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<b>let </b><font color="Maroon">IT1</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="scmfsa_2.html#K3">FinSeq-Locations</a> , <font color="Maroon">IT2</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="scmfsa_2.html#K3">FinSeq-Locations</a> ;<br/>

<b>given </b><font color="Maroon">UIL1</font> being   <a href="funct_2.html#NM1">Function</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <a href="finsub_1.html#K5">Fin</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> <b> such that </b><a NAME="E1:45_1_2"/><i><font color="Green">E37</font></i>: 
( ( for <font color="Olive">i</font> being  <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  holds  <font color="Maroon">UIL1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a>  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Olive">i</font> ) &amp; <font color="Maroon">IT1</font> <a href="hidden.html#R1">=</a>  <a href="card_3.html#K3">Union</a> <span class="p1">(<span class="default"><font color="Maroon">UIL1</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">p</font></span>)</span> )
 ;<br/>

<b>given </b><font color="Maroon">UIL2</font> being   <a href="funct_2.html#NM1">Function</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <a href="finsub_1.html#K5">Fin</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> <b> such that </b><a NAME="E2:45_1_2"/><i><font color="Green">E38</font></i>: 
( ( for <font color="Olive">i</font> being  <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  holds  <font color="Maroon">UIL2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a>  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Olive">i</font> ) &amp; <font color="Maroon">IT2</font> <a href="hidden.html#R1">=</a>  <a href="card_3.html#K3">Union</a> <span class="p1">(<span class="default"><font color="Maroon">UIL2</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">p</font></span>)</span> )
 ;<br/>

<a NAME="E3:45_1_2"/>
for <font color="Olive">c</font> being   <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  holds  <font color="Maroon">UIL1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">UIL2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c</font> be    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>

<b>reconsider </b><font color="Maroon">d</font> = <font color="Maroon">c</font> as   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ;<br/>
<b>thus </b><font color="Maroon">UIL1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font> = 
 <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">d</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">UIL2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font>
<b>by </b><i/>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:45_1_2"/>
<font color="Maroon">IT1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">IT2</font>
 <b>by </b><i>, , <a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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