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<b>let </b><font color="Maroon">I</font> be   <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/>

<b>consider </b><font color="Maroon">UIL</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><br/><a NAME="E2:54"/><i><font color="Green">E32</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">UIL</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;  <a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="card_3.html#K3">Union</a> <span class="p1">(<span class="default"><font color="Maroon">UIL</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">I</font></span>)</span> )
 <b>by </b><i><a class="txt" href="sf_mastr.html#E5:54"><i><font color="Green">E35</font></i></a></i>;<br/>
<b>consider </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><br/><a NAME="E4:54"/><i><font color="Green">E33</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;  <a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> <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> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="sf_mastr.html#E5:54"><i><font color="Green">E35</font></i></a></i>;<br/>
<a NAME="E5:54"/><i><font color="Green">E35</font></i>: 
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">UIL</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="54_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">UIL</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>
<a NAME="E6:54"/><i><font color="Green">E36</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">UIL</font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E7:54"/>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T71">RELAT_1:71</a></i>;<br/>
<a NAME="E8:54"/><b>then </b><i><font color="Green">E37</font></i>: 
<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K13">goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="funct_7.html#K2">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K13">goto</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_7.html#D3">FUNCT_7:def 3</a></i>;<br/>
<i><font color="Green">E38</font></i>: <font color="Maroon">UIL</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="txt" href="sf_mastr.html#E2:54"><i><font color="Green">E32</font></i></a></i>
;<br/>
<i><font color="Green">E39</font></i>: <font color="Maroon">UIL</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K13">goto</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> = 
 <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K13">goto</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="txt" href="sf_mastr.html#E2:54"><i><font color="Green">E32</font></i></a></i>
;<br/>
<font color="Maroon">UIL</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span> = 
<font color="Maroon">UIL</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K13">goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">I</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#D1">SCMFSA6A:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">UIL</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K13">goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">I</font>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<font color="Maroon">UIL</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">I</font>
<b>by </b><i>, , , , </i>
;<br/>
<b>hence </b><a NAME="E12:54"/>
 <a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="sf_mastr.html#K4" target="_self">UsedInt*Loc</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">I</font></span>)</span>
 <b>by </b><i>, , , <a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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