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

<b>let </b><font color="Maroon" title="c1">s1</font>, <font color="Maroon" title="c2">s2</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/>

<a NAME="E1:40"/><i><font color="Green" title="E21">A1</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p3">(<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><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p3">(<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><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></i>;<br/>
<a NAME="E2:40"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p3">(<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><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 
<b>by </b><i><a class="ref" href="ami_3.html#T36" title="AMI_3:th.36">AMI_3:36</a>, <a class="ref" href="scmfsa_2.html#T8" title="SCMFSA_2:th.8">SCMFSA_2:8</a></i>;<br/>
<a NAME="E3:40"/><b>then </b><i><font color="Green" title="E22">A2</font></i>: 
<a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">s1</font>
 
<b>by </b><i><a class="txt" href="scmfsa6a.html#E1:40"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E4:40"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p3">(<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><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 
<b>by </b><i><a class="ref" href="ami_3.html#T36" title="AMI_3:th.36">AMI_3:36</a>, <a class="ref" href="scmfsa_2.html#T8" title="SCMFSA_2:th.8">SCMFSA_2:8</a></i>;<br/>
<a NAME="E5:40"/><b>then </b><i><font color="Green" title="E23">A3</font></i>: 
<a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">s2</font>
 
<b>by </b><i><a class="txt" href="scmfsa6a.html#E1:40"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<div><i><font color="Green" title="E24">A4</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="40_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:40_1"/><i><font color="Green" title="E25">A5</font></i>: 
( ( for <font color="Olive" title="b1">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  holds  <font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Olive" title="b1">a</font> ) &amp; ( for <font color="Olive" title="b1">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Olive" title="b1">f</font> ) )
 ;<br/><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:40_1_1"/><i><font color="Green" title="E26">A6</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> 
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="40_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:40_1_1_1"/>
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  or  not <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="40_1_1_1_1"><b>suppose </b></a><a NAME="E1:40_1_1_1_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a> 
 ;<br/><div class="add"><a NAME="E2:40_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c3">x</font> is    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T11" title="SCMFSA_2:th.11">SCMFSA_2:11</a></i>;<br/><b>hence </b><a NAME="E3:40_1_1_1_1"/>
<font color="Maroon" title="c1">s1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E1:40_1"><i><font color="Green" title="E25">A5</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="40_1_1_1_2"><b>suppose </b></a><a NAME="E1:40_1_1_1_2"/>
not <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a> 
 ;<br/><div class="add"><a NAME="E2:40_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> 
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E1:40_1_1"><i><font color="Green" title="E26">A6</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E3:40_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c3">x</font> is    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T12" title="SCMFSA_2:th.12">SCMFSA_2:12</a></i>;<br/><b>hence </b><a NAME="E4:40_1_1_1_2"/>
<font color="Maroon" title="c1">s1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E1:40_1"><i><font color="Green" title="E25">A5</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="40_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:40_2"/><i><font color="Green" title="E25">A7</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a>  holds <br/><font color="Maroon" title="c1">s1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 ;<br/><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon" title="c3">a</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ;<br/><a NAME="E1:40_2_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T9" title="SCMFSA_2:th.9">SCMFSA_2:9</a></i>;<br/><a NAME="E2:40_2_1"/><b>then </b>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><b>hence </b><a NAME="E3:40_2_1"/>
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E1:40_2"><i><font color="Green" title="E25">A7</font></i></a></i>;<br/></div>
<b>end;</b></div><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon" title="c3">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ;<br/><a NAME="E1:40_2_2"/>
<font color="Maroon" title="c3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T10" title="SCMFSA_2:th.10">SCMFSA_2:10</a></i>;<br/><a NAME="E2:40_2_2"/><b>then </b>
<font color="Maroon" title="c3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><b>hence </b><a NAME="E3:40_2_2"/>
<font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Maroon" title="c3">f</font>
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E1:40_2"><i><font color="Green" title="E25">A7</font></i></a></i>;<br/></div>
<b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E8:40"/>
( ( ( for <font color="Olive" title="b1">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  holds  <font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Olive" title="b1">a</font> ) &amp; ( for <font color="Olive" title="b1">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <font color="Maroon" title="c1">s1</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Olive" title="b1">f</font> ) ) iff <font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="scmfsa6a.html#E3:40"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="scmfsa6a.html#E5:40"><i><font color="Green" title="E23">A3</font></i></a>, <a class="txt" href="scmfsa6a.html#E6:40"><i><font color="Green" title="E24">A4</font></i></a>, <a class="ref" href="scmfsa6a.html#T9" target="_self" title="SCMFSA6A:th.9">Th9</a></i>;<br/>


</div>
