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

<b>let </b><font color="Maroon">aa</font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>let </b><font color="Maroon">I</font> be   <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/>



<b>assume </b><a NAME="E1:16"/><i><font color="Green">E35</font></i>: 
not <font color="Maroon">aa</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">I</font>
 ;<br/>

<b>let </b><font color="Maroon">i</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="scmfsa7b.html#D4">SCMFSA7B:def 4</a><br/>

<b>assume </b><a NAME="E2:16"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">I</font>
 ;<br/>

<a NAME="E3:16"/><b>then </b>
 <a href="sf_mastr.html#K1">UsedIntLoc</a> <font color="Maroon">i</font> <a href="tarski.html#R1">c=</a>  <a href="sf_mastr.html#K2">UsedIntLoc</a> <font color="Maroon">I</font>
 
<b>by </b><i><a class="ref" href="sf_mastr.html#T23">SF_MASTR:23</a></i>;<br/>
<a NAME="E4:16"/><b>then </b><i><font color="Green">E36</font></i>: 
not <font color="Maroon">aa</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1">UsedIntLoc</a> <font color="Maroon">i</font>
 
<b>by </b><i/>;<br/>
<a NAME="E5:16"/><i><font color="Green">E37</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 11 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T35">SCMFSA_2:35</a></i>;<br/>
<a NAME="E6:16"/><i><font color="Green">E38</font></i>: 
(  not  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 10 <a href="nat_1.html#K1">+</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 10 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 11 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/>
<a NAME="E7:16"/><i><font color="Green">E39</font></i>: 
(  not  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 9 <a href="nat_1.html#K1">+</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 8 <a href="nat_1.html#K1">+</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 10 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/>
<a NAME="E8:16"/><i><font color="Green">E40</font></i>: 
(  not  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 8 <a href="nat_1.html#K1">+</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 7 <a href="nat_1.html#K1">+</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 9 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:16_1"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 0 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 2 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 3 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 4 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 5 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 6 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 7 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 8 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 9 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 10 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 11 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 12 )
 </span><b>by </b><i>, , , , <a class="ref" href="cqc_the1.html#T9">CQC_THE1:9</a>, <a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_1"><b>suppose </b></a><a NAME="E1:16_1_1"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:16_1_1"/><b>then </b>
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T122">SCMFSA_2:122</a></i>;<br/><b>hence </b><a NAME="E3:16_1_1"/>
<font color="Maroon">i</font> <a href="scmfsa7b.html#R3">does_not_destroy</a> <font color="Maroon">aa</font>
 <b>by </b><i><a class="ref" href="scmfsa7b.html#T11">SCMFSA7B:11</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_2"><b>suppose </b></a><a NAME="E1:16_1_2"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:16_1_2"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T54">SCMFSA_2:54</a></i>;<br/><a NAME="E4:16_1_2"/>
 <a href="sf_mastr.html#K1">UsedIntLoc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i>, <a class="ref" href="sf_mastr.html#T18">SF_MASTR:18</a></i>;<br/><a NAME="E5:16_1_2"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1">UsedIntLoc</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E6:16_1_2"/>
<font color="Maroon">i</font> <a href="scmfsa7b.html#R3">does_not_destroy</a> <font color="Maroon">aa</font>
 <b>by </b><i>, , <a class="ref" href="scmfsa7b.html#T12">SCMFSA7B:12</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_3"><b>suppose </b></a><a NAME="E1:16_1_3"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:16_1_3"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T55">SCMFSA_2:55</a></i>;<br/><a NAME="E4:16_1_3"/>
 <a href="sf_mastr.html#K1">UsedIntLoc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i>, <a class="ref" href="sf_mastr.html#T18">SF_MASTR:18</a></i>;<br/><a NAME="E5:16_1_3"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1">UsedIntLoc</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E6:16_1_3"/>
<font color="Maroon">i</font> <a href="scmfsa7b.html#R3">does_not_destroy</a> <font color="Maroon">aa</font>
 <b>by </b><i>, , <a class="ref" href="scmfsa7b.html#T13">SCMFSA7B:13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_4"><b>suppose </b></a><a NAME="E1:16_1_4"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 3
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:16_1_4"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T56">SCMFSA_2:56</a></i>;<br/><a NAME="E4:16_1_4"/>
 <a href="sf_mastr.html#K1">UsedIntLoc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i>, <a class="ref" href="sf_mastr.html#T18">SF_MASTR:18</a></i>;<br/><a NAME="E5:16_1_4"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1">UsedIntLoc</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E6:16_1_4"/>
<font color="Maroon">i</font> <a href="scmfsa7b.html#R3">does_not_destroy</a> <font color="Maroon">aa</font>
 <b>by </b><i>, , <a class="ref" href="scmfsa7b.html#T14">SCMFSA7B:14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_5"><b>suppose </b></a><a NAME="E1:16_1_5"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 4
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:16_1_5"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T57">SCMFSA_2:57</a></i>;<br/><a NAME="E4:16_1_5"/>
 <a href="sf_mastr.html#K1">UsedIntLoc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i>, <a class="ref" href="sf_mastr.html#T18">SF_MASTR:18</a></i>;<br/><a NAME="E5:16_1_5"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1">UsedIntLoc</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E6:16_1_5"/>
<font color="Maroon">i</font> <a href="scmfsa7b.html#R3">does_not_destroy</a> <font color="Maroon">aa</font>
 <b>by </b><i>, , <a class="ref" href="scmfsa7b.html#T15">SCMFSA7B:15</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_6"><b>suppose </b></a><a NAME="E1:16_1_6"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 5
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:16_1_6"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T58">SCMFSA_2:58</a></i>;<br/><a NAME="E4:16_1_6"/>
 <a href="sf_mastr.html#K1">UsedIntLoc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i>, <a class="ref" href="sf_mastr.html#T18">SF_MASTR:18</a></i>;<br/><a NAME="E5:16_1_6"/><b>then </b>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1">UsedIntLoc</a> <font color="Maroon">i</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1">UsedIntLoc</a> <font color="Maroon">i</font> )
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E6:16_1_6"/>
<font color="Maroon">i</font> <a href="scmfsa7b.html#R3">does_not_destroy</a> <font color="Maroon">aa</font>
 <b>by </b><i>, , <a class="ref" href="scmfsa7b.html#T16">SCMFSA7B:16</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_7"><b>suppose </b></a><a NAME="E1:16_1_7"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 6
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">l</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:16_1_7"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Maroon">l</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T59">SCMFSA_2:59</a></i>;<br/><b>thus </b><a NAME="E4:16_1_7"/>
<font color="Maroon">i</font> <a href="scmfsa7b.html#R3">does_not_destroy</a> <font color="Maroon">aa</font>
 <b>by </b><i>, <a class="ref" href="scmfsa7b.html#T17">SCMFSA7B:17</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_8"><b>suppose </b></a><a NAME="E1:16_1_8"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 7
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">l</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:16_1_8"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">l</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T60">SCMFSA_2:60</a></i>;<br/><b>thus </b><a NAME="E4:16_1_8"/>
<font color="Maroon">i</font> <a href="scmfsa7b.html#R3">does_not_destroy</a> <font color="Maroon">aa</font>
 <b>by </b><i>, <a class="ref" href="scmfsa7b.html#T18">SCMFSA7B:18</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_9"><b>suppose </b></a><a NAME="E1:16_1_9"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 8
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">l</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:16_1_9"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">l</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T61">SCMFSA_2:61</a></i>;<br/><b>thus </b><a NAME="E4:16_1_9"/>
<font color="Maroon">i</font> <a href="scmfsa7b.html#R3">does_not_destroy</a> <font color="Maroon">aa</font>
 <b>by </b><i>, <a class="ref" href="scmfsa7b.html#T19">SCMFSA7B:19</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_10"><b>suppose </b></a><a NAME="E1:16_1_10"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 9
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:16_1_10"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">f</font>,<font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T62">SCMFSA_2:62</a></i>;<br/><a NAME="E4:16_1_10"/>
 <a href="sf_mastr.html#K1">UsedIntLoc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i>, <a class="ref" href="sf_mastr.html#T21">SF_MASTR:21</a></i>;<br/><a NAME="E5:16_1_10"/><b>then </b>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1">UsedIntLoc</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E6:16_1_10"/>
<font color="Maroon">i</font> <a href="scmfsa7b.html#R3">does_not_destroy</a> <font color="Maroon">aa</font>
 <b>by </b><i>, , <a class="ref" href="scmfsa7b.html#T20">SCMFSA7B:20</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_11"><b>suppose </b></a><a NAME="E1:16_1_11"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 10
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:16_1_11"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>,<font color="Maroon">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T63">SCMFSA_2:63</a></i>;<br/><b>thus </b><a NAME="E4:16_1_11"/>
<font color="Maroon">i</font> <a href="scmfsa7b.html#R3">does_not_destroy</a> <font color="Maroon">aa</font>
 <b>by </b><i>, <a class="ref" href="scmfsa7b.html#T21">SCMFSA7B:21</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_12"><b>suppose </b></a><a NAME="E1:16_1_12"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 11
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:16_1_12"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T64">SCMFSA_2:64</a></i>;<br/><a NAME="E4:16_1_12"/>
 <a href="sf_mastr.html#K1">UsedIntLoc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, <a class="ref" href="sf_mastr.html#T22">SF_MASTR:22</a></i>;<br/><a NAME="E5:16_1_12"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1">UsedIntLoc</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:16_1_12"/>
<font color="Maroon">i</font> <a href="scmfsa7b.html#R3">does_not_destroy</a> <font color="Maroon">aa</font>
 <b>by </b><i>, , <a class="ref" href="scmfsa7b.html#T22">SCMFSA7B:22</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_13"><b>suppose </b></a><a NAME="E1:16_1_13"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 12
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:16_1_13"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T65">SCMFSA_2:65</a></i>;<br/><b>thus </b><a NAME="E4:16_1_13"/>
<font color="Maroon">i</font> <a href="scmfsa7b.html#R3">does_not_destroy</a> <font color="Maroon">aa</font>
 <b>by </b><i>, <a class="ref" href="scmfsa7b.html#T23">SCMFSA7B:23</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
