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

<b>let </b><font color="Maroon">i</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon">t</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>





<b>assume </b><a NAME="E1:89"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span> &amp; <font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span> &amp;  <a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <font color="Maroon">t</font> )
 ;<br/>

<b>set </b><font color="Maroon">Es</font> =  <a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font>;<br/>
<b>set </b><font color="Maroon">Et</font> =  <a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font>;<br/>
<b>set </b><font color="Maroon">Ui</font> =  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font>;<br/>
<b>set </b><font color="Maroon">UFi</font> =  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font>;<br/>
<i><font color="Green">E33</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> = 
the <a href="struct_0.html#U1">carrier</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>
;<br/>
<a NAME="E3:89"/><i><font color="Green">E35</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 11 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T35">SCMFSA_2:35</a></i>;<br/>
<a NAME="E4:89"/><i><font color="Green">E36</font></i>: 
(  not  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 10 <a href="nat_1.html#K1">+</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 10 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 11 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/>
<a NAME="E5:89"/><i><font color="Green">E37</font></i>: 
(  not  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 9 <a href="nat_1.html#K1">+</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 8 <a href="nat_1.html#K1">+</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 10 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/>
<a NAME="E6:89"/><i><font color="Green">E38</font></i>: 
(  not  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 8 <a href="nat_1.html#K1">+</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 7 <a href="nat_1.html#K1">+</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 9 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:89_2"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 0 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 2 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 3 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 4 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 5 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 6 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 7 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 8 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 9 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 10 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 11 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 12 )
 </span><b>by </b><i><a class="ref" href="sf_mastr.html#T7" target="_self">Th7</a>, <a class="ref" href="sf_mastr.html#T8" target="_self">Th8</a>, <a class="ref" href="sf_mastr.html#T9" target="_self">Th9</a>, , <a class="ref" href="cqc_the1.html#T9">CQC_THE1:9</a>, <a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_1"><b>suppose </b></a><a NAME="E1:89_2_1"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:89_2_1"/><b>then </b>
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T122">SCMFSA_2:122</a></i>;<br/><a NAME="E3:89_2_1"/><b>then </b>
(  <a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> &amp;  <a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> )
 <b>by </b><i><a class="ref" href="ami_1.html#D8">AMI_1:def 8</a></i>;<br/><b>hence </b><a NAME="E4:89_2_1"/>
(  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span> )
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_2"><b>suppose </b></a><a NAME="E1:89_2_2"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:89_2_2"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T54">SCMFSA_2:54</a></i>;<br/><b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">t</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/><a NAME="E5:89_2_2"/><i><font color="Green">E80</font></i>: 
(  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K2">}</a></span> &amp;  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i>, , <a class="txt" href="sf_mastr.html#E1:89"><i><font color="Green">E32</font></i></a></i>;<br/><a NAME="E6:89_2_2"/><b>then </b><i><font color="Green">E81</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> )
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E7:89_2_2"/><b>then </b>
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><a NAME="E8:89_2_2"/><b>then </b><i><font color="Green">E82</font></i>: 
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> )
 <b>by </b><i>, <a class="ref" href="sf_mastr.html#T12" target="_self">Th12</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><a NAME="E9:89_2_2"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> or <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> )
 ;<br/><a NAME="E10:89_2_2"/><b>then </b>
( <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T89">SCMFSA_2:89</a></i>;<br/><b>hence </b><a NAME="E11:89_2_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="sf_mastr.html#T6" target="_self">Th6</a>, <a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a>, <a class="ref" href="ami_3.html#T25">AMI_3:25</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span> = 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_3"><b>suppose </b></a><a NAME="E1:89_2_3"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:89_2_3"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T55">SCMFSA_2:55</a></i>;<br/><b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">t</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/><a NAME="E5:89_2_3"/><i><font color="Green">E84</font></i>: 
(  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K2">}</a></span> &amp;  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i>, , <a class="txt" href="sf_mastr.html#E1:89"><i><font color="Green">E32</font></i></a></i>;<br/><a NAME="E6:89_2_3"/><b>then </b><i><font color="Green">E85</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> )
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E7:89_2_3"/><b>then </b>
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><a NAME="E8:89_2_3"/><b>then </b><i><font color="Green">E86</font></i>: 
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> )
 <b>by </b><i>, <a class="ref" href="sf_mastr.html#T12" target="_self">Th12</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><a NAME="E9:89_2_3"/><i><font color="Green">E87</font></i>: 
( <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="89_2_3_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_3_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:89_2_3_2_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> or <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_3_2_1_1"><b>case </b></a><a NAME="E1:89_2_3_2_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:89_2_3_2_1_1"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_3_2_1_2"><b>case </b></a><a NAME="E1:89_2_3_2_1_2"/>
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:89_2_3_2_1_2"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T90">SCMFSA_2:90</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E11:89_2_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="sf_mastr.html#T6" target="_self">Th6</a>, <a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a>, <a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a>, <a class="ref" href="ami_3.html#T25">AMI_3:25</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span> = 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_4"><b>suppose </b></a><a NAME="E1:89_2_4"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 3
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:89_2_4"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T56">SCMFSA_2:56</a></i>;<br/><b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">t</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/><a NAME="E5:89_2_4"/><i><font color="Green">E89</font></i>: 
(  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K2">}</a></span> &amp;  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i>, , <a class="txt" href="sf_mastr.html#E1:89"><i><font color="Green">E32</font></i></a></i>;<br/><a NAME="E6:89_2_4"/><b>then </b><i><font color="Green">E90</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> )
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E7:89_2_4"/><b>then </b>
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><a NAME="E8:89_2_4"/><b>then </b><i><font color="Green">E91</font></i>: 
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> )
 <b>by </b><i>, <a class="ref" href="sf_mastr.html#T12" target="_self">Th12</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><a NAME="E9:89_2_4"/><i><font color="Green">E175</font></i>: 
( <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="89_2_4_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_4_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:89_2_4_2_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> or <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_4_2_1_1"><b>case </b></a><a NAME="E1:89_2_4_2_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:89_2_4_2_1_1"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_4_2_1_2"><b>case </b></a><a NAME="E1:89_2_4_2_1_2"/>
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:89_2_4_2_1_2"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T91">SCMFSA_2:91</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E11:89_2_4"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="sf_mastr.html#T6" target="_self">Th6</a>, <a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a>, <a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a>, <a class="ref" href="ami_3.html#T25">AMI_3:25</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span> = 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_5"><b>suppose </b></a><a NAME="E1:89_2_5"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 4
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:89_2_5"/><i><font color="Green">E176</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T57">SCMFSA_2:57</a></i>;<br/><b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">t</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/><a NAME="E5:89_2_5"/><i><font color="Green">E177</font></i>: 
(  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K2">}</a></span> &amp;  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i>, , <a class="txt" href="sf_mastr.html#E1:89"><i><font color="Green">E32</font></i></a></i>;<br/><a NAME="E6:89_2_5"/><b>then </b><i><font color="Green">E178</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> )
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E7:89_2_5"/><b>then </b>
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><a NAME="E8:89_2_5"/><b>then </b><i><font color="Green">E179</font></i>: 
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> )
 <b>by </b><i>, <a class="ref" href="sf_mastr.html#T12" target="_self">Th12</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><a NAME="E9:89_2_5"/><i><font color="Green">E180</font></i>: 
( <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="89_2_5_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_5_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:89_2_5_2_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> or <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_5_2_1_1"><b>case </b></a><a NAME="E1:89_2_5_2_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:89_2_5_2_1_1"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_5_2_1_2"><b>case </b></a><a NAME="E1:89_2_5_2_1_2"/>
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:89_2_5_2_1_2"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T92">SCMFSA_2:92</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E11:89_2_5"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="sf_mastr.html#T6" target="_self">Th6</a>, <a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a>, <a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a>, <a class="ref" href="ami_3.html#T25">AMI_3:25</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span> = 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_6"><b>suppose </b></a><a NAME="E1:89_2_6"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 5
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:89_2_6"/><i><font color="Green">E181</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T58">SCMFSA_2:58</a></i>;<br/><a NAME="E4:89_2_6"/><i><font color="Green">E182</font></i>: 
(  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K2">}</a></span> &amp;  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i>, , <a class="txt" href="sf_mastr.html#E1:89"><i><font color="Green">E32</font></i></a></i>;<br/><a NAME="E5:89_2_6"/><b>then </b><i><font color="Green">E183</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> )
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E6:89_2_6"/><b>then </b>
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><a NAME="E7:89_2_6"/><b>then </b><i><font color="Green">E184</font></i>: 
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> )
 <b>by </b><i>, <a class="ref" href="sf_mastr.html#T12" target="_self">Th12</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_6_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:89_2_6_1_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> or <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_6_1_1_1"><b>suppose </b></a><a NAME="E1:89_2_6_1_1_1"/><i><font color="Green">E185</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">t</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a>, <a class="ref" href="scmfsa_2.html#T94">SCMFSA_2:94</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a>, <a class="ref" href="scmfsa_2.html#T94">SCMFSA_2:94</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/><a NAME="E3:89_2_6_1_1_1"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a>, <a class="ref" href="scmfsa_2.html#T94">SCMFSA_2:94</a></i>;<br/><b>hence </b><a NAME="E4:89_2_6_1_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="sf_mastr.html#T6" target="_self">Th6</a>, <a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a>, <a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a>, <a class="ref" href="ami_3.html#T25">AMI_3:25</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span> = 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_6_1_1_2"><b>suppose </b></a><a NAME="E1:89_2_6_1_1_2"/><i><font color="Green">E186</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">t</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/><a NAME="E3:89_2_6_1_1_2"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a>, <a class="ref" href="scmfsa_2.html#T93">SCMFSA_2:93</a></i>;<br/><b>hence </b><a NAME="E4:89_2_6_1_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="sf_mastr.html#T6" target="_self">Th6</a>, <a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a>, <a class="ref" href="ami_3.html#T25">AMI_3:25</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span> = 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_7"><b>suppose </b></a><a NAME="E1:89_2_7"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 6
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">l</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:89_2_7"/><i><font color="Green">E187</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Maroon">l</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T59">SCMFSA_2:59</a></i>;<br/><b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
<font color="Maroon">l</font>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/><a NAME="E5:89_2_7"/><i><font color="Green">E188</font></i>: 
(  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i>, , <a class="txt" href="sf_mastr.html#E1:89"><i><font color="Green">E32</font></i></a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span> = 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
;<br/><br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span> = 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_8"><b>suppose </b></a><a NAME="E1:89_2_8"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 7
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">l</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:89_2_8"/><i><font color="Green">E189</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">l</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T60">SCMFSA_2:60</a></i>;<br/><a NAME="E4:89_2_8"/><i><font color="Green">E190</font></i>: 
(  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i>, , <a class="txt" href="sf_mastr.html#E1:89"><i><font color="Green">E32</font></i></a></i>;<br/><a NAME="E5:89_2_8"/><b>then </b><i><font color="Green">E191</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E6:89_2_8"/><b>then </b>
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><a NAME="E7:89_2_8"/><b>then </b><i><font color="Green">E192</font></i>: 
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="sf_mastr.html#T12" target="_self">Th12</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_8_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:89_2_8_1_1"/>
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_8_1_1_1"><b>suppose </b></a><a NAME="E1:89_2_8_1_1_1"/><i><font color="Green">E193</font></i>: 
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
<font color="Maroon">l</font>
<b>by </b><i>, <a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a>, <a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_8_1_1_2"><b>suppose </b></a><a NAME="E1:89_2_8_1_1_2"/><i><font color="Green">E194</font></i>: 
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span>
<b>by </b><i>, <a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, , <a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a>, <a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div><a NAME="E9:89_2_8"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T96">SCMFSA_2:96</a></i>;<br/><b>hence </b><a NAME="E10:89_2_8"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="sf_mastr.html#T6" target="_self">Th6</a>, <a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span> = 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_9"><b>suppose </b></a><a NAME="E1:89_2_9"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 8
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">l</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:89_2_9"/><i><font color="Green">E195</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">l</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T61">SCMFSA_2:61</a></i>;<br/><a NAME="E4:89_2_9"/><i><font color="Green">E196</font></i>: 
(  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i>, , <a class="txt" href="sf_mastr.html#E1:89"><i><font color="Green">E32</font></i></a></i>;<br/><a NAME="E5:89_2_9"/><b>then </b><i><font color="Green">E197</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E6:89_2_9"/><b>then </b>
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><a NAME="E7:89_2_9"/><b>then </b><i><font color="Green">E198</font></i>: 
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="sf_mastr.html#T12" target="_self">Th12</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_9_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:89_2_9_1_1"/>
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_9_1_1_1"><b>suppose </b></a><a NAME="E1:89_2_9_1_1_1"/><i><font color="Green">E199</font></i>: 
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
<font color="Maroon">l</font>
<b>by </b><i>, <a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a>, <a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_9_1_1_2"><b>suppose </b></a><a NAME="E1:89_2_9_1_1_2"/><i><font color="Green">E200</font></i>: 
<font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/><div class="add"><b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span>
<b>by </b><i>, <a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, , <a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a>, <a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div><a NAME="E9:89_2_9"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>;<br/><b>hence </b><a NAME="E10:89_2_9"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="sf_mastr.html#T6" target="_self">Th6</a>, <a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span> = 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_10"><b>suppose </b></a><a NAME="E1:89_2_10"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 9
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:89_2_10"/><i><font color="Green">E201</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">f</font>,<font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T62">SCMFSA_2:62</a></i>;<br/><b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">t</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/><a NAME="E5:89_2_10"/><i><font color="Green">E202</font></i>: 
(  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K2">}</a></span> &amp;  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">f</font></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i>, , <a class="txt" href="sf_mastr.html#E2:89"><i><font color="Green">E33</font></i></a></i>;<br/><a NAME="E6:89_2_10"/><b>then </b><i><font color="Green">E203</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> &amp; <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font> )
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E7:89_2_10"/><b>then </b>
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">f</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><a NAME="E8:89_2_10"/><b>then </b><i><font color="Green">E204</font></i>: 
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> )
 <b>by </b><i>, <a class="ref" href="sf_mastr.html#T12" target="_self">Th12</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><b>consider </b><font color="Maroon">m</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E10:89_2_10"/><i><font color="Green">E205</font></i>: 
( <font color="Maroon">m</font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">m</font> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>;<br/><b>consider </b><font color="Maroon">n</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E12:89_2_10"/><i><font color="Green">E206</font></i>: 
( <font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">n</font> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>;<br/><a NAME="E13:89_2_10"/><i><font color="Green">E207</font></i>: 
( <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="89_2_10_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_10_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:89_2_10_2_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> or <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_10_2_1_1"><b>case </b></a><a NAME="E1:89_2_10_2_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><b>thus </b><a NAME="E2:89_2_10_2_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a>, <a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a>, <a class="ref" href="sf_mastr.html#T15" target="_self">Th15</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_10_2_1_2"><b>case </b></a><a NAME="E1:89_2_10_2_1_2"/>
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:89_2_10_2_1_2"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E15:89_2_10"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="sf_mastr.html#T6" target="_self">Th6</a>, <a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a>, <a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a>, <a class="ref" href="sf_mastr.html#T15" target="_self">Th15</a>, <a class="ref" href="ami_3.html#T25">AMI_3:25</a></i>;<br/><b>thus </b><a NAME="E16:89_2_10"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="sf_mastr.html#T6" target="_self">Th6</a>, <a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a>, <a class="ref" href="sf_mastr.html#T16" target="_self">Th16</a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_11"><b>suppose </b></a><a NAME="E1:89_2_11"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 10
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:89_2_11"/><i><font color="Green">E208</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>,<font color="Maroon">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T63">SCMFSA_2:63</a></i>;<br/><b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">t</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/><a NAME="E5:89_2_11"/><i><font color="Green">E209</font></i>: 
(  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K2">}</a></span> &amp;  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">f</font></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i>, , <a class="txt" href="sf_mastr.html#E2:89"><i><font color="Green">E33</font></i></a></i>;<br/><a NAME="E6:89_2_11"/><b>then </b><i><font color="Green">E210</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> &amp; <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font> )
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E7:89_2_11"/><b>then </b>
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">f</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><a NAME="E8:89_2_11"/><b>then </b><i><font color="Green">E211</font></i>: 
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> )
 <b>by </b><i>, <a class="ref" href="sf_mastr.html#T12" target="_self">Th12</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><b>consider </b><font color="Maroon">m</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E10:89_2_11"/><i><font color="Green">E212</font></i>: 
( <font color="Maroon">m</font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font></span>)</span> <a href="funct_7.html#K2">+*</a> <font color="Maroon">m</font>,<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>;<br/><b>consider </b><font color="Maroon">n</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E12:89_2_11"/><i><font color="Green">E213</font></i>: 
( <font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font></span>)</span> <a href="funct_7.html#K2">+*</a> <font color="Maroon">n</font>,<span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>;<br/><a NAME="E13:89_2_11"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">b</font> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>;<br/><b>hence </b><a NAME="E14:89_2_11"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="sf_mastr.html#T6" target="_self">Th6</a>, <a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a>, <a class="ref" href="ami_3.html#T25">AMI_3:25</a></i>;<br/><b>thus </b><a NAME="E15:89_2_11"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="sf_mastr.html#T6" target="_self">Th6</a>, <a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a>, <a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a>, <a class="ref" href="sf_mastr.html#T15" target="_self">Th15</a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_12"><b>suppose </b></a><a NAME="E1:89_2_12"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 11
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:89_2_12"/><i><font color="Green">E214</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T64">SCMFSA_2:64</a></i>;<br/><b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">t</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/><a NAME="E5:89_2_12"/><i><font color="Green">E215</font></i>: 
(  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">f</font></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i>, , </i>;<br/><a NAME="E6:89_2_12"/><b>then </b><i><font color="Green">E216</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> &amp; <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font> )
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E7:89_2_12"/><b>then </b>
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">f</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><a NAME="E8:89_2_12"/><b>then </b><i><font color="Green">E217</font></i>: 
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> )
 <b>by </b><i>, <a class="ref" href="sf_mastr.html#T12" target="_self">Th12</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><a NAME="E9:89_2_12"/><i><font color="Green">E218</font></i>: 
( <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>;<br/><b>hence </b><a NAME="E10:89_2_12"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="sf_mastr.html#T6" target="_self">Th6</a>, <a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><b>thus </b><a NAME="E11:89_2_12"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="sf_mastr.html#T6" target="_self">Th6</a>, <a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a>, <a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="89_2_13"><b>suppose </b></a><a NAME="E1:89_2_13"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 12
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:89_2_13"/><i><font color="Green">E219</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T65">SCMFSA_2:65</a></i>;<br/><b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">t</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
;<br/><a NAME="E5:89_2_13"/><i><font color="Green">E220</font></i>: 
(  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">f</font></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i>, , </i>;<br/><a NAME="E6:89_2_13"/><b>then </b><i><font color="Green">E221</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font> &amp; <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font> )
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E7:89_2_13"/><b>then </b>
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">f</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><a NAME="E8:89_2_13"/><b>then </b><i><font color="Green">E222</font></i>: 
( <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> &amp; <font color="Maroon">s</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> )
 <b>by </b><i>, <a class="ref" href="sf_mastr.html#T12" target="_self">Th12</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><b>consider </b><font color="Maroon">m</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E10:89_2_13"/><i><font color="Green">E223</font></i>: 
( <font color="Maroon">m</font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> <a href="finseq_2.html#K2">|-&gt;</a> 0 )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>;<br/><b>consider </b><font color="Maroon">n</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E12:89_2_13"/><i><font color="Green">E224</font></i>: 
( <font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="finseq_2.html#K2">|-&gt;</a> 0 )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>;<br/><a NAME="E13:89_2_13"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font> )
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>;<br/><b>hence </b><a NAME="E14:89_2_13"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K1" target="_self">UsedIntLoc</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="sf_mastr.html#T6" target="_self">Th6</a>, <a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><b>thus </b><a NAME="E15:89_2_13"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">t</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" target="_self">UsedInt*Loc</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="sf_mastr.html#T6" target="_self">Th6</a>, <a class="ref" href="sf_mastr.html#T11" target="_self">Th11</a>, <a class="ref" href="sf_mastr.html#T13" target="_self">Th13</a>, <a class="ref" href="sf_mastr.html#T14" target="_self">Th14</a>, <a class="ref" href="sf_mastr.html#T15" target="_self">Th15</a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
