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<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/>

<b>assume </b><b>that </b><br/><a NAME="E1:76"/><i><font color="Green" title="E43">A1</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c1">s1</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="c2">s2</font>
 <b>and </b><br/><a NAME="E2:76"/><i><font color="Green" title="E44">A2</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>
 <b>and </b><br/><a NAME="E3:76"/><i><font color="Green" title="E45">A3</font></i>: 
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>
 <b>and </b><br/><a NAME="E4:76"/><i><font color="Green" title="E46">A4</font></i>: 
for <font color="Olive" title="b1">i</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  holds  <font color="Maroon" title="c1">s1</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Olive" title="b1">i</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c3">g1</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E6:76"/><i><font color="Green" title="E47">A5</font></i>: 
( <font color="Maroon" title="c1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g1</font> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-OK</a>  &amp; ( 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="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-OK</a>  holds <br/><font color="Maroon" title="c3">g1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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="Olive" title="b1">x</font> ) )
 <b>by </b><i><a class="ref" href="card_3.html#D5" title="CARD_3:def.5">CARD_3:def 5</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">g2</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E8:76"/><i><font color="Green" title="E48">A6</font></i>: 
( <font color="Maroon" title="c2">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g2</font> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c4">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-OK</a>  &amp; ( 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="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-OK</a>  holds <br/><font color="Maroon" title="c4">g2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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="Olive" title="b1">x</font> ) )
 <b>by </b><i><a class="ref" href="card_3.html#D5" title="CARD_3:def.5">CARD_3:def 5</a></i>;<br/>
<a NAME="E9:76"/><i><font color="Green" title="E49">A7</font></i>: 
(  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">g1</font> &amp;  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c4">g2</font> )
 
<b>by </b><i><a class="txt" href="scmfsa_2.html#E6:76"><i><font color="Green" title="E47">A5</font></i></a>, <a class="txt" href="scmfsa_2.html#E8:76"><i><font color="Green" title="E48">A6</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:76_1"/><i><font color="Green" title="E50">A8</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 ;<br/><a NAME="E2:76_1"/>
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</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="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K1" title="SCMFSA_1:func.1">SCM+FSA-Data-Loc</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Data*-Loc</a>  or <font color="Maroon" title="c5">x</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>  )
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E1:76_1"><i><font color="Green" title="E50">A8</font></i></a>, <a class="ref" href="scmfsa_2.html#T7" target="_self" title="SCMFSA_2:th.7">Th7</a>, <a class="ref" href="scmfsa_1.html#T8" title="SCMFSA_1:th.8">SCMFSA_1:8</a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E3:76_1"/><b>then </b><i><font color="Green" title="E51">A9</font></i>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<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="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K1" title="SCMFSA_1:func.1">SCM+FSA-Data-Loc</a>  or <font color="Maroon" title="c5">x</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>  or <font color="Maroon" title="c5">x</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>  )
 <b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="76_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:76_1_1"/>
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<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="tarski.html#K1" title="TARSKI:func.1">}</a></span> or <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_1.html#K1" title="SCMFSA_1:func.1">SCM+FSA-Data-Loc</a>  or <font color="Maroon" title="c5">x</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>  or <font color="Maroon" title="c5">x</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>  )
 </span><b>by </b><i><a class="txt" href="scmfsa_2.html#E3:76_1"><i><font color="Green" title="E51">A9</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="76_1_1_1"><b>suppose </b></a><a NAME="E1:76_1_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<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="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:76_1_1_1"/><b>then </b><i><font color="Green" title="E52">A10</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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> 
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:76_1_1_1"/>
<font color="Maroon" title="c1">s1</font> <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> <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> <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>
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E1:76"><i><font color="Green" title="E43">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E4:76_1_1_1"/>
<font color="Maroon" title="c3">g1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E6:76"><i><font color="Green" title="E47">A5</font></i></a>, <a class="txt" href="scmfsa_2.html#E8:76"><i><font color="Green" title="E48">A6</font></i></a>, <a class="txt" href="scmfsa_2.html#E2:76_1_1_1"><i><font color="Green" title="E52">A10</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="76_1_1_2"><b>suppose </b></a><a NAME="E1:76_1_1_2"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_1.html#K1" title="SCMFSA_1:func.1">SCM+FSA-Data-Loc</a> 
 ;<br/><div class="add"><a NAME="E2:76_1_1_2"/><b>then </b>
<font color="Maroon" title="c5">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#D4" target="_self" title="SCMFSA_2:def.4">Def4</a></i>;<br/><b>hence </b><a NAME="E3:76_1_1_2"/>
<font color="Maroon" title="c3">g1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E2:76"><i><font color="Green" title="E44">A2</font></i></a>, <a class="txt" href="scmfsa_2.html#E6:76"><i><font color="Green" title="E47">A5</font></i></a>, <a class="txt" href="scmfsa_2.html#E8:76"><i><font color="Green" title="E48">A6</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="76_1_1_3"><b>suppose </b></a><a NAME="E1:76_1_1_3"/>
<font color="Maroon" title="c5">x</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> 
 ;<br/><div class="add"><a NAME="E2:76_1_1_3"/><b>then </b>
<font color="Maroon" title="c5">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#D5" target="_self" title="SCMFSA_2:def.5">Def5</a></i>;<br/><b>hence </b><a NAME="E3:76_1_1_3"/>
<font color="Maroon" title="c3">g1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E3:76"><i><font color="Green" title="E45">A3</font></i></a>, <a class="txt" href="scmfsa_2.html#E6:76"><i><font color="Green" title="E47">A5</font></i></a>, <a class="txt" href="scmfsa_2.html#E8:76"><i><font color="Green" title="E48">A6</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="76_1_1_4"><b>suppose </b></a><a NAME="E1:76_1_1_4"/>
<font color="Maroon" title="c5">x</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/><div class="add"><b>hence </b><a NAME="E2:76_1_1_4"/>
<font color="Maroon" title="c3">g1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E4:76"><i><font color="Green" title="E46">A4</font></i></a>, <a class="txt" href="scmfsa_2.html#E6:76"><i><font color="Green" title="E47">A5</font></i></a>, <a class="txt" href="scmfsa_2.html#E8:76"><i><font color="Green" title="E48">A6</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E11:76"/>
<font color="Maroon" title="c1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font>
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E6:76"><i><font color="Green" title="E47">A5</font></i></a>, <a class="txt" href="scmfsa_2.html#E8:76"><i><font color="Green" title="E48">A6</font></i></a>, <a class="txt" href="scmfsa_2.html#E9:76"><i><font color="Green" title="E49">A7</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/>


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