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\begin{verbatim}#|

 Copyright (C) 1994 by Yuan Yu.  All Rights Reserved.

 This script is hereby placed in the public domain, and therefore unlimited
 editing and redistribution is permitted.

 NO WARRANTY

 Yuan Yu PROVIDES ABSOLUTELY NO WARRANTY.  THE EVENT SCRIPT IS PROVIDED "AS IS"
 WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESS OR IMPLIED, INCLUDING, BUT NOT
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 SCRIPT IS WITH YOU.  SHOULD THE SCRIPT PROVE DEFECTIVE, YOU ASSUME THE COST OF
 ALL NECESSARY SERVICING, REPAIR OR CORRECTION.

 IN NO EVENT WILL Yuan Yu 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
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 PARTIES), EVEN IF YOU HAVE ADVISED US OF THE POSSIBILITY OF SUCH DAMAGES, OR
 FOR ANY CLAIM BY ANY OTHER PARTY.

|#

\end{verbatim}
\noindent{\sc Event}:   Start with the library {\tt{"mc20-2"}} using the compiled version.

\addvspace{18pt}
\begin{verbatim};          Proof of the Correctness of the STRCMP Function
#|
This is part of our effort to verify the Berkeley string library.  The 
Berkeley string library is widely used as part of the Berkeley Unix OS.

This is the source code of strcmp function in the Berkeley string library.

/* compare (unsigned) char s1[] to s2[] */
int
strcmp(s1, s2)
	register const char *s1, *s2;
{
	while (*s1 == *s2++)
		if (*s1++ == 0)
			return (0);
	return (*(unsigned char *)s1 - *(unsigned char *)--s2);
}

The MC68020 assembly code of the C function strcmp on SUN-3 is given as 
follows.  This binary is generated by "gcc -O".

0x2528 <strcmp>:        linkw fp,#0
0x252c <strcmp+4>:      movel d2,sp@-
0x252e <strcmp+6>:      moveal fp@(8),a0
0x2532 <strcmp+10>:     moveal fp@(12),a1
0x2536 <strcmp+14>:     bra 0x2540 <strcmp+24>
0x2538 <strcmp+16>:     tstb a0@+
0x253a <strcmp+18>:     bne 0x2540 <strcmp+24>
0x253c <strcmp+20>:     clrl d0
0x253e <strcmp+22>:     bra 0x2550 <strcmp+40>
0x2540 <strcmp+24>:     moveb a0@,d2
0x2542 <strcmp+26>:     cmpb a1@+,d2
0x2544 <strcmp+28>:     beq 0x2538 <strcmp+16>
0x2546 <strcmp+30>:     clrl d0
0x2548 <strcmp+32>:     moveb a0@,d0
0x254a <strcmp+34>:     clrl d1
0x254c <strcmp+36>:     moveb a1@-,d1
0x254e <strcmp+38>:     subl d1,d0
0x2550 <strcmp+40>:     movel fp@(-4),d2
0x2554 <strcmp+44>:     unlk fp
0x2556 <strcmp+46>:     rts

The machine code of the above program is:

<strcmp>:      0x4e56  0x0000  0x2f02  0x206e  0x0008  0x226e  0x000c  0x6008
<strcmp+16>:   0x4a18  0x6604  0x4280  0x6010  0x1410  0xb419  0x67f2  0x4280
<strcmp+32>:   0x1010  0x4281  0x1221  0x9081  0x242e  0xfffc  0x4e5e  0x4e75

'(78      86      0       0       47      2       32      110
  0       8       34      110     0       12      96      8
  74      24      102     4       66      128     96      16
  20      16      180     25      103     242     66      128
  16      16      66      129     18      33      144     129
  36      46      255     252     78      94      78      117)
|#

; in the logic, the above program is defined by (strcmp-code).
\end{verbatim}\begin{tabbing}{\sc Definition}:\index{strcmp-code} \\  
\=\+{\sc{strcmp-code}}\index{strcmp-code} \\ 
$=$$\;\;\;\;${\tt{'}}{\tt{(}}\=\+{\tt{78}}{\tt{ }}{\tt{86}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{47}}{\tt{ }}{\tt{2}}{\tt{ }}{\tt{32}}{\tt{ }}{\tt{110}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{34}}{\tt{ }}{\tt{110}}{\tt{ }}{\tt{0}}{\tt{ }}{\tt{12}}{\tt{ }}{\tt{96}}{\tt{ }}{\tt{8}}{\tt{ }}{\tt{74}}{\tt{ }}{\tt{24}}{\tt{ }}{\tt{102}} \\ 
{\tt{4}}{\tt{ }}{\tt{66}}{\tt{ }}{\tt{128}}{\tt{ }}{\tt{96}}{\tt{ }}{\tt{16}}{\tt{ }}{\tt{20}}{\tt{ }}{\tt{16}}{\tt{ }}{\tt{180}}{\tt{ }}{\tt{25}}{\tt{ }}{\tt{103}}{\tt{ }}{\tt{242}}{\tt{ }}{\tt{66}}{\tt{ }}{\tt{128}}{\tt{ }}{\tt{16}}{\tt{ }}{\tt{16}}{\tt{ }}{\tt{66}} \\ 
{\tt{129}}{\tt{ }}{\tt{18}}{\tt{ }}{\tt{33}}{\tt{ }}{\tt{144}}{\tt{ }}{\tt{129}}{\tt{ }}{\tt{36}}{\tt{ }}{\tt{46}}{\tt{ }}{\tt{255}}{\tt{ }}{\tt{252}}{\tt{ }}{\tt{78}}{\tt{ }}{\tt{94}}{\tt{ }}{\tt{78}}{\tt{ }}{\tt{117}}{\tt{)}}\-\-
\end{tabbing}

\begin{tabbing}{\sc Conservative Axiom}:  strcmp-load \\ \index{strcmp-load}
\=\+{\rm{strcmp-loadp}}\,({\it{s\/}})\index{strcmp-loadp} \\ 
$=$$\;\;\;\;$(\=\+{\rm{evenp}}\,({\sc{strcmp-addr}}\index{strcmp-addr})\index{evenp} \\ 
$\wedge$$\;\;\;\;$({\sc{strcmp-addr}}\index{strcmp-addr} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;${\rm{nat-rangep}}\,({\sc{strcmp-addr}}\index{strcmp-addr}, {\tt{32}})\index{nat-rangep} \\ 
$\wedge$$\;\;\;\;${\rm{rom-addrp}}\,({\sc{strcmp-addr}}\index{strcmp-addr}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\tt{48}})\index{rom-addrp} \\ 
$\wedge$$\;\;\;\;${\rm{mcode-addrp}}\,({\sc{strcmp-addr}}\index{strcmp-addr}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\sc{strcmp-code}}\index{strcmp-code})\index{mcode-addrp})\-\-
\end{tabbing}\noindent Simultaneously, we introduce the new function symbols {\it strcmp-loadp\/} and {\it strcmp-addr\/}.

\begin{tabbing}{\sc Theorem}:  stepn-strcmp-loadp \\ \index{stepn-strcmp-loadp}
{\rm{strcmp-loadp}}\,({\rm{stepn}}\,({\it{s\/}}, {\it{n\/}})\index{stepn})\index{strcmp-loadp} $=$ {\rm{strcmp-loadp}}\,({\it{s\/}})\index{strcmp-loadp}
\end{tabbing}

\begin{verbatim}; the computation time of the program.
\end{verbatim}\begin{tabbing}{\sc Definition}:\index{strcmp1-t} \\  
\=\+{\rm{strcmp1-t}}\,({\it{i\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{lst2\/}})\index{strcmp1-t} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{i\/}} $<$ {\it{n1\/}} \\ 
{\bf then }\=\+{\bf if }{\rm{get-nth}}\,({\it{i\/}}, {\it{lst1\/}})\index{get-nth} $=$ {\rm{get-nth}}\,({\it{i\/}}, {\it{lst2\/}})\index{get-nth} \\ 
{\bf then }\=\+{\bf if }{\rm{get-nth}}\,({\it{i\/}}, {\it{lst1\/}})\index{get-nth} $=$ {\sc{null}}\index{null}$\;\;${\bf then }{\tt{10}} \\ 
{\bf else }{\rm{splus}}\,({\tt{5}}, {\rm{strcmp1-t}}\,($1\;+$ {\it{i\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{lst2\/}})\index{strcmp1-t})\index{splus}$\;${\bf  endif}\- \\ 
{\bf else }{\tt{11}}$\;${\bf  endif}\- \\ 
{\bf else }{\tt{0}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{tabbing}{\sc Definition}:\index{strcmp-t} \\  
{\rm{strcmp-t}}\,({\it{n1\/}}, {\it{lst1\/}}, {\it{lst2\/}})\index{strcmp-t} $=$ {\rm{splus}}\,({\tt{5}}, {\rm{strcmp1-t}}\,({\tt{0}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{lst2\/}})\index{strcmp1-t})\index{splus}
\end{tabbing}

\begin{verbatim}; an induction hint.
\end{verbatim}\begin{tabbing}{\sc Definition}:\index{strcmp-induct} \\  
\=\+{\rm{strcmp-induct}}\,({\it{s\/}}, {\it{i*\/}}, {\it{i\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{lst2\/}})\index{strcmp-induct} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\it{i\/}} $<$ {\it{n1\/}} \\ 
{\bf then }\=\+{\bf if }{\rm{get-nth}}\,({\it{i\/}}, {\it{lst1\/}})\index{get-nth} $=$ {\rm{get-nth}}\,({\it{i\/}}, {\it{lst2\/}})\index{get-nth} \\ 
{\bf then }\=\+{\bf if }{\rm{get-nth}}\,({\it{i\/}}, {\it{lst1\/}})\index{get-nth} $=$ {\sc{null}}\index{null}$\;\;${\bf then }{\bf{t}} \\ 
{\bf else }{\rm{strcmp-induct}}\,(\=\+{\rm{stepn}}\,({\it{s\/}}, {\tt{5}})\index{stepn}, \\ 
{\rm{add}}\,({\tt{32}}, {\it{i*\/}}, {\tt{1}})\index{add}, \\ 
$1\;+$ {\it{i\/}}, \\ 
{\it{n1\/}}, \\ 
{\it{lst1\/}}, \\ 
{\it{lst2\/}})\-\index{strcmp-induct}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\- \\ 
{\bf else }{\bf{t}}$\;${\bf  endif}\-\-
\end{tabbing}

\begin{verbatim}; the preconditions on the initial state.
\end{verbatim}\begin{tabbing}{\sc Definition}:\index{strcmp-statep} \\  
\=\+{\rm{strcmp-statep}}\,({\it{s\/}}, {\it{str1\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{str2\/}}, {\it{n2\/}}, {\it{lst2\/}})\index{strcmp-statep} \\ 
$=$$\;\;\;\;$(\=\+({\rm{mc-status}}\,({\it{s\/}})\index{mc-status} $=$ {\tt{'}}{\tt{running}}) \\ 
$\wedge$$\;\;\;\;${\rm{strcmp-loadp}}\,({\it{s\/}})\index{strcmp-loadp} \\ 
$\wedge$$\;\;\;\;$({\rm{mc-pc}}\,({\it{s\/}})\index{mc-pc} $=$ {\sc{strcmp-addr}}\index{strcmp-addr}) \\ 
$\wedge$$\;\;\;\;${\rm{ram-addrp}}\,({\rm{sub}}\,({\tt{32}}, {\tt{8}}, {\rm{read-sp}}\,({\it{s\/}})\index{read-sp})\index{sub}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\tt{20}})\index{ram-addrp} \\ 
$\wedge$$\;\;\;\;${\rm{ram-addrp}}\,({\it{str1\/}}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\it{n1\/}})\index{ram-addrp} \\ 
$\wedge$$\;\;\;\;${\rm{mem-lst}}\,({\tt{1}}, {\it{str1\/}}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\it{n1\/}}, {\it{lst1\/}})\index{mem-lst} \\ 
$\wedge$$\;\;\;\;${\rm{ram-addrp}}\,({\it{str2\/}}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\it{n2\/}})\index{ram-addrp} \\ 
$\wedge$$\;\;\;\;${\rm{mem-lst}}\,({\tt{1}}, {\it{str2\/}}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\it{n2\/}}, {\it{lst2\/}})\index{mem-lst} \\ 
$\wedge$$\;\;\;\;${\rm{disjoint}}\,({\rm{sub}}\,({\tt{32}}, {\tt{8}}, {\rm{read-sp}}\,({\it{s\/}})\index{read-sp})\index{sub}, {\tt{20}}, {\it{str1\/}}, {\it{n1\/}})\index{disjoint} \\ 
$\wedge$$\;\;\;\;${\rm{disjoint}}\,({\rm{sub}}\,({\tt{32}}, {\tt{8}}, {\rm{read-sp}}\,({\it{s\/}})\index{read-sp})\index{sub}, {\tt{20}}, {\it{str2\/}}, {\it{n2\/}})\index{disjoint} \\ 
$\wedge$$\;\;\;\;$({\it{str1\/}} $=$ {\rm{read-mem}}\,({\rm{add}}\,({\tt{32}}, {\rm{read-sp}}\,({\it{s\/}})\index{read-sp}, {\tt{4}})\index{add}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\tt{4}})\index{read-mem}) \\ 
$\wedge$$\;\;\;\;$({\it{str2\/}} $=$ {\rm{read-mem}}\,({\rm{add}}\,({\tt{32}}, {\rm{read-sp}}\,({\it{s\/}})\index{read-sp}, {\tt{8}})\index{add}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\tt{4}})\index{read-mem}) \\ 
$\wedge$$\;\;\;\;${\rm{stringp}}\,({\tt{0}}, {\it{n1\/}}, {\it{lst1\/}})\index{stringp} \\ 
$\wedge$$\;\;\;\;$({\it{n1\/}} $\leq$ {\it{n2\/}}) \\ 
$\wedge$$\;\;\;\;$({\it{n1\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$({\it{n2\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;${\rm{uint-rangep}}\,({\it{n2\/}}, {\tt{32}})\index{uint-rangep})\-\-
\end{tabbing}

\begin{verbatim}; an intermediate state.
\end{verbatim}\begin{tabbing}{\sc Definition}:\index{strcmp-s0p} \\  
\=\+{\rm{strcmp-s0p}}\,({\it{s\/}}, {\it{i*\/}}, {\it{i\/}}, {\it{str1\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{str2\/}}, {\it{n2\/}}, {\it{lst2\/}})\index{strcmp-s0p} \\ 
$=$$\;\;\;\;$(\=\+({\rm{mc-status}}\,({\it{s\/}})\index{mc-status} $=$ {\tt{'}}{\tt{running}}) \\ 
$\wedge$$\;\;\;\;${\rm{evenp}}\,({\rm{mc-pc}}\,({\it{s\/}})\index{mc-pc})\index{evenp} \\ 
$\wedge$$\;\;\;\;${\rm{rom-addrp}}\,({\rm{sub}}\,({\tt{32}}, {\tt{24}}, {\rm{mc-pc}}\,({\it{s\/}})\index{mc-pc})\index{sub}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\tt{48}})\index{rom-addrp} \\ 
$\wedge$$\;\;\;\;${\rm{mcode-addrp}}\,({\rm{sub}}\,({\tt{32}}, {\tt{24}}, {\rm{mc-pc}}\,({\it{s\/}})\index{mc-pc})\index{sub}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\sc{strcmp-code}}\index{strcmp-code})\index{mcode-addrp} \\ 
$\wedge$$\;\;\;\;${\rm{ram-addrp}}\,({\rm{sub}}\,({\tt{32}}, {\tt{4}}, {\rm{read-an}}\,({\tt{32}}, {\tt{6}}, {\it{s\/}})\index{read-an})\index{sub}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\tt{20}})\index{ram-addrp} \\ 
$\wedge$$\;\;\;\;${\rm{ram-addrp}}\,({\it{str1\/}}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\it{n1\/}})\index{ram-addrp} \\ 
$\wedge$$\;\;\;\;${\rm{mem-lst}}\,({\tt{1}}, {\it{str1\/}}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\it{n1\/}}, {\it{lst1\/}})\index{mem-lst} \\ 
$\wedge$$\;\;\;\;${\rm{ram-addrp}}\,({\it{str2\/}}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\it{n2\/}})\index{ram-addrp} \\ 
$\wedge$$\;\;\;\;${\rm{mem-lst}}\,({\tt{1}}, {\it{str2\/}}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\it{n2\/}}, {\it{lst2\/}})\index{mem-lst} \\ 
$\wedge$$\;\;\;\;${\rm{disjoint}}\,({\rm{sub}}\,({\tt{32}}, {\tt{4}}, {\rm{read-an}}\,({\tt{32}}, {\tt{6}}, {\it{s\/}})\index{read-an})\index{sub}, {\tt{20}}, {\it{str1\/}}, {\it{n1\/}})\index{disjoint} \\ 
$\wedge$$\;\;\;\;${\rm{disjoint}}\,({\rm{sub}}\,({\tt{32}}, {\tt{4}}, {\rm{read-an}}\,({\tt{32}}, {\tt{6}}, {\it{s\/}})\index{read-an})\index{sub}, {\tt{20}}, {\it{str2\/}}, {\it{n2\/}})\index{disjoint} \\ 
$\wedge$$\;\;\;\;${\rm{equal*}}\,({\rm{read-an}}\,({\tt{32}}, {\tt{0}}, {\it{s\/}})\index{read-an}, {\rm{add}}\,({\tt{32}}, {\it{str1\/}}, {\it{i*\/}})\index{add})\index{equal*} \\ 
$\wedge$$\;\;\;\;${\rm{equal*}}\,({\rm{read-an}}\,({\tt{32}}, {\tt{1}}, {\it{s\/}})\index{read-an}, {\rm{add}}\,({\tt{32}}, {\it{str2\/}}, {\it{i*\/}})\index{add})\index{equal*} \\ 
$\wedge$$\;\;\;\;$({\it{i\/}} $=$ {\rm{nat-to-uint}}\,({\it{i*\/}})\index{nat-to-uint}) \\ 
$\wedge$$\;\;\;\;${\rm{stringp}}\,({\it{i\/}}, {\it{n1\/}}, {\it{lst1\/}})\index{stringp} \\ 
$\wedge$$\;\;\;\;$({\it{i\/}} $<$ {\it{n1\/}}) \\ 
$\wedge$$\;\;\;\;$({\it{n1\/}} $\leq$ {\it{n2\/}}) \\ 
$\wedge$$\;\;\;\;$({\it{i*\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;${\rm{nat-rangep}}\,({\it{i*\/}}, {\tt{32}})\index{nat-rangep} \\ 
$\wedge$$\;\;\;\;$({\it{n1\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;$({\it{n2\/}} $\in\;${\bf{N}}${}$) \\ 
$\wedge$$\;\;\;\;${\rm{uint-rangep}}\,({\it{n2\/}}, {\tt{32}})\index{uint-rangep})\-\-
\end{tabbing}

\begin{verbatim}; from the initial state s to s0: s --> s0.
\end{verbatim}\begin{tabbing}{\sc Theorem}:  strcmp-s-s0 \\ \index{strcmp-s-s0}
\=\+{\rm{strcmp-statep}}\,({\it{s\/}}, {\it{str1\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{str2\/}}, {\it{n2\/}}, {\it{lst2\/}})\index{strcmp-statep} \\ 
$\rightarrow$$\;\;\;\;${\rm{strcmp-s0p}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{5}})\index{stepn}, {\tt{0}}, {\tt{0}}, {\it{str1\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{str2\/}}, {\it{n2\/}}, {\it{lst2\/}})\index{strcmp-s0p}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  strcmp-s-s0-else \\ \index{strcmp-s-s0-else}
\=\+{\rm{strcmp-statep}}\,({\it{s\/}}, {\it{str1\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{str2\/}}, {\it{n2\/}}, {\it{lst2\/}})\index{strcmp-statep} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{linked-rts-addr}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{5}})\index{stepn})\index{linked-rts-addr} $=$ {\rm{rts-addr}}\,({\it{s\/}})\index{rts-addr}) \\ 
$\wedge$$\;\;\;\;$({\rm{linked-a6}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{5}})\index{stepn})\index{linked-a6} $=$ {\rm{read-an}}\,({\tt{32}}, {\tt{6}}, {\it{s\/}})\index{read-an}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{read-rn}}\,({\tt{32}}, {\tt{14}}, {\rm{mc-rfile}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{5}})\index{stepn})\index{mc-rfile})\index{read-rn} \\ 
$=$$\;\;\;\;${\rm{sub}}\,({\tt{32}}, {\tt{4}}, {\rm{read-sp}}\,({\it{s\/}})\index{read-sp})\index{sub})\- \\ 
$\wedge$$\;\;\;\;$({\rm{rn-saved}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{5}})\index{stepn})\index{rn-saved} $=$ {\rm{read-dn}}\,({\tt{32}}, {\tt{2}}, {\it{s\/}})\index{read-dn}))\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  strcmp-s-s0-rfile \\ \index{strcmp-s-s0-rfile}
\=\+({\rm{strcmp-statep}}\,({\it{s\/}}, {\it{str1\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{str2\/}}, {\it{n2\/}}, {\it{lst2\/}})\index{strcmp-statep} $\wedge$ {\rm{d3-7a2-5p}}\,({\it{rn\/}})\index{d3-7a2-5p}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{read-rn}}\,({\it{oplen\/}}, {\it{rn\/}}, {\rm{mc-rfile}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{5}})\index{stepn})\index{mc-rfile})\index{read-rn} \\ 
$=$$\;\;\;\;${\rm{read-rn}}\,({\it{oplen\/}}, {\it{rn\/}}, {\rm{mc-rfile}}\,({\it{s\/}})\index{mc-rfile})\index{read-rn})\-\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  strcmp-s-s0-mem \\ \index{strcmp-s-s0-mem}
\=\+(\=\+{\rm{strcmp-statep}}\,({\it{s\/}}, {\it{str1\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{str2\/}}, {\it{n2\/}}, {\it{lst2\/}})\index{strcmp-statep} \\ 
$\wedge$$\;\;\;\;${\rm{disjoint}}\,({\it{x\/}}, {\it{k\/}}, {\rm{sub}}\,({\tt{32}}, {\tt{8}}, {\rm{read-sp}}\,({\it{s\/}})\index{read-sp})\index{sub}, {\tt{20}})\index{disjoint})\- \\ 
$\rightarrow$$\;\;\;\;$({\rm{read-mem}}\,({\it{x\/}}, {\rm{mc-mem}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{5}})\index{stepn})\index{mc-mem}, {\it{k\/}})\index{read-mem} $=$ {\rm{read-mem}}\,({\it{x\/}}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\it{k\/}})\index{read-mem})\-
\end{tabbing}
	      
\begin{verbatim}; from s0 to exit: s0 --> sn.
; base case 1: s0 --> sn.  lst1[i] =\= lst2[i].
\end{verbatim}\begin{tabbing}{\sc Theorem}:  strcmp-s0-sn-base1 \\ \index{strcmp-s0-sn-base1}
\=\+(\=\+{\rm{strcmp-s0p}}\,({\it{s\/}}, {\it{i*\/}}, {\it{i\/}}, {\it{str1\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{str2\/}}, {\it{n2\/}}, {\it{lst2\/}})\index{strcmp-s0p} \\ 
$\wedge$$\;\;\;\;$({\rm{get-nth}}\,({\it{i\/}}, {\it{lst1\/}})\index{get-nth} $\not=$ {\rm{get-nth}}\,({\it{i\/}}, {\it{lst2\/}})\index{get-nth}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{mc-status}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{11}})\index{stepn})\index{mc-status} $=$ {\tt{'}}{\tt{running}}) \\ 
$\wedge$$\;\;\;\;$({\rm{mc-pc}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{11}})\index{stepn})\index{mc-pc} $=$ {\rm{linked-rts-addr}}\,({\it{s\/}})\index{linked-rts-addr}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{iread-dn}}\,({\tt{32}}, {\tt{0}}, {\rm{stepn}}\,({\it{s\/}}, {\tt{11}})\index{stepn})\index{iread-dn} \\ 
$=$$\;\;\;\;${\rm{idifference}}\,({\rm{get-nth}}\,({\it{i\/}}, {\it{lst1\/}})\index{get-nth}, {\rm{get-nth}}\,({\it{i\/}}, {\it{lst2\/}})\index{get-nth})\index{idifference})\- \\ 
$\wedge$$\;\;\;\;$({\rm{read-rn}}\,({\tt{32}}, {\tt{14}}, {\rm{mc-rfile}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{11}})\index{stepn})\index{mc-rfile})\index{read-rn} $=$ {\rm{linked-a6}}\,({\it{s\/}})\index{linked-a6}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{read-rn}}\,({\tt{32}}, {\tt{15}}, {\rm{mc-rfile}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{11}})\index{stepn})\index{mc-rfile})\index{read-rn} \\ 
$=$$\;\;\;\;${\rm{add}}\,({\tt{32}}, {\rm{read-an}}\,({\tt{32}}, {\tt{6}}, {\it{s\/}})\index{read-an}, {\tt{8}})\index{add})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{read-mem}}\,({\it{x\/}}, {\rm{mc-mem}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{11}})\index{stepn})\index{mc-mem}, {\it{k\/}})\index{read-mem} \\ 
$=$$\;\;\;\;${\rm{read-mem}}\,({\it{x\/}}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\it{k\/}})\index{read-mem})\-)\-\-
\end{tabbing}
		   
\begin{tabbing}{\sc Theorem}:  strcmp-s0-sn-rfile-base1 \\ \index{strcmp-s0-sn-rfile-base1}
\=\+(\=\+{\rm{strcmp-s0p}}\,({\it{s\/}}, {\it{i*\/}}, {\it{i\/}}, {\it{str1\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{str2\/}}, {\it{n2\/}}, {\it{lst2\/}})\index{strcmp-s0p} \\ 
$\wedge$$\;\;\;\;$({\rm{get-nth}}\,({\it{i\/}}, {\it{lst1\/}})\index{get-nth} $\not=$ {\rm{get-nth}}\,({\it{i\/}}, {\it{lst2\/}})\index{get-nth}) \\ 
$\wedge$$\;\;\;\;$({\it{oplen\/}} $\leq$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{d2-7a2-5p}}\,({\it{rn\/}})\index{d2-7a2-5p})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{read-rn}}\,({\it{oplen\/}}, {\it{rn\/}}, {\rm{mc-rfile}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{11}})\index{stepn})\index{mc-rfile})\index{read-rn} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{d3-7a2-5p}}\,({\it{rn\/}})\index{d3-7a2-5p}$\;\;${\bf then }{\rm{read-rn}}\,({\it{oplen\/}}, {\it{rn\/}}, {\rm{mc-rfile}}\,({\it{s\/}})\index{mc-rfile})\index{read-rn} \\ 
{\bf else }{\rm{head}}\,({\rm{rn-saved}}\,({\it{s\/}})\index{rn-saved}, {\it{oplen\/}})\index{head}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{verbatim}; base case 2: s0 --> sn.  lst[i] = lst2[i] and lst[i] = 0.
\end{verbatim}\begin{tabbing}{\sc Theorem}:  strcmp-s0-sn-base2 \\ \index{strcmp-s0-sn-base2}
\=\+(\=\+{\rm{strcmp-s0p}}\,({\it{s\/}}, {\it{i*\/}}, {\it{i\/}}, {\it{str1\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{str2\/}}, {\it{n2\/}}, {\it{lst2\/}})\index{strcmp-s0p} \\ 
$\wedge$$\;\;\;\;$({\rm{get-nth}}\,({\it{i\/}}, {\it{lst1\/}})\index{get-nth} $=$ {\rm{get-nth}}\,({\it{i\/}}, {\it{lst2\/}})\index{get-nth}) \\ 
$\wedge$$\;\;\;\;$({\rm{get-nth}}\,({\it{i\/}}, {\it{lst1\/}})\index{get-nth} $=$ {\tt{0}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{mc-status}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{10}})\index{stepn})\index{mc-status} $=$ {\tt{'}}{\tt{running}}) \\ 
$\wedge$$\;\;\;\;$({\rm{mc-pc}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{10}})\index{stepn})\index{mc-pc} $=$ {\rm{linked-rts-addr}}\,({\it{s\/}})\index{linked-rts-addr}) \\ 
$\wedge$$\;\;\;\;$({\rm{iread-dn}}\,({\tt{32}}, {\tt{0}}, {\rm{stepn}}\,({\it{s\/}}, {\tt{10}})\index{stepn})\index{iread-dn} $=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\rm{read-rn}}\,({\tt{32}}, {\tt{14}}, {\rm{mc-rfile}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{10}})\index{stepn})\index{mc-rfile})\index{read-rn} $=$ {\rm{linked-a6}}\,({\it{s\/}})\index{linked-a6}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{read-rn}}\,({\tt{32}}, {\tt{15}}, {\rm{mc-rfile}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{10}})\index{stepn})\index{mc-rfile})\index{read-rn} \\ 
$=$$\;\;\;\;${\rm{add}}\,({\tt{32}}, {\rm{read-an}}\,({\tt{32}}, {\tt{6}}, {\it{s\/}})\index{read-an}, {\tt{8}})\index{add})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{read-mem}}\,({\it{x\/}}, {\rm{mc-mem}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{10}})\index{stepn})\index{mc-mem}, {\it{k\/}})\index{read-mem} \\ 
$=$$\;\;\;\;${\rm{read-mem}}\,({\it{x\/}}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\it{k\/}})\index{read-mem})\-)\-\-
\end{tabbing}			  

\begin{tabbing}{\sc Theorem}:  strcmp-s0-sn-rfile-base2 \\ \index{strcmp-s0-sn-rfile-base2}
\=\+(\=\+{\rm{strcmp-s0p}}\,({\it{s\/}}, {\it{i*\/}}, {\it{i\/}}, {\it{str1\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{str2\/}}, {\it{n2\/}}, {\it{lst2\/}})\index{strcmp-s0p} \\ 
$\wedge$$\;\;\;\;$({\rm{get-nth}}\,({\it{i\/}}, {\it{lst1\/}})\index{get-nth} $=$ {\rm{get-nth}}\,({\it{i\/}}, {\it{lst2\/}})\index{get-nth}) \\ 
$\wedge$$\;\;\;\;$({\rm{get-nth}}\,({\it{i\/}}, {\it{lst1\/}})\index{get-nth} $=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;$({\it{oplen\/}} $\leq$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{d2-7a2-5p}}\,({\it{rn\/}})\index{d2-7a2-5p})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{read-rn}}\,({\it{oplen\/}}, {\it{rn\/}}, {\rm{mc-rfile}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{10}})\index{stepn})\index{mc-rfile})\index{read-rn} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{d3-7a2-5p}}\,({\it{rn\/}})\index{d3-7a2-5p}$\;\;${\bf then }{\rm{read-rn}}\,({\it{oplen\/}}, {\it{rn\/}}, {\rm{mc-rfile}}\,({\it{s\/}})\index{mc-rfile})\index{read-rn} \\ 
{\bf else }{\rm{head}}\,({\rm{rn-saved}}\,({\it{s\/}})\index{rn-saved}, {\it{oplen\/}})\index{head}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{verbatim}; induction case: s0 --> s0. lst[i] = lst2[i] and lst[i] =\= 0.
\end{verbatim}\begin{tabbing}{\sc Theorem}:  strcmp-s0-s0 \\ \index{strcmp-s0-s0}
\=\+(\=\+{\rm{strcmp-s0p}}\,({\it{s\/}}, {\it{i*\/}}, {\it{i\/}}, {\it{str1\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{str2\/}}, {\it{n2\/}}, {\it{lst2\/}})\index{strcmp-s0p} \\ 
$\wedge$$\;\;\;\;$({\rm{get-nth}}\,({\it{i\/}}, {\it{lst1\/}})\index{get-nth} $=$ {\rm{get-nth}}\,({\it{i\/}}, {\it{lst2\/}})\index{get-nth}) \\ 
$\wedge$$\;\;\;\;$({\rm{get-nth}}\,({\it{i\/}}, {\it{lst1\/}})\index{get-nth} $\not=$ {\tt{0}}))\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{strcmp-s0p}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{5}})\index{stepn}, {\rm{add}}\,({\tt{32}}, {\it{i*\/}}, {\tt{1}})\index{add}, $1\;+$ {\it{i\/}}, {\it{str1\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{str2\/}}, {\it{n2\/}}, {\it{lst2\/}})\index{strcmp-s0p} \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{read-rn}}\,({\tt{32}}, {\tt{14}}, {\rm{mc-rfile}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{5}})\index{stepn})\index{mc-rfile})\index{read-rn} \\ 
$=$$\;\;\;\;${\rm{read-rn}}\,({\tt{32}}, {\tt{14}}, {\rm{mc-rfile}}\,({\it{s\/}})\index{mc-rfile})\index{read-rn})\- \\ 
$\wedge$$\;\;\;\;$({\rm{linked-a6}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{5}})\index{stepn})\index{linked-a6} $=$ {\rm{linked-a6}}\,({\it{s\/}})\index{linked-a6}) \\ 
$\wedge$$\;\;\;\;$({\rm{linked-rts-addr}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{5}})\index{stepn})\index{linked-rts-addr} $=$ {\rm{linked-rts-addr}}\,({\it{s\/}})\index{linked-rts-addr}) \\ 
$\wedge$$\;\;\;\;$({\rm{rn-saved}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{5}})\index{stepn})\index{rn-saved} $=$ {\rm{rn-saved}}\,({\it{s\/}})\index{rn-saved}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{read-mem}}\,({\it{x\/}}, {\rm{mc-mem}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{5}})\index{stepn})\index{mc-mem}, {\it{k\/}})\index{read-mem} \\ 
$=$$\;\;\;\;${\rm{read-mem}}\,({\it{x\/}}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\it{k\/}})\index{read-mem})\-)\-\-
\end{tabbing}			  

\begin{tabbing}{\sc Theorem}:  strcmp-s0-s0-rfile \\ \index{strcmp-s0-s0-rfile}
\=\+(\=\+{\rm{strcmp-s0p}}\,({\it{s\/}}, {\it{i*\/}}, {\it{i\/}}, {\it{str1\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{str2\/}}, {\it{n2\/}}, {\it{lst2\/}})\index{strcmp-s0p} \\ 
$\wedge$$\;\;\;\;$({\rm{get-nth}}\,({\it{i\/}}, {\it{lst1\/}})\index{get-nth} $=$ {\rm{get-nth}}\,({\it{i\/}}, {\it{lst2\/}})\index{get-nth}) \\ 
$\wedge$$\;\;\;\;$({\rm{get-nth}}\,({\it{i\/}}, {\it{lst1\/}})\index{get-nth} $\not=$ {\tt{0}}) \\ 
$\wedge$$\;\;\;\;${\rm{d3-7a2-5p}}\,({\it{rn\/}})\index{d3-7a2-5p})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{read-rn}}\,({\it{oplen\/}}, {\it{rn\/}}, {\rm{mc-rfile}}\,({\rm{stepn}}\,({\it{s\/}}, {\tt{5}})\index{stepn})\index{mc-rfile})\index{read-rn} \\ 
$=$$\;\;\;\;${\rm{read-rn}}\,({\it{oplen\/}}, {\it{rn\/}}, {\rm{mc-rfile}}\,({\it{s\/}})\index{mc-rfile})\index{read-rn})\-\-
\end{tabbing}

\begin{verbatim}; put together.  s0 --> sn.
\end{verbatim}\begin{tabbing}{\sc Theorem}:  strcmp-s0p-info \\ \index{strcmp-s0p-info}
{\rm{strcmp-s0p}}\,({\it{s\/}}, {\it{i*\/}}, {\it{i\/}}, {\it{str1\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{str2\/}}, {\it{n2\/}}, {\it{lst2\/}})\index{strcmp-s0p} $\rightarrow$ (({\it{i\/}} $<$ {\it{n1\/}}) $=$ {\bf{t}})
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  strcmp-s0-sn \\ \index{strcmp-s0-sn}
\=\+{\bf let }\=\+{\it{sn\/}}{\bf $\;$ be$\;\;$}{\rm{stepn}}\,({\it{s\/}}, {\rm{strcmp1-t}}\,({\it{i\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{lst2\/}})\index{strcmp1-t})\index{stepn}\- \\ 
{\bf in} \\ 
\=\+{\rm{strcmp-s0p}}\,({\it{s\/}}, {\it{i*\/}}, {\it{i\/}}, {\it{str1\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{str2\/}}, {\it{n2\/}}, {\it{lst2\/}})\index{strcmp-s0p} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{mc-status}}\,({\it{sn\/}})\index{mc-status} $=$ {\tt{'}}{\tt{running}}) \\ 
$\wedge$$\;\;\;\;$({\rm{mc-pc}}\,({\it{sn\/}})\index{mc-pc} $=$ {\rm{linked-rts-addr}}\,({\it{s\/}})\index{linked-rts-addr}) \\ 
$\wedge$$\;\;\;\;$({\rm{iread-dn}}\,({\tt{32}}, {\tt{0}}, {\it{sn\/}})\index{iread-dn} $=$ {\rm{strcmp}}\,({\it{i\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{lst2\/}})\index{strcmp}) \\ 
$\wedge$$\;\;\;\;$({\rm{read-rn}}\,({\tt{32}}, {\tt{14}}, {\rm{mc-rfile}}\,({\it{sn\/}})\index{mc-rfile})\index{read-rn} $=$ {\rm{linked-a6}}\,({\it{s\/}})\index{linked-a6}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{read-rn}}\,({\tt{32}}, {\tt{15}}, {\rm{mc-rfile}}\,({\it{sn\/}})\index{mc-rfile})\index{read-rn} \\ 
$=$$\;\;\;\;${\rm{add}}\,({\tt{32}}, {\rm{read-an}}\,({\tt{32}}, {\tt{6}}, {\it{s\/}})\index{read-an}, {\tt{8}})\index{add})\- \\ 
$\wedge$$\;\;\;\;$({\rm{read-mem}}\,({\it{x\/}}, {\rm{mc-mem}}\,({\it{sn\/}})\index{mc-mem}, {\it{k\/}})\index{read-mem} $=$ {\rm{read-mem}}\,({\it{x\/}}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\it{k\/}})\index{read-mem}))\-\-$\;${\bf  endlet}\-
\end{tabbing}

\begin{tabbing}{\sc Theorem}:  strcmp-s0-sn-rfile \\ \index{strcmp-s0-sn-rfile}
\=\+(\=\+{\rm{strcmp-s0p}}\,({\it{s\/}}, {\it{i*\/}}, {\it{i\/}}, {\it{str1\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{str2\/}}, {\it{n2\/}}, {\it{lst2\/}})\index{strcmp-s0p} \\ 
$\wedge$$\;\;\;\;$({\it{oplen\/}} $\leq$ {\tt{32}}) \\ 
$\wedge$$\;\;\;\;${\rm{d2-7a2-5p}}\,({\it{rn\/}})\index{d2-7a2-5p})\- \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{read-rn}}\,({\it{oplen\/}}, {\it{rn\/}}, {\rm{mc-rfile}}\,({\rm{stepn}}\,({\it{s\/}}, {\rm{strcmp1-t}}\,({\it{i\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{lst2\/}})\index{strcmp1-t})\index{stepn})\index{mc-rfile})\index{read-rn} \\ 
$=$$\;\;\;\;$\=\+{\bf if }{\rm{d3-7a2-5p}}\,({\it{rn\/}})\index{d3-7a2-5p}$\;\;${\bf then }{\rm{read-rn}}\,({\it{oplen\/}}, {\it{rn\/}}, {\rm{mc-rfile}}\,({\it{s\/}})\index{mc-rfile})\index{read-rn} \\ 
{\bf else }{\rm{head}}\,({\rm{rn-saved}}\,({\it{s\/}})\index{rn-saved}, {\it{oplen\/}})\index{head}$\;${\bf  endif}\-)\-\-
\end{tabbing}

\begin{verbatim}; the correctness of strcmp.
\end{verbatim}\begin{tabbing}{\sc Theorem}:  strcmp-correctness \\ \index{strcmp-correctness}
\=\+{\bf let }\=\+{\it{sn\/}}{\bf $\;$ be$\;\;$}{\rm{stepn}}\,({\it{s\/}}, {\rm{strcmp-t}}\,({\it{n1\/}}, {\it{lst1\/}}, {\it{lst2\/}})\index{strcmp-t})\index{stepn}\- \\ 
{\bf in} \\ 
\=\+{\rm{strcmp-statep}}\,({\it{s\/}}, {\it{str1\/}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{str2\/}}, {\it{n2\/}}, {\it{lst2\/}})\index{strcmp-statep} \\ 
$\rightarrow$$\;\;\;\;$(\=\+({\rm{mc-status}}\,({\it{sn\/}})\index{mc-status} $=$ {\tt{'}}{\tt{running}}) \\ 
$\wedge$$\;\;\;\;$({\rm{mc-pc}}\,({\it{sn\/}})\index{mc-pc} $=$ {\rm{rts-addr}}\,({\it{s\/}})\index{rts-addr}) \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{read-rn}}\,({\tt{32}}, {\tt{14}}, {\rm{mc-rfile}}\,({\it{sn\/}})\index{mc-rfile})\index{read-rn} \\ 
$=$$\;\;\;\;${\rm{read-rn}}\,({\tt{32}}, {\tt{14}}, {\rm{mc-rfile}}\,({\it{s\/}})\index{mc-rfile})\index{read-rn})\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{read-rn}}\,({\tt{32}}, {\tt{15}}, {\rm{mc-rfile}}\,({\it{sn\/}})\index{mc-rfile})\index{read-rn} \\ 
$=$$\;\;\;\;${\rm{add}}\,({\tt{32}}, {\rm{read-an}}\,({\tt{32}}, {\tt{7}}, {\it{s\/}})\index{read-an}, {\tt{4}})\index{add})\- \\ 
$\wedge$$\;\;\;\;$(\=\+(({\it{oplen\/}} $\leq$ {\tt{32}}) $\wedge$ {\rm{d2-7a2-5p}}\,({\it{rn\/}})\index{d2-7a2-5p}) \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{read-rn}}\,({\it{oplen\/}}, {\it{rn\/}}, {\rm{mc-rfile}}\,({\it{sn\/}})\index{mc-rfile})\index{read-rn} \\ 
$=$$\;\;\;\;${\rm{read-rn}}\,({\it{oplen\/}}, {\it{rn\/}}, {\rm{mc-rfile}}\,({\it{s\/}})\index{mc-rfile})\index{read-rn})\-)\- \\ 
$\wedge$$\;\;\;\;$(\=\+{\rm{disjoint}}\,({\it{x\/}}, {\it{k\/}}, {\rm{sub}}\,({\tt{32}}, {\tt{8}}, {\rm{read-sp}}\,({\it{s\/}})\index{read-sp})\index{sub}, {\tt{20}})\index{disjoint} \\ 
$\rightarrow$$\;\;\;\;$(\=\+{\rm{read-mem}}\,({\it{x\/}}, {\rm{mc-mem}}\,({\it{sn\/}})\index{mc-mem}, {\it{k\/}})\index{read-mem} \\ 
$=$$\;\;\;\;${\rm{read-mem}}\,({\it{x\/}}, {\rm{mc-mem}}\,({\it{s\/}})\index{mc-mem}, {\it{k\/}})\index{read-mem})\-)\- \\ 
$\wedge$$\;\;\;\;$({\rm{iread-dn}}\,({\tt{32}}, {\tt{0}}, {\it{sn\/}})\index{iread-dn} $=$ {\rm{strcmp}}\,({\tt{0}}, {\it{n1\/}}, {\it{lst1\/}}, {\it{lst2\/}})\index{strcmp}))\-\-$\;${\bf  endlet}\-
\end{tabbing}


\noindent{\sc Event}:   Disable strcmp-t.

\addvspace{18pt}

\begin{verbatim}; some properties of strcmp.
; see file cstring.events.

\end{verbatim}
\noindent{\sc Event}:   Make the library {\tt{"strcmp"}} and compile it.

\addvspace{18pt}

%\end{list}
\printindex
\end{document}
