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

<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/>





<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ,  <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ] means ( ( for <font color="Olive">b<sub>1</sub></font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon">a<sub>1</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>2</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>1</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  holds <font color="Maroon">a<sub>1</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>2</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>1</sub></font> ) );<br/>
<b>assume </b><a NAME="E1:45"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>]
 ;<br/>

<b>assume </b><a NAME="E2:45"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="scmfsa7b.html#R1">does_not_refer</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<b>assume </b><a NAME="E3:45"/><i><font color="Green">E42</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E4:45"/><i><font color="Green">E43</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></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="E5:45"/><i><font color="Green">E44</font></i>: 
(  not  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></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">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 10 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></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="E6:45"/><i><font color="Green">E45</font></i>: 
(  not  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></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">c<sub>5</sub></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">c<sub>5</sub></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="E7:45"/><i><font color="Green">E46</font></i>: 
(  not  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></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">c<sub>5</sub></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">c<sub>5</sub></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><i><font color="Green">E47</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>assume </b><a NAME="E1:45_1"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_1_1"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 2 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 4 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 5 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 6 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 7 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 8 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 9 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 10 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 11 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 12 )
 </span><b>by </b><i><a class="txt" href="scmfsa8b.html#E4:45"><i><font color="Green">E43</font></i></a>, <a class="txt" href="scmfsa8b.html#E5:45"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scmfsa8b.html#E6:45"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scmfsa8b.html#E7:45"><i><font color="Green">E46</font></i></a>, <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="45_1_1_1"><b>suppose </b></a><a NAME="E1:45_1_1_1"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:45_1_1_1"/><b>then </b><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></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><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#D8">AMI_1:def 8</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1"><i><font color="Green">E48</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E2:45_1_1_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="ami_1.html#D8">AMI_1:def 8</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_2"><b>suppose </b></a><a NAME="E1:45_1_1_2"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:45_1_1_2"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T54">SCMFSA_2:54</a></i>;<br/><a NAME="E4:45_1_1_2"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E2:45"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa7b.html#D1">SCMFSA7B:def 1</a></i>;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_1_1_2_1_1"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> or <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:45_1_1_2_1_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E4:45_1_1_2"><i><font color="Green">E50</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1_1_2_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:45_1_1_2_1_1_2"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1"><i><font color="Green">E48</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1_1_2_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_3"><b>suppose </b></a><a NAME="E1:45_1_1_3"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:45_1_1_3"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T55">SCMFSA_2:55</a></i>;<br/><a NAME="E4:45_1_1_3"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E2:45"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_1_1_3"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa7b.html#D1">SCMFSA7B:def 1</a></i>;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_1_1_3_1_1"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> or <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_3_1_1_1"><b>suppose </b></a><a NAME="E1:45_1_1_3_1_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_3"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1"><i><font color="Green">E48</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E4:45_1_1_3"><i><font color="Green">E50</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_3"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1_1_3_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_3_1_1_2"><b>suppose </b></a><a NAME="E1:45_1_1_3_1_1_2"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_3"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1"><i><font color="Green">E48</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_3"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1_1_3_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_4"><b>suppose </b></a><a NAME="E1:45_1_1_4"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:45_1_1_4"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T56">SCMFSA_2:56</a></i>;<br/><a NAME="E4:45_1_1_4"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E2:45"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_1_1_4"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa7b.html#D1">SCMFSA7B:def 1</a></i>;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_4_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_1_1_4_1_1"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> or <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_4_1_1_1"><b>suppose </b></a><a NAME="E1:45_1_1_4_1_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_4"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1"><i><font color="Green">E48</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E4:45_1_1_4"><i><font color="Green">E50</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_4"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1_1_4_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_4_1_1_2"><b>suppose </b></a><a NAME="E1:45_1_1_4_1_1_2"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_4"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1"><i><font color="Green">E48</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_4"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1_1_4_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_5"><b>suppose </b></a><a NAME="E1:45_1_1_5"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 4
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:45_1_1_5"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T57">SCMFSA_2:57</a></i>;<br/><a NAME="E4:45_1_1_5"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E2:45"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_1_1_5"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa7b.html#D1">SCMFSA7B:def 1</a></i>;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_5_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_1_1_5_1_1"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> or <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_5_1_1_1"><b>suppose </b></a><a NAME="E1:45_1_1_5_1_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_5"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1"><i><font color="Green">E48</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E4:45_1_1_5"><i><font color="Green">E50</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_5"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1_1_5_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_5_1_1_2"><b>suppose </b></a><a NAME="E1:45_1_1_5_1_1_2"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_5"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1"><i><font color="Green">E48</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_5"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1_1_5_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_6"><b>suppose </b></a><a NAME="E1:45_1_1_6"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 5
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:45_1_1_6"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T58">SCMFSA_2:58</a></i>;<br/><a NAME="E4:45_1_1_6"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E2:45"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_1_1_6"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa7b.html#D1">SCMFSA7B:def 1</a></i>;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_6_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_1_1_6_1_1"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> or ( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font> ) or ( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_6_1_1_1"><b>suppose </b></a><a NAME="E1:45_1_1_6_1_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_6"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E4:45_1_1_6"><i><font color="Green">E50</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E4:45_1_1_6"><i><font color="Green">E50</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_6"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1_1_6_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_6_1_1_2"><b>suppose </b></a><a NAME="E1:45_1_1_6_1_1_2"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font> )
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_6"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E4:45_1_1_6"><i><font color="Green">E50</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E4:45_1_1_6"><i><font color="Green">E50</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_6"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1_1_6_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_6_1_1_3"><b>suppose </b></a><a NAME="E1:45_1_1_6_1_1_3"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font> )
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_6"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1"><i><font color="Green">E48</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_6"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1_1_6_1_1_3"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_7"><b>suppose </b></a><a NAME="E1:45_1_1_7"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 6
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></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="E3:45_1_1_7"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T59">SCMFSA_2:59</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_7"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1"><i><font color="Green">E48</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_7"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_8"><b>suppose </b></a><a NAME="E1:45_1_1_8"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 7
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:45_1_1_8"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T60">SCMFSA_2:60</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_8"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1"><i><font color="Green">E48</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_8"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_9"><b>suppose </b></a><a NAME="E1:45_1_1_9"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 8
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:45_1_1_9"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T61">SCMFSA_2:61</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_9"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1"><i><font color="Green">E48</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_9"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_10"><b>suppose </b></a><a NAME="E1:45_1_1_10"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 9
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>10</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:45_1_1_10"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T62">SCMFSA_2:62</a></i>;<br/><a NAME="E4:45_1_1_10"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E2:45"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_1_1_10"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa7b.html#D1">SCMFSA7B:def 1</a></i>;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_10_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_1_1_10_1_1"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> or <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_10_1_1_1"><b>suppose </b></a><a NAME="E1:45_1_1_10_1_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:45_1_1_10_1_1_1"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E4:45_1_1_10_1_1_1"/><i><font color="Green">E53</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E6:45_1_1_10_1_1_1"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E7:45_1_1_10_1_1_1"/><i><font color="Green">E55</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45_1_1_10_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>;<br/><a NAME="E8:45_1_1_10_1_1_1"/>
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>10</sub></font> )
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E4:45_1_1_10"><i><font color="Green">E50</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_1_1_10_1_1_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scmfsa8b.html#E6:45_1_1_10_1_1_1"><i><font color="Green">E54</font></i></a></i>;<br/><b>hence </b><a NAME="E9:45_1_1_10_1_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_10"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E4:45_1_1_10_1_1_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmfsa8b.html#E7:45_1_1_10_1_1_1"><i><font color="Green">E55</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_10_1_1_2"><b>suppose </b></a><a NAME="E1:45_1_1_10_1_1_2"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_10"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1"><i><font color="Green">E48</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_10"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1_1_10_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_11"><b>suppose </b></a><a NAME="E1:45_1_1_11"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 10
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>10</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:45_1_1_11"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T63">SCMFSA_2:63</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_11"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1"><i><font color="Green">E48</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_11"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_12"><b>suppose </b></a><a NAME="E1:45_1_1_12"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 11
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:45_1_1_12"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T64">SCMFSA_2:64</a></i>;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_12_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_1_1_12_1_1"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> or <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_12_1_1_1"><b>suppose </b></a><a NAME="E1:45_1_1_12_1_1_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_12"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_12"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1_1_12_1_1_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_12_1_1_2"><b>suppose </b></a><a NAME="E1:45_1_1_12_1_1_2"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_12"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1"><i><font color="Green">E48</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_12"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1_1_12_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1_13"><b>suppose </b></a><a NAME="E1:45_1_1_13"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 12
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:45_1_1_13"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T65">SCMFSA_2:65</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_13"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_1"><i><font color="Green">E48</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_1_1_13"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_2_1"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 2 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 4 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 5 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 6 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 7 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 8 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 9 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 10 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 11 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 12 )
 </span><b>by </b><i><a class="txt" href="scmfsa8b.html#E4:45"><i><font color="Green">E43</font></i></a>, <a class="txt" href="scmfsa8b.html#E5:45"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scmfsa8b.html#E6:45"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scmfsa8b.html#E7:45"><i><font color="Green">E46</font></i></a>, <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="45_2_1_1"><b>suppose </b></a><a NAME="E1:45_2_1_1"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:45_2_1_1"/><b>then </b><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>5</sub></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><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#D8">AMI_1:def 8</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E2:45_2_1_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="ami_1.html#D8">AMI_1:def 8</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_2_1_2"><b>suppose </b></a><a NAME="E1:45_2_1_2"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:45_2_1_2"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T54">SCMFSA_2:54</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_2"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_2"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_2_1_3"><b>suppose </b></a><a NAME="E1:45_2_1_3"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:45_2_1_3"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T55">SCMFSA_2:55</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_3"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_3"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_2_1_4"><b>suppose </b></a><a NAME="E1:45_2_1_4"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:45_2_1_4"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T56">SCMFSA_2:56</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_4"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_4"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_2_1_5"><b>suppose </b></a><a NAME="E1:45_2_1_5"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 4
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:45_2_1_5"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T57">SCMFSA_2:57</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_5"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_5"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_2_1_6"><b>suppose </b></a><a NAME="E1:45_2_1_6"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 5
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:45_2_1_6"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T58">SCMFSA_2:58</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_6"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_6"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_2_1_7"><b>suppose </b></a><a NAME="E1:45_2_1_7"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 6
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></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="E3:45_2_1_7"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T59">SCMFSA_2:59</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_7"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_7"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_2_1_8"><b>suppose </b></a><a NAME="E1:45_2_1_8"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 7
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:45_2_1_8"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T60">SCMFSA_2:60</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_8"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_8"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_2_1_9"><b>suppose </b></a><a NAME="E1:45_2_1_9"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 8
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:45_2_1_9"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T61">SCMFSA_2:61</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_9"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_9"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_2_1_10"><b>suppose </b></a><a NAME="E1:45_2_1_10"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 9
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>10</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:45_2_1_10"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T62">SCMFSA_2:62</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_10"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_10"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_2_1_11"><b>suppose </b></a><a NAME="E1:45_2_1_11"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 10
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>10</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:45_2_1_11"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T63">SCMFSA_2:63</a></i>;<br/><a NAME="E4:45_2_1_11"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E2:45"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_2_1_11"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa7b.html#D1">SCMFSA7B:def 1</a></i>;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_2_1_11_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_2_1_11_1_1"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> or <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_2_1_11_1_1_1"><b>suppose </b></a><a NAME="E1:45_2_1_11_1_1_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 ;<br/><div class="add"><b>consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:45_2_1_11_1_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E4:45_2_1_11_1_1_1"/><i><font color="Green">E52</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="funct_7.html#K2">+*</a> <font color="Maroon">c<sub>11</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E6:45_2_1_11_1_1_1"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E7:45_2_1_11_1_1_1"/><i><font color="Green">E54</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="funct_7.html#K2">+*</a> <font color="Maroon">c<sub>12</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>;<br/><a NAME="E8:45_2_1_11_1_1_1"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E4:45_2_1_11"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_2_1_11_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="txt" href="scmfsa8b.html#E6:45_2_1_11_1_1_1"><i><font color="Green">E53</font></i></a></i>;<br/><a NAME="E9:45_2_1_11_1_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E4:45_2_1_11"><i><font color="Green">E49</font></i></a></i>;<br/><b>hence </b><a NAME="E10:45_2_1_11_1_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_2_1_11"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_2_1_11_1_1_1"><i><font color="Green">E50</font></i></a>, <a class="txt" href="scmfsa8b.html#E4:45_2_1_11_1_1_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scmfsa8b.html#E7:45_2_1_11_1_1_1"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmfsa8b.html#E8:45_2_1_11_1_1_1"><i><font color="Green">E55</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_2_1_11_1_1_2"><b>suppose </b></a><a NAME="E1:45_2_1_11_1_1_2"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_11"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_11"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_2_1_11_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_2_1_12"><b>suppose </b></a><a NAME="E1:45_2_1_12"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 11
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:45_2_1_12"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T64">SCMFSA_2:64</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_12"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_12"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_2_1_13"><b>suppose </b></a><a NAME="E1:45_2_1_13"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 12
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:45_2_1_13"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T65">SCMFSA_2:65</a></i>;<br/><a NAME="E4:45_2_1_13"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E2:45"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_2_1_13"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa7b.html#D1">SCMFSA7B:def 1</a></i>;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_2_1_13_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_2_1_13_1_1"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> or <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_2_1_13_1_1_1"><b>suppose </b></a><a NAME="E1:45_2_1_13_1_1_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/><div class="add"><b>consider </b><font color="Maroon">c<sub>10</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:45_2_1_13_1_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E4:45_2_1_13_1_1_1"/><i><font color="Green">E52</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="finseq_2.html#K2">|-&gt;</a> 0
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E6:45_2_1_13_1_1_1"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E7:45_2_1_13_1_1_1"/><i><font color="Green">E54</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="finseq_2.html#K2">|-&gt;</a> 0
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>;<br/><b>thus </b><a NAME="E8:45_2_1_13_1_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_2_1_13"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmfsa8b.html#E4:45_2_1_13"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_2_1_13_1_1_1"><i><font color="Green">E50</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_2_1_13_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="txt" href="scmfsa8b.html#E4:45_2_1_13_1_1_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scmfsa8b.html#E6:45_2_1_13_1_1_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmfsa8b.html#E7:45_2_1_13_1_1_1"><i><font color="Green">E54</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_2_1_13_1_1_2"><b>suppose </b></a><a NAME="E1:45_2_1_13_1_1_2"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_13"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_2_1_13"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_2_1_13_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E10:45"/>
<font color="Maroon">S<sub>1</sub></font>[ <a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>, <a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>]
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E8:45"><i><font color="Green">E47</font></i></a></i>;<br/>

<div><i><font color="Green">E48</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="45_3"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_3_1"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 2 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 4 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 5 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 6 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 7 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 8 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 9 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 10 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 11 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 12 )
 </span><b>by </b><i><a class="txt" href="scmfsa8b.html#E4:45"><i><font color="Green">E43</font></i></a>, <a class="txt" href="scmfsa8b.html#E5:45"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scmfsa8b.html#E6:45"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scmfsa8b.html#E7:45"><i><font color="Green">E46</font></i></a>, <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="45_3_1_1"><b>suppose </b></a><a NAME="E1:45_3_1_1"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:45_3_1_1"/><b>then </b><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></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><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D8">AMI_1:def 8</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45"><i><font color="Green">E42</font></i></a>, <a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E2:45_3_1_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="ami_1.html#D8">AMI_1:def 8</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_3_1_2"><b>suppose </b></a><a NAME="E1:45_3_1_2"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:45_3_1_2"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T54">SCMFSA_2:54</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_3_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_3_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_3_1_3"><b>suppose </b></a><a NAME="E1:45_3_1_3"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:45_3_1_3"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T55">SCMFSA_2:55</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_3_1_3"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_3_1_3"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_3_1_4"><b>suppose </b></a><a NAME="E1:45_3_1_4"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:45_3_1_4"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T56">SCMFSA_2:56</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_3_1_4"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_3_1_4"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_3_1_5"><b>suppose </b></a><a NAME="E1:45_3_1_5"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 4
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:45_3_1_5"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T57">SCMFSA_2:57</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_3_1_5"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_3_1_5"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_3_1_6"><b>suppose </b></a><a NAME="E1:45_3_1_6"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 5
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:45_3_1_6"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T58">SCMFSA_2:58</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_3_1_6"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_3_1_6"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_3_1_7"><b>suppose </b></a><a NAME="E1:45_3_1_7"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 6
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>7</sub></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="E3:45_3_1_7"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T59">SCMFSA_2:59</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_3_1_7"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_3_1_7"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_3_1_8"><b>suppose </b></a><a NAME="E1:45_3_1_8"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 7
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:45_3_1_8"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T60">SCMFSA_2:60</a></i>;<br/><a NAME="E4:45_3_1_8"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E2:45"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_3_1_8"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa7b.html#D1">SCMFSA7B:def 1</a></i>;<br/><a NAME="E5:45_3_1_8"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a></i>;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_3_1_8_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_3_1_8_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_3_1_8_1_1_1"><b>suppose </b></a><a NAME="E1:45_3_1_8_1_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_3_1_8"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_3_1_8"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E5:45_3_1_8"><i><font color="Green">E50</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_3_1_8_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_3_1_8_1_1_2"><b>suppose </b></a><a NAME="E1:45_3_1_8_1_1_2"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_3_1_8"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_3_1_8"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E5:45_3_1_8"><i><font color="Green">E50</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_3_1_8_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_3_1_9"><b>suppose </b></a><a NAME="E1:45_3_1_9"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 8
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:45_3_1_9"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T61">SCMFSA_2:61</a></i>;<br/><a NAME="E4:45_3_1_9"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E2:45"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_3_1_9"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa7b.html#D1">SCMFSA7B:def 1</a></i>;<br/><a NAME="E5:45_3_1_9"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E1:45"><i><font color="Green">E40</font></i></a></i>;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_3_1_9_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_3_1_9_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or <font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_3_1_9_1_1_1"><b>suppose </b></a><a NAME="E1:45_3_1_9_1_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_3_1_9"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_3_1_9"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E5:45_3_1_9"><i><font color="Green">E50</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_3_1_9_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_3_1_9_1_1_2"><b>suppose </b></a><a NAME="E1:45_3_1_9_1_1_2"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_3_1_9"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_3_1_9"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa8b.html#E5:45_3_1_9"><i><font color="Green">E50</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:45_3_1_9_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_3_1_10"><b>suppose </b></a><a NAME="E1:45_3_1_10"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 9
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:45_3_1_10"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T62">SCMFSA_2:62</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_3_1_10"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_3_1_10"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_3_1_11"><b>suppose </b></a><a NAME="E1:45_3_1_11"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 10
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>9</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:45_3_1_11"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T63">SCMFSA_2:63</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_3_1_11"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_3_1_11"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_3_1_12"><b>suppose </b></a><a NAME="E1:45_3_1_12"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 11
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>7</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:45_3_1_12"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T64">SCMFSA_2:64</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_3_1_12"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_3_1_12"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_3_1_13"><b>suppose </b></a><a NAME="E1:45_3_1_13"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 12
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>7</sub></font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">c<sub>8</sub></font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:45_3_1_13"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T65">SCMFSA_2:65</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45_3_1_13"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E3:45"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:45_3_1_13"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E12:45"/>
(  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> &amp;  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>;<br/>
<b>hence </b><a NAME="E13:45"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa8b.html#E11:45"><i><font color="Green">E48</font></i></a></i>;<br/>


</div>
