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

<b>let </b><font color="Maroon">s1</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">s2</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">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">i</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:43"/><i><font color="Green">E29</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <font color="Maroon">s2</font>
 <b>and </b><br/><a NAME="E2:43"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 ;<br/>

<b>set </b><font color="Maroon">D</font> = <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> ;<br/>
<b>consider </b><font color="Maroon">k1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E4:43"/><i><font color="Green">E31</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">k1</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T21">SCMFSA_2:21</a></i>;<br/>
<a NAME="E5:43"/><i><font color="Green">E32</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa_2.html#K7">Next</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <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">s2</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1"><b>proof </b></a><div class="add">

<b>thus </b><span class="p1">(<span class="default"><a href="scmfsa_2.html#K7">Next</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font> = 
<span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><font color="Maroon">k1</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T32">SCMFSA_2:32</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">k1</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_4.html#D1">SCMFSA_4:def 1</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">k1</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>

<br/>.= 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><font color="Maroon">k1</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_2.html#T32">SCMFSA_2:32</a></i>
<br/>.= 
 <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">s2</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="scmfsa_4.html#D1">SCMFSA_4:def 1</a></i>
;<br/>


</div><b>end;</b></div>
<div><i><font color="Green">E33</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_2"><b>now </b></a><div class="add"><b>assume </b><b>that </b><br/><a NAME="E1:43_2"/><i><font color="Green">E34</font></i>: 
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 6 or 8 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> )
 <b>and </b><br/><a NAME="E2:43_2"/><i><font color="Green">E38</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><b>set </b><font color="Maroon">I</font> =  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font>;<br/><a NAME="E3:43_2"/><i><font color="Green">E40</font></i>: 
not  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K9">{</a><span class="default">0,6,7,8</span><a href="domain_1.html#K9">}</a></span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:43_2_1"/><i><font color="Green">E41</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K9">{</a><span class="default">0,6,7,8</span><a href="domain_1.html#K9">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:43_2_1_1"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 0 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 6 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 7 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 8 )
 </span><b>by </b><i><a class="txt" href="scmfsa6a.html#E1:43"><i><font color="Green">E29</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_2_1_1_1"><b>suppose </b></a><a NAME="E1:43_2_1_1_1"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:43_2_1_1_1"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_2_1_1_2"><b>suppose </b></a><a NAME="E1:43_2_1_1_2"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 6
 ;<br/><div class="add"><b>hence </b><a NAME="E2:43_2_1_1_2"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_2_1_1_3"><b>suppose </b></a><a NAME="E1:43_2_1_1_3"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 7
 ;<br/><div class="add"><b>hence </b><a NAME="E2:43_2_1_1_3"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_2_1_1_4"><b>suppose </b></a><a NAME="E1:43_2_1_1_4"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 8
 ;<br/><div class="add"><b>hence </b><a NAME="E2:43_2_1_1_4"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E4:43_2"/>
not  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K8">{</a><span class="default">6,7,8</span><a href="domain_1.html#K8">}</a></span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:43_2_2"/><i><font color="Green">E42</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K8">{</a><span class="default">6,7,8</span><a href="domain_1.html#K8">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:43_2_2_1"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 6 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 7 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 8 )
 </span><b>by </b><i><a class="txt" href="scmfsa6a.html#E1:43"><i><font color="Green">E29</font></i></a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_2_2_1_1"><b>suppose </b></a><a NAME="E1:43_2_2_1_1"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 6
 ;<br/><div class="add"><b>hence </b><a NAME="E2:43_2_2_1_1"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_2_2_1_2"><b>suppose </b></a><a NAME="E1:43_2_2_1_2"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 7
 ;<br/><div class="add"><b>hence </b><a NAME="E2:43_2_2_1_2"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_2_2_1_3"><b>suppose </b></a><a NAME="E1:43_2_2_1_3"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 8
 ;<br/><div class="add"><b>hence </b><a NAME="E2:43_2_2_1_3"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E5:43_2"/><b>then </b><i><font color="Green">E43</font></i>: 
 <a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="scmfsa_4.html#D3">SCMFSA_4:def 3</a></i>;<br/> <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">i</font>,<font color="Maroon">s1</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</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/>.= 
 <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">s1</font></span>)</span>
<b>by </b><i>, </i>
;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</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="scmfsa6a.html#E1:43"><i><font color="Green">E29</font></i></a>, </i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E7:43"/><i><font color="Green">E44</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 11 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T35">SCMFSA_2:35</a></i>;<br/>
<a NAME="E8:43"/><i><font color="Green">E45</font></i>: 
(  not  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 10 <a href="nat_1.html#K1">+</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 10 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 11 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/>
<a NAME="E9:43"/><i><font color="Green">E91</font></i>: 
(  not  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 9 <a href="nat_1.html#K1">+</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 8 <a href="nat_1.html#K1">+</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 10 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/>
<a NAME="E10:43"/><i><font color="Green">E92</font></i>: 
(  not  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 8 <a href="nat_1.html#K1">+</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 7 <a href="nat_1.html#K1">+</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 9 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:43_3"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 0 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 2 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 3 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 4 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 5 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 6 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 7 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 8 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 9 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 10 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 11 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 12 )
 </span><b>by </b><i>, , , <a class="txt" href="scmfsa6a.html#E1:43"><i><font color="Green">E29</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="43_3_1"><b>suppose </b></a><a NAME="E1:43_3_1"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:43_3_1"/><b>then </b><i><font color="Green">E93</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T122">SCMFSA_2:122</a></i>;<br/><a NAME="E3:43_3_1"/><b>then </b>
(  <a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s1</font> &amp;  <a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> )
 <b>by </b><i><a class="ref" href="ami_1.html#D8">AMI_1:def 8</a></i>;<br/><b>hence </b><a NAME="E4:43_3_1"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font> <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> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> )
 <b>by </b><i>, , <a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a>, <a class="ref" href="scmfsa_4.html#T8">SCMFSA_4:8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_2"><b>suppose </b></a><a NAME="E1:43_3_2"/><i><font color="Green">E94</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">db</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:43_3_2"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T54">SCMFSA_2:54</a></i>;<br/><a NAME="E4:43_3_2"/><i><font color="Green">E96</font></i>: 
 <a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_4.html#T9">SCMFSA_4:9</a></i>;<br/><b>thus </b><a NAME="E5:43_3_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font> <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> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a></i>;<br/><div><i><font color="Green">E97</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:43_3_2_1_1"/>
( <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> or <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_2_1_1_1"><b>suppose </b></a><a NAME="E1:43_3_2_1_1_1"/><i><font color="Green">E98</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</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">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</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="43_3_2_1_1_2"><b>suppose </b></a><a NAME="E1:43_3_2_1_1_2"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</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">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</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><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">f</font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>
;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:43_3_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E6:43"><i><font color="Green">E33</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_3"><b>suppose </b></a><a NAME="E1:43_3_3"/><i><font color="Green">E100</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">db</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:43_3_3"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T55">SCMFSA_2:55</a></i>;<br/><a NAME="E4:43_3_3"/><i><font color="Green">E102</font></i>: 
 <a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_4.html#T10">SCMFSA_4:10</a></i>;<br/><b>thus </b><a NAME="E5:43_3_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font> <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> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a></i>;<br/><div><i><font color="Green">E103</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:43_3_3_1_1"/>
( <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> or <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_3_1_1_1"><b>suppose </b></a><a NAME="E1:43_3_3_1_1_1"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font>
 ;<br/><div class="add"><a NAME="E2:43_3_3_1_1_1"/>
( <font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> &amp; <font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font> )
 <b>by </b><i>, </i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</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> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</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="43_3_3_1_1_2"><b>suppose </b></a><a NAME="E1:43_3_3_1_1_2"/><i><font color="Green">E105</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</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">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</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><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_3_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">f</font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>
;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:43_3_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E6:43"><i><font color="Green">E33</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_4"><b>suppose </b></a><a NAME="E1:43_3_4"/><i><font color="Green">E106</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 3
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">db</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:43_3_4"/><i><font color="Green">E107</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T56">SCMFSA_2:56</a></i>;<br/><a NAME="E4:43_3_4"/><i><font color="Green">E108</font></i>: 
 <a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_4.html#T11">SCMFSA_4:11</a></i>;<br/><b>thus </b><a NAME="E5:43_3_4"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font> <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> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a></i>;<br/><div><i><font color="Green">E110</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_4_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_4_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:43_3_4_1_1"/>
( <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> or <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_4_1_1_1"><b>suppose </b></a><a NAME="E1:43_3_4_1_1_1"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font>
 ;<br/><div class="add"><a NAME="E2:43_3_4_1_1_1"/>
( <font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> &amp; <font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font> )
 <b>by </b><i>, </i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</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> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</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="43_3_4_1_1_2"><b>suppose </b></a><a NAME="E1:43_3_4_1_1_2"/><i><font color="Green">E112</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</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">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</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><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_4_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">f</font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>
;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:43_3_4"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E6:43"><i><font color="Green">E33</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_5"><b>suppose </b></a><a NAME="E1:43_3_5"/><i><font color="Green">E113</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 4
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">db</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:43_3_5"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T57">SCMFSA_2:57</a></i>;<br/><b>thus </b><a NAME="E4:43_3_5"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font> <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> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a></i>;<br/><a NAME="E5:43_3_5"/><i><font color="Green">E115</font></i>: 
 <a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_4.html#T12">SCMFSA_4:12</a></i>;<br/><div><i><font color="Green">E116</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_5_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_5_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:43_3_5_1_1"/>
( <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> or <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_5_1_1_1"><b>suppose </b></a><a NAME="E1:43_3_5_1_1_1"/><i><font color="Green">E117</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font>
 ;<br/><div class="add"><a NAME="E2:43_3_5_1_1_1"/>
( <font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> &amp; <font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font> )
 <b>by </b><i>, </i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</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> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</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="43_3_5_1_1_2"><b>suppose </b></a><a NAME="E1:43_3_5_1_1_2"/><i><font color="Green">E118</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</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">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</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><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_5_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">f</font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>
;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:43_3_5"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E6:43"><i><font color="Green">E33</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_6"><b>suppose </b></a><a NAME="E1:43_3_6"/><i><font color="Green">E119</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 5
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">db</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:43_3_6"/><i><font color="Green">E120</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T58">SCMFSA_2:58</a></i>;<br/><a NAME="E4:43_3_6"/><i><font color="Green">E121</font></i>: 
 <a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_4.html#T13">SCMFSA_4:13</a></i>;<br/><b>thus </b><a NAME="E5:43_3_6"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font> <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> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a></i>;<br/><div><i><font color="Green">E122</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_6_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_6_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:43_3_6_1_1"/>
( <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">db</font> or ( <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">db</font> ) or ( <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">db</font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_6_1_1_1"><b>suppose </b></a><a NAME="E1:43_3_6_1_1_1"/><i><font color="Green">E123</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">db</font>
 ;<br/><div class="add"><a NAME="E2:43_3_6_1_1_1"/>
( <font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> &amp; <font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font> )
 <b>by </b><i>, </i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</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> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</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="43_3_6_1_1_2"><b>suppose </b></a><a NAME="E1:43_3_6_1_1_2"/><i><font color="Green">E124</font></i>: 
( <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">db</font> )
 ;<br/><div class="add"><a NAME="E2:43_3_6_1_1_2"/>
( <font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> &amp; <font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font> )
 <b>by </b><i>, </i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font></span>)</span> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</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> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</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="43_3_6_1_1_3"><b>suppose </b></a><a NAME="E1:43_3_6_1_1_3"/><i><font color="Green">E125</font></i>: 
( <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">db</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">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</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><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_6_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">f</font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>
;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:43_3_6"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E6:43"><i><font color="Green">E33</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_7"><b>suppose </b></a><a NAME="E1:43_3_7"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 6
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">loc</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="E3:43_3_7"/><i><font color="Green">E126</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Maroon">loc</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T59">SCMFSA_2:59</a></i>;<br/><a NAME="E4:43_3_7"/><i><font color="Green">E127</font></i>: 
 <a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <span class="p1">(<span class="default"><font color="Maroon">loc</font> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a>, <a class="ref" href="scmfsa_4.html#T14">SCMFSA_4:14</a></i>;<br/> <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">i</font>,<font color="Maroon">s1</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</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/>.= 
<font color="Maroon">loc</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a>, <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</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="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/><br/><div><i><font color="Green">E128</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_7_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a>, <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</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="hs2(this)" href="javascript:()" title="43_3_7_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">f</font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a>, <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>
;<br/></div><b>end;</b></div><b>hence </b><a NAME="E9:43_3_7"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_8"><b>suppose </b></a><a NAME="E1:43_3_8"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 7
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">loc</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:43_3_8"/><i><font color="Green">E129</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">loc</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T60">SCMFSA_2:60</a></i>;<br/><a NAME="E4:43_3_8"/><i><font color="Green">E130</font></i>: 
 <a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p1">(<span class="default"><font color="Maroon">loc</font> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a>, <a class="ref" href="scmfsa_4.html#T15">SCMFSA_4:15</a></i>;<br/><div><i><font color="Green">E131</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_8_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
;<br/></div><b>end;</b></div><div><i><font color="Green">E132</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_8_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">f</font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
;<br/></div><b>end;</b></div><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_8_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:43_3_8_3_1"/>
( <font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</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="43_3_8_3_1_1"><b>suppose </b></a><a NAME="E1:43_3_8_3_1_1"/><i><font color="Green">E133</font></i>: 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:43_3_8_3_1_1"/><b>then </b><i><font color="Green">E134</font></i>: 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i>, </i>;<br/> <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">i</font>,<font color="Maroon">s1</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</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/>.= 
<font color="Maroon">loc</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a>, , <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</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="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa6a.html#T8" target="_self">Th8</a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_8_3_1_2"><b>suppose </b></a><a NAME="E1:43_3_8_3_1_2"/><i><font color="Green">E135</font></i>: 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:43_3_8_3_1_2"/><b>then </b><i><font color="Green">E136</font></i>: 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i>, </i>;<br/> <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">i</font>,<font color="Maroon">s1</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</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/>.= 
 <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">s1</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a>, , <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</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="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa6a.html#T8" target="_self">Th8</a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div><b>thus </b><a NAME="E8:43_3_8"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</font></i></a>, <a class="txt" href="scmfsa6a.html#E6:43"><i><font color="Green">E33</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_9"><b>suppose </b></a><a NAME="E1:43_3_9"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 8
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">loc</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:43_3_9"/><i><font color="Green">E137</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">loc</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T61">SCMFSA_2:61</a></i>;<br/><a NAME="E4:43_3_9"/><i><font color="Green">E138</font></i>: 
 <a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <span class="p1">(<span class="default"><font color="Maroon">loc</font> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a>, <a class="ref" href="scmfsa_4.html#T16">SCMFSA_4:16</a></i>;<br/><div><i><font color="Green">E139</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_9_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
;<br/></div><b>end;</b></div><div><i><font color="Green">E140</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_9_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">f</font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
;<br/></div><b>end;</b></div><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_9_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:43_3_9_3_1"/>
( <font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or <font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</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="43_3_9_3_1_1"><b>suppose </b></a><a NAME="E1:43_3_9_3_1_1"/><i><font color="Green">E141</font></i>: 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:43_3_9_3_1_1"/><b>then </b><i><font color="Green">E142</font></i>: 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i>, </i>;<br/> <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">i</font>,<font color="Maroon">s1</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</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/>.= 
<font color="Maroon">loc</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a>, , <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</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="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa6a.html#T8" target="_self">Th8</a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_9_3_1_2"><b>suppose </b></a><a NAME="E1:43_3_9_3_1_2"/><i><font color="Green">E143</font></i>: 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/><div class="add"><a NAME="E2:43_3_9_3_1_2"/><b>then </b><i><font color="Green">E144</font></i>: 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i>, </i>;<br/> <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">i</font>,<font color="Maroon">s1</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</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/>.= 
 <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">s1</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a>, , <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</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="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa6a.html#T8" target="_self">Th8</a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div><b>thus </b><a NAME="E8:43_3_9"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</font></i></a>, <a class="txt" href="scmfsa6a.html#E6:43"><i><font color="Green">E33</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_10"><b>suppose </b></a><a NAME="E1:43_3_10"/><i><font color="Green">E145</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 9
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">db</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:43_3_10"/><i><font color="Green">E146</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">f</font>,<font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T62">SCMFSA_2:62</a></i>;<br/><a NAME="E4:43_3_10"/><i><font color="Green">E147</font></i>: 
 <a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_4.html#T17">SCMFSA_4:17</a></i>;<br/><b>thus </b><a NAME="E5:43_3_10"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font> <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> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a></i>;<br/><div><i><font color="Green">E148</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_10_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_10_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:43_3_10_1_1"/>
( <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> or <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_10_1_1_1"><b>suppose </b></a><a NAME="E1:43_3_10_1_1_1"/><i><font color="Green">E149</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">m</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:43_3_10_1_1_1"/><i><font color="Green">E150</font></i>: 
<font color="Maroon">m</font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font></span>)</span>
 <b>and </b><br/><a NAME="E4:43_3_10_1_1_1"/><i><font color="Green">E151</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">da</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">f</font>,<font color="Maroon">db</font></span>)</span>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">m</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">m2</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E6:43_3_10_1_1_1"/><i><font color="Green">E152</font></i>: 
<font color="Maroon">m2</font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font></span>)</span>
 <b>and </b><br/><a NAME="E7:43_3_10_1_1_1"/><i><font color="Green">E153</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">da</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">f</font>,<font color="Maroon">db</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">m2</font>
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>;<br/><a NAME="E8:43_3_10_1_1_1"/>
( <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m2</font> &amp; <font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> )
 <b>by </b><i>, <a class="ref" href="scmfsa6a.html#T8" target="_self">Th8</a>, , </i>;<br/><b>hence </b><a NAME="E9:43_3_10_1_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa6a.html#T9" target="_self">Th9</a>, , <a class="ref" href="scmfsa_4.html#T17">SCMFSA_4:17</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_10_1_1_2"><b>suppose </b></a><a NAME="E1:43_3_10_1_1_2"/><i><font color="Green">E154</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</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">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</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><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_10_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">f</font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>
;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:43_3_10"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E6:43"><i><font color="Green">E33</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_11"><b>suppose </b></a><a NAME="E1:43_3_11"/><i><font color="Green">E155</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 10
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">db</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:43_3_11"/><i><font color="Green">E156</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>,<font color="Maroon">db</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">da</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T63">SCMFSA_2:63</a></i>;<br/><a NAME="E4:43_3_11"/><i><font color="Green">E157</font></i>: 
 <a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_4.html#T18">SCMFSA_4:18</a></i>;<br/><b>thus </b><a NAME="E5:43_3_11"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font> <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> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a></i>;<br/><div><i><font color="Green">E158</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_11_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</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="hs2(this)" href="javascript:()" title="43_3_11_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">g</font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_11_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:43_3_11_2_1"/>
( <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> or <font color="Maroon">g</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">f</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_11_2_1_1"><b>suppose </b></a><a NAME="E1:43_3_11_2_1_1"/><i><font color="Green">E168</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 ;<br/><div class="add"><b>consider </b><font color="Maroon">m1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:43_3_11_2_1_1"/><i><font color="Green">E170</font></i>: 
<font color="Maroon">m1</font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font></span>)</span>
 <b>and </b><br/><a NAME="E4:43_3_11_2_1_1"/><i><font color="Green">E171</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">f</font>,<font color="Maroon">db</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">da</font></span>)</span>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font></span>)</span> <a href="funct_7.html#K2">+*</a> <font color="Maroon">m1</font>,<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</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">m2</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E6:43_3_11_2_1_1"/><i><font color="Green">E172</font></i>: 
<font color="Maroon">m2</font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font></span>)</span>
 <b>and </b><br/><a NAME="E7:43_3_11_2_1_1"/><i><font color="Green">E173</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">f</font>,<font color="Maroon">db</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">da</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font></span>)</span> <a href="funct_7.html#K2">+*</a> <font color="Maroon">m2</font>,<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>;<br/><a NAME="E8:43_3_11_2_1_1"/>
( <font color="Maroon">m1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m2</font> &amp; <font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> &amp; <font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> )
 <b>by </b><i>, <a class="ref" href="scmfsa6a.html#T8" target="_self">Th8</a>, , </i>;<br/><b>hence </b><a NAME="E9:43_3_11_2_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, , <a class="ref" href="scmfsa6a.html#T9" target="_self">Th9</a>, , <a class="ref" href="scmfsa_4.html#T18">SCMFSA_4:18</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_11_2_1_2"><b>suppose </b></a><a NAME="E1:43_3_11_2_1_2"/><i><font color="Green">E174</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">f</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">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">g</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">g</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">g</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">g</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</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><b>hence </b><a NAME="E8:43_3_11"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E6:43"><i><font color="Green">E33</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_12"><b>suppose </b></a><a NAME="E1:43_3_12"/><i><font color="Green">E175</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 11
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:43_3_12"/><i><font color="Green">E176</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T64">SCMFSA_2:64</a></i>;<br/><a NAME="E4:43_3_12"/><i><font color="Green">E177</font></i>: 
 <a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_4.html#T19">SCMFSA_4:19</a></i>;<br/><b>thus </b><a NAME="E5:43_3_12"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font> <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> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a></i>;<br/><div><i><font color="Green">E178</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_12_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_12_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:43_3_12_1_1"/>
( <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> or <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_12_1_1_1"><b>suppose </b></a><a NAME="E1:43_3_12_1_1_1"/><i><font color="Green">E179</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</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">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</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">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</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="43_3_12_1_1_2"><b>suppose </b></a><a NAME="E1:43_3_12_1_1_2"/><i><font color="Green">E180</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</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">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</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><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_12_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">f</font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:43_3_12"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E6:43"><i><font color="Green">E33</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_13"><b>suppose </b></a><a NAME="E1:43_3_13"/><i><font color="Green">E181</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 12
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:43_3_13"/><i><font color="Green">E182</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">da</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T65">SCMFSA_2:65</a></i>;<br/><a NAME="E4:43_3_13"/><i><font color="Green">E183</font></i>: 
 <a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_4.html#T20">SCMFSA_4:20</a></i>;<br/><b>thus </b><a NAME="E5:43_3_13"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">n</font> <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> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="scmfsa6a.html#E2:43"><i><font color="Green">E30</font></i></a></i>;<br/><div><i><font color="Green">E184</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_13_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3_13_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">g</font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_13_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:43_3_13_2_1"/>
( <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> or <font color="Maroon">g</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">f</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_13_2_1_1"><b>suppose </b></a><a NAME="E1:43_3_13_2_1_1"/><i><font color="Green">E185</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 ;<br/><div class="add"><b>consider </b><font color="Maroon">m1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:43_3_13_2_1_1"/><i><font color="Green">E186</font></i>: 
<font color="Maroon">m1</font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font></span>)</span>
 <b>and </b><br/><a NAME="E4:43_3_13_2_1_1"/><i><font color="Green">E187</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">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">da</font></span>)</span>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m1</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">m2</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E6:43_3_13_2_1_1"/><i><font color="Green">E188</font></i>: 
<font color="Maroon">m2</font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font></span>)</span>
 <b>and </b><br/><a NAME="E7:43_3_13_2_1_1"/><i><font color="Green">E189</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">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">da</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m2</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="E8:43_3_13_2_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">g</font>
 <b>by </b><i>, <a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</font></i></a>, , <a class="ref" href="scmfsa6a.html#T8" target="_self">Th8</a>, <a class="ref" href="scmfsa6a.html#T9" target="_self">Th9</a>, , , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_3_13_2_1_2"><b>suppose </b></a><a NAME="E1:43_3_13_2_1_2"/><i><font color="Green">E190</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">f</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">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">g</font> = 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">g</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">g</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">g</font>
<b>by </b><i><a class="txt" href="scmfsa6a.html#E4:43"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:43"><i><font color="Green">E32</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><b>hence </b><a NAME="E8:43_3_13"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E6:43"><i><font color="Green">E33</font></i></a>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
