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

<b>let </b><font color="Maroon">p</font> be  <a href="ami_3.html#V1">programmed</a>  <a href="ami_1.html#M1">FinPartState</a> of  <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon">l</font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon">ic</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>





<b>set </b><font color="Maroon">pl</font> = <font color="Maroon">p</font> <a href="scmfsa_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="ami_3.html#K14">.--&gt;</a> <font color="Maroon">ic</font></span>)</span>;<br/>
<b>assume </b><a NAME="E1:6"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">l</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font> &amp;  ex <font color="Olive">pc</font> being  <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  st <br/>( <font color="Olive">pc</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font> &amp;  <a href="sf_mastr.html#K3">UsedInt*Loc</a> <font color="Olive">pc</font> <a href="hidden.html#R1">=</a>  <a href="sf_mastr.html#K3">UsedInt*Loc</a> <font color="Maroon">ic</font> ) )
 ;<br/>

<b>then </b><i><font color="Green">E41</font></i>: <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="scmfsa_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="ami_3.html#K14">.--&gt;</a> <font color="Maroon">ic</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font> = 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="funct_7.html#K2">+*</a> <font color="Maroon">l</font>,<font color="Maroon">ic</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font>
<b>by </b><i><a class="ref" href="funct_7.html#D3">FUNCT_7:def 3</a></i>
<br/>.= 
<font color="Maroon">ic</font>
<b>by </b><i>, <a class="ref" href="funct_7.html#T33">FUNCT_7:33</a></i>
;<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="E4:6"/><i><font color="Green">E43</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">UsedInt*Loc</a> <font color="Olive">i</font> ) &amp;  <a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</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">p</font></span>)</span> )
 <b>by </b><i><a class="ref" href="sf_mastr.html#D4">SF_MASTR:def 4</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="E6:6"/><i><font color="Green">E45</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">UsedInt*Loc</a> <font color="Olive">i</font> ) &amp;  <a href="sf_mastr.html#K4">UsedInt*Loc</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="scmfsa_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="ami_3.html#K14">.--&gt;</a> <font color="Maroon">ic</font></span>)</span></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"><font color="Maroon">p</font> <a href="scmfsa_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">l</font> <a href="ami_3.html#K14">.--&gt;</a> <font color="Maroon">ic</font></span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="sf_mastr.html#D4">SF_MASTR:def 4</a></i>;<br/>
<a NAME="E7:6"/>
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="6_2"><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">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="E8:6"/><b>then </b><i><font color="Green">E47</font></i>: 
<font color="Maroon">UIL</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">UIL2</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>
<b>set </b><font color="Maroon">f</font> = <font color="Maroon">UIL</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">p</font>;<br/>
<b>set </b><font color="Maroon">g</font> = <font color="Maroon">UIL</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="scmfsa_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="ami_3.html#K14">.--&gt;</a> <font color="Maroon">ic</font></span>)</span></span>)</span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_3"><b>now </b></a><div class="add"><a NAME="E1:6_3"/><i><font color="Green">E49</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="scmfsa_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="ami_3.html#K14">.--&gt;</a> <font color="Maroon">ic</font></span>)</span></span>)</span>
 <b>by </b><i>, </i>;<br/><a NAME="E2:6_3"/>
 <a href="relat_1.html#K1">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="E3:6_3"/><b>then </b><i><font color="Green">E50</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">UIL</font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="scmfsa_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="ami_3.html#K14">.--&gt;</a> <font color="Maroon">ic</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">UIL</font> )
 <b>by </b><i><a class="ref" href="scmfsa_4.html#T1">SCMFSA_4:1</a></i>;<br/><a NAME="E4:6_3"/><b>then </b><i><font color="Green">E51</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">UIL</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>;<br/><b>hence </b><a NAME="E5:6_3"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">UIL</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <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"><font color="Maroon">p</font> <a href="scmfsa_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">l</font> <a href="ami_3.html#K14">.--&gt;</a> <font color="Maroon">ic</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, , <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E6:6_3"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">UIL</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">p</font></span>)</span>
 ;<br/><a NAME="E7:6_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="scmfsa_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="ami_3.html#K14">.--&gt;</a> <font color="Maroon">ic</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="scmfsa_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="ami_3.html#K14">.--&gt;</a> <font color="Maroon">ic</font></span>)</span></span>)</span>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><b>then reconsider </b><font color="Maroon">plx</font> = <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="scmfsa_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="ami_3.html#K14">.--&gt;</a> <font color="Maroon">ic</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> as   <a href="ami_1.html#NM3">Instruction</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/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="6_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:6_3_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">l</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">l</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="6_3_1_1"><b>suppose </b></a><a NAME="E1:6_3_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">l</font>
 ;<br/><div class="add"><a NAME="E2:6_3_1_1"/><b>then </b>
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">l</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:6_3_1_1"/><b>then </b>
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="ami_3.html#K14">.--&gt;</a> <font color="Maroon">ic</font></span>)</span>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/><a NAME="E4:6_3_1_1"/><b>then </b>
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="scmfsa_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="ami_3.html#K14">.--&gt;</a> <font color="Maroon">ic</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon">UIL</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">p</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">UIL</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">plx</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</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"><font color="Maroon">p</font> <a href="scmfsa_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">l</font> <a href="ami_3.html#K14">.--&gt;</a> <font color="Maroon">ic</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , , <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="6_3_1_2"><b>suppose </b></a><a NAME="E1:6_3_1_2"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">l</font>
 ;<br/><div class="add"><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">UIL</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">p</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">UIL</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>
<br/>.= 
 <a href="sf_mastr.html#K3">UsedInt*Loc</a> <font color="Maroon">plx</font>
<b>by </b><i>, , , </i>
<br/>.= 
<font color="Maroon">UIL</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">plx</font>
<b>by </b><i>, </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"><font color="Maroon">p</font> <a href="scmfsa_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">l</font> <a href="ami_3.html#K14">.--&gt;</a> <font color="Maroon">ic</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , , <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E10:6"/>
 <a href="sf_mastr.html#K4">UsedInt*Loc</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="sf_mastr.html#K4">UsedInt*Loc</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="scmfsa_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="ami_3.html#K14">.--&gt;</a> <font color="Maroon">ic</font></span>)</span></span>)</span>
 <b>by </b><i>, , , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


</div>
