\index{mapup-error}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{mapup-svcid}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\it{os\/}})\-\index{mapup-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{mapup-cpu}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\it{os\/}})\index{mapup-cpu})\-\index{putnth})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-receive-handler-path4-case1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-receive-handler-path4-case2 \\ \index{mapup-cpu-os-svc-receive-handle!r-path4-case2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}) \\ 
$\wedge$$\;\;\;\;$({\it{taskid\/}} $\not=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-receive-handler-path4-case2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-receive-handler-path4 \\ \index{mapup-cpu-os-svc-receive-handle!r-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{mapup-cpu} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
{\bf then }{\rm{putnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{3}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc}, \\ 
{\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\index{putnth})\-\index{putnth} \\ 
{\bf else }{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-svc-receive-handler-path4 \\ \index{mapup-regs-os-svc-receive-handle!r-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{mapup-regs} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
{\bf then }{\rm{putnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{3}}, \\ 
{\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\index{putnth} \\ 
{\bf else }{\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-svc-receive-handler-path4 \\ \index{mapup-cc-os-svc-receive-handler!-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-svc-receive-handler-path4 \\ \index{mapup-error-os-svc-receive-hand!ler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-svc-receive-handler-path4 \\ \index{mapup-svcflag-os-svc-receive-ha!ndler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf else }{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-svc-receive-handler-path4 \\ \index{mapup-svcid-os-svc-receive-hand!ler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-svc-receive-handler-path4 \\ \index{mapup-task-os-svc-receive-handle!r-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{mapup-task} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
{\bf then }{\rm{os-store-message}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfirst}, \\ 
{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\index{tm-set-svcflag})\-\index{os-store-message} \\ 
{\bf else }{\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-receive-handler-path4-case1 \\ \index{mapup-tasks-os-svc-receive-hand!ler-path4-case1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} $<$ {\it{taskid\/}})))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-receive-handler-path4-case1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-receive-handler-path4-case2 \\ \index{mapup-tasks-os-svc-receive-hand!ler-path4-case2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} $<$ {\it{taskid\/}} \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{os-store-message}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfirst}, \\ 
{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
$-$$\;\;\;\;${\it{taskid\/}}\-, \\ 
{\rm{mapup-tasks}}\,(\=\+{\it{taskid\/}}, \\ 
{\it{os\/}})\-\index{mapup-tasks})\-\index{getnth})\-\index{tm-set-svcflag})\-\index{os-store-message}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} $-$ {\it{taskid\/}}, \\ 
{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-receive-handler-path4-case2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-receive-handler-path4-support \\ \index{mapup-os-tasks-os-svc-receive-h!andler-path4-support}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{os-store-message}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfirst}, \\ 
{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{getnth})\-\index{tm-set-svcflag})\-\index{os-store-message}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-receive-handler-path4-support.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-receive-handler-path4 \\ \index{mapup-os-tasks-os-svc-receive-h!andler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{os-store-message}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qfirst}, \\ 
{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{getnth})\-\index{tm-set-svcflag})\-\index{os-store-message}, \\ 
{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-svc-receive-handler-path4 \\ \index{mapup-os-ibuffers-os-svc-receive!-handler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-svc-receive-handler-path4 \\ \index{mapup-os-obuffers-os-svc-receive!-handler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-svc-receive-handler-path4-support \\ \index{mapup-os-mbuffers-os-svc-receive!-handler-path4-support}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{deq2}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\index{deq2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-svc-receive-handler-path4-support.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-svc-receive-handler-path4 \\ \index{mapup-os-mbuffers-os-svc-receive!-handler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{deq2}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\index{deq2})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-svc-receive-handler-path4 \\ \index{mapup-queue-os-readyq-os-svc-re!ceive-handler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-svc-receive-handler-path4 \\ \index{mapup-os-status-table-os-svc-re!ceive-handler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-svc-receive-handler-path4 \\ \index{tm-clock-os-svc-receive-handler!-path4}
{\rm{tm-clock}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-svc-receive-handler-path4 \\ \index{tm-iports-os-svc-receive-handle!r-path4}
{\rm{tm-iports}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-svc-receive-handler-path4 \\ \index{tm-oports-os-svc-receive-handle!r-path4}
{\rm{tm-oports}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-svc-receive-handler-path4 \\ \index{tm-rwstate-os-svc-receive-handle!r-path4}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-rwstate}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{tm-rwstate} $=$ {\rm{tm-rwstate}}\,({\it{os\/}})\index{tm-rwstate})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-ak-waiting-to-sendp-mapup-os \\ \index{not-ak-waiting-to-sendp-mapup-o!s}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ (\=\+(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{2}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{1}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid})\-\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{ak-waiting-to-sendp}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-waiting-to-sendp})\-
\end{tabbing}


\noindent{\sc Event}:   Disable not-ak-waiting-to-sendp-mapup-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-svc-receive-handler-path4 \\ \index{correctness-of-os-svc-receive-h!andler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-mbuffer}}\,(\=\+{\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-mbuffer})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ (\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{2}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{1}} \\ 
$+$$\;\;\;\;$(\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{os-srcid}}\,(\=\+{\it{os\/}}, \\ 
{\tt{'}}{\tt{16}})\-\index{os-srcid})\-\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid})\-)\-))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-svc-receive-handler-path4}}\,({\it{os\/}})\index{os-svc-receive-handler-path4})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-execute-receive}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-execute-receive})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-svc-receive-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-svc-receive-handler \\ \index{correctness-of-os-svc-receive-h!andler}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) $\wedge$ (({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{1}})))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-svc-receive-handler}}\,({\it{os\/}})\index{os-svc-receive-handler})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-execute-receive}}\,(\=\+{\rm{os-srcid}}\,({\it{os\/}}, {\tt{'}}{\tt{16}})\index{os-srcid}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-execute-receive})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-svc-receive-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-svc-tyi-handler-path1 \\ \index{mapup-base-os-svc-tyi-handler-p!ath1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-svc-tyi-handler-path1 \\ \index{mapup-limit-os-svc-tyi-handler-p!ath1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-svc-tyi-handler-path1 \\ \index{getseg-tm-memory-os-svc-tyi-han!dler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-tyi-handler-path1 \\ \index{mapup-cpu-os-svc-tyi-handler-pat!h1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-svc-tyi-handler-path1 \\ \index{mapup-regs-os-svc-tyi-handler-p!ath1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-svc-tyi-handler-path1 \\ \index{mapup-cc-os-svc-tyi-handler-pat!h1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-svc-tyi-handler-path1 \\ \index{mapup-error-os-svc-tyi-handler-p!ath1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-svc-tyi-handler-path1 \\ \index{mapup-svcflag-os-svc-tyi-handle!r-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-svc-tyi-handler-path1 \\ \index{mapup-svcid-os-svc-tyi-handler-p!ath1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-svc-tyi-handler-path1 \\ \index{mapup-task-os-svc-tyi-handler-p!ath1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-tyi-handler-path1 \\ \index{mapup-tasks-os-svc-tyi-handler-p!ath1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ({\it{taskid\/}} $\in\;${\bf{N}}${}$))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-tyi-handler-path1 \\ \index{mapup-os-tasks-os-svc-tyi-handle!r-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{mapup-os-tasks}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{mapup-os-tasks} $=$ {\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-svc-tyi-handler-path1 \\ \index{mapup-os-ibuffers-os-svc-tyi-ha!ndler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-svc-tyi-handler-path1 \\ \index{mapup-os-obuffers-os-svc-tyi-ha!ndler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-svc-tyi-handler-path1 \\ \index{mapup-os-mbuffers-os-svc-tyi-ha!ndler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-svc-tyi-handler-path1 \\ \index{mapup-queue-os-readyq-os-svc-tyi!-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{deq}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{deq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-svc-tyi-handler-path1 \\ \index{mapup-os-status-table-os-svc-tyi!-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{5}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-svc-tyi-handler-path1 \\ \index{tm-rwstate-os-svc-tyi-handler-p!ath1}
{\rm{tm-rwstate}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{tm-rwstate} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-svc-tyi-handler-path1 \\ \index{tm-clock-os-svc-tyi-handler-pat!h1}
{\rm{tm-clock}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-svc-tyi-handler-path1 \\ \index{tm-iports-os-svc-tyi-handler-pat!h1}
{\rm{tm-iports}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-svc-tyi-handler-path1 \\ \index{tm-oports-os-svc-tyi-handler-pat!h1}
{\rm{tm-oports}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-svc-tyi-handler-path1 \\ \index{correctness-of-os-svc-tyi-handle!r-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{3}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qemptyp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qemptyp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-svc-tyi-handler-path1}}\,({\it{os\/}})\index{os-svc-tyi-handler-path1})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-execute-input}}\,({\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, {\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-execute-input})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-svc-tyi-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-svc-tyi-handler-path2 \\ \index{mapup-base-os-svc-tyi-handler-p!ath2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-svc-tyi-handler-path2 \\ \index{mapup-limit-os-svc-tyi-handler-p!ath2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-svc-tyi-handler-path2 \\ \index{getseg-tm-memory-os-svc-tyi-han!dler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-svc-tyi-handler-path2.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 TM-CPU-OS-SVC-TYI-HANDLER-PATH2-CROCK
 (REWRITE)
 (IMPLIES
  (AND (GOOD-OS OS)
       (NOT (TM-WAITING OS)))
  (EQUAL
   (TM-CPU (OS-SVC-TYI-HANDLER-PATH2 OS))
   (CONS
    (GETNTH '0
            (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                         OS))
    (CONS
     (GETNTH '1
             (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                          OS))
     (CONS
      (GETNTH '2
              (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                           OS))
      (CONS
       (GETNTH '3
               (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                            OS))
       (CONS
        (GETNTH '4
                (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                             OS))
        (CONS
         (GETNTH '5
                 (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                              OS))
         (CONS
          (GETNTH '6
                  (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                               OS))
          (CONS
           (GETNTH '7
                   (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                OS))
           (CONS
            (TM-PACK-PSW
                      (OS-NEW-CC (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                 OS)
                      (OS-NEW-ERROR (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                    OS)
                      (OS-NEW-SVCFLAG (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                      OS)
                      (OS-NEW-SVCID (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                    OS))
            'NIL)))))))))))
 ((ENABLE OS-SVC-TYI-HANDLER-PATH2 TM-CPU TM-R0 TM-R1 TM-R2 TM-R3 TM-R4 TM-R5
          TM-R6 TM-R7)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable tm-cpu-os-svc-tyi-handler-path2-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-svc-tyi-handler-path2-case1 \\ \index{tm-cpu-os-svc-tyi-handler-path2!-case1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfirst}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qfirst} \\ 
$=$$\;\;\;\;${\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-task-table}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{os-task-table})\index{table})\-\index{getnth})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-svc-tyi-handler-path2-case2 \\ \index{tm-cpu-os-svc-tyi-handler-path2!-case2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfirst}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qfirst} \\ 
$\not=$$\;\;\;\;${\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-task-table}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{os-task-table})\index{table})\-\index{getnth})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-svc-tyi-handler-path2 \\ \index{tm-cpu-os-svc-tyi-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-task-table}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{os-task-table})\index{table})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-tyi-handler-path2 \\ \index{mapup-cpu-os-svc-tyi-handler-pat!h2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-svc-tyi-handler-path2 \\ \index{mapup-regs-os-svc-tyi-handler-p!ath2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-svc-tyi-handler-path2 \\ \index{mapup-cc-os-svc-tyi-handler-pat!h2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-svc-tyi-handler-path2 \\ \index{mapup-error-os-svc-tyi-handler-p!ath2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-svc-tyi-handler-path2 \\ \index{mapup-svcflag-os-svc-tyi-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-svc-tyi-handler-path2 \\ \index{mapup-svcid-os-svc-tyi-handler-p!ath2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-svc-tyi-handler-path2 \\ \index{mapup-task-os-svc-tyi-handler-p!ath2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-tyi-handler-path2 \\ \index{mapup-tasks-os-svc-tyi-handler-p!ath2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$({\it{taskid\/}} $\in\;${\bf{N}}${}$))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-tyi-handler-path2 \\ \index{mapup-os-tasks-os-svc-tyi-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{mapup-os-tasks}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{mapup-os-tasks} $=$ {\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-svc-tyi-handler-path2 \\ \index{mapup-os-ibuffers-os-svc-tyi-ha!ndler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-svc-tyi-handler-path2 \\ \index{mapup-os-obuffers-os-svc-tyi-ha!ndler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-svc-tyi-handler-path2 \\ \index{mapup-os-mbuffers-os-svc-tyi-ha!ndler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-svc-tyi-handler-path2 \\ \index{mapup-queue-os-readyq-os-svc-tyi!-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{deq}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{deq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-svc-tyi-handler-path2 \\ \index{mapup-os-status-table-os-svc-tyi!-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{5}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-svc-tyi-handler-path2 \\ \index{tm-clock-os-svc-tyi-handler-pat!h2}
{\rm{tm-clock}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{tm-clock} $=$ {\tt{'}}{\tt{1000}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-svc-tyi-handler-path2 \\ \index{tm-iports-os-svc-tyi-handler-pat!h2}
{\rm{tm-iports}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-svc-tyi-handler-path2 \\ \index{tm-oports-os-svc-tyi-handler-pat!h2}
{\rm{tm-oports}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-svc-tyi-handler-path2 \\ \index{tm-rwstate-os-svc-tyi-handler-p!ath2}
{\rm{tm-rwstate}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{tm-rwstate} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-svc-tyi-handler-path2 \\ \index{correctness-of-os-svc-tyi-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{3}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qemptyp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qemptyp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-svc-tyi-handler-path2}}\,({\it{os\/}})\index{os-svc-tyi-handler-path2})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-execute-input}}\,({\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, {\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-execute-input})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-svc-tyi-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-svc-tyi-handler-path3 \\ \index{mapup-base-os-svc-tyi-handler-p!ath3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-svc-tyi-handler-path3 \\ \index{mapup-limit-os-svc-tyi-handler-p!ath3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-svc-tyi-handler-path3 \\ \index{getseg-tm-memory-os-svc-tyi-han!dler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-svc-tyi-handler-path3 \\ \index{tm-cpu-os-svc-tyi-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{3}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{tm-cc}}\,({\it{os\/}})\index{tm-cc}, \\ 
{\rm{tm-error}}\,({\it{os\/}})\index{tm-error}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu})\-\index{putnth})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-tyi-handler-path3-case1 \\ \index{mapup-cpu-os-svc-tyi-handler-pat!h3-case1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{3}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{mapup-cc}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\it{os\/}})\-\index{mapup-cc}, \\ 
{\rm{mapup-error}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\it{os\/}})\-\index{mapup-error}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{mapup-svcid}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\it{os\/}})\-\index{mapup-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{mapup-cpu}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\it{os\/}})\index{mapup-cpu})\-\index{putnth})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-tyi-handler-path3-case1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-tyi-handler-path3-case2 \\ \index{mapup-cpu-os-svc-tyi-handler-pat!h3-case2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}) \\ 
$\wedge$$\;\;\;\;$({\it{taskid\/}} $\not=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-tyi-handler-path3-case2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-tyi-handler-path3 \\ \index{mapup-cpu-os-svc-tyi-handler-pat!h3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{mapup-cpu} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
{\bf then }{\rm{putnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{3}}, \\ 
{\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc}, \\ 
{\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\index{putnth})\-\index{putnth} \\ 
{\bf else }{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-svc-tyi-handler-path3 \\ \index{mapup-regs-os-svc-tyi-handler-p!ath3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{mapup-regs} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
{\bf then }{\rm{putnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfirst}, \\ 
{\tt{'}}{\tt{3}}, \\ 
{\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\index{putnth} \\ 
{\bf else }{\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-svc-tyi-handler-path3 \\ \index{mapup-cc-os-svc-tyi-handler-pat!h3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-svc-tyi-handler-path3 \\ \index{mapup-error-os-svc-tyi-handler-p!ath3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-svc-tyi-handler-path3 \\ \index{mapup-svcflag-os-svc-tyi-handle!r-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf else }{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-svc-tyi-handler-path3 \\ \index{mapup-svcid-os-svc-tyi-handler-p!ath3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-svc-tyi-handler-path3 \\ \index{mapup-task-os-svc-tyi-handler-p!ath3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{mapup-task} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
{\bf then }{\rm{os-store-message}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfirst}, \\ 
{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\index{tm-set-svcflag})\-\index{os-store-message} \\ 
{\bf else }{\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-tyi-handler-path3-case1 \\ \index{mapup-tasks-os-svc-tyi-handler-p!ath3-case1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} $<$ {\it{taskid\/}})))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-tyi-handler-path3-case1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-tyi-handler-path3-case2 \\ \index{mapup-tasks-os-svc-tyi-handler-p!ath3-case2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} $<$ {\it{taskid\/}} \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{os-store-message}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfirst}, \\ 
{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
$-$$\;\;\;\;${\it{taskid\/}}\-, \\ 
{\rm{mapup-tasks}}\,(\=\+{\it{taskid\/}}, \\ 
{\it{os\/}})\-\index{mapup-tasks})\-\index{getnth})\-\index{tm-set-svcflag})\-\index{os-store-message}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} $-$ {\it{taskid\/}}, \\ 
{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-tyi-handler-path3-case2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-tyi-handler-path3-support \\ \index{mapup-os-tasks-os-svc-tyi-handle!r-path3-support}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{os-store-message}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfirst}, \\ 
{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{getnth})\-\index{tm-set-svcflag})\-\index{os-store-message}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-tyi-handler-path3-support.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-tyi-handler-path3 \\ \index{mapup-os-tasks-os-svc-tyi-handle!r-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{os-store-message}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfirst}, \\ 
{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{getnth})\-\index{tm-set-svcflag})\-\index{os-store-message}, \\ 
{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-svc-tyi-handler-path3 \\ \index{mapup-os-ibuffers-os-svc-tyi-ha!ndler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{deq-ith-buffer}}\,({\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, {\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\index{deq-ith-buffer})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-svc-tyi-handler-path3 \\ \index{mapup-os-obuffers-os-svc-tyi-ha!ndler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-svc-tyi-handler-path3 \\ \index{mapup-os-mbuffers-os-svc-tyi-ha!ndler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-svc-tyi-handler-path3 \\ \index{mapup-queue-os-readyq-os-svc-tyi!-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-svc-tyi-handler-path3 \\ \index{mapup-os-status-table-os-svc-tyi!-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-svc-tyi-handler-path3 \\ \index{tm-clock-os-svc-tyi-handler-pat!h3}
{\rm{tm-clock}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-svc-tyi-handler-path3 \\ \index{tm-iports-os-svc-tyi-handler-pat!h3}
{\rm{tm-iports}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-svc-tyi-handler-path3 \\ \index{tm-oports-os-svc-tyi-handler-pat!h3}
{\rm{tm-oports}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-svc-tyi-handler-path3 \\ \index{tm-rwstate-os-svc-tyi-handler-p!ath3}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-rwstate}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{tm-rwstate} $=$ {\rm{tm-rwstate}}\,({\it{os\/}})\index{tm-rwstate})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-svc-tyi-handler-path3 \\ \index{correctness-of-os-svc-tyi-handle!r-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{3}}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-svc-tyi-handler-path3}}\,({\it{os\/}})\index{os-svc-tyi-handler-path3})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-execute-input}}\,({\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, {\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-execute-input})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-svc-tyi-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-svc-tyi-handler \\ \index{correctness-of-os-svc-tyi-handle!r}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) $\wedge$ (({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{3}})))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-svc-tyi-handler}}\,({\it{os\/}})\index{os-svc-tyi-handler})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-execute-input}}\,({\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, {\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-execute-input})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-svc-tyi-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-svc-tyo-handler-path1 \\ \index{mapup-base-os-svc-tyo-handler-p!ath1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-svc-tyo-handler-path1 \\ \index{mapup-limit-os-svc-tyo-handler-p!ath1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-svc-tyo-handler-path1 \\ \index{getseg-tm-memory-os-svc-tyo-han!dler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-tyo-handler-path1 \\ \index{mapup-cpu-os-svc-tyo-handler-pat!h1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-svc-tyo-handler-path1 \\ \index{mapup-regs-os-svc-tyo-handler-p!ath1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-svc-tyo-handler-path1 \\ \index{mapup-cc-os-svc-tyo-handler-pat!h1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-svc-tyo-handler-path1 \\ \index{mapup-error-os-svc-tyo-handler-p!ath1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-svc-tyo-handler-path1 \\ \index{mapup-svcflag-os-svc-tyo-handle!r-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-svc-tyo-handler-path1 \\ \index{mapup-svcid-os-svc-tyo-handler-p!ath1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-svc-tyo-handler-path1 \\ \index{mapup-task-os-svc-tyo-handler-p!ath1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-tyo-handler-path1 \\ \index{mapup-tasks-os-svc-tyo-handler-p!ath1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ({\it{taskid\/}} $\in\;${\bf{N}}${}$))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-tyo-handler-path1 \\ \index{mapup-os-tasks-os-svc-tyo-handle!r-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{mapup-os-tasks}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{mapup-os-tasks} $=$ {\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-svc-tyo-handler-path1 \\ \index{mapup-os-ibuffers-os-svc-tyo-ha!ndler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-svc-tyo-handler-path1 \\ \index{mapup-os-obuffers-os-svc-tyo-ha!ndler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-svc-tyo-handler-path1 \\ \index{mapup-os-mbuffers-os-svc-tyo-ha!ndler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-svc-tyo-handler-path1 \\ \index{mapup-queue-os-readyq-os-svc-ty!o-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{deq}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{deq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-svc-tyo-handler-path1 \\ \index{mapup-os-status-table-os-svc-ty!o-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{4}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-svc-tyo-handler-path1 \\ \index{tm-rwstate-os-svc-tyo-handler-p!ath1}
{\rm{tm-rwstate}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{tm-rwstate} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-svc-tyo-handler-path1 \\ \index{tm-clock-os-svc-tyo-handler-pat!h1}
{\rm{tm-clock}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-svc-tyo-handler-path1 \\ \index{tm-iports-os-svc-tyo-handler-pat!h1}
{\rm{tm-iports}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-svc-tyo-handler-path1 \\ \index{tm-oports-os-svc-tyo-handler-pat!h1}
{\rm{tm-oports}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-getnth-for-obuffers \\ \index{mapup-queue-getnth-for-obuffers}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{id\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{getnth}}\,({\it{id\/}}, {\rm{table}}\,({\tt{'}}{\tt{8}}, {\rm{os-obuffers}}\,({\it{os\/}})\index{os-obuffers})\index{table})\index{getnth})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,({\it{id\/}}, {\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-getnth-for-obuffers.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-array-qfullp-obuffers-instance \\ \index{correctness-of-array-qfullp-obu!ffers-instance}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ ({\tt{'}}{\tt{4}} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{array-qfullp}}\,({\it{queue\/}})\index{array-qfullp} $=$ {\rm{qfullp}}\,({\rm{mapup-queue}}\,({\it{queue\/}})\index{mapup-queue}, {\tt{'}}{\tt{4}})\index{qfullp})\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-array-qfullp-obuffers-instance.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-svc-tyo-handler-path1 \\ \index{correctness-of-os-svc-tyo-handle!r-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qfullp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-svc-tyo-handler-path1}}\,({\it{os\/}})\index{os-svc-tyo-handler-path1})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-execute-output}}\,(\=\+{\rm{os-message}}\,({\it{os\/}})\index{os-message}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-execute-output})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-svc-tyo-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-svc-tyo-handler-path2 \\ \index{mapup-base-os-svc-tyo-handler-p!ath2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-svc-tyo-handler-path2 \\ \index{mapup-limit-os-svc-tyo-handler-p!ath2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-svc-tyo-handler-path2 \\ \index{getseg-tm-memory-os-svc-tyo-han!dler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-svc-tyo-handler-path2.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 TM-CPU-OS-SVC-TYO-HANDLER-PATH2-CROCK
 (REWRITE)
 (IMPLIES
  (AND (GOOD-OS OS)
       (NOT (TM-WAITING OS)))
  (EQUAL
   (TM-CPU (OS-SVC-TYO-HANDLER-PATH2 OS))
   (CONS
    (GETNTH '0
            (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                         OS))
    (CONS
     (GETNTH '1
             (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                          OS))
     (CONS
      (GETNTH '2
              (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                           OS))
      (CONS
       (GETNTH '3
               (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                            OS))
       (CONS
        (GETNTH '4
                (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                             OS))
        (CONS
         (GETNTH '5
                 (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                              OS))
         (CONS
          (GETNTH '6
                  (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                               OS))
          (CONS
           (GETNTH '7
                   (OS-NEW-REGS (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                OS))
           (CONS
            (TM-PACK-PSW
                      (OS-NEW-CC (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                 OS)
                      (OS-NEW-ERROR (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                    OS)
                      (OS-NEW-SVCFLAG (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                      OS)
                      (OS-NEW-SVCID (ARRAY-QFIRST (ARRAY-DEQ (OS-READYQ OS)))
                                    OS))
            'NIL)))))))))))
 ((ENABLE OS-SVC-TYO-HANDLER-PATH2 TM-CPU TM-R0 TM-R1 TM-R2 TM-R3 TM-R4 TM-R5
          TM-R6 TM-R7)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable tm-cpu-os-svc-tyo-handler-path2-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-svc-tyo-handler-path2-case1 \\ \index{tm-cpu-os-svc-tyo-handler-path2!-case1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfirst}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qfirst} \\ 
$=$$\;\;\;\;${\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-task-table}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{os-task-table})\index{table})\-\index{getnth})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-svc-tyo-handler-path2-case2 \\ \index{tm-cpu-os-svc-tyo-handler-path2!-case2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfirst}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qfirst} \\ 
$\not=$$\;\;\;\;${\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-task-table}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{os-task-table})\index{table})\-\index{getnth})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-svc-tyo-handler-path2 \\ \index{tm-cpu-os-svc-tyo-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{9}}, {\rm{os-task-table}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{os-task-table})\index{table})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-tyo-handler-path2 \\ \index{mapup-cpu-os-svc-tyo-handler-pat!h2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-svc-tyo-handler-path2 \\ \index{mapup-regs-os-svc-tyo-handler-p!ath2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-svc-tyo-handler-path2 \\ \index{mapup-cc-os-svc-tyo-handler-pat!h2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-svc-tyo-handler-path2 \\ \index{mapup-error-os-svc-tyo-handler-p!ath2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-svc-tyo-handler-path2 \\ \index{mapup-svcflag-os-svc-tyo-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-svc-tyo-handler-path2 \\ \index{mapup-svcid-os-svc-tyo-handler-p!ath2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-svc-tyo-handler-path2 \\ \index{mapup-task-os-svc-tyo-handler-p!ath2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-tyo-handler-path2 \\ \index{mapup-tasks-os-svc-tyo-handler-p!ath2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}) \\ 
$\wedge$$\;\;\;\;$({\it{taskid\/}} $\in\;${\bf{N}}${}$))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-tyo-handler-path2 \\ \index{mapup-os-tasks-os-svc-tyo-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{mapup-os-tasks}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{mapup-os-tasks} $=$ {\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-svc-tyo-handler-path2 \\ \index{mapup-os-ibuffers-os-svc-tyo-ha!ndler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-svc-tyo-handler-path2 \\ \index{mapup-os-obuffers-os-svc-tyo-ha!ndler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-svc-tyo-handler-path2 \\ \index{mapup-os-mbuffers-os-svc-tyo-ha!ndler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-svc-tyo-handler-path2 \\ \index{mapup-queue-os-readyq-os-svc-ty!o-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{deq}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{deq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-svc-tyo-handler-path2 \\ \index{mapup-os-status-table-os-svc-ty!o-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{4}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-svc-tyo-handler-path2 \\ \index{tm-clock-os-svc-tyo-handler-pat!h2}
{\rm{tm-clock}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{tm-clock} $=$ {\tt{'}}{\tt{1000}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-svc-tyo-handler-path2 \\ \index{tm-iports-os-svc-tyo-handler-pat!h2}
{\rm{tm-iports}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-svc-tyo-handler-path2 \\ \index{tm-oports-os-svc-tyo-handler-pat!h2}
{\rm{tm-oports}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-svc-tyo-handler-path2 \\ \index{tm-rwstate-os-svc-tyo-handler-p!ath2}
{\rm{tm-rwstate}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{tm-rwstate} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-svc-tyo-handler-path2 \\ \index{correctness-of-os-svc-tyo-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qfullp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{array-deq}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-deq})\index{array-qemptyp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-svc-tyo-handler-path2}}\,({\it{os\/}})\index{os-svc-tyo-handler-path2})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-execute-output}}\,(\=\+{\rm{os-message}}\,({\it{os\/}})\index{os-message}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-execute-output})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-svc-tyo-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-svc-tyo-handler-path3 \\ \index{mapup-base-os-svc-tyo-handler-p!ath3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-svc-tyo-handler-path3 \\ \index{mapup-limit-os-svc-tyo-handler-p!ath3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-svc-tyo-handler-path3 \\ \index{getseg-tm-memory-os-svc-tyo-han!dler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-svc-tyo-handler-path3 \\ \index{tm-cpu-os-svc-tyo-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,({\rm{tm-cc}}\,({\it{os\/}})\index{tm-cc}, {\rm{tm-error}}\,({\it{os\/}})\index{tm-error}, {\tt{'}}{\tt{0}}, {\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid})\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-tyo-handler-path3-case1 \\ \index{mapup-cpu-os-svc-tyo-handler-pat!h3-case1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{mapup-cc}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\it{os\/}})\index{mapup-cc}, \\ 
{\rm{mapup-error}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\it{os\/}})\index{mapup-error}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{mapup-svcid}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\it{os\/}})\index{mapup-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{mapup-cpu}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\it{os\/}})\index{mapup-cpu})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-tyo-handler-path3-case1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-tyo-handler-path3-case2 \\ \index{mapup-cpu-os-svc-tyo-handler-pat!h3-case2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}) \\ 
$\wedge$$\;\;\;\;$({\it{taskid\/}} $\not=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-tyo-handler-path3-case2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-tyo-handler-path3 \\ \index{mapup-cpu-os-svc-tyo-handler-pat!h3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{mapup-cpu} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
{\bf then }{\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc}, \\ 
{\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\index{putnth} \\ 
{\bf else }{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-svc-tyo-handler-path3 \\ \index{mapup-regs-os-svc-tyo-handler-p!ath3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-svc-tyo-handler-path3 \\ \index{mapup-cc-os-svc-tyo-handler-pat!h3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-svc-tyo-handler-path3 \\ \index{mapup-error-os-svc-tyo-handler-p!ath3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-svc-tyo-handler-path3 \\ \index{mapup-svcflag-os-svc-tyo-handle!r-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf else }{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-svc-tyo-handler-path3 \\ \index{mapup-svcid-os-svc-tyo-handler-p!ath3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-svc-tyo-handler-path3 \\ \index{mapup-task-os-svc-tyo-handler-p!ath3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{mapup-task} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
{\bf then }{\rm{tm-set-svcflag}}\,({\tt{'}}{\tt{0}}, {\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\index{tm-set-svcflag} \\ 
{\bf else }{\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-tyo-handler-path3-case1 \\ \index{mapup-tasks-os-svc-tyo-handler-p!ath3-case1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} $<$ {\it{taskid\/}})))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-tyo-handler-path3-case1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-tyo-handler-path3-case2 \\ \index{mapup-tasks-os-svc-tyo-handler-p!ath3-case2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} $<$ {\it{taskid\/}} \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
$-$$\;\;\;\;${\it{taskid\/}}\-, \\ 
{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\index{getnth})\-\index{tm-set-svcflag}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} $-$ {\it{taskid\/}}, \\ 
{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-tyo-handler-path3-case2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-tyo-handler-path3-support \\ \index{mapup-os-tasks-os-svc-tyo-handle!r-path3-support}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{getnth})\-\index{tm-set-svcflag}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-tyo-handler-path3-support.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-tyo-handler-path3 \\ \index{mapup-os-tasks-os-svc-tyo-handle!r-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{getnth})\-\index{tm-set-svcflag}, \\ 
{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-svc-tyo-handler-path3 \\ \index{mapup-os-ibuffers-os-svc-tyo-ha!ndler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-svc-tyo-handler-path3 \\ \index{mapup-os-obuffers-os-svc-tyo-ha!ndler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{enq-ith-buffer}}\,(\=\+{\rm{os-message}}\,({\it{os\/}})\index{os-message}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\index{enq-ith-buffer})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-svc-tyo-handler-path3 \\ \index{mapup-os-mbuffers-os-svc-tyo-ha!ndler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-svc-tyo-handler-path3 \\ \index{mapup-queue-os-readyq-os-svc-ty!o-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-svc-tyo-handler-path3 \\ \index{mapup-os-status-table-os-svc-ty!o-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-svc-tyo-handler-path3 \\ \index{tm-clock-os-svc-tyo-handler-pat!h3}
{\rm{tm-clock}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-svc-tyo-handler-path3 \\ \index{tm-iports-os-svc-tyo-handler-pat!h3}
{\rm{tm-iports}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-svc-tyo-handler-path3 \\ \index{tm-oports-os-svc-tyo-handler-pat!h3}
\=\+{\rm{tm-oports}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-post-output-interrupt}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-post-output-interrupt}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-svc-tyo-handler-path3 \\ \index{tm-rwstate-os-svc-tyo-handler-p!ath3}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-rwstate}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{tm-rwstate} $=$ {\rm{tm-rwstate}}\,({\it{os\/}})\index{tm-rwstate})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-svc-tyo-handler-path3 \\ \index{correctness-of-os-svc-tyo-handle!r-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-oport-idlep}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\-\index{tm-oport-idlep})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-svc-tyo-handler-path3}}\,({\it{os\/}})\index{os-svc-tyo-handler-path3})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-execute-output}}\,(\=\+{\rm{os-message}}\,({\it{os\/}})\index{os-message}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-execute-output})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-svc-tyo-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-svc-tyo-handler-path4 \\ \index{mapup-base-os-svc-tyo-handler-p!ath4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-svc-tyo-handler-path4 \\ \index{mapup-limit-os-svc-tyo-handler-p!ath4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-svc-tyo-handler-path4 \\ \index{getseg-tm-memory-os-svc-tyo-han!dler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-svc-tyo-handler-path4 \\ \index{tm-cpu-os-svc-tyo-handler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,({\rm{tm-cc}}\,({\it{os\/}})\index{tm-cc}, {\rm{tm-error}}\,({\it{os\/}})\index{tm-error}, {\tt{'}}{\tt{0}}, {\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid})\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-tyo-handler-path4-case1 \\ \index{mapup-cpu-os-svc-tyo-handler-pat!h4-case1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{mapup-cc}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\it{os\/}})\index{mapup-cc}, \\ 
{\rm{mapup-error}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\it{os\/}})\index{mapup-error}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{mapup-svcid}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\it{os\/}})\index{mapup-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{mapup-cpu}}\,({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, {\it{os\/}})\index{mapup-cpu})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-tyo-handler-path4-case1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-tyo-handler-path4-case2 \\ \index{mapup-cpu-os-svc-tyo-handler-pat!h4-case2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}) \\ 
$\wedge$$\;\;\;\;$({\it{taskid\/}} $\not=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-tyo-handler-path4-case2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-svc-tyo-handler-path4 \\ \index{mapup-cpu-os-svc-tyo-handler-pat!h4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{mapup-cpu} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
{\bf then }{\rm{putnth}}\,(\=\+{\rm{tm-pack-psw}}\,(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc}, \\ 
{\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error}, \\ 
{\tt{'}}{\tt{0}}, \\ 
{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\index{tm-pack-psw}, \\ 
{\tt{'}}{\tt{8}}, \\ 
{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\index{putnth} \\ 
{\bf else }{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-svc-tyo-handler-path4 \\ \index{mapup-regs-os-svc-tyo-handler-p!ath4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-svc-tyo-handler-path4 \\ \index{mapup-cc-os-svc-tyo-handler-pat!h4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-svc-tyo-handler-path4 \\ \index{mapup-error-os-svc-tyo-handler-p!ath4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-svc-tyo-handler-path4 \\ \index{mapup-svcflag-os-svc-tyo-handle!r-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}$\;\;${\bf then }{\tt{'}}{\tt{0}} \\ 
{\bf else }{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-svc-tyo-handler-path4 \\ \index{mapup-svcid-os-svc-tyo-handler-p!ath4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-svc-tyo-handler-path4 \\ \index{mapup-task-os-svc-tyo-handler-p!ath4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}}))))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{mapup-task} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{taskid\/}} $=$ {\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
{\bf then }{\rm{tm-set-svcflag}}\,({\tt{'}}{\tt{0}}, {\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\index{tm-set-svcflag} \\ 
{\bf else }{\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task}$\;${\bf  endif}\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-tyo-handler-path4-case1 \\ \index{mapup-tasks-os-svc-tyo-handler-p!ath4-case1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} $<$ {\it{taskid\/}})))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-tyo-handler-path4-case1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-svc-tyo-handler-path4-case2 \\ \index{mapup-tasks-os-svc-tyo-handler-p!ath4-case2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+({\it{taskid\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$\=\+{\bf if }{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} $<$ {\it{taskid\/}} \\ 
{\bf then }{\tt{'}}{\tt{*1*false}} \\ 
{\bf else }{\tt{'}}{\tt{*1*true}}$\;${\bf  endif}\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} \\ 
$-$$\;\;\;\;${\it{taskid\/}}\-, \\ 
{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\index{getnth})\-\index{tm-set-svcflag}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst} $-$ {\it{taskid\/}}, \\ 
{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-svc-tyo-handler-path4-case2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-tyo-handler-path4-support \\ \index{mapup-os-tasks-os-svc-tyo-handle!r-path4-support}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{getnth})\-\index{tm-set-svcflag}, \\ 
{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-tyo-handler-path4-support.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-svc-tyo-handler-path4 \\ \index{mapup-os-tasks-os-svc-tyo-handle!r-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\rm{tm-set-svcflag}}\,(\=\+{\tt{'}}{\tt{0}}, \\ 
{\rm{getnth}}\,(\=\+{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{getnth})\-\index{tm-set-svcflag}, \\ 
{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-svc-tyo-handler-path4 \\ \index{mapup-os-ibuffers-os-svc-tyo-ha!ndler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-svc-tyo-handler-path4 \\ \index{mapup-os-obuffers-os-svc-tyo-ha!ndler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{enq-ith-buffer}}\,(\=\+{\rm{os-message}}\,({\it{os\/}})\index{os-message}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\index{enq-ith-buffer})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-svc-tyo-handler-path4 \\ \index{mapup-os-mbuffers-os-svc-tyo-ha!ndler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-svc-tyo-handler-path4 \\ \index{mapup-queue-os-readyq-os-svc-ty!o-handler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-svc-tyo-handler-path4 \\ \index{mapup-os-status-table-os-svc-ty!o-handler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-svc-tyo-handler-path4 \\ \index{tm-clock-os-svc-tyo-handler-pat!h4}
{\rm{tm-clock}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-svc-tyo-handler-path4 \\ \index{tm-iports-os-svc-tyo-handler-pat!h4}
{\rm{tm-iports}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-svc-tyo-handler-path4 \\ \index{tm-oports-os-svc-tyo-handler-pat!h4}
{\rm{tm-oports}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-svc-tyo-handler-path4 \\ \index{tm-rwstate-os-svc-tyo-handler-p!ath4}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-rwstate}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{tm-rwstate} $=$ {\rm{tm-rwstate}}\,({\it{os\/}})\index{tm-rwstate})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-svc-tyo-handler-path4 \\ \index{correctness-of-os-svc-tyo-handle!r-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) \\ 
$\wedge$$\;\;\;\;$(\=\+(({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}}) \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-oport-idlep}}\,(\=\+{\rm{array-qfirst}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{array-qfirst}, \\ 
{\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\-\index{tm-oport-idlep}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-svc-tyo-handler-path4}}\,({\it{os\/}})\index{os-svc-tyo-handler-path4})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-execute-output}}\,(\=\+{\rm{os-message}}\,({\it{os\/}})\index{os-message}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-execute-output})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-svc-tyo-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-svc-tyo-handler \\ \index{correctness-of-os-svc-tyo-handle!r}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}) $\wedge$ (({\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid} ${}${\bf{mod}}${}$ {\tt{'}}{\tt{4}}) $=$ {\tt{'}}{\tt{2}})))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-svc-tyo-handler}}\,({\it{os\/}})\index{os-svc-tyo-handler})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-execute-output}}\,(\=\+{\rm{os-message}}\,({\it{os\/}})\index{os-message}, \\ 
{\rm{os-current-taskid}}\,({\it{os\/}})\index{os-current-taskid}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-execute-output})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-svc-tyo-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-waiting-input-handler-path1 \\ \index{mapup-base-os-waiting-input-han!dler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-waiting-input-handler-path1 \\ \index{mapup-limit-os-waiting-input-ha!ndler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-waiting-input-handler-path1 \\ \index{getseg-tm-memory-os-waiting-inp!ut-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-waiting-input-handler-path1.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 TM-CPU-OS-WAITING-INPUT-HANDLER-PATH1-CROCK
 (REWRITE)
 (EQUAL
  (TM-CPU (OS-WAITING-INPUT-HANDLER-PATH1 OS))
  (CONS
   (GETNTH '0
           (GETSEG '0
                   '8
                   (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                           (TABLE '9 (OS-TASK-TABLE OS)))))
   (CONS
    (GETNTH '1
            (GETSEG '0
                    '8
                    (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TABLE '9 (OS-TASK-TABLE OS)))))
    (CONS
     (GETNTH '2
             (GETSEG '0
                     '8
                     (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                             (TABLE '9 (OS-TASK-TABLE OS)))))
     (CONS
      (GETNTH '3
              (GETSEG '0
                      '8
                      (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                              (TABLE '9 (OS-TASK-TABLE OS)))))
      (CONS
       (GETNTH '4
               (GETSEG '0
                       '8
                       (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                               (TABLE '9 (OS-TASK-TABLE OS)))))
       (CONS
        (GETNTH '5
                (GETSEG '0
                        '8
                        (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                (TABLE '9 (OS-TASK-TABLE OS)))))
        (CONS
         (GETNTH '6
                 (GETSEG '0
                         '8
                         (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                 (TABLE '9 (OS-TASK-TABLE OS)))))
         (CONS
          (GETNTH '7
                  (GETSEG '0
                          '8
                          (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                  (TABLE '9 (OS-TASK-TABLE OS)))))
          (CONS
           (TM-PACK-PSW
            (TM-UNPACK-CC
             (GETNTH (PLUS '8
                           (TIMES '9
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     (OS-TASK-TABLE OS)))
            (TM-UNPACK-ERROR
             (GETNTH (PLUS '8
                           (TIMES '9
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     (OS-TASK-TABLE OS)))
            (TM-UNPACK-SVCFLAG
             (GETNTH (PLUS '8
                           (TIMES '9
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     (OS-TASK-TABLE OS)))
            (TM-UNPACK-SVCID
             (GETNTH (PLUS '8
                           (TIMES '9
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     (OS-TASK-TABLE OS))))
           'NIL))))))))))
 ((ENABLE OS-WAITING-INPUT-HANDLER-PATH1 TM-CPU TM-R0 TM-R1 TM-R2 TM-R3 TM-R4
          TM-R5 TM-R6 TM-R7 TM-UNPACK-CC TM-UNPACK-ERROR TM-UNPACK-SVCFLAG
          TM-UNPACK-SVCID)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable tm-cpu-os-waiting-input-handler-path1-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-waiting-input-handler-path1 \\ \index{tm-cpu-os-waiting-input-handler!-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{os-current-taskid}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{os-task-table}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{os-task-table})\-\index{table})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-waiting-input-handler-path1 \\ \index{mapup-cpu-os-waiting-input-hand!ler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-waiting-input-handler-path1 \\ \index{mapup-regs-os-waiting-input-han!dler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-waiting-input-handler-path1 \\ \index{mapup-cc-os-waiting-input-handle!r-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-waiting-input-handler-path1 \\ \index{mapup-error-os-waiting-input-ha!ndler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-waiting-input-handler-path1 \\ \index{mapup-svcflag-os-waiting-input-!handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-waiting-input-handler-path1 \\ \index{mapup-svcid-os-waiting-input-ha!ndler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-waiting-input-handler-path1 \\ \index{mapup-task-os-waiting-input-han!dler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-waiting-input-handler-path1 \\ \index{mapup-tasks-os-waiting-input-ha!ndler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ ({\it{taskid\/}} $\in\;${\bf{N}}${}$)))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-waiting-input-handler-path1 \\ \index{mapup-os-tasks-os-waiting-input!-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-waiting-input-handler-path1 \\ \index{mapup-os-ibuffers-os-waiting-inp!ut-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{qreplace-ith-buffer}}\,(\=\+{\rm{tm-overflow-char}}\,({\rm{tm-ichar}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{getnth})\index{tm-ichar})\index{tm-overflow-char}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\index{qreplace-ith-buffer})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-waiting-input-handler-path1 \\ \index{mapup-os-obuffers-os-waiting-inp!ut-handler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-waiting-input-handler-path1 \\ \index{mapup-os-mbuffers-os-waiting-inp!ut-handler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-waiting-input-handler-path1 \\ \index{mapup-queue-os-readyq-os-waitin!g-input-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{enq}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\-\index{enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-waiting-input-handler-path1 \\ \index{mapup-os-status-table-os-waitin!g-input-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-waiting-input-handler-path1 \\ \index{tm-rwstate-os-waiting-input-han!dler-path1}
{\rm{tm-rwstate}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{tm-rwstate} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-waiting-input-handler-path1 \\ \index{tm-clock-os-waiting-input-handle!r-path1}
{\rm{tm-clock}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{tm-clock} $=$ {\tt{'}}{\tt{1000}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-waiting-input-handler-path1 \\ \index{tm-iports-os-waiting-input-hand!ler-path1}
\=\+{\rm{tm-iports}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-clear-input-interrupt}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-clear-input-interrupt}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-waiting-input-handler-path1 \\ \index{tm-oports-os-waiting-input-hand!ler-path1}
{\rm{tm-oports}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-waiting-to-inputp-mapup-os \\ \index{ak-waiting-to-inputp-mapup-os}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{ak-waiting-to-inputp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-waiting-to-inputp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable ak-waiting-to-inputp-mapup-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-array-qfullp-ibuffers-instance \\ \index{correctness-of-array-qfullp-ibu!ffers-instance}
\=\+({\rm{array-queuep}}\,({\it{queue\/}})\index{array-queuep} $\wedge$ ({\tt{'}}{\tt{4}} $=$ {\rm{getnth}}\,({\tt{'}}{\tt{3}}, {\it{queue\/}})\index{getnth})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{array-qfullp}}\,({\it{queue\/}})\index{array-qfullp} $=$ {\rm{qfullp}}\,({\rm{mapup-queue}}\,({\it{queue\/}})\index{mapup-queue}, {\tt{'}}{\tt{4}})\index{qfullp})\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-array-qfullp-ibuffers-instance.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-waiting-input-handler-path1 \\ \index{correctness-of-os-waiting-input!-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-waiting-input-handler-path1}}\,({\it{os\/}})\index{os-waiting-input-handler-path1})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-waiting-input-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-waiting-input-interrupt-hand!ler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-waiting-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-waiting-input-handler-path2 \\ \index{mapup-base-os-waiting-input-han!dler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-waiting-input-handler-path2 \\ \index{mapup-limit-os-waiting-input-ha!ndler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-waiting-input-handler-path2 \\ \index{getseg-tm-memory-os-waiting-inp!ut-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-waiting-input-handler-path2.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 TM-CPU-OS-WAITING-INPUT-HANDLER-PATH2-CROCK
 (REWRITE)
 (EQUAL
  (TM-CPU (OS-WAITING-INPUT-HANDLER-PATH2 OS))
  (CONS
   (GETNTH '0
           (GETSEG '0
                   '8
                   (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                           (TABLE '9 (OS-TASK-TABLE OS)))))
   (CONS
    (GETNTH '1
            (GETSEG '0
                    '8
                    (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TABLE '9 (OS-TASK-TABLE OS)))))
    (CONS
     (GETNTH '2
             (GETSEG '0
                     '8
                     (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                             (TABLE '9 (OS-TASK-TABLE OS)))))
     (CONS
      (GETNTH '3
              (GETSEG '0
                      '8
                      (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                              (TABLE '9 (OS-TASK-TABLE OS)))))
      (CONS
       (GETNTH '4
               (GETSEG '0
                       '8
                       (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                               (TABLE '9 (OS-TASK-TABLE OS)))))
       (CONS
        (GETNTH '5
                (GETSEG '0
                        '8
                        (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                (TABLE '9 (OS-TASK-TABLE OS)))))
        (CONS
         (GETNTH '6
                 (GETSEG '0
                         '8
                         (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                 (TABLE '9 (OS-TASK-TABLE OS)))))
         (CONS
          (GETNTH '7
                  (GETSEG '0
                          '8
                          (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                  (TABLE '9 (OS-TASK-TABLE OS)))))
          (CONS
           (TM-PACK-PSW
            (TM-UNPACK-CC
             (GETNTH (PLUS '8
                           (TIMES '9
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     (OS-TASK-TABLE OS)))
            (TM-UNPACK-ERROR
             (GETNTH (PLUS '8
                           (TIMES '9
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     (OS-TASK-TABLE OS)))
            (TM-UNPACK-SVCFLAG
             (GETNTH (PLUS '8
                           (TIMES '9
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     (OS-TASK-TABLE OS)))
            (TM-UNPACK-SVCID
             (GETNTH (PLUS '8
                           (TIMES '9
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     (OS-TASK-TABLE OS))))
           'NIL))))))))))
 ((ENABLE OS-WAITING-INPUT-HANDLER-PATH2 TM-CPU TM-R0 TM-R1 TM-R2 TM-R3 TM-R4
          TM-R5 TM-R6 TM-R7 TM-UNPACK-CC TM-UNPACK-ERROR TM-UNPACK-SVCFLAG
          TM-UNPACK-SVCID)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable tm-cpu-os-waiting-input-handler-path2-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-waiting-input-handler-path2 \\ \index{tm-cpu-os-waiting-input-handler!-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{os-task-table}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{os-task-table})\-\index{table})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-waiting-input-handler-path2 \\ \index{mapup-cpu-os-waiting-input-hand!ler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-waiting-input-handler-path2 \\ \index{mapup-regs-os-waiting-input-han!dler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-waiting-input-handler-path2 \\ \index{mapup-cc-os-waiting-input-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-waiting-input-handler-path2 \\ \index{mapup-error-os-waiting-input-ha!ndler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-waiting-input-handler-path2 \\ \index{mapup-svcflag-os-waiting-input-!handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-waiting-input-handler-path2 \\ \index{mapup-svcid-os-waiting-input-ha!ndler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-waiting-input-handler-path2 \\ \index{mapup-task-os-waiting-input-han!dler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-waiting-input-handler-path2 \\ \index{mapup-tasks-os-waiting-input-ha!ndler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ ({\it{taskid\/}} $\in\;${\bf{N}}${}$)))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-waiting-input-handler-path2 \\ \index{mapup-os-tasks-os-waiting-input!-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-waiting-input-handler-path2 \\ \index{mapup-os-ibuffers-os-waiting-inp!ut-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{enq-ith-buffer}}\,(\=\+{\rm{tm-overflow-char}}\,({\rm{tm-ichar}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{getnth})\index{tm-ichar})\index{tm-overflow-char}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\index{enq-ith-buffer})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-waiting-input-handler-path2 \\ \index{mapup-os-obuffers-os-waiting-inp!ut-handler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-waiting-input-handler-path2 \\ \index{mapup-os-mbuffers-os-waiting-inp!ut-handler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-waiting-input-handler-path2 \\ \index{mapup-queue-os-readyq-os-waitin!g-input-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{enq}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\-\index{enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-waiting-input-handler-path2 \\ \index{mapup-os-status-table-os-waitin!g-input-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-waiting-input-handler-path2 \\ \index{tm-rwstate-os-waiting-input-han!dler-path2}
{\rm{tm-rwstate}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{tm-rwstate} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-waiting-input-handler-path2 \\ \index{tm-clock-os-waiting-input-handle!r-path2}
{\rm{tm-clock}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{tm-clock} $=$ {\tt{'}}{\tt{1000}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-waiting-input-handler-path2 \\ \index{tm-iports-os-waiting-input-hand!ler-path2}
\=\+{\rm{tm-iports}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-clear-input-interrupt}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-clear-input-interrupt}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-waiting-input-handler-path2 \\ \index{tm-oports-os-waiting-input-hand!ler-path2}
{\rm{tm-oports}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-waiting-input-handler-path2 \\ \index{correctness-of-os-waiting-input!-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-waiting-input-handler-path2}}\,({\it{os\/}})\index{os-waiting-input-handler-path2})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-waiting-input-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-waiting-input-interrupt-hand!ler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-waiting-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-waiting-input-handler-path3 \\ \index{mapup-base-os-waiting-input-han!dler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-waiting-input-handler-path3 \\ \index{mapup-limit-os-waiting-input-ha!ndler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-waiting-input-handler-path3 \\ \index{getseg-tm-memory-os-waiting-inp!ut-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-waiting-input-handler-path3.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 TM-CPU-OS-WAITING-INPUT-HANDLER-PATH3-CROCK
 (REWRITE)
 (EQUAL
  (TM-CPU (OS-WAITING-INPUT-HANDLER-PATH3 OS))
  (CONS
   (GETNTH '0
           (GETSEG '0
                   '8
                   (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                           (TABLE '9 (OS-TASK-TABLE OS)))))
   (CONS
    (GETNTH '1
            (GETSEG '0
                    '8
                    (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                            (TABLE '9 (OS-TASK-TABLE OS)))))
    (CONS
     (GETNTH '2
             (GETSEG '0
                     '8
                     (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                             (TABLE '9 (OS-TASK-TABLE OS)))))
     (CONS
      (GETNTH '3
              (GETSEG '0
                      '8
                      (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                              (TABLE '9 (OS-TASK-TABLE OS)))))
      (CONS
       (GETNTH '4
               (GETSEG '0
                       '8
                       (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                               (TABLE '9 (OS-TASK-TABLE OS)))))
       (CONS
        (GETNTH '5
                (GETSEG '0
                        '8
                        (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                (TABLE '9 (OS-TASK-TABLE OS)))))
        (CONS
         (GETNTH '6
                 (GETSEG '0
                         '8
                         (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                 (TABLE '9 (OS-TASK-TABLE OS)))))
         (CONS
          (GETNTH '7
                  (GETSEG '0
                          '8
                          (GETNTH (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))
                                  (TABLE '9 (OS-TASK-TABLE OS)))))
          (CONS
           (TM-PACK-PSW
            (TM-UNPACK-CC
             (GETNTH (PLUS '8
                           (TIMES '9
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     (OS-TASK-TABLE OS)))
            (TM-UNPACK-ERROR
             (GETNTH (PLUS '8
                           (TIMES '9
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     (OS-TASK-TABLE OS)))
            (TM-UNPACK-SVCFLAG
             (GETNTH (PLUS '8
                           (TIMES '9
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     (OS-TASK-TABLE OS)))
            (TM-UNPACK-SVCID
             (GETNTH (PLUS '8
                           (TIMES '9
                                  (TM-INTERRUPTING-INPUT-PORT (TM-IPORTS OS))))
                     (OS-TASK-TABLE OS))))
           'NIL))))))))))
 ((ENABLE OS-WAITING-INPUT-HANDLER-PATH3 TM-CPU TM-R0 TM-R1 TM-R2 TM-R3 TM-R4
          TM-R5 TM-R6 TM-R7 TM-UNPACK-CC TM-UNPACK-ERROR TM-UNPACK-SVCFLAG
          TM-UNPACK-SVCID)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable tm-cpu-os-waiting-input-handler-path3-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-waiting-input-handler-path3 \\ \index{tm-cpu-os-waiting-input-handler!-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{os-current-taskid}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{os-task-table}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{os-task-table})\-\index{table})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-waiting-input-handler-path3 \\ \index{mapup-cpu-os-waiting-input-hand!ler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-waiting-input-handler-path3 \\ \index{mapup-regs-os-waiting-input-han!dler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-waiting-input-handler-path3 \\ \index{mapup-cc-os-waiting-input-handle!r-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-waiting-input-handler-path3 \\ \index{mapup-error-os-waiting-input-ha!ndler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-waiting-input-handler-path3 \\ \index{mapup-svcflag-os-waiting-input-!handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-waiting-input-handler-path3 \\ \index{mapup-svcid-os-waiting-input-ha!ndler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-waiting-input-handler-path3 \\ \index{mapup-task-os-waiting-input-han!dler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-waiting-input-handler-path3 \\ \index{mapup-tasks-os-waiting-input-ha!ndler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ ({\it{taskid\/}} $\in\;${\bf{N}}${}$)))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-waiting-input-handler-path3 \\ \index{mapup-os-tasks-os-waiting-input!-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-waiting-input-handler-path3 \\ \index{mapup-os-ibuffers-os-waiting-inp!ut-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{enq-ith-buffer}}\,(\=\+{\rm{tm-ichar}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{getnth})\index{tm-ichar}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\index{enq-ith-buffer})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-waiting-input-handler-path3 \\ \index{mapup-os-obuffers-os-waiting-inp!ut-handler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-waiting-input-handler-path3 \\ \index{mapup-os-mbuffers-os-waiting-inp!ut-handler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-waiting-input-handler-path3 \\ \index{mapup-queue-os-readyq-os-waitin!g-input-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{enq}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\-\index{enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-waiting-input-handler-path3 \\ \index{mapup-os-status-table-os-waitin!g-input-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-waiting-input-handler-path3 \\ \index{tm-rwstate-os-waiting-input-han!dler-path3}
{\rm{tm-rwstate}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{tm-rwstate} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-waiting-input-handler-path3 \\ \index{tm-clock-os-waiting-input-handle!r-path3}
{\rm{tm-clock}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{tm-clock} $=$ {\tt{'}}{\tt{1000}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-waiting-input-handler-path3 \\ \index{tm-iports-os-waiting-input-hand!ler-path3}
\=\+{\rm{tm-iports}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-clear-input-interrupt}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-clear-input-interrupt}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-waiting-input-handler-path3 \\ \index{tm-oports-os-waiting-input-hand!ler-path3}
{\rm{tm-oports}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-waiting-input-handler-path3 \\ \index{correctness-of-os-waiting-input!-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-waiting-input-handler-path3}}\,({\it{os\/}})\index{os-waiting-input-handler-path3})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-waiting-input-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-waiting-input-interrupt-hand!ler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-waiting-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-waiting-input-handler-path4 \\ \index{mapup-base-os-waiting-input-han!dler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-waiting-input-handler-path4 \\ \index{mapup-limit-os-waiting-input-ha!ndler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-waiting-input-handler-path4 \\ \index{getseg-tm-memory-os-waiting-inp!ut-handler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-waiting-input-handler-path4 \\ \index{mapup-cpu-os-waiting-input-hand!ler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-waiting-input-handler-path4 \\ \index{mapup-regs-os-waiting-input-han!dler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-waiting-input-handler-path4 \\ \index{mapup-cc-os-waiting-input-handle!r-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-waiting-input-handler-path4 \\ \index{mapup-error-os-waiting-input-ha!ndler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-waiting-input-handler-path4 \\ \index{mapup-svcflag-os-waiting-input-!handler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-waiting-input-handler-path4 \\ \index{mapup-svcid-os-waiting-input-ha!ndler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-waiting-input-handler-path4 \\ \index{mapup-task-os-waiting-input-han!dler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-waiting-input-handler-path4 \\ \index{mapup-tasks-os-waiting-input-ha!ndler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ ({\it{taskid\/}} $\in\;${\bf{N}}${}$))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-waiting-input-handler-path4 \\ \index{mapup-os-tasks-os-waiting-input!-handler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-waiting-input-handler-path4 \\ \index{mapup-os-ibuffers-os-waiting-inp!ut-handler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{qreplace-ith-buffer}}\,(\=\+{\rm{tm-overflow-char}}\,({\rm{tm-ichar}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{getnth})\index{tm-ichar})\index{tm-overflow-char}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\index{qreplace-ith-buffer})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-waiting-input-handler-path4 \\ \index{mapup-os-obuffers-os-waiting-inp!ut-handler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-waiting-input-handler-path4 \\ \index{mapup-os-mbuffers-os-waiting-inp!ut-handler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-waiting-input-handler-path4 \\ \index{tm-rwstate-os-waiting-input-han!dler-path4}
{\rm{tm-rwstate}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{tm-rwstate} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-waiting-input-handler-path4 \\ \index{tm-clock-os-waiting-input-handle!r-path4}
{\rm{tm-clock}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-waiting-input-handler-path4 \\ \index{tm-iports-os-waiting-input-hand!ler-path4}
\=\+{\rm{tm-iports}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-clear-input-interrupt}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-clear-input-interrupt}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-waiting-input-handler-path4 \\ \index{tm-oports-os-waiting-input-hand!ler-path4}
{\rm{tm-oports}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-ak-waiting-to-inputp-mapup-os \\ \index{not-ak-waiting-to-inputp-mapup-!os}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{ak-waiting-to-inputp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-waiting-to-inputp})\-
\end{tabbing}


\noindent{\sc Event}:   Disable not-ak-waiting-to-inputp-mapup-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-waiting-input-handler-path4 \\ \index{correctness-of-os-waiting-input!-handler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-waiting-input-handler-path4}}\,({\it{os\/}})\index{os-waiting-input-handler-path4})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-waiting-input-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-waiting-input-interrupt-hand!ler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-waiting-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-waiting-input-handler-path5 \\ \index{mapup-base-os-waiting-input-han!dler-path5}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-waiting-input-handler-path5 \\ \index{mapup-limit-os-waiting-input-ha!ndler-path5}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-waiting-input-handler-path5 \\ \index{getseg-tm-memory-os-waiting-inp!ut-handler-path5}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-waiting-input-handler-path5 \\ \index{mapup-cpu-os-waiting-input-hand!ler-path5}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-waiting-input-handler-path5 \\ \index{mapup-regs-os-waiting-input-han!dler-path5}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-waiting-input-handler-path5 \\ \index{mapup-cc-os-waiting-input-handle!r-path5}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-waiting-input-handler-path5 \\ \index{mapup-error-os-waiting-input-ha!ndler-path5}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-waiting-input-handler-path5 \\ \index{mapup-svcflag-os-waiting-input-!handler-path5}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-waiting-input-handler-path5 \\ \index{mapup-svcid-os-waiting-input-ha!ndler-path5}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-waiting-input-handler-path5 \\ \index{mapup-task-os-waiting-input-han!dler-path5}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-waiting-input-handler-path5 \\ \index{mapup-tasks-os-waiting-input-ha!ndler-path5}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ ({\it{taskid\/}} $\in\;${\bf{N}}${}$))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-waiting-input-handler-path5 \\ \index{mapup-os-tasks-os-waiting-input!-handler-path5}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-waiting-input-handler-path5 \\ \index{mapup-os-ibuffers-os-waiting-inp!ut-handler-path5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{enq-ith-buffer}}\,(\=\+{\rm{tm-overflow-char}}\,({\rm{tm-ichar}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{getnth})\index{tm-ichar})\index{tm-overflow-char}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\index{enq-ith-buffer})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-waiting-input-handler-path5 \\ \index{mapup-os-obuffers-os-waiting-inp!ut-handler-path5}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-waiting-input-handler-path5 \\ \index{mapup-os-mbuffers-os-waiting-inp!ut-handler-path5}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-waiting-input-handler-path5 \\ \index{tm-rwstate-os-waiting-input-han!dler-path5}
{\rm{tm-rwstate}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{tm-rwstate} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-waiting-input-handler-path5 \\ \index{tm-clock-os-waiting-input-handle!r-path5}
{\rm{tm-clock}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-waiting-input-handler-path5 \\ \index{tm-iports-os-waiting-input-hand!ler-path5}
\=\+{\rm{tm-iports}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-clear-input-interrupt}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-clear-input-interrupt}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-waiting-input-handler-path5 \\ \index{tm-oports-os-waiting-input-hand!ler-path5}
{\rm{tm-oports}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-waiting-input-handler-path5 \\ \index{correctness-of-os-waiting-input!-handler-path5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-waiting-input-handler-path5}}\,({\it{os\/}})\index{os-waiting-input-handler-path5})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-waiting-input-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-waiting-input-interrupt-hand!ler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-waiting-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-waiting-input-handler-path6 \\ \index{mapup-base-os-waiting-input-han!dler-path6}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-waiting-input-handler-path6 \\ \index{mapup-limit-os-waiting-input-ha!ndler-path6}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-waiting-input-handler-path6 \\ \index{getseg-tm-memory-os-waiting-inp!ut-handler-path6}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-waiting-input-handler-path6 \\ \index{mapup-cpu-os-waiting-input-hand!ler-path6}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-waiting-input-handler-path6 \\ \index{mapup-regs-os-waiting-input-han!dler-path6}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-waiting-input-handler-path6 \\ \index{mapup-cc-os-waiting-input-handle!r-path6}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-waiting-input-handler-path6 \\ \index{mapup-error-os-waiting-input-ha!ndler-path6}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-waiting-input-handler-path6 \\ \index{mapup-svcflag-os-waiting-input-!handler-path6}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-waiting-input-handler-path6 \\ \index{mapup-svcid-os-waiting-input-ha!ndler-path6}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-waiting-input-handler-path6 \\ \index{mapup-task-os-waiting-input-han!dler-path6}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-waiting-input-handler-path6 \\ \index{mapup-tasks-os-waiting-input-ha!ndler-path6}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ ({\it{taskid\/}} $\in\;${\bf{N}}${}$))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-waiting-input-handler-path6 \\ \index{mapup-os-tasks-os-waiting-input!-handler-path6}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-waiting-input-handler-path6 \\ \index{mapup-os-ibuffers-os-waiting-inp!ut-handler-path6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{enq-ith-buffer}}\,(\=\+{\rm{tm-ichar}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{getnth})\index{tm-ichar}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\index{enq-ith-buffer})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-waiting-input-handler-path6 \\ \index{mapup-os-obuffers-os-waiting-inp!ut-handler-path6}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-waiting-input-handler-path6 \\ \index{mapup-os-mbuffers-os-waiting-inp!ut-handler-path6}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-waiting-input-handler-path6 \\ \index{tm-rwstate-os-waiting-input-han!dler-path6}
{\rm{tm-rwstate}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{tm-rwstate} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-waiting-input-handler-path6 \\ \index{tm-clock-os-waiting-input-handle!r-path6}
{\rm{tm-clock}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-waiting-input-handler-path6 \\ \index{tm-iports-os-waiting-input-hand!ler-path6}
\=\+{\rm{tm-iports}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-clear-input-interrupt}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-clear-input-interrupt}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-waiting-input-handler-path6 \\ \index{tm-oports-os-waiting-input-hand!ler-path6}
{\rm{tm-oports}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-waiting-input-handler-path6 \\ \index{correctness-of-os-waiting-input!-handler-path6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-waiting-input-handler-path6}}\,({\it{os\/}})\index{os-waiting-input-handler-path6})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-waiting-input-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-waiting-input-interrupt-hand!ler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-waiting-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-waiting-input-handler \\ \index{correctness-of-os-waiting-input!-handler}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-waiting-input-handler}}\,({\it{os\/}})\index{os-waiting-input-handler})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-waiting-input-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-waiting-input-interrupt-hand!ler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-waiting-input-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-running-input-handler-path1 \\ \index{mapup-base-os-running-input-han!dler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-running-input-handler-path1 \\ \index{mapup-limit-os-running-input-ha!ndler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-running-input-handler-path1 \\ \index{getseg-tm-memory-os-running-inp!ut-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-running-input-handler-path1-crock \\ \index{tm-cpu-os-running-input-handler!-path1-crock}
{\rm{tm-cpu}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{tm-cpu} $=$ {\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-running-input-handler-path1-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-running-input-handler-path1 \\ \index{tm-cpu-os-running-input-handler!-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{os-current-taskid}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{os-task-table}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{os-task-table})\-\index{table})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-running-input-handler-path1 \\ \index{mapup-cpu-os-running-input-hand!ler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-running-input-handler-path1 \\ \index{mapup-regs-os-running-input-han!dler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-running-input-handler-path1 \\ \index{mapup-cc-os-running-input-handle!r-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-running-input-handler-path1 \\ \index{mapup-error-os-running-input-ha!ndler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-running-input-handler-path1 \\ \index{mapup-svcflag-os-running-input-!handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-running-input-handler-path1 \\ \index{mapup-svcid-os-running-input-ha!ndler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-running-input-handler-path1 \\ \index{mapup-task-os-running-input-han!dler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-running-input-handler-path1 \\ \index{mapup-tasks-os-running-input-ha!ndler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$({\it{taskid\/}} $\in\;${\bf{N}}${}$))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-running-input-handler-path1 \\ \index{mapup-os-tasks-os-running-input!-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-running-input-handler-path1 \\ \index{mapup-os-ibuffers-os-running-inp!ut-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{qreplace-ith-buffer}}\,(\=\+{\rm{tm-overflow-char}}\,({\rm{tm-ichar}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{getnth})\index{tm-ichar})\index{tm-overflow-char}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\index{qreplace-ith-buffer})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-running-input-handler-path1 \\ \index{mapup-os-obuffers-os-running-inp!ut-handler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-running-input-handler-path1 \\ \index{mapup-os-mbuffers-os-running-inp!ut-handler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-running-input-handler-path1 \\ \index{mapup-queue-os-readyq-os-runnin!g-input-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{enq}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\-\index{enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-running-input-handler-path1 \\ \index{mapup-os-status-table-os-runnin!g-input-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-running-input-handler-path1 \\ \index{tm-rwstate-os-running-input-han!dler-path1}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-rwstate}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{tm-rwstate} $=$ {\rm{tm-rwstate}}\,({\it{os\/}})\index{tm-rwstate})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-running-input-handler-path1 \\ \index{tm-clock-os-running-input-handle!r-path1}
{\rm{tm-clock}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-running-input-handler-path1 \\ \index{tm-iports-os-running-input-hand!ler-path1}
\=\+{\rm{tm-iports}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-clear-input-interrupt}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-clear-input-interrupt}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-running-input-handler-path1 \\ \index{tm-oports-os-running-input-hand!ler-path1}
{\rm{tm-oports}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-running-input-handler-path1 \\ \index{correctness-of-os-running-input!-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-running-input-handler-path1}}\,({\it{os\/}})\index{os-running-input-handler-path1})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-running-input-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-running-input-interrupt-hand!ler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-running-input-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-running-input-handler-path2 \\ \index{mapup-base-os-running-input-han!dler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-running-input-handler-path2 \\ \index{mapup-limit-os-running-input-ha!ndler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-running-input-handler-path2 \\ \index{getseg-tm-memory-os-running-inp!ut-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-running-input-handler-path2-crock \\ \index{tm-cpu-os-running-input-handler!-path2-crock}
{\rm{tm-cpu}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{tm-cpu} $=$ {\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-running-input-handler-path2-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-running-input-handler-path2 \\ \index{tm-cpu-os-running-input-handler!-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{os-task-table}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{os-task-table})\-\index{table})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-running-input-handler-path2 \\ \index{mapup-cpu-os-running-input-hand!ler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-running-input-handler-path2 \\ \index{mapup-regs-os-running-input-han!dler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-running-input-handler-path2 \\ \index{mapup-cc-os-running-input-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-running-input-handler-path2 \\ \index{mapup-error-os-running-input-ha!ndler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-running-input-handler-path2 \\ \index{mapup-svcflag-os-running-input-!handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-running-input-handler-path2 \\ \index{mapup-svcid-os-running-input-ha!ndler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-running-input-handler-path2 \\ \index{mapup-task-os-running-input-han!dler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-running-input-handler-path2 \\ \index{mapup-tasks-os-running-input-ha!ndler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$({\it{taskid\/}} $\in\;${\bf{N}}${}$))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-running-input-handler-path2 \\ \index{mapup-os-tasks-os-running-input!-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-running-input-handler-path2 \\ \index{mapup-os-ibuffers-os-running-inp!ut-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{enq-ith-buffer}}\,(\=\+{\rm{tm-overflow-char}}\,({\rm{tm-ichar}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{getnth})\index{tm-ichar})\index{tm-overflow-char}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\index{enq-ith-buffer})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-running-input-handler-path2 \\ \index{mapup-os-obuffers-os-running-inp!ut-handler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-running-input-handler-path2 \\ \index{mapup-os-mbuffers-os-running-inp!ut-handler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-running-input-handler-path2 \\ \index{mapup-queue-os-readyq-os-runnin!g-input-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{enq}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\-\index{enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-running-input-handler-path2 \\ \index{mapup-os-status-table-os-runnin!g-input-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-running-input-handler-path2 \\ \index{tm-rwstate-os-running-input-han!dler-path2}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-rwstate}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{tm-rwstate} $=$ {\rm{tm-rwstate}}\,({\it{os\/}})\index{tm-rwstate})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-running-input-handler-path2 \\ \index{tm-clock-os-running-input-handle!r-path2}
{\rm{tm-clock}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-running-input-handler-path2 \\ \index{tm-iports-os-running-input-hand!ler-path2}
\=\+{\rm{tm-iports}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-clear-input-interrupt}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-clear-input-interrupt}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-running-input-handler-path2 \\ \index{tm-oports-os-running-input-hand!ler-path2}
{\rm{tm-oports}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-running-input-handler-path2 \\ \index{correctness-of-os-running-input!-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-running-input-handler-path2}}\,({\it{os\/}})\index{os-running-input-handler-path2})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-running-input-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-running-input-interrupt-hand!ler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-running-input-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-running-input-handler-path3 \\ \index{mapup-base-os-running-input-han!dler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-running-input-handler-path3 \\ \index{mapup-limit-os-running-input-ha!ndler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-running-input-handler-path3 \\ \index{getseg-tm-memory-os-running-inp!ut-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-running-input-handler-path3-crock \\ \index{tm-cpu-os-running-input-handler!-path3-crock}
{\rm{tm-cpu}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{tm-cpu} $=$ {\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-running-input-handler-path3-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-running-input-handler-path3 \\ \index{tm-cpu-os-running-input-handler!-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{os-current-taskid}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{os-task-table}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{os-task-table})\-\index{table})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-running-input-handler-path3 \\ \index{mapup-cpu-os-running-input-hand!ler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-running-input-handler-path3 \\ \index{mapup-regs-os-running-input-han!dler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-running-input-handler-path3 \\ \index{mapup-cc-os-running-input-handle!r-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-running-input-handler-path3 \\ \index{mapup-error-os-running-input-ha!ndler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-running-input-handler-path3 \\ \index{mapup-svcflag-os-running-input-!handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-running-input-handler-path3 \\ \index{mapup-svcid-os-running-input-ha!ndler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-running-input-handler-path3 \\ \index{mapup-task-os-running-input-han!dler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-running-input-handler-path3 \\ \index{mapup-tasks-os-running-input-ha!ndler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$({\it{taskid\/}} $\in\;${\bf{N}}${}$))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-running-input-handler-path3 \\ \index{mapup-os-tasks-os-running-input!-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-running-input-handler-path3 \\ \index{mapup-os-ibuffers-os-running-inp!ut-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{enq-ith-buffer}}\,(\=\+{\rm{tm-ichar}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{getnth})\index{tm-ichar}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\index{enq-ith-buffer})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-running-input-handler-path3 \\ \index{mapup-os-obuffers-os-running-inp!ut-handler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-running-input-handler-path3 \\ \index{mapup-os-mbuffers-os-running-inp!ut-handler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-running-input-handler-path3 \\ \index{mapup-queue-os-readyq-os-runnin!g-input-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{enq}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\-\index{enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-running-input-handler-path3 \\ \index{mapup-os-status-table-os-runnin!g-input-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-running-input-handler-path3 \\ \index{tm-rwstate-os-running-input-han!dler-path3}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-rwstate}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{tm-rwstate} $=$ {\rm{tm-rwstate}}\,({\it{os\/}})\index{tm-rwstate})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-running-input-handler-path3 \\ \index{tm-clock-os-running-input-handle!r-path3}
{\rm{tm-clock}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-running-input-handler-path3 \\ \index{tm-iports-os-running-input-hand!ler-path3}
\=\+{\rm{tm-iports}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-clear-input-interrupt}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-clear-input-interrupt}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-running-input-handler-path3 \\ \index{tm-oports-os-running-input-hand!ler-path3}
{\rm{tm-oports}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-running-input-handler-path3 \\ \index{correctness-of-os-running-input!-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-running-input-handler-path3}}\,({\it{os\/}})\index{os-running-input-handler-path3})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-running-input-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-running-input-interrupt-hand!ler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-running-input-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-running-input-handler-path4 \\ \index{mapup-base-os-running-input-han!dler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-running-input-handler-path4 \\ \index{mapup-limit-os-running-input-ha!ndler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-running-input-handler-path4 \\ \index{getseg-tm-memory-os-running-inp!ut-handler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-running-input-handler-path4-crock \\ \index{tm-cpu-os-running-input-handler!-path4-crock}
{\rm{tm-cpu}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{tm-cpu} $=$ {\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-running-input-handler-path4-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-running-input-handler-path4 \\ \index{tm-cpu-os-running-input-handler!-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{os-current-taskid}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{os-task-table}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{os-task-table})\-\index{table})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-running-input-handler-path4 \\ \index{mapup-cpu-os-running-input-hand!ler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-running-input-handler-path4 \\ \index{mapup-regs-os-running-input-han!dler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-running-input-handler-path4 \\ \index{mapup-cc-os-running-input-handle!r-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-running-input-handler-path4 \\ \index{mapup-error-os-running-input-ha!ndler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-running-input-handler-path4 \\ \index{mapup-svcflag-os-running-input-!handler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-running-input-handler-path4 \\ \index{mapup-svcid-os-running-input-ha!ndler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-running-input-handler-path4 \\ \index{mapup-task-os-running-input-han!dler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-running-input-handler-path4 \\ \index{mapup-tasks-os-running-input-ha!ndler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ ({\it{taskid\/}} $\in\;${\bf{N}}${}$)))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-running-input-handler-path4 \\ \index{mapup-os-tasks-os-running-input!-handler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-running-input-handler-path4 \\ \index{mapup-os-ibuffers-os-running-inp!ut-handler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{qreplace-ith-buffer}}\,(\=\+{\rm{tm-overflow-char}}\,({\rm{tm-ichar}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{getnth})\index{tm-ichar})\index{tm-overflow-char}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\index{qreplace-ith-buffer})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-running-input-handler-path4 \\ \index{mapup-os-obuffers-os-running-inp!ut-handler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-running-input-handler-path4 \\ \index{mapup-os-mbuffers-os-running-inp!ut-handler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-running-input-handler-path4 \\ \index{tm-rwstate-os-running-input-han!dler-path4}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-rwstate}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{tm-rwstate} $=$ {\rm{tm-rwstate}}\,({\it{os\/}})\index{tm-rwstate})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-running-input-handler-path4 \\ \index{tm-clock-os-running-input-handle!r-path4}
{\rm{tm-clock}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-running-input-handler-path4 \\ \index{tm-iports-os-running-input-hand!ler-path4}
\=\+{\rm{tm-iports}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-clear-input-interrupt}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-clear-input-interrupt}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-running-input-handler-path4 \\ \index{tm-oports-os-running-input-hand!ler-path4}
{\rm{tm-oports}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-running-input-handler-path4 \\ \index{correctness-of-os-running-input!-handler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-running-input-handler-path4}}\,({\it{os\/}})\index{os-running-input-handler-path4})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-running-input-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-running-input-interrupt-hand!ler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-running-input-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-running-input-handler-path5 \\ \index{mapup-base-os-running-input-han!dler-path5}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-running-input-handler-path5 \\ \index{mapup-limit-os-running-input-ha!ndler-path5}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-running-input-handler-path5 \\ \index{getseg-tm-memory-os-running-inp!ut-handler-path5}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-running-input-handler-path5-crock \\ \index{tm-cpu-os-running-input-handler!-path5-crock}
{\rm{tm-cpu}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{tm-cpu} $=$ {\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-running-input-handler-path5-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-running-input-handler-path5 \\ \index{tm-cpu-os-running-input-handler!-path5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{os-current-taskid}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{os-task-table}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{os-task-table})\-\index{table})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-running-input-handler-path5 \\ \index{mapup-cpu-os-running-input-hand!ler-path5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-running-input-handler-path5 \\ \index{mapup-regs-os-running-input-han!dler-path5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-running-input-handler-path5 \\ \index{mapup-cc-os-running-input-handle!r-path5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-running-input-handler-path5 \\ \index{mapup-error-os-running-input-ha!ndler-path5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-running-input-handler-path5 \\ \index{mapup-svcflag-os-running-input-!handler-path5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-running-input-handler-path5 \\ \index{mapup-svcid-os-running-input-ha!ndler-path5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-running-input-handler-path5 \\ \index{mapup-task-os-running-input-han!dler-path5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-running-input-handler-path5 \\ \index{mapup-tasks-os-running-input-ha!ndler-path5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ ({\it{taskid\/}} $\in\;${\bf{N}}${}$)))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-running-input-handler-path5 \\ \index{mapup-os-tasks-os-running-input!-handler-path5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-running-input-handler-path5 \\ \index{mapup-os-ibuffers-os-running-inp!ut-handler-path5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{enq-ith-buffer}}\,(\=\+{\rm{tm-overflow-char}}\,({\rm{tm-ichar}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{getnth})\index{tm-ichar})\index{tm-overflow-char}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\index{enq-ith-buffer})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-running-input-handler-path5 \\ \index{mapup-os-obuffers-os-running-inp!ut-handler-path5}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-running-input-handler-path5 \\ \index{mapup-os-mbuffers-os-running-inp!ut-handler-path5}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-running-input-handler-path5 \\ \index{tm-rwstate-os-running-input-han!dler-path5}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-rwstate}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{tm-rwstate} $=$ {\rm{tm-rwstate}}\,({\it{os\/}})\index{tm-rwstate})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-running-input-handler-path5 \\ \index{tm-clock-os-running-input-handle!r-path5}
{\rm{tm-clock}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-running-input-handler-path5 \\ \index{tm-iports-os-running-input-hand!ler-path5}
\=\+{\rm{tm-iports}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-clear-input-interrupt}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-clear-input-interrupt}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-running-input-handler-path5 \\ \index{tm-oports-os-running-input-hand!ler-path5}
{\rm{tm-oports}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-running-input-handler-path5 \\ \index{correctness-of-os-running-input!-handler-path5}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;${\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp})\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-running-input-handler-path5}}\,({\it{os\/}})\index{os-running-input-handler-path5})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-running-input-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-running-input-interrupt-hand!ler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-running-input-handler-path5.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-running-input-handler-path6 \\ \index{mapup-base-os-running-input-han!dler-path6}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-running-input-handler-path6 \\ \index{mapup-limit-os-running-input-ha!ndler-path6}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-running-input-handler-path6 \\ \index{getseg-tm-memory-os-running-inp!ut-handler-path6}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-running-input-handler-path6-crock \\ \index{tm-cpu-os-running-input-handler!-path6-crock}
{\rm{tm-cpu}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{tm-cpu} $=$ {\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-running-input-handler-path6-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-running-input-handler-path6 \\ \index{tm-cpu-os-running-input-handler!-path6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{os-current-taskid}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{os-task-table}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{os-task-table})\-\index{table})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-running-input-handler-path6 \\ \index{mapup-cpu-os-running-input-hand!ler-path6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-running-input-handler-path6 \\ \index{mapup-regs-os-running-input-han!dler-path6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-running-input-handler-path6 \\ \index{mapup-cc-os-running-input-handle!r-path6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-running-input-handler-path6 \\ \index{mapup-error-os-running-input-ha!ndler-path6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-running-input-handler-path6 \\ \index{mapup-svcflag-os-running-input-!handler-path6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-running-input-handler-path6 \\ \index{mapup-svcid-os-running-input-ha!ndler-path6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-running-input-handler-path6 \\ \index{mapup-task-os-running-input-han!dler-path6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-running-input-handler-path6 \\ \index{mapup-tasks-os-running-input-ha!ndler-path6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ ({\it{taskid\/}} $\in\;${\bf{N}}${}$)))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-running-input-handler-path6 \\ \index{mapup-os-tasks-os-running-input!-handler-path6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-running-input-handler-path6 \\ \index{mapup-os-ibuffers-os-running-inp!ut-handler-path6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{enq-ith-buffer}}\,(\=\+{\rm{tm-ichar}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{getnth})\index{tm-ichar}, \\ 
{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\index{enq-ith-buffer})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-running-input-handler-path6 \\ \index{mapup-os-obuffers-os-running-inp!ut-handler-path6}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-running-input-handler-path6 \\ \index{mapup-os-mbuffers-os-running-inp!ut-handler-path6}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-running-input-handler-path6 \\ \index{tm-rwstate-os-running-input-han!dler-path6}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-rwstate}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{tm-rwstate} $=$ {\rm{tm-rwstate}}\,({\it{os\/}})\index{tm-rwstate})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-running-input-handler-path6 \\ \index{tm-clock-os-running-input-handle!r-path6}
{\rm{tm-clock}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-running-input-handler-path6 \\ \index{tm-iports-os-running-input-hand!ler-path6}
\=\+{\rm{tm-iports}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{tm-iports} \\ 
$=$$\;\;\;\;${\rm{tm-clear-input-interrupt}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-clear-input-interrupt}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-running-input-handler-path6 \\ \index{tm-oports-os-running-input-hand!ler-path6}
{\rm{tm-oports}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{tm-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-running-input-handler-path6 \\ \index{correctness-of-os-running-input!-handler-path6}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{5}})\- \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{array-qfullp}}\,({\rm{os-current-ibuffer}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\it{os\/}})\-\index{os-current-ibuffer})\index{array-qfullp}) \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{tm-iport-errorp}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\-\index{tm-iport-errorp}))\-)\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-running-input-handler-path6}}\,({\it{os\/}})\index{os-running-input-handler-path6})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-running-input-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-running-input-interrupt-hand!ler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-running-input-handler-path6.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-running-input-handler \\ \index{correctness-of-os-running-input!-handler}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-running-input-handler}}\,({\it{os\/}})\index{os-running-input-handler})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-running-input-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-running-input-interrupt-hand!ler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-running-input-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-waiting-output-handler-path1 \\ \index{mapup-base-os-waiting-output-ha!ndler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-waiting-output-handler-path1 \\ \index{mapup-limit-os-waiting-output-h!andler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-waiting-output-handler-path1 \\ \index{getseg-tm-memory-os-waiting-outp!ut-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-waiting-output-handler-path1.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 TM-CPU-OS-WAITING-OUTPUT-HANDLER-PATH1-CROCK
 (REWRITE)
 (EQUAL
  (TM-CPU (OS-WAITING-OUTPUT-HANDLER-PATH1 OS))
  (CONS
   (GETNTH '0
           (GETSEG '0
                   '8
                   (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                           (TABLE '9 (OS-TASK-TABLE OS)))))
   (CONS
    (GETNTH '1
            (GETSEG '0
                    '8
                    (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                            (TABLE '9 (OS-TASK-TABLE OS)))))
    (CONS
     (GETNTH '2
             (GETSEG '0
                     '8
                     (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                             (TABLE '9 (OS-TASK-TABLE OS)))))
     (CONS
      (GETNTH '3
              (GETSEG '0
                      '8
                      (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                              (TABLE '9 (OS-TASK-TABLE OS)))))
      (CONS
       (GETNTH '4
               (GETSEG '0
                       '8
                       (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                               (TABLE '9 (OS-TASK-TABLE OS)))))
       (CONS
        (GETNTH '5
                (GETSEG '0
                        '8
                        (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                (TABLE '9 (OS-TASK-TABLE OS)))))
        (CONS
         (GETNTH '6
                 (GETSEG '0
                         '8
                         (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                 (TABLE '9 (OS-TASK-TABLE OS)))))
         (CONS
          (GETNTH '7
                  (GETSEG '0
                          '8
                          (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                  (TABLE '9 (OS-TASK-TABLE OS)))))
          (CONS
           (TM-PACK-PSW
            (TM-UNPACK-CC
             (GETNTH
                    (PLUS '8
                          (TIMES '9
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    (OS-TASK-TABLE OS)))
            (TM-UNPACK-ERROR
             (GETNTH
                    (PLUS '8
                          (TIMES '9
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    (OS-TASK-TABLE OS)))
            (TM-UNPACK-SVCFLAG
             (GETNTH
                    (PLUS '8
                          (TIMES '9
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    (OS-TASK-TABLE OS)))
            (TM-UNPACK-SVCID
             (GETNTH
                    (PLUS '8
                          (TIMES '9
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    (OS-TASK-TABLE OS))))
           'NIL))))))))))
 ((ENABLE OS-WAITING-OUTPUT-HANDLER-PATH1 TM-CPU TM-R0 TM-R1 TM-R2 TM-R3 TM-R4
          TM-R5 TM-R6 TM-R7 TM-UNPACK-CC TM-UNPACK-ERROR TM-UNPACK-SVCFLAG
          TM-UNPACK-SVCID)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable tm-cpu-os-waiting-output-handler-path1-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-waiting-output-handler-path1 \\ \index{tm-cpu-os-waiting-output-handle!r-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{os-current-taskid}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{os-task-table}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{os-task-table})\-\index{table})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-waiting-output-handler-path1 \\ \index{mapup-cpu-os-waiting-output-han!dler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-waiting-output-handler-path1 \\ \index{mapup-regs-os-waiting-output-ha!ndler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-waiting-output-handler-path1 \\ \index{mapup-cc-os-waiting-output-hand!ler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-waiting-output-handler-path1 \\ \index{mapup-error-os-waiting-output-h!andler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-waiting-output-handler-path1 \\ \index{mapup-svcflag-os-waiting-output!-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-waiting-output-handler-path1 \\ \index{mapup-svcid-os-waiting-output-h!andler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-waiting-output-handler-path1 \\ \index{mapup-task-os-waiting-output-ha!ndler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-waiting-output-handler-path1 \\ \index{mapup-tasks-os-waiting-output-h!andler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} $\wedge$ ({\it{taskid\/}} $\in\;${\bf{N}}${}$)))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-waiting-output-handler-path1 \\ \index{mapup-os-tasks-os-waiting-output!-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-waiting-output-handler-path1 \\ \index{mapup-os-ibuffers-os-waiting-outp!ut-handler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-waiting-output-handler-path1 \\ \index{mapup-os-obuffers-os-waiting-outp!ut-handler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-waiting-output-handler-path1 \\ \index{mapup-os-mbuffers-os-waiting-outp!ut-handler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-waiting-output-handler-path1 \\ \index{mapup-queue-os-readyq-os-waitin!g-output-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{enq}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\-\index{enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-waiting-output-handler-path1 \\ \index{mapup-os-status-table-os-waitin!g-output-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-waiting-output-handler-path1 \\ \index{tm-rwstate-os-waiting-output-ha!ndler-path1}
{\rm{tm-rwstate}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{tm-rwstate} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-waiting-output-handler-path1 \\ \index{tm-clock-os-waiting-output-hand!ler-path1}
{\rm{tm-clock}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{tm-clock} $=$ {\tt{'}}{\tt{1000}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-waiting-output-handler-path1 \\ \index{tm-iports-os-waiting-output-han!dler-path1}
{\rm{tm-iports}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-waiting-output-handler-path1 \\ \index{tm-oports-os-waiting-output-han!dler-path1}
\=\+{\rm{tm-oports}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-clear-output-interrupt}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\-\index{tm-clear-output-interrupt}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-waiting-to-outputp-mapup-os \\ \index{ak-waiting-to-outputp-mapup-os}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;${\rm{ak-waiting-to-outputp}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-waiting-to-outputp}\-
\end{tabbing}


\noindent{\sc Event}:   Disable ak-waiting-to-outputp-mapup-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-waiting-output-handler-path1 \\ \index{correctness-of-os-waiting-output!-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-waiting-output-handler-path1}}\,({\it{os\/}})\index{os-waiting-output-handler-path1})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-waiting-output-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-waiting-output-interrupt-han!dler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-waiting-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-waiting-output-handler-path2 \\ \index{mapup-base-os-waiting-output-ha!ndler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-waiting-output-handler-path2 \\ \index{mapup-limit-os-waiting-output-h!andler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-waiting-output-handler-path2 \\ \index{getseg-tm-memory-os-waiting-outp!ut-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-waiting-output-handler-path2.

\addvspace{18pt}

%\item 
\begin{verbatim}


(PROVE-LEMMA
 TM-CPU-OS-WAITING-OUTPUT-HANDLER-PATH2-CROCK
 (REWRITE)
 (EQUAL
  (TM-CPU (OS-WAITING-OUTPUT-HANDLER-PATH2 OS))
  (CONS
   (GETNTH '0
           (GETSEG '0
                   '8
                   (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                           (TABLE '9 (OS-TASK-TABLE OS)))))
   (CONS
    (GETNTH '1
            (GETSEG '0
                    '8
                    (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                            (TABLE '9 (OS-TASK-TABLE OS)))))
    (CONS
     (GETNTH '2
             (GETSEG '0
                     '8
                     (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                             (TABLE '9 (OS-TASK-TABLE OS)))))
     (CONS
      (GETNTH '3
              (GETSEG '0
                      '8
                      (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                              (TABLE '9 (OS-TASK-TABLE OS)))))
      (CONS
       (GETNTH '4
               (GETSEG '0
                       '8
                       (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                               (TABLE '9 (OS-TASK-TABLE OS)))))
       (CONS
        (GETNTH '5
                (GETSEG '0
                        '8
                        (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                (TABLE '9 (OS-TASK-TABLE OS)))))
        (CONS
         (GETNTH '6
                 (GETSEG '0
                         '8
                         (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                 (TABLE '9 (OS-TASK-TABLE OS)))))
         (CONS
          (GETNTH '7
                  (GETSEG '0
                          '8
                          (GETNTH (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))
                                  (TABLE '9 (OS-TASK-TABLE OS)))))
          (CONS
           (TM-PACK-PSW
            (TM-UNPACK-CC
             (GETNTH
                    (PLUS '8
                          (TIMES '9
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    (OS-TASK-TABLE OS)))
            (TM-UNPACK-ERROR
             (GETNTH
                    (PLUS '8
                          (TIMES '9
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    (OS-TASK-TABLE OS)))
            (TM-UNPACK-SVCFLAG
             (GETNTH
                    (PLUS '8
                          (TIMES '9
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    (OS-TASK-TABLE OS)))
            (TM-UNPACK-SVCID
             (GETNTH
                    (PLUS '8
                          (TIMES '9
                                 (TM-INTERRUPTING-OUTPUT-PORT (TM-OPORTS OS))))
                    (OS-TASK-TABLE OS))))
           'NIL))))))))))
 ((ENABLE OS-WAITING-OUTPUT-HANDLER-PATH2 TM-CPU TM-R0 TM-R1 TM-R2 TM-R3 TM-R4
          TM-R5 TM-R6 TM-R7 TM-UNPACK-CC TM-UNPACK-ERROR TM-UNPACK-SVCFLAG
          TM-UNPACK-SVCID)
  (ENABLE-THEORY TM-SHELLS GROUND-ZERO)
  (DISABLE-THEORY T)))
\end{verbatim}



\noindent{\sc Event}:   Disable tm-cpu-os-waiting-output-handler-path2-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-waiting-output-handler-path2 \\ \index{tm-cpu-os-waiting-output-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{os-task-table}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{os-task-table})\-\index{table})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-waiting-output-handler-path2 \\ \index{mapup-cpu-os-waiting-output-han!dler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-waiting-output-handler-path2 \\ \index{mapup-regs-os-waiting-output-ha!ndler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-waiting-output-handler-path2 \\ \index{mapup-cc-os-waiting-output-hand!ler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-waiting-output-handler-path2 \\ \index{mapup-error-os-waiting-output-h!andler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-waiting-output-handler-path2 \\ \index{mapup-svcflag-os-waiting-output!-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-waiting-output-handler-path2 \\ \index{mapup-svcid-os-waiting-output-h!andler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-waiting-output-handler-path2 \\ \index{mapup-task-os-waiting-output-ha!ndler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-waiting-output-handler-path2 \\ \index{mapup-tasks-os-waiting-output-h!andler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} $\wedge$ ({\it{taskid\/}} $\in\;${\bf{N}}${}$)))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-waiting-output-handler-path2 \\ \index{mapup-os-tasks-os-waiting-output!-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-waiting-output-handler-path2 \\ \index{mapup-os-ibuffers-os-waiting-outp!ut-handler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-waiting-output-handler-path2 \\ \index{mapup-os-obuffers-os-waiting-outp!ut-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{deq-ith-buffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\index{deq-ith-buffer})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-waiting-output-handler-path2 \\ \index{mapup-os-mbuffers-os-waiting-outp!ut-handler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-waiting-output-handler-path2 \\ \index{mapup-queue-os-readyq-os-waitin!g-output-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{enq}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\-\index{enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-waiting-output-handler-path2 \\ \index{mapup-os-status-table-os-waitin!g-output-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-waiting-output-handler-path2 \\ \index{tm-rwstate-os-waiting-output-ha!ndler-path2}
{\rm{tm-rwstate}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{tm-rwstate} $=$ {\tt{'}}{\tt{0}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-waiting-output-handler-path2 \\ \index{tm-clock-os-waiting-output-hand!ler-path2}
{\rm{tm-clock}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{tm-clock} $=$ {\tt{'}}{\tt{1000}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-waiting-output-handler-path2 \\ \index{tm-iports-os-waiting-output-han!dler-path2}
{\rm{tm-iports}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-waiting-output-handler-path2 \\ \index{tm-oports-os-waiting-output-han!dler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-oports}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-start-output}}\,(\=\+{\rm{qfirst}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\index{getnth})\index{qfirst}, \\ 
{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\-\index{tm-start-output})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-waiting-output-handler-path2 \\ \index{correctness-of-os-waiting-output!-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-waiting-output-handler-path2}}\,({\it{os\/}})\index{os-waiting-output-handler-path2})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-waiting-output-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-waiting-output-interrupt-han!dler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-waiting-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-waiting-output-handler-path3 \\ \index{mapup-base-os-waiting-output-ha!ndler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-waiting-output-handler-path3 \\ \index{mapup-limit-os-waiting-output-h!andler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-waiting-output-handler-path3 \\ \index{getseg-tm-memory-os-waiting-outp!ut-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-waiting-output-handler-path3 \\ \index{mapup-cpu-os-waiting-output-han!dler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-waiting-output-handler-path3 \\ \index{mapup-regs-os-waiting-output-ha!ndler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-waiting-output-handler-path3 \\ \index{mapup-cc-os-waiting-output-hand!ler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-waiting-output-handler-path3 \\ \index{mapup-error-os-waiting-output-h!andler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-waiting-output-handler-path3 \\ \index{mapup-svcflag-os-waiting-output!-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-waiting-output-handler-path3 \\ \index{mapup-svcid-os-waiting-output-h!andler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-waiting-output-handler-path3 \\ \index{mapup-task-os-waiting-output-ha!ndler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-waiting-output-handler-path3 \\ \index{mapup-tasks-os-waiting-output-h!andler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ ({\it{taskid\/}} $\in\;${\bf{N}}${}$))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-waiting-output-handler-path3 \\ \index{mapup-os-tasks-os-waiting-output!-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-waiting-output-handler-path3 \\ \index{mapup-os-ibuffers-os-waiting-outp!ut-handler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-waiting-output-handler-path3 \\ \index{mapup-os-obuffers-os-waiting-outp!ut-handler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-waiting-output-handler-path3 \\ \index{mapup-os-mbuffers-os-waiting-outp!ut-handler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-waiting-output-handler-path3 \\ \index{tm-rwstate-os-waiting-output-ha!ndler-path3}
{\rm{tm-rwstate}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{tm-rwstate} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-waiting-output-handler-path3 \\ \index{tm-clock-os-waiting-output-hand!ler-path3}
{\rm{tm-clock}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-waiting-output-handler-path3 \\ \index{tm-iports-os-waiting-output-han!dler-path3}
{\rm{tm-iports}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-waiting-output-handler-path3 \\ \index{tm-oports-os-waiting-output-han!dler-path3}
\=\+{\rm{tm-oports}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-clear-output-interrupt}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\-\index{tm-clear-output-interrupt}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-ak-waiting-to-outputp-mapup-os \\ \index{not-ak-waiting-to-outputp-mapup!-os}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+{\tt{'}}{\tt{2}} $*$ {\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{4}})\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{ak-waiting-to-outputp}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-waiting-to-outputp})\-
\end{tabbing}


\noindent{\sc Event}:   Disable not-ak-waiting-to-outputp-mapup-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-waiting-output-handler-path3 \\ \index{correctness-of-os-waiting-output!-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-waiting-output-handler-path3}}\,({\it{os\/}})\index{os-waiting-output-handler-path3})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-waiting-output-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-waiting-output-interrupt-han!dler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-waiting-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-waiting-output-handler-path4 \\ \index{mapup-base-os-waiting-output-ha!ndler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-waiting-output-handler-path4 \\ \index{mapup-limit-os-waiting-output-h!andler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-waiting-output-handler-path4 \\ \index{getseg-tm-memory-os-waiting-outp!ut-handler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-waiting-output-handler-path4 \\ \index{mapup-cpu-os-waiting-output-han!dler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-waiting-output-handler-path4 \\ \index{mapup-regs-os-waiting-output-ha!ndler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-waiting-output-handler-path4 \\ \index{mapup-cc-os-waiting-output-hand!ler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-waiting-output-handler-path4 \\ \index{mapup-error-os-waiting-output-h!andler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-waiting-output-handler-path4 \\ \index{mapup-svcflag-os-waiting-output!-handler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-waiting-output-handler-path4 \\ \index{mapup-svcid-os-waiting-output-h!andler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-waiting-output-handler-path4 \\ \index{mapup-task-os-waiting-output-ha!ndler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ (({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-waiting-output-handler-path4 \\ \index{mapup-tasks-os-waiting-output-h!andler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} $\wedge$ ({\it{taskid\/}} $\in\;${\bf{N}}${}$))) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-waiting-output-handler-path4 \\ \index{mapup-os-tasks-os-waiting-output!-handler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-waiting-output-handler-path4 \\ \index{mapup-os-ibuffers-os-waiting-outp!ut-handler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-waiting-output-handler-path4 \\ \index{mapup-os-obuffers-os-waiting-outp!ut-handler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{deq-ith-buffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\index{deq-ith-buffer})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-waiting-output-handler-path4 \\ \index{mapup-os-mbuffers-os-waiting-outp!ut-handler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-waiting-output-handler-path4 \\ \index{tm-rwstate-os-waiting-output-ha!ndler-path4}
{\rm{tm-rwstate}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{tm-rwstate} $=$ {\tt{'}}{\tt{1}}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-waiting-output-handler-path4 \\ \index{tm-clock-os-waiting-output-hand!ler-path4}
{\rm{tm-clock}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-waiting-output-handler-path4 \\ \index{tm-iports-os-waiting-output-han!dler-path4}
{\rm{tm-iports}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-waiting-output-handler-path4 \\ \index{tm-oports-os-waiting-output-han!dler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-oports}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-start-output}}\,(\=\+{\rm{qfirst}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\index{getnth})\index{qfirst}, \\ 
{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\-\index{tm-start-output})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-waiting-output-handler-path4 \\ \index{correctness-of-os-waiting-output!-handler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-waiting-output-handler-path4}}\,({\it{os\/}})\index{os-waiting-output-handler-path4})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-waiting-output-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-waiting-output-interrupt-han!dler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-waiting-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-waiting-output-handler \\ \index{correctness-of-os-waiting-output!-handler}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} $\wedge$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-waiting-output-handler}}\,({\it{os\/}})\index{os-waiting-output-handler})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-waiting-output-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-waiting-output-interrupt-han!dler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-waiting-output-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-running-output-handler-path1 \\ \index{mapup-base-os-running-output-ha!ndler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-running-output-handler-path1 \\ \index{mapup-limit-os-running-output-h!andler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-running-output-handler-path1 \\ \index{getseg-tm-memory-os-running-outp!ut-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-running-output-handler-path1-crock \\ \index{tm-cpu-os-running-output-handle!r-path1-crock}
{\rm{tm-cpu}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{tm-cpu} $=$ {\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-running-output-handler-path1-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-running-output-handler-path1 \\ \index{tm-cpu-os-running-output-handle!r-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{os-current-taskid}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{os-task-table}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{os-task-table})\-\index{table})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-running-output-handler-path1 \\ \index{mapup-cpu-os-running-output-han!dler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-running-output-handler-path1 \\ \index{mapup-regs-os-running-output-ha!ndler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-running-output-handler-path1 \\ \index{mapup-cc-os-running-output-hand!ler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-running-output-handler-path1 \\ \index{mapup-error-os-running-output-h!andler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-running-output-handler-path1 \\ \index{mapup-svcflag-os-running-output!-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-running-output-handler-path1 \\ \index{mapup-svcid-os-running-output-h!andler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-running-output-handler-path1 \\ \index{mapup-task-os-running-output-ha!ndler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-running-output-handler-path1 \\ \index{mapup-tasks-os-running-output-h!andler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$({\it{taskid\/}} $\in\;${\bf{N}}${}$))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-running-output-handler-path1 \\ \index{mapup-os-tasks-os-running-output!-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-running-output-handler-path1 \\ \index{mapup-os-ibuffers-os-running-outp!ut-handler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-running-output-handler-path1 \\ \index{mapup-os-obuffers-os-running-outp!ut-handler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-running-output-handler-path1 \\ \index{mapup-os-mbuffers-os-running-outp!ut-handler-path1}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-running-output-handler-path1 \\ \index{mapup-queue-os-readyq-os-runnin!g-output-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{enq}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\-\index{enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-running-output-handler-path1 \\ \index{mapup-os-status-table-os-runnin!g-output-handler-path1}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-running-output-handler-path1 \\ \index{tm-rwstate-os-running-output-ha!ndler-path1}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-rwstate}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{tm-rwstate} $=$ {\rm{tm-rwstate}}\,({\it{os\/}})\index{tm-rwstate})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-running-output-handler-path1 \\ \index{tm-clock-os-running-output-hand!ler-path1}
{\rm{tm-clock}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-running-output-handler-path1 \\ \index{tm-iports-os-running-output-han!dler-path1}
{\rm{tm-iports}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-running-output-handler-path1 \\ \index{tm-oports-os-running-output-han!dler-path1}
\=\+{\rm{tm-oports}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-clear-output-interrupt}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\-\index{tm-clear-output-interrupt}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-running-output-handler-path1 \\ \index{correctness-of-os-running-output!-handler-path1}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-running-output-handler-path1}}\,({\it{os\/}})\index{os-running-output-handler-path1})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-running-output-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-running-output-interrupt-han!dler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-running-output-handler-path1.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-running-output-handler-path2 \\ \index{mapup-base-os-running-output-ha!ndler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-running-output-handler-path2 \\ \index{mapup-limit-os-running-output-h!andler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-running-output-handler-path2 \\ \index{getseg-tm-memory-os-running-outp!ut-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-running-output-handler-path2-crock \\ \index{tm-cpu-os-running-output-handle!r-path2-crock}
{\rm{tm-cpu}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{tm-cpu} $=$ {\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-running-output-handler-path2-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-running-output-handler-path2 \\ \index{tm-cpu-os-running-output-handle!r-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{os-current-taskid}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{os-task-table}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{os-task-table})\-\index{table})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-running-output-handler-path2 \\ \index{mapup-cpu-os-running-output-han!dler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-running-output-handler-path2 \\ \index{mapup-regs-os-running-output-ha!ndler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-running-output-handler-path2 \\ \index{mapup-cc-os-running-output-hand!ler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-running-output-handler-path2 \\ \index{mapup-error-os-running-output-h!andler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-running-output-handler-path2 \\ \index{mapup-svcflag-os-running-output!-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-running-output-handler-path2 \\ \index{mapup-svcid-os-running-output-h!andler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-running-output-handler-path2 \\ \index{mapup-task-os-running-output-ha!ndler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-running-output-handler-path2 \\ \index{mapup-tasks-os-running-output-h!andler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$({\it{taskid\/}} $\in\;${\bf{N}}${}$))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-running-output-handler-path2 \\ \index{mapup-os-tasks-os-running-output!-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-running-output-handler-path2 \\ \index{mapup-os-ibuffers-os-running-outp!ut-handler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-running-output-handler-path2 \\ \index{mapup-os-obuffers-os-running-outp!ut-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{deq-ith-buffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\index{deq-ith-buffer})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-running-output-handler-path2 \\ \index{mapup-os-mbuffers-os-running-outp!ut-handler-path2}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-queue-os-readyq-os-running-output-handler-path2 \\ \index{mapup-queue-os-readyq-os-runnin!g-output-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{os-readyq})\index{mapup-queue} \\ 
$=$$\;\;\;\;${\rm{enq}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\-\index{enq})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-queue-os-readyq-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-status-table-os-running-output-handler-path2 \\ \index{mapup-os-status-table-os-runnin!g-output-handler-path2}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{os-status-table})\index{table} \\ 
$=$$\;\;\;\;${\rm{putnth}}\,(\=\+{\tt{'}}{\tt{(}}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{)}}, \\ 
{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{table}}\,({\tt{'}}{\tt{2}}, {\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\index{table})\-\index{putnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-status-table-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-running-output-handler-path2 \\ \index{tm-rwstate-os-running-output-ha!ndler-path2}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-rwstate}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{tm-rwstate} $=$ {\rm{tm-rwstate}}\,({\it{os\/}})\index{tm-rwstate})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-running-output-handler-path2 \\ \index{tm-clock-os-running-output-hand!ler-path2}
{\rm{tm-clock}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-running-output-handler-path2 \\ \index{tm-iports-os-running-output-han!dler-path2}
{\rm{tm-iports}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-running-output-handler-path2 \\ \index{tm-oports-os-running-output-han!dler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-oports}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-start-output}}\,(\=\+{\rm{qfirst}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\index{getnth})\index{qfirst}, \\ 
{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\-\index{tm-start-output})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-running-output-handler-path2 \\ \index{correctness-of-os-running-output!-handler-path2}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-running-output-handler-path2}}\,({\it{os\/}})\index{os-running-output-handler-path2})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-running-output-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-running-output-interrupt-han!dler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-running-output-handler-path2.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-running-output-handler-path3 \\ \index{mapup-base-os-running-output-ha!ndler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-running-output-handler-path3 \\ \index{mapup-limit-os-running-output-h!andler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-running-output-handler-path3 \\ \index{getseg-tm-memory-os-running-outp!ut-handler-path3}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-running-output-handler-path3-crock \\ \index{tm-cpu-os-running-output-handle!r-path3-crock}
{\rm{tm-cpu}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{tm-cpu} $=$ {\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-running-output-handler-path3-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-running-output-handler-path3 \\ \index{tm-cpu-os-running-output-handle!r-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{os-current-taskid}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{os-task-table}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{os-task-table})\-\index{table})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-running-output-handler-path3 \\ \index{mapup-cpu-os-running-output-han!dler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-running-output-handler-path3 \\ \index{mapup-regs-os-running-output-ha!ndler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-running-output-handler-path3 \\ \index{mapup-cc-os-running-output-hand!ler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-running-output-handler-path3 \\ \index{mapup-error-os-running-output-h!andler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-running-output-handler-path3 \\ \index{mapup-svcflag-os-running-output!-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-running-output-handler-path3 \\ \index{mapup-svcid-os-running-output-h!andler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-running-output-handler-path3 \\ \index{mapup-task-os-running-output-ha!ndler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-running-output-handler-path3 \\ \index{mapup-tasks-os-running-output-h!andler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} $\wedge$ ({\it{taskid\/}} $\in\;${\bf{N}}${}$)))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-running-output-handler-path3 \\ \index{mapup-os-tasks-os-running-output!-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-running-output-handler-path3 \\ \index{mapup-os-ibuffers-os-running-outp!ut-handler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-running-output-handler-path3 \\ \index{mapup-os-obuffers-os-running-outp!ut-handler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-running-output-handler-path3 \\ \index{mapup-os-mbuffers-os-running-outp!ut-handler-path3}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-running-output-handler-path3 \\ \index{tm-rwstate-os-running-output-ha!ndler-path3}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-rwstate}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{tm-rwstate} $=$ {\rm{tm-rwstate}}\,({\it{os\/}})\index{tm-rwstate})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-running-output-handler-path3 \\ \index{tm-clock-os-running-output-hand!ler-path3}
{\rm{tm-clock}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-running-output-handler-path3 \\ \index{tm-iports-os-running-output-han!dler-path3}
{\rm{tm-iports}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-running-output-handler-path3 \\ \index{tm-oports-os-running-output-han!dler-path3}
\=\+{\rm{tm-oports}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-clear-output-interrupt}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\-\index{tm-clear-output-interrupt}\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-running-output-handler-path3 \\ \index{correctness-of-os-running-output!-handler-path3}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;${\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp})\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-running-output-handler-path3}}\,({\it{os\/}})\index{os-running-output-handler-path3})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-running-output-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-running-output-interrupt-han!dler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-running-output-handler-path3.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-base-os-running-output-handler-path4 \\ \index{mapup-base-os-running-output-ha!ndler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{mapup-base} \\ 
$=$$\;\;\;\;${\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-base-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-limit-os-running-output-handler-path4 \\ \index{mapup-limit-os-running-output-h!andler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-limit}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{mapup-limit} \\ 
$=$$\;\;\;\;${\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-limit-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getseg-tm-memory-os-running-output-handler-path4 \\ \index{getseg-tm-memory-os-running-outp!ut-handler-path4}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{tm-memory})\-\index{getseg} \\ 
$=$$\;\;\;\;${\rm{getseg}}\,(\=\+{\rm{mapup-base}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-base}, \\ 
{\rm{mapup-limit}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-limit}, \\ 
{\rm{tm-memory}}\,({\it{os\/}})\index{tm-memory})\-\index{getseg})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable getseg-tm-memory-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-running-output-handler-path4-crock \\ \index{tm-cpu-os-running-output-handle!r-path4-crock}
{\rm{tm-cpu}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{tm-cpu} $=$ {\rm{tm-cpu}}\,({\it{os\/}})\index{tm-cpu}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-running-output-handler-path4-crock.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-cpu-os-running-output-handler-path4 \\ \index{tm-cpu-os-running-output-handle!r-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-cpu}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{tm-cpu} \\ 
$=$$\;\;\;\;${\rm{getnth}}\,(\=\+{\rm{os-current-taskid}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{os-current-taskid}, \\ 
{\rm{table}}\,(\=\+{\tt{'}}{\tt{9}}, \\ 
{\rm{os-task-table}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{os-task-table})\-\index{table})\-\index{getnth})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-cpu-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-os-running-output-handler-path4 \\ \index{mapup-cpu-os-running-output-han!dler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{mapup-cpu} \\ 
$=$$\;\;\;\;${\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-regs-os-running-output-handler-path4 \\ \index{mapup-regs-os-running-output-ha!ndler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-regs}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{mapup-regs} \\ 
$=$$\;\;\;\;${\rm{mapup-regs}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-regs-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cc-os-running-output-handler-path4 \\ \index{mapup-cc-os-running-output-hand!ler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-cc}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{mapup-cc} \\ 
$=$$\;\;\;\;${\rm{mapup-cc}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cc})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cc-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-error-os-running-output-handler-path4 \\ \index{mapup-error-os-running-output-h!andler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-error}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{mapup-error} \\ 
$=$$\;\;\;\;${\rm{mapup-error}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-error-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcflag-os-running-output-handler-path4 \\ \index{mapup-svcflag-os-running-output!-handler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{mapup-svcflag} \\ 
$=$$\;\;\;\;${\rm{mapup-svcflag}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcflag-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-svcid-os-running-output-handler-path4 \\ \index{mapup-svcid-os-running-output-h!andler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-svcid}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{mapup-svcid} \\ 
$=$$\;\;\;\;${\rm{mapup-svcid}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-svcid-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-os-running-output-handler-path4 \\ \index{mapup-task-os-running-output-ha!ndler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(({\it{taskid\/}} $\in\;${\bf{N}}${}$) $\wedge$ ({\it{taskid\/}} $<$ {\tt{'}}{\tt{16}})))\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-os-running-output-handler-path4 \\ \index{mapup-tasks-os-running-output-h!andler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} $\wedge$ ({\it{taskid\/}} $\in\;${\bf{N}}${}$)))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tasks-os-running-output-handler-path4 \\ \index{mapup-os-tasks-os-running-output!-handler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-tasks}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{mapup-os-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tasks-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-ibuffers-os-running-output-handler-path4 \\ \index{mapup-os-ibuffers-os-running-outp!ut-handler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-ibuffers}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{mapup-os-ibuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-ibuffers}}\,({\it{os\/}})\index{mapup-os-ibuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-ibuffers-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-obuffers-os-running-output-handler-path4 \\ \index{mapup-os-obuffers-os-running-outp!ut-handler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-obuffers}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{mapup-os-obuffers} \\ 
$=$$\;\;\;\;${\rm{deq-ith-buffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\index{deq-ith-buffer})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-obuffers-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-mbuffers-os-running-output-handler-path4 \\ \index{mapup-os-mbuffers-os-running-outp!ut-handler-path4}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os-mbuffers}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{mapup-os-mbuffers} \\ 
$=$$\;\;\;\;${\rm{mapup-os-mbuffers}}\,({\it{os\/}})\index{mapup-os-mbuffers})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-mbuffers-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-rwstate-os-running-output-handler-path4 \\ \index{tm-rwstate-os-running-output-ha!ndler-path4}
\=\+({\rm{good-tm}}\,({\it{os\/}})\index{good-tm} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{tm-rwstate}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{tm-rwstate} $=$ {\rm{tm-rwstate}}\,({\it{os\/}})\index{tm-rwstate})\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-rwstate-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-clock-os-running-output-handler-path4 \\ \index{tm-clock-os-running-output-hand!ler-path4}
{\rm{tm-clock}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{tm-clock} $=$ {\rm{tm-clock}}\,({\it{os\/}})\index{tm-clock}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-clock-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-iports-os-running-output-handler-path4 \\ \index{tm-iports-os-running-output-han!dler-path4}
{\rm{tm-iports}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{tm-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports}
\end{tabbing}


\noindent{\sc Event}:   Disable tm-iports-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-oports-os-running-output-handler-path4 \\ \index{tm-oports-os-running-output-han!dler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-oports}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{tm-oports} \\ 
$=$$\;\;\;\;${\rm{tm-start-output}}\,(\=\+{\rm{qfirst}}\,({\rm{getnth}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-os-obuffers}}\,({\it{os\/}})\index{mapup-os-obuffers})\-\index{getnth})\index{qfirst}, \\ 
{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\-\index{tm-start-output})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-oports-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-running-output-handler-path4 \\ \index{correctness-of-os-running-output!-handler-path4}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} \\ 
$\wedge$$\;\;\;\;$(\=\+($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) \\ 
$\wedge$$\;\;\;\;$(\=\+(\=\+{\rm{getnth}}\,(\=\+\=\+{\tt{'}}{\tt{2}} \\ 
$*$$\;\;\;\;${\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}\-, \\ 
{\rm{os-status-table}}\,({\it{os\/}})\index{os-status-table})\-\index{getnth} \\ 
$\not=$$\;\;\;\;${\tt{'}}{\tt{4}})\- \\ 
$\wedge$$\;\;\;\;$($\neg$ {\rm{array-qemptyp}}\,({\rm{os-current-obuffer}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\it{os\/}})\-\index{os-current-obuffer})\index{array-qemptyp}))\-)\-)\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-running-output-handler-path4}}\,({\it{os\/}})\index{os-running-output-handler-path4})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-running-output-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-running-output-interrupt-han!dler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-running-output-handler-path4.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-os-running-output-handler \\ \index{correctness-of-os-running-output!-handler}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$({\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-running-output-handler}}\,({\it{os\/}})\index{os-running-output-handler})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-running-output-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-running-output-interrupt-han!dler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-os-running-output-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-svcid-mapup-task \\ \index{tm-svcid-mapup-task}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-svcid}}\,({\rm{mapup-task}}\,({\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, {\it{os\/}})\index{mapup-task})\index{tm-svcid} \\ 
$=$$\;\;\;\;${\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-svcid-mapup-task.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  getnth-mapup-tasks-corollary \\ \index{getnth-mapup-tasks-corollary}
\=\+(({\it{i\/}} $<$ {\tt{'}}{\tt{16}}) $\wedge$ ({\it{i\/}} $\in\;${\bf{N}}${}$)) \\ 
$\rightarrow$$\;\;\;\;$({\rm{getnth}}\,({\it{i\/}}, {\rm{mapup-tasks}}\,({\tt{'}}{\tt{0}}, {\it{os\/}})\index{mapup-tasks})\index{getnth} $=$ {\rm{mapup-task}}\,({\it{i\/}}, {\it{os\/}})\index{mapup-task})\-
\end{tabbing}


\noindent{\sc Event}:   Disable getnth-mapup-tasks-corollary.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-svcid-mapup-os-tasks \\ \index{tm-svcid-mapup-os-tasks}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-svcid}}\,({\rm{getnth}}\,(\=\+{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{getnth})\index{tm-svcid} \\ 
$=$$\;\;\;\;${\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-svcid-mapup-os-tasks.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-svcid-getnth-ak-pstates \\ \index{tm-svcid-getnth-ak-pstates}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-svcid}}\,({\rm{getnth}}\,(\=\+{\rm{qfirst}}\,({\rm{ak-readyq}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-readyq})\index{qfirst}, \\ 
{\rm{ak-pstates}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-pstates})\-\index{getnth})\index{tm-svcid} \\ 
$=$$\;\;\;\;${\rm{tm-svcid}}\,({\it{os\/}})\index{tm-svcid})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-svcid-getnth-ak-pstates.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-regs-mapup-task \\ \index{tm-regs-mapup-task}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-regs}}\,({\rm{mapup-task}}\,({\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, {\it{os\/}})\index{mapup-task})\index{tm-regs} \\ 
$=$$\;\;\;\;${\rm{tm-regs}}\,({\it{os\/}})\index{tm-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-regs-mapup-task.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-regs-mapup-os-tasks \\ \index{tm-regs-mapup-os-tasks}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-regs}}\,({\rm{getnth}}\,({\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, {\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\index{getnth})\index{tm-regs} \\ 
$=$$\;\;\;\;${\rm{tm-regs}}\,({\it{os\/}})\index{tm-regs})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-regs-mapup-os-tasks.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-regs-getnth-ak-pstates \\ \index{tm-regs-getnth-ak-pstates}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+(\=\+{\rm{tm-r2}}\,({\rm{getnth}}\,(\=\+{\rm{qfirst}}\,({\rm{ak-readyq}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-readyq})\index{qfirst}, \\ 
{\rm{ak-pstates}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-pstates})\-\index{getnth})\index{tm-r2} \\ 
$=$$\;\;\;\;${\rm{tm-r2}}\,({\it{os\/}})\index{tm-r2})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{tm-r3}}\,({\rm{getnth}}\,(\=\+{\rm{qfirst}}\,({\rm{ak-readyq}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-readyq})\index{qfirst}, \\ 
{\rm{ak-pstates}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-pstates})\-\index{getnth})\index{tm-r3} \\ 
$=$$\;\;\;\;${\rm{tm-r3}}\,({\it{os\/}})\index{tm-r3})\-)\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-regs-getnth-ak-pstates.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-readyq-mapup-os \\ \index{ak-readyq-mapup-os}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ ({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue} $=$ {\rm{ak-readyq}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-readyq})
\end{tabbing}


\noindent{\sc Event}:   Disable ak-readyq-mapup-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-svc-handler \\ \index{correctness-of-svc-handler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ (($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting}) $\wedge$ ($\neg$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp}))) \\ 
$\rightarrow$$\;\;\;\;$({\rm{mapup-os}}\,({\rm{os-svc-handler}}\,({\it{os\/}})\index{os-svc-handler})\index{mapup-os} $=$ {\rm{ak-svc-handler}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-svc-handler})\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-svc-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-waiting-mapup-os \\ \index{ak-waiting-mapup-os}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ ({\rm{ak-waiting}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-waiting} $=$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})
\end{tabbing}


\noindent{\sc Event}:   Disable ak-waiting-mapup-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-iports-mapup-os \\ \index{ak-iports-mapup-os}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ ({\rm{ak-iports}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-iports} $=$ {\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})
\end{tabbing}


\noindent{\sc Event}:   Disable ak-iports-mapup-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-input-interrupt-handler \\ \index{correctness-of-input-interrupt-!handler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-input-interruptp}}\,({\rm{tm-iports}}\,({\it{os\/}})\index{tm-iports})\index{tm-some-input-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-input-interrupt-handler}}\,({\it{os\/}})\index{os-input-interrupt-handler})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-input-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-input-port}}\,({\rm{ak-iports}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-iports})\index{tm-interrupting-input-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-input-interrupt-handler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-input-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-oports-mapup-os \\ \index{ak-oports-mapup-os}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ ({\rm{ak-oports}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-oports} $=$ {\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})
\end{tabbing}


\noindent{\sc Event}:   Disable ak-oports-mapup-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-output-interrupt-handler \\ \index{correctness-of-output-interrupt!-handler}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{tm-some-output-interruptp}}\,({\rm{tm-oports}}\,({\it{os\/}})\index{tm-oports})\index{tm-some-output-interruptp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-output-interrupt-handler}}\,({\it{os\/}})\index{os-output-interrupt-handler})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-output-interrupt-handler}}\,(\=\+{\rm{tm-interrupting-output-port}}\,({\rm{ak-oports}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-oports})\index{tm-interrupting-output-port}, \\ 
{\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\-\index{ak-output-interrupt-handler})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-output-interrupt-handler.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-error-mapup-task \\ \index{tm-error-mapup-task}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-error}}\,({\rm{mapup-task}}\,({\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, {\it{os\/}})\index{mapup-task})\index{tm-error} \\ 
$=$$\;\;\;\;${\rm{tm-error}}\,({\it{os\/}})\index{tm-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-error-mapup-task.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-error-mapup-os-tasks \\ \index{tm-error-mapup-os-tasks}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-error}}\,({\rm{getnth}}\,(\=\+{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{getnth})\index{tm-error} \\ 
$=$$\;\;\;\;${\rm{tm-error}}\,({\it{os\/}})\index{tm-error})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-error-mapup-os-tasks.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-svcflag-mapup-task \\ \index{tm-svcflag-mapup-task}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-svcflag}}\,({\rm{mapup-task}}\,({\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, {\it{os\/}})\index{mapup-task})\index{tm-svcflag} \\ 
$=$$\;\;\;\;${\rm{tm-svcflag}}\,({\it{os\/}})\index{tm-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-svcflag-mapup-task.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  tm-svcflag-mapup-os-tasks \\ \index{tm-svcflag-mapup-os-tasks}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{tm-svcflag}}\,({\rm{getnth}}\,(\=\+{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{getnth})\index{tm-svcflag} \\ 
$=$$\;\;\;\;${\rm{tm-svcflag}}\,({\it{os\/}})\index{tm-svcflag})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable tm-svcflag-mapup-os-tasks.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-mapup-task \\ \index{not-tm-in-supervisor-mode-mapup!-task}
$\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task})\index{tm-in-supervisor-mode}
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-mapup-task.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  not-tm-in-supervisor-mode-getnth-mapup-os-tasks \\ \index{not-tm-in-supervisor-mode-getnt!h-mapup-os-tasks}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$($\neg$ {\rm{tm-in-supervisor-mode}}\,({\rm{getnth}}\,(\=\+{\rm{qfirst}}\,({\rm{mapup-queue}}\,({\rm{os-readyq}}\,({\it{os\/}})\index{os-readyq})\index{mapup-queue})\index{qfirst}, \\ 
{\rm{mapup-os-tasks}}\,({\it{os\/}})\index{mapup-os-tasks})\-\index{getnth})\index{tm-in-supervisor-mode})\-
\end{tabbing}


\noindent{\sc Event}:   Disable not-tm-in-supervisor-mode-getnth-mapup-os-tasks.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-input-interruptp-mapup-os \\ \index{ak-input-interruptp-mapup-os}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$({\rm{ak-input-interruptp}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-input-interruptp} $=$ {\rm{tm-input-interruptp}}\,({\it{os\/}})\index{tm-input-interruptp})\-
\end{tabbing}


\noindent{\sc Event}:   Disable ak-input-interruptp-mapup-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-output-interruptp-mapup-os \\ \index{ak-output-interruptp-mapup-os}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$({\rm{ak-output-interruptp}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-output-interruptp} $=$ {\rm{tm-output-interruptp}}\,({\it{os\/}})\index{tm-output-interruptp})\-
\end{tabbing}


\noindent{\sc Event}:   Disable ak-output-interruptp-mapup-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-errorp-mapup-os \\ \index{ak-errorp-mapup-os}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{ak-errorp}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-errorp} $=$ {\rm{tm-errorp}}\,({\it{os\/}})\index{tm-errorp})\-
\end{tabbing}


\noindent{\sc Event}:   Disable ak-errorp-mapup-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-svc-interruptp-mapup-os \\ \index{ak-svc-interruptp-mapup-os}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ ($\neg$ {\rm{tm-waiting}}\,({\it{os\/}})\index{tm-waiting})) \\ 
$\rightarrow$$\;\;\;\;$({\rm{ak-svc-interruptp}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-svc-interruptp} $=$ {\rm{tm-svc-interruptp}}\,({\it{os\/}})\index{tm-svc-interruptp})\-
\end{tabbing}


\noindent{\sc Event}:   Disable ak-svc-interruptp-mapup-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  ak-clock-interruptp-mapup-os \\ \index{ak-clock-interruptp-mapup-os}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$({\rm{ak-clock-interruptp}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-clock-interruptp} $=$ {\rm{tm-clock-interruptp}}\,({\it{os\/}})\index{tm-clock-interruptp})\-
\end{tabbing}


\noindent{\sc Event}:   Disable ak-clock-interruptp-mapup-os.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-step-implements-ak-step \\ \index{os-step-implements-ak-step}
{\rm{good-os}}\,({\it{os\/}})\index{good-os} $\rightarrow$ ({\rm{mapup-os}}\,({\rm{os-step}}\,({\it{os\/}})\index{os-step})\index{mapup-os} $=$ {\rm{ak-step}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-step})
\end{tabbing}


\noindent{\sc Event}:   Disable os-step-implements-ak-step.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-cpu-tm-post-interrupt \\ \index{mapup-cpu-tm-post-interrupt}
{\rm{mapup-cpu}}\,({\it{taskid\/}}, {\rm{tm-post-interrupt}}\,({\it{interrupt\/}}, {\it{os\/}})\index{tm-post-interrupt})\index{mapup-cpu} $=$ {\rm{mapup-cpu}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-cpu}
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-cpu-tm-post-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-task-tm-post-interrupt \\ \index{mapup-task-tm-post-interrupt}
\=\+{\rm{mapup-task}}\,({\it{taskid\/}}, {\rm{tm-post-interrupt}}\,({\it{interrupt\/}}, {\it{os\/}})\index{tm-post-interrupt})\index{mapup-task} \\ 
$=$$\;\;\;\;${\rm{mapup-task}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-task}\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-task-tm-post-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-tasks-tm-post-interrupt \\ \index{mapup-tasks-tm-post-interrupt}
\=\+{\rm{mapup-tasks}}\,({\it{taskid\/}}, {\rm{tm-post-interrupt}}\,({\it{interrupt\/}}, {\it{os\/}})\index{tm-post-interrupt})\index{mapup-tasks} \\ 
$=$$\;\;\;\;${\rm{mapup-tasks}}\,({\it{taskid\/}}, {\it{os\/}})\index{mapup-tasks}\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-tasks-tm-post-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  mapup-os-tm-post-interrupt \\ \index{mapup-os-tm-post-interrupt}
\=\+{\rm{mapup-os}}\,({\rm{tm-post-interrupt}}\,({\it{interrupt\/}}, {\it{os\/}})\index{tm-post-interrupt})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-post-interrupt}}\,({\it{interrupt\/}}, {\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-post-interrupt}\-
\end{tabbing}


\noindent{\sc Event}:   Disable mapup-os-tm-post-interrupt.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{bak-processor} \\  
\=\+{\rm{bak-processor}}\,({\it{ak\/}}, {\it{oracle\/}})\index{bak-processor} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{listp}}\,({\it{oracle\/}}) \\ 
{\bf then }{\rm{ak-step}}\,({\rm{ak-post-interrupt}}\,(\=\+{\rm{car}}\,({\it{oracle\/}}), \\ 
{\rm{bak-processor}}\,({\it{ak\/}}, {\rm{cdr}}\,({\it{oracle\/}}))\index{bak-processor})\-\index{ak-post-interrupt})\index{ak-step} \\ 
{\bf else }{\it{ak\/}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  bak-implements-ak \\ \index{bak-implements-ak}
{\rm{bak-processor}}\,({\it{ak\/}}, {\it{oracle\/}})\index{bak-processor} $=$ {\rm{ak-processor}}\,({\it{ak\/}}, {\rm{reverse}}\,({\it{oracle\/}})\index{reverse})\index{ak-processor}
\end{tabbing}


\noindent{\sc Event}:   Disable bak-implements-ak.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  bos-implements-bak \\ \index{bos-implements-bak}
\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{bos-processor}}\,({\it{os\/}}, {\it{oracle\/}})\index{bos-processor})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{bak-processor}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os}, {\it{oracle\/}})\index{bak-processor})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable bos-implements-bak.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  os-implements-ak \\ \index{os-implements-ak}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{plistp}}\,({\it{oracle\/}})\index{plistp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{os-processor}}\,({\it{os\/}}, {\it{oracle\/}})\index{os-processor})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-processor}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os}, {\it{oracle\/}})\index{ak-processor})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable os-implements-ak.

\addvspace{18pt}

\begin{tabbing}{\sc Theorem}:  correctness-of-operating-system \\ \index{correctness-of-operating-system}
\=\+({\rm{good-os}}\,({\it{os\/}})\index{good-os} $\wedge$ {\rm{plistp}}\,({\it{oracle\/}})\index{plistp}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{mapup-os}}\,({\rm{tm-processor}}\,({\it{os\/}}, {\rm{os-oracle}}\,({\it{os\/}}, {\it{oracle\/}})\index{os-oracle})\index{tm-processor})\index{mapup-os} \\ 
$=$$\;\;\;\;${\rm{ak-processor}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os}, {\it{oracle\/}})\index{ak-processor})\-\-
\end{tabbing}


\noindent{\sc Event}:   Disable correctness-of-operating-system.

\addvspace{18pt}

\begin{tabbing}{\sc Definition}:\index{project-ith-task}$\;\;$
{\rm{project-ith-task}}\,({\it{i\/}}, {\it{os\/}})\index{project-ith-task} $=$ {\rm{project}}\,({\it{i\/}}, {\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{project}
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  os-implements-parallel-tasks \\ \index{os-implements-parallel-tasks}
\=\+(\=\+{\rm{good-os}}\,({\it{os\/}})\index{good-os} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{plistp}}\,({\it{oracle\/}})\index{plistp} \\ 
$\wedge$$\;\;\;\;${\rm{finite-numberp}}\,({\it{i\/}}, {\rm{length}}\,({\rm{ak-pstates}}\,({\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os})\index{ak-pstates})\index{length})\index{finite-numberp})\-)\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{project-ith-task}}\,({\it{i\/}}, {\rm{tm-processor}}\,({\it{os\/}}, {\rm{os-oracle}}\,({\it{os\/}}, {\it{oracle\/}})\index{os-oracle})\index{tm-processor})\index{project-ith-task} \\ 
$=$$\;\;\;\;${\rm{task-processor}}\,(\=\+{\rm{project-ith-task}}\,({\it{i\/}}, {\it{os\/}})\index{project-ith-task}, \\ 
{\it{i\/}}, \\ 
{\rm{control-oracle}}\,({\it{i\/}}, {\rm{mapup-os}}\,({\it{os\/}})\index{mapup-os}, {\it{oracle\/}})\index{control-oracle})\-\index{task-processor})\-\-
\end{tabbing}
%\end{list}
\printindex
\end{document}
