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

<b>let </b><font color="Maroon" title="c1">I</font> be   <a href="scmfsa6a.html#NM1" title="SCMFSA6A:NM.1">Macro-Instruction</a>;<br/>

<b>consider </b><font color="Maroon" title="c2">UIL</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="ami_1.html#U3" title="AMI_1:sel.3">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> , <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> <b> such that </b><br/><a NAME="E2:50"/><i><font color="Green" title="E41">A1</font></i>: 
( ( for <font color="Olive" title="b1">i</font> being  <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  holds  <font color="Maroon" title="c2">UIL</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sf_mastr.html#K3" title="SF_MASTR:func.3">UsedInt*Loc</a> <font color="Olive" title="b1">i</font> ) &amp;  <a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">UIL</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c1">I</font></span>)</span> )
 <b>by </b><i><a class="ref" href="sf_mastr.html#D4" target="_self" title="SF_MASTR:def.4">Def4</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c3">UIL2</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="ami_1.html#U3" title="AMI_1:sel.3">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> , <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> <b> such that </b><br/><a NAME="E4:50"/><i><font color="Green" title="E42">A2</font></i>: 
( ( for <font color="Olive" title="b1">i</font> being  <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  holds  <font color="Maroon" title="c3">UIL2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sf_mastr.html#K3" title="SF_MASTR:func.3">UsedInt*Loc</a> <font color="Olive" title="b1">i</font> ) &amp;  <a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">UIL2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="sf_mastr.html#D4" target="_self" title="SF_MASTR:def.4">Def4</a></i>;<br/>
<a NAME="E5:50"/><i><font color="Green" title="E43">A3</font></i>: 
for <font color="Olive" title="b1">c</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="ami_1.html#U3" title="AMI_1:sel.3">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  holds  <font color="Maroon" title="c2">UIL</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">UIL2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">c</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="ami_1.html#U3" title="AMI_1:sel.3">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/>

<b>reconsider </b><font color="Maroon" title="c5">d</font> = <font color="Maroon" title="c4">c</font> as   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  ;<br/>
<b>thus </b><font color="Maroon" title="c2">UIL</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">c</font> = 
 <a href="sf_mastr.html#K3" title="SF_MASTR:func.3">UsedInt*Loc</a> <font color="Maroon" title="c5">d</font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E2:50"><i><font color="Green" title="E41">A1</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c3">UIL2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">c</font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E4:50"><i><font color="Green" title="E42">A2</font></i></a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E6:50"/><i><font color="Green" title="E44">A4</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">UIL</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E7:50"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Instructions</a> of <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> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></i>;<br/>
<a NAME="E8:50"/><b>then </b><i><font color="Green" title="E45">A5</font></i>: 
<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</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="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_7.html#D3" title="FUNCT_7:def.3">FUNCT_7:def 3</a></i>;<br/>
<i><font color="Green" title="E46">A6</font></i>: <font color="Maroon" title="c2">UIL</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> = 
 <a href="sf_mastr.html#K3" title="SF_MASTR:func.3">UsedInt*Loc</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</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="sf_mastr.html#E2:50"><i><font color="Green" title="E41">A1</font></i></a></i>
<br/>.= 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<b>by </b><i><a class="ref" href="sf_mastr.html#T36" target="_self" title="SF_MASTR:th.36">Th36</a></i>
;<br/>
<i><font color="Green" title="E47">A7</font></i>: <font color="Maroon" title="c2">UIL</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span> = 
 <a href="sf_mastr.html#K3" title="SF_MASTR:func.3">UsedInt*Loc</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sf_mastr.html#E2:50"><i><font color="Green" title="E41">A1</font></i></a></i>
<br/>.= 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<b>by </b><i><a class="ref" href="sf_mastr.html#T36" target="_self" title="SF_MASTR:th.36">Th36</a></i>
;<br/>
<font color="Maroon" title="c2">UIL</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c1">I</font></span>)</span> = 
<font color="Maroon" title="c2">UIL</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p0">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c1">I</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#D1" title="SCMFSA6A:def.1">SCMFSA6A:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">UIL</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p0">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">I</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c1">I</font>
<b>by </b><i><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>
<br/>.= 
<font color="Maroon" title="c2">UIL</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c1">I</font>
<b>by </b><i><a class="txt" href="sf_mastr.html#E6:50"><i><font color="Green" title="E44">A4</font></i></a>, <a class="txt" href="sf_mastr.html#E8:50"><i><font color="Green" title="E45">A5</font></i></a>, <a class="txt" href="sf_mastr.html#E9:50"><i><font color="Green" title="E46">A6</font></i></a>, <a class="txt" href="sf_mastr.html#E10:50"><i><font color="Green" title="E47">A7</font></i></a>, <a class="ref" href="funct_7.html#T110" title="FUNCT_7:th.110">FUNCT_7:110</a></i>
;<br/>
<b>hence </b><a NAME="E12:50"/>
 <a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1" title="SCMFSA6A:func.1">Directed</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E2:50"><i><font color="Green" title="E41">A1</font></i></a>, <a class="txt" href="sf_mastr.html#E4:50"><i><font color="Green" title="E42">A2</font></i></a>, <a class="txt" href="sf_mastr.html#E5:50"><i><font color="Green" title="E43">A3</font></i></a>, <a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>


</div>
