<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">a</font> be   <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">aa</font>, <font color="Olive" title="b2">bb</font>, <font color="Olive" title="b3">cc</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <br/>  for <font color="Olive" title="b4">I</font> being   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of   st <font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">aa</font> &amp; <font color="Olive" title="b1">aa</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p1">(<span class="default"><span class="p2"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Olive" title="b2">bb</font>,<font color="Olive" title="b3">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Olive" title="b4">I</font></span>)</span></span>)</span> &amp;  not <font color="Olive" title="b4">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Olive" title="b1">aa</font> holds <br/> not  <a href="sfmastr3.html#K2" title="SFMASTR3:func.2">for-up</a> (<font color="Maroon" title="c1">a</font>,<font color="Olive" title="b2">bb</font>,<font color="Olive" title="b3">cc</font>,<font color="Olive" title="b4">I</font>) <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Olive" title="b1">aa</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">aa</font>, <font color="Maroon" title="c3">bb</font>, <font color="Maroon" title="c4">cc</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">I</font> being   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of   st <font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">aa</font> &amp; <font color="Maroon" title="c2">aa</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p1">(<span class="default"><span class="p2"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Olive" title="b1">I</font></span>)</span></span>)</span> &amp;  not <font color="Olive" title="b1">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c2">aa</font> holds <br/> not  <a href="sfmastr3.html#K2" title="SFMASTR3:func.2">for-up</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font>,<font color="Olive" title="b1">I</font>) <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c2">aa</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">I</font> be   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">aa</font> &amp; <font color="Maroon" title="c2">aa</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p1">(<span class="default"><span class="p2"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span> &amp;  not <font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c2">aa</font> implies  not  <a href="sfmastr3.html#K2" title="SFMASTR3:func.2">for-up</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font>,<font color="Maroon" title="c5">I</font>) <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c2">aa</font> )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:28"/><span class="lab"><font color="Green" title="E25">A1</font></span>: 
<font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">aa</font>
 <span class="kw">and </span><br/><a NAME="E2:28"/><span class="lab"><font color="Green" title="E26">A2</font></span>: 
<font color="Maroon" title="c2">aa</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p1">(<span class="default"><span class="p2"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:28"/><span class="lab"><font color="Green" title="E27">A3</font></span>: 
 not <font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c2">aa</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not  <a href="sfmastr3.html#K2" title="SFMASTR3:func.2">for-up</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font>,<font color="Maroon" title="c5">I</font>) <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c2">aa</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">aux</font> = 1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p1">(<span class="default"><span class="p2"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">i2</font> =  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<span class="p1">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p2">(<span class="default"><span class="p3"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>);<br/>
<a NAME="E4:28"/><span class="lab"><font color="Green" title="E28">A4</font></span>: 
 not  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<span class="p1">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p2">(<span class="default"><span class="p3"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>) <a href="scmfsa7b.html#R3" title="SCMFSA7B:pred.3">destroys</a> <font color="Maroon" title="c2">aa</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="ref" href="scmfsa7b.html#T7" title="SCMFSA7B:th.7">SCMFSA7B:7</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">i3</font> = <font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c3">bb</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">i1</font> =  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<span class="p1">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p2">(<span class="default"><span class="p3"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">bb</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c10">i0</font> = <span class="p1">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p2">(<span class="default"><span class="p3"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">cc</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">I03</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p5">(<span class="default"><span class="p0"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p0">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">cc</font></span>)</span> <a href="scmfsa6a.html#K7" title="SCMFSA6A:func.7">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<span class="p4">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p5">(<span class="default"><span class="p0"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p0">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">bb</font>)</span>)</span></span>)</span> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<span class="p3">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p4">(<span class="default"><span class="p5"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p5">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c3">bb</font></span>)</span>;<br/>
<a NAME="E5:28"/>
(  not <span class="p1">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p2">(<span class="default"><span class="p3"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">cc</font> <a href="scmfsa7b.html#R3" title="SCMFSA7B:pred.3">destroys</a> <font color="Maroon" title="c2">aa</font> &amp;  not  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<span class="p1">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p2">(<span class="default"><span class="p3"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">bb</font>) <a href="scmfsa7b.html#R3" title="SCMFSA7B:pred.3">destroys</a> <font color="Maroon" title="c2">aa</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="ref" href="scmfsa7b.html#T6" title="SCMFSA7B:th.6">SCMFSA7B:6</a>, <a class="ref" href="scmfsa7b.html#T8" title="SCMFSA7B:th.8">SCMFSA7B:8</a></span>;<br/>
<a NAME="E6:28"/><span class="kw">then </span>
 not <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p4">(<span class="default"><span class="p5"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p5">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">cc</font></span>)</span> <a href="scmfsa6a.html#K7" title="SCMFSA6A:func.7">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<span class="p3">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p4">(<span class="default"><span class="p5"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p5">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">bb</font>)</span>)</span></span>)</span> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p3">(<span class="default"><span class="p4"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c2">aa</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:28"><span class="lab"><font color="Green" title="E28">A4</font></span></a>, <a class="ref" href="scmfsa8c.html#T54" title="SCMFSA8C:th.54">SCMFSA8C:54</a>, <a class="ref" href="scmfsa8c.html#T55" title="SCMFSA8C:th.55">SCMFSA8C:55</a></span>;<br/>
<a NAME="E7:28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A5</font></span>: 
 not <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p5">(<span class="default"><span class="p0"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p0">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">cc</font></span>)</span> <a href="scmfsa6a.html#K7" title="SCMFSA6A:func.7">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<span class="p4">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p5">(<span class="default"><span class="p0"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p0">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">bb</font>)</span>)</span></span>)</span> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<span class="p3">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p4">(<span class="default"><span class="p5"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p5">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c3">bb</font></span>)</span> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c2">aa</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="ref" href="scmfsa7b.html#T6" title="SCMFSA7B:th.6">SCMFSA7B:6</a>, <a class="ref" href="scmfsa8c.html#T54" title="SCMFSA8C:th.54">SCMFSA8C:54</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">IB</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c5">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Maroon" title="c1">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p3">(<span class="default"><span class="p4"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">I4</font> =  <a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> (<span class="p1">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p2">(<span class="default"><span class="p3"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Maroon" title="c1">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<span class="p3">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p4">(<span class="default"><span class="p5"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p5">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>);<br/>
<a NAME="E8:28"/>
 not <font color="Maroon" title="c5">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Maroon" title="c1">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c2">aa</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E27">A3</font></span></a>, <a class="ref" href="scmfsa7b.html#T7" title="SCMFSA7B:th.7">SCMFSA7B:7</a>, <a class="ref" href="scmfsa8c.html#T54" title="SCMFSA8C:th.54">SCMFSA8C:54</a></span>;<br/>
<a NAME="E9:28"/><span class="kw">then </span>
 not <span class="p1">(<span class="default"><font color="Maroon" title="c5">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Maroon" title="c1">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<span class="p2">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p3">(<span class="default"><span class="p4"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p4">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c2">aa</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="ref" href="scmfsa7b.html#T8" title="SCMFSA7B:th.8">SCMFSA7B:8</a>, <a class="ref" href="scmfsa8c.html#T54" title="SCMFSA8C:th.54">SCMFSA8C:54</a></span>;<br/>
<a NAME="E10:28"/><span class="kw">then </span>
 not  <a href="scmfsa_9.html#K2" title="SCMFSA_9:func.2">while&gt;0</a> (<span class="p1">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p2">(<span class="default"><span class="p3"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Maroon" title="c1">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<span class="p3">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p4">(<span class="default"><span class="p5"><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font></span><a href="sfmastr1.html#K3" title="SFMASTR1:func.3">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p5">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>) <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c2">aa</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sfmastr3.html#T8" target="_self" title="SFMASTR3:th.8">Th14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:28"/>
 not  <a href="sfmastr3.html#K2" title="SFMASTR3:func.2">for-up</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">bb</font>,<font color="Maroon" title="c4">cc</font>,<font color="Maroon" title="c5">I</font>) <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c2">aa</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:28"><span class="lab"><font color="Green" title="E29">A5</font></span></a>, <a class="ref" href="scmfsa8c.html#T52" title="SCMFSA8C:th.52">SCMFSA8C:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
