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

<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ;<br/><b>let </b><font color="Maroon" title="c3">s</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/>





<b>consider </b><font color="Maroon" title="c4">A</font>, <font color="Maroon" title="c5">B</font> being    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> <b> such that </b><br/><a NAME="E2:79"/><i><font color="Green" title="E46">A1</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A</font>
 <b>and </b><br/><a NAME="E3:79"/><i><font color="Green" title="E47">A2</font></i>: 
<font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">B</font>
 <b>and </b><br/><a NAME="E4:79"/><i><font color="Green" title="E48">A3</font></i>: 
 <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">AddTo</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K4" title="AMI_3:func.4">AddTo</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#D12" target="_self" title="SCMFSA_2:def.12">Def12</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">S</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Instr-Loc</a>  <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K4" title="AMI_3:func.4">AddTo</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font></span>)</span></span>)</span> as   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <b>by </b><i><a class="ref" href="scmfsa_1.html#T18" title="SCMFSA_1:th.18">SCMFSA_1:18</a></i>;<br/>
<a NAME="E6:79"/><i><font color="Green" title="E49">A4</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">S</font>
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T88" target="_self" title="SCMFSA_2:th.88">Th88</a></i>;<br/>
<a NAME="E7:79"/><i><font color="Green" title="E50">A5</font></i>: 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">AddTo</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_3.html#K4" title="AMI_3:func.4">AddTo</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c6">S</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Instr-Loc</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa_2.html#E4:79"><i><font color="Green" title="E48">A3</font></i></a>, <a class="ref" href="scmfsa_2.html#T75" target="_self" title="SCMFSA_2:th.75">Th75</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">AddTo</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K4" title="AMI_3:func.4">AddTo</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c6">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_2.html#T78" target="_self" title="SCMFSA_2:th.78">Th78</a></i>
<br/>.= 
 <a href="ami_3.html#K11" title="AMI_3:func.11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">S</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_3.html#T9" title="AMI_3:th.9">AMI_3:9</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c3">s</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E6:79"><i><font color="Green" title="E49">A4</font></i></a>, <a class="ref" href="scmfsa_2.html#T33" target="_self" title="SCMFSA_2:th.33">Th33</a></i>
;<br/><br/>

<b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">AddTo</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c1">a</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K4" title="AMI_3:func.4">AddTo</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c6">S</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">A</font>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E2:79"><i><font color="Green" title="E46">A1</font></i></a>, <a class="txt" href="scmfsa_2.html#E7:79"><i><font color="Green" title="E50">A5</font></i></a>, <a class="ref" href="scmfsa_2.html#T79" target="_self" title="SCMFSA_2:th.79">Th79</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">B</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_3.html#T9" title="AMI_3:th.9">AMI_3:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">b</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E3:79"><i><font color="Green" title="E47">A2</font></i></a>, <a class="ref" href="scmfsa_2.html#T80" target="_self" title="SCMFSA_2:th.80">Th80</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">b</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E2:79"><i><font color="Green" title="E46">A1</font></i></a>, <a class="ref" href="scmfsa_2.html#T80" target="_self" title="SCMFSA_2:th.80">Th80</a></i>
;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon" title="c7">c</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ;<br/><b>assume </b><a NAME="E1:79_3"/><i><font color="Green" title="E51">A6</font></i>: 
<font color="Maroon" title="c7">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">a</font>
 ;<br/><b>reconsider </b><font color="Maroon" title="c8">C</font> = <font color="Maroon" title="c7">c</font> as    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#T25" target="_self" title="SCMFSA_2:th.25">Th25</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">AddTo</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c7">c</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K4" title="AMI_3:func.4">AddTo</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c6">S</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c8">C</font>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E7:79"><i><font color="Green" title="E50">A5</font></i></a>, <a class="ref" href="scmfsa_2.html#T79" target="_self" title="SCMFSA_2:th.79">Th79</a></i>
<br/>.= 
<font color="Maroon" title="c6">S</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c8">C</font>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E2:79"><i><font color="Green" title="E46">A1</font></i></a>, <a class="txt" href="scmfsa_2.html#E1:79_3"><i><font color="Green" title="E51">A6</font></i></a>, <a class="ref" href="ami_3.html#T9" title="AMI_3:th.9">AMI_3:9</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c7">c</font>
<b>by </b><i><a class="ref" href="scmfsa_2.html#T80" target="_self" title="SCMFSA_2:th.80">Th80</a></i>
;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c7">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ;<br/>

<a NAME="E11:79"/><i><font color="Green" title="E51">A7</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Instr-Loc</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Instr-Loc</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="79_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:79_4"/>
<font color="Maroon" title="c7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Instr-Loc</a> 
 ;<br/><a NAME="E2:79_4"/><b>then </b><i><font color="Green" title="E52">A8</font></i>: 
<a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-OK</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Instr</a> 
 <b>by </b><i><a class="ref" href="scmfsa_1.html#T11" title="SCMFSA_1:th.11">SCMFSA_1:11</a></i>;<br/><a NAME="E3:79_4"/>
<font color="Maroon" title="c7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Data*-Loc</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#D5" target="_self" title="SCMFSA_2:def.5">Def5</a></i>;<br/><b>hence </b><a NAME="E4:79_4"/>
contradiction
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E2:79_4"><i><font color="Green" title="E52">A8</font></i></a>, <a class="ref" href="scmfsa_1.html#T12" title="SCMFSA_1:th.12">SCMFSA_1:12</a>, <a class="ref" href="scmfsa_1.html#T13" title="SCMFSA_1:th.13">SCMFSA_1:13</a></i>;<br/></div><b>end;</b></div>
<a NAME="E13:79"/><b>then </b><i><font color="Green" title="E52">A9</font></i>: 
not <font color="Maroon" title="c7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Instr-Loc</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa_2.html#E11:79"><i><font color="Green" title="E51">A7</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E14:79"/><i><font color="Green" title="E53">A10</font></i>: 
not <font color="Maroon" title="c7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K4" title="AMI_3:func.4">AddTo</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c6">S</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T68" target="_self" title="SCMFSA_2:th.68">Th68</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">AddTo</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Maroon" title="c7">f</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_3.html#K4" title="AMI_3:func.4">AddTo</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c6">S</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">f</font>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E7:79"><i><font color="Green" title="E50">A5</font></i></a>, <a class="txt" href="scmfsa_2.html#E13:79"><i><font color="Green" title="E52">A9</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Maroon" title="c7">f</font>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E14:79"><i><font color="Green" title="E53">A10</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
;<br/>


</div>
