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

<b>let </b><font color="Maroon">s1</font> be   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a> , <font color="Maroon">s2</font> be   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a> ;<br/>

<b>assume </b><a NAME="E1:37"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 ;<br/>

<a NAME="E2:37"/>
 <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E3:37"/><b>then </b><i><font color="Green">E35</font></i>: 
 <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E4:37"/><i><font color="Green">E45</font></i>: 
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="ami_3.html#K1">SCM</a> 
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E5:37"/><b>then </b>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">s1</font>
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E6:37"/><b>then </b><i><font color="Green">E52</font></i>: 
 <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_5.html#T16" target="_self">Th16</a>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/>
<a NAME="E7:37"/>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">s2</font>
 
<b>by </b><i>, <a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E8:37"/><b>then </b><i><font color="Green">E54</font></i>: 
 <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_5.html#T16" target="_self">Th16</a>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/>
<i><font color="Green">E55</font></i>:  <a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></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="ami_3.html#K1">SCM</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="ami_5.html#T18" target="_self">Th18</a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">s2</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
;<br/>
<b>let </b><font color="Maroon">l</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> ;<br/>

<a NAME="E10:37"/><i><font color="Green">E56</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">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="ami_3.html#K1">SCM</a> 
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E11:37"/><i><font color="Green">E57</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">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="ami_3.html#K1">SCM</a> 
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E12:37"/><i><font color="Green">E58</font></i>: 
 <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="tarski.html#R1">c=</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E13:37"/><i><font color="Green">E86</font></i>: 
 <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="tarski.html#R1">c=</a>  <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">l</font>,<font color="Maroon">s1</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E14:37"/><i><font color="Green">E94</font></i>: 
 <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="tarski.html#R1">c=</a>  <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">l</font>,<font color="Maroon">s2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E1:37"><i><font color="Green">E34</font></i></a></i>;<br/>
<a NAME="E15:37"/><i><font color="Green">E102</font></i>: 
 <a href="ami_5.html#K1" target="_self">InsCode</a> <font color="Maroon">l</font> <a href="xxreal_0.html#R1">&lt;=</a> 8
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:37_2"/>
(  <a href="ami_5.html#K1" target="_self">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 0 or  <a href="ami_5.html#K1" target="_self">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 1 or  <a href="ami_5.html#K1" target="_self">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 2 or  <a href="ami_5.html#K1" target="_self">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 3 or  <a href="ami_5.html#K1" target="_self">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 4 or  <a href="ami_5.html#K1" target="_self">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 5 or  <a href="ami_5.html#K1" target="_self">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 6 or  <a href="ami_5.html#K1" target="_self">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 7 or  <a href="ami_5.html#K1" target="_self">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 8 )
 </span><b>by </b><i><a class="ref" href="ami_5.html#T20" target="_self">Th20</a>, <a class="ref" href="cqc_the1.html#T9">CQC_THE1:9</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1"><b>suppose </b></a><a NAME="E1:37_2_1"/>
 <a href="ami_5.html#K1" target="_self">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:37_2_1"/><b>then </b><i><font color="Green">E103</font></i>: 
<font color="Maroon">l</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="ami_3.html#K1">SCM</a> 
 <b>by </b><i/>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> = 
<font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_1.html#D8">AMI_1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_1.html#D8">AMI_1:def 8</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_2"><b>suppose </b></a><a NAME="E1:37_2_2"/>
 <a href="ami_5.html#K1" target="_self">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">db</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E3:37_2_2"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="ami_3.html#K3">:=</a> <font color="Maroon">db</font>
 <b>by </b><i/>;<br/><a NAME="E4:37_2_2"/>
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green">E105</font></i>:  <a href="ami_2.html#K2">SCM-Data-Loc</a>  = 
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T46">ZFMISC_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
;<br/><a NAME="E6:37_2_2"/>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><a NAME="E7:37_2_2"/><b>then </b>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <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">l</font>,<font color="Maroon">s1</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_5.html#T19" target="_self">Th19</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E8:37_2_2"/><b>then </b><i><font color="Green">E106</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E9:37_2_2"/>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><a NAME="E10:37_2_2"/><b>then </b>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <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">l</font>,<font color="Maroon">s2</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E11:37_2_2"/><b>then </b><i><font color="Green">E107</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E12:37_2_2"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:37_2_2_2"/><i><font color="Green">E108</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<a NAME="E2:37_2_2_2"/><b>then </b><i><font color="Green">E109</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:37_2_2_2"/><i><font color="Green">E110</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as    <a href="ami_3.html#M1">Data-Location</a>  <b>by </b><i>, <a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/>
<a NAME="E5:37_2_2_2"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font>
 
<b>by </b><i><a class="txt" href="ami_5.html#E4:37"><i><font color="Green">E45</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E6:37_2_2_2"/><i><font color="Green">E112</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="ami_3.html#T8">AMI_3:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></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/>.= 
<font color="Maroon">s2</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="ami_3.html#T8">AMI_3:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/>


</div><b>end;</b></div><a NAME="E13:37_2_2"/><b>then </b><i><font color="Green">E113</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></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">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="ami_5.html#T22" target="_self">Th22</a>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E14:37_2_2"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">db</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font> = 
<font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">db</font>
<b>by </b><i>, <a class="ref" href="ami_3.html#T8">AMI_3:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">db</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">db</font>
<b>by </b><i>, <a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font>
<b>by </b><i>, <a class="ref" href="ami_3.html#T8">AMI_3:8</a></i>
;<br/><a NAME="E16:37_2_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="txt" href="ami_5.html#E1:37"><i><font color="Green">E34</font></i></a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><a NAME="E17:37_2_2"/><b>then </b><i><font color="Green">E115</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i>, <a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</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="ami_3.html#K1">SCM</a> </span>)</span> = 
 <a href="ami_3.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_3.html#T8">AMI_3:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</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="ami_3.html#K1">SCM</a> </span>)</span>
<b>by </b><i>, , <a class="ref" href="ami_3.html#T8">AMI_3:8</a></i>
;<br/><a NAME="E19:37_2_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="txt" href="ami_5.html#E1:37"><i><font color="Green">E34</font></i></a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><b>hence </b><a NAME="E20:37_2_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></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">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_5.html#E4:37"><i><font color="Green">E45</font></i></a>, <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_3"><b>suppose </b></a><a NAME="E1:37_2_3"/>
 <a href="ami_5.html#K1" target="_self">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">db</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E3:37_2_3"/><i><font color="Green">E116</font></i>: 
<font color="Maroon">l</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K4">AddTo</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i/>;<br/><a NAME="E4:37_2_3"/>
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green">E117</font></i>:  <a href="ami_2.html#K2">SCM-Data-Loc</a>  = 
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T46">ZFMISC_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
;<br/><a NAME="E6:37_2_3"/>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><a NAME="E7:37_2_3"/><b>then </b>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <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">l</font>,<font color="Maroon">s1</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_5.html#T19" target="_self">Th19</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E8:37_2_3"/><b>then </b><i><font color="Green">E118</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E9:37_2_3"/>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><a NAME="E10:37_2_3"/><b>then </b>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <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">l</font>,<font color="Maroon">s2</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E11:37_2_3"/><b>then </b><i><font color="Green">E119</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E12:37_2_3"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_3_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:37_2_3_2"/><i><font color="Green">E120</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<a NAME="E2:37_2_3_2"/><b>then </b><i><font color="Green">E121</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:37_2_3_2"/><i><font color="Green">E122</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as    <a href="ami_3.html#M1">Data-Location</a>  <b>by </b><i>, <a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/>
<a NAME="E5:37_2_3_2"/><i><font color="Green">E123</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font>
 
<b>by </b><i><a class="txt" href="ami_5.html#E4:37"><i><font color="Green">E45</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E6:37_2_3_2"/><i><font color="Green">E124</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="ami_3.html#T9">AMI_3:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></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/>.= 
<font color="Maroon">s2</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="ami_3.html#T9">AMI_3:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/>


</div><b>end;</b></div><a NAME="E13:37_2_3"/><b>then </b><i><font color="Green">E125</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></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">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="ami_5.html#T22" target="_self">Th22</a>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E14:37_2_3"/><i><font color="Green">E126</font></i>: 
<font color="Maroon">db</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/><a NAME="E15:37_2_3"/><i><font color="Green">E127</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green">E128</font></i>: <font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font>
<b>by </b><i>, <a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, <a class="txt" href="ami_5.html#E4:37"><i><font color="Green">E45</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><i><font color="Green">E129</font></i>: <font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">db</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">db</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">db</font>
<b>by </b><i>, <a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">db</font></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_3.html#T9">AMI_3:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font>
<b>by </b><i>, , , <a class="ref" href="ami_3.html#T9">AMI_3:9</a></i>
;<br/><a NAME="E19:37_2_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="txt" href="ami_5.html#E1:37"><i><font color="Green">E34</font></i></a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><a NAME="E20:37_2_3"/><b>then </b><i><font color="Green">E130</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i>, <a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</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="ami_3.html#K1">SCM</a> </span>)</span> = 
 <a href="ami_3.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_3.html#T9">AMI_3:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</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="ami_3.html#K1">SCM</a> </span>)</span>
<b>by </b><i>, , <a class="ref" href="ami_3.html#T9">AMI_3:9</a></i>
;<br/><a NAME="E22:37_2_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="txt" href="ami_5.html#E1:37"><i><font color="Green">E34</font></i></a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><b>hence </b><a NAME="E23:37_2_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></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">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="ami_5.html#T25" target="_self">Th25</a>, <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_4"><b>suppose </b></a><a NAME="E1:37_2_4"/>
 <a href="ami_5.html#K1" target="_self">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 3
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">db</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E3:37_2_4"/><i><font color="Green">E131</font></i>: 
<font color="Maroon">l</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K5">SubFrom</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i/>;<br/><a NAME="E4:37_2_4"/>
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green">E132</font></i>:  <a href="ami_2.html#K2">SCM-Data-Loc</a>  = 
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T46">ZFMISC_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
;<br/><a NAME="E6:37_2_4"/>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><a NAME="E7:37_2_4"/><b>then </b>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <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">l</font>,<font color="Maroon">s1</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_5.html#T19" target="_self">Th19</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E8:37_2_4"/><b>then </b><i><font color="Green">E133</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E9:37_2_4"/>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><a NAME="E10:37_2_4"/><b>then </b>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <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">l</font>,<font color="Maroon">s2</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E11:37_2_4"/><b>then </b><i><font color="Green">E134</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E12:37_2_4"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_4_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:37_2_4_2"/><i><font color="Green">E135</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<a NAME="E2:37_2_4_2"/><b>then </b><i><font color="Green">E136</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:37_2_4_2"/><i><font color="Green">E137</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as    <a href="ami_3.html#M1">Data-Location</a>  <b>by </b><i>, <a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/>
<a NAME="E5:37_2_4_2"/><i><font color="Green">E138</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font>
 
<b>by </b><i><a class="txt" href="ami_5.html#E4:37"><i><font color="Green">E45</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E6:37_2_4_2"/><i><font color="Green">E139</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="ami_3.html#T10">AMI_3:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></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/>.= 
<font color="Maroon">s2</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="ami_3.html#T10">AMI_3:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/>


</div><b>end;</b></div><a NAME="E13:37_2_4"/><b>then </b><i><font color="Green">E140</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></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">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="ami_5.html#T22" target="_self">Th22</a>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E14:37_2_4"/><i><font color="Green">E141</font></i>: 
<font color="Maroon">db</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/><a NAME="E15:37_2_4"/><i><font color="Green">E142</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green">E143</font></i>: <font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font>
<b>by </b><i>, <a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, <a class="txt" href="ami_5.html#E4:37"><i><font color="Green">E45</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><i><font color="Green">E144</font></i>: <font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">db</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">db</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">db</font>
<b>by </b><i>, <a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">db</font></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_3.html#T10">AMI_3:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font>
<b>by </b><i>, , , <a class="ref" href="ami_3.html#T10">AMI_3:10</a></i>
;<br/><a NAME="E19:37_2_4"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="txt" href="ami_5.html#E1:37"><i><font color="Green">E34</font></i></a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><a NAME="E20:37_2_4"/><b>then </b><i><font color="Green">E145</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i>, <a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</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="ami_3.html#K1">SCM</a> </span>)</span> = 
 <a href="ami_3.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_3.html#T10">AMI_3:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</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="ami_3.html#K1">SCM</a> </span>)</span>
<b>by </b><i>, , <a class="ref" href="ami_3.html#T10">AMI_3:10</a></i>
;<br/><a NAME="E22:37_2_4"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="txt" href="ami_5.html#E1:37"><i><font color="Green">E34</font></i></a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><b>hence </b><a NAME="E23:37_2_4"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></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">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="ami_5.html#T25" target="_self">Th25</a>, <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_5"><b>suppose </b></a><a NAME="E1:37_2_5"/>
 <a href="ami_5.html#K1" target="_self">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 4
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">db</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E3:37_2_5"/><i><font color="Green">E146</font></i>: 
<font color="Maroon">l</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K6">MultBy</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i/>;<br/><a NAME="E4:37_2_5"/>
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green">E147</font></i>:  <a href="ami_2.html#K2">SCM-Data-Loc</a>  = 
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T46">ZFMISC_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
;<br/><a NAME="E6:37_2_5"/>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><a NAME="E7:37_2_5"/><b>then </b>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <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">l</font>,<font color="Maroon">s1</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_5.html#T19" target="_self">Th19</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E8:37_2_5"/><b>then </b><i><font color="Green">E148</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E9:37_2_5"/>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><a NAME="E10:37_2_5"/><b>then </b>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <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">l</font>,<font color="Maroon">s2</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E11:37_2_5"/><b>then </b><i><font color="Green">E149</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E12:37_2_5"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_5_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:37_2_5_2"/><i><font color="Green">E150</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<a NAME="E2:37_2_5_2"/><b>then </b><i><font color="Green">E151</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:37_2_5_2"/><i><font color="Green">E152</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as    <a href="ami_3.html#M1">Data-Location</a>  <b>by </b><i>, <a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/>
<a NAME="E5:37_2_5_2"/><i><font color="Green">E153</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font>
 
<b>by </b><i><a class="txt" href="ami_5.html#E4:37"><i><font color="Green">E45</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E6:37_2_5_2"/><i><font color="Green">E154</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="ami_3.html#T11">AMI_3:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></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/>.= 
<font color="Maroon">s2</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="ami_3.html#T11">AMI_3:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/>


</div><b>end;</b></div><a NAME="E13:37_2_5"/><b>then </b><i><font color="Green">E155</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></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">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="ami_5.html#T22" target="_self">Th22</a>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E14:37_2_5"/><i><font color="Green">E156</font></i>: 
<font color="Maroon">db</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/><a NAME="E15:37_2_5"/><i><font color="Green">E157</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green">E158</font></i>: <font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font>
<b>by </b><i>, <a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, <a class="txt" href="ami_5.html#E4:37"><i><font color="Green">E45</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><i><font color="Green">E159</font></i>: <font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">db</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">db</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">db</font>
<b>by </b><i>, <a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">db</font></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_3.html#T11">AMI_3:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font>
<b>by </b><i>, , , <a class="ref" href="ami_3.html#T11">AMI_3:11</a></i>
;<br/><a NAME="E19:37_2_5"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="txt" href="ami_5.html#E1:37"><i><font color="Green">E34</font></i></a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><a NAME="E20:37_2_5"/><b>then </b><i><font color="Green">E160</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i>, <a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</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="ami_3.html#K1">SCM</a> </span>)</span> = 
 <a href="ami_3.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_3.html#T11">AMI_3:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</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="ami_3.html#K1">SCM</a> </span>)</span>
<b>by </b><i>, , <a class="ref" href="ami_3.html#T11">AMI_3:11</a></i>
;<br/><a NAME="E22:37_2_5"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="txt" href="ami_5.html#E1:37"><i><font color="Green">E34</font></i></a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><b>hence </b><a NAME="E23:37_2_5"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></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">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="ami_5.html#T25" target="_self">Th25</a>, <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_6"><b>suppose </b></a><a NAME="E1:37_2_6"/>
 <a href="ami_5.html#K1" target="_self">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 5
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">db</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E3:37_2_6"/><i><font color="Green">E161</font></i>: 
<font color="Maroon">l</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K7">Divide</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E4:37_2_6"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></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">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_6_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_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="E1:37_2_6_1_1"/>
( <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">db</font> or <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">db</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_6_1_1_1"><b>suppose </b></a><a NAME="E1:37_2_6_1_1_1"/><i><font color="Green">E162</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">db</font>
 ;<br/><div class="add"><a NAME="E2:37_2_6_1_1_1"/>
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green">E163</font></i>:  <a href="ami_2.html#K2">SCM-Data-Loc</a>  = 
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T46">ZFMISC_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
;<br/><a NAME="E4:37_2_6_1_1_1"/>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><a NAME="E5:37_2_6_1_1_1"/><b>then </b>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <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">l</font>,<font color="Maroon">s1</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_5.html#T19" target="_self">Th19</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E6:37_2_6_1_1_1"/><b>then </b><i><font color="Green">E164</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E7:37_2_6_1_1_1"/>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><a NAME="E8:37_2_6_1_1_1"/><b>then </b>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <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">l</font>,<font color="Maroon">s2</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E9:37_2_6_1_1_1"/><b>then </b><i><font color="Green">E165</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E10:37_2_6_1_1_1"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_6_1_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:37_2_6_1_1_1_2"/><i><font color="Green">E166</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<a NAME="E2:37_2_6_1_1_1_2"/><b>then </b><i><font color="Green">E167</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:37_2_6_1_1_1_2"/><i><font color="Green">E168</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as    <a href="ami_3.html#M1">Data-Location</a>  <b>by </b><i><a class="txt" href="ami_5.html#E4:37"><i><font color="Green">E45</font></i></a>, <a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/>
<a NAME="E5:37_2_6_1_1_1_2"/><i><font color="Green">E169</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E6:37_2_6_1_1_1_2"/><i><font color="Green">E170</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E4:37"><i><font color="Green">E45</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="ami_5.html#T25" target="_self">Th25</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="ami_5.html#T25" target="_self">Th25</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , , </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/>


</div><b>end;</b></div><a NAME="E11:37_2_6_1_1_1"/><b>then </b><i><font color="Green">E171</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></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">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i>, <a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E12:37_2_6_1_1_1"/><i><font color="Green">E172</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green">E173</font></i>: <font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font>
<b>by </b><i>, <a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, <a class="txt" href="ami_5.html#E4:37"><i><font color="Green">E45</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font>
<b>by </b><i>, , , </i>
;<br/><a NAME="E15:37_2_6_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="txt" href="ami_5.html#E1:37"><i><font color="Green">E34</font></i></a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><a NAME="E16:37_2_6_1_1_1"/><b>then </b><i><font color="Green">E174</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_5.html#T22" target="_self">Th22</a>, , <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</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="ami_3.html#K1">SCM</a> </span>)</span> = 
 <a href="ami_3.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</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="ami_3.html#K1">SCM</a> </span>)</span>
<b>by </b><i>, , , </i>
;<br/><a NAME="E18:37_2_6_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="txt" href="ami_5.html#E1:37"><i><font color="Green">E34</font></i></a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><b>hence </b><a NAME="E19:37_2_6_1_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></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">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i>, <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_6_1_1_2"><b>suppose </b></a><a NAME="E1:37_2_6_1_1_2"/><i><font color="Green">E175</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">db</font>
 ;<br/><div class="add"><a NAME="E2:37_2_6_1_1_2"/><i><font color="Green">E176</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/><a NAME="E3:37_2_6_1_1_2"/>
<font color="Maroon">db</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green">E177</font></i>:  <a href="ami_2.html#K2">SCM-Data-Loc</a>  = 
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span>
<b>by </b><i><a class="ref" href="ami_5.html#T22" target="_self">Th22</a>, <a class="ref" href="zfmisc_1.html#T48">ZFMISC_1:48</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
;<br/><a NAME="E5:37_2_6_1_1_2"/>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><a NAME="E6:37_2_6_1_1_2"/><b>then </b>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span> <a href="tarski.html#R1">c=</a>  <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">l</font>,<font color="Maroon">s1</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_5.html#T19" target="_self">Th19</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E7:37_2_6_1_1_2"/><b>then </b><i><font color="Green">E178</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span>
 <b>by </b><i><a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E8:37_2_6_1_1_2"/>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><a NAME="E9:37_2_6_1_1_2"/><b>then </b>
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span> <a href="tarski.html#R1">c=</a>  <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">l</font>,<font color="Maroon">s2</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E10:37_2_6_1_1_2"/><b>then </b><i><font color="Green">E179</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span>
 <b>by </b><i><a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E11:37_2_6_1_1_2"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_6_1_1_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:37_2_6_1_1_2_2"/><i><font color="Green">E180</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span>
 ;<br/>

<a NAME="E2:37_2_6_1_1_2_2"/><b>then </b><i><font color="Green">E181</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:37_2_6_1_1_2_2"/><i><font color="Green">E182</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E4:37"><i><font color="Green">E45</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as    <a href="ami_3.html#M1">Data-Location</a>  <b>by </b><i>, <a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/>
<a NAME="E5:37_2_6_1_1_2_2"/><i><font color="Green">E183</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">db</font> )
 
<b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E6:37_2_6_1_1_2_2"/><i><font color="Green">E184</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E4:37"><i><font color="Green">E45</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="ami_5.html#T25" target="_self">Th25</a>, <a class="ref" href="ami_3.html#T12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></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/>.= 
<font color="Maroon">s2</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="ami_5.html#T25" target="_self">Th25</a>, <a class="ref" href="ami_3.html#T12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="txt" href="ami_5.html#E4:37"><i><font color="Green">E45</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/>


</div><b>end;</b></div><a NAME="E12:37_2_6_1_1_2"/><b>then </b><i><font color="Green">E185</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span></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">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E13:37_2_6_1_1_2"/><i><font color="Green">E186</font></i>: 
<font color="Maroon">db</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/><a NAME="E14:37_2_6_1_1_2"/><i><font color="Green">E187</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green">E188</font></i>: <font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font>
<b>by </b><i>, <a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><i><font color="Green">E189</font></i>: <font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">db</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">db</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">db</font>
<b>by </b><i>, <a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><i><font color="Green">E190</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font></span>)</span> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">db</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="ami_3.html#T12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font>
<b>by </b><i>, , <a class="ref" href="ami_5.html#T25" target="_self">Th25</a>, , <a class="ref" href="ami_3.html#T12">AMI_3:12</a></i>
;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">db</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">db</font></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_3.html#T12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">db</font>
<b>by </b><i>, <a class="ref" href="ami_5.html#T25" target="_self">Th25</a>, , <a class="ref" href="ami_3.html#T12">AMI_3:12</a></i>
;<br/><a NAME="E19:37_2_6_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">da</font>,<font color="Maroon">db</font></span><a href="domain_1.html#K7">}</a></span>
 <b>by </b><i>, <a class="txt" href="ami_5.html#E1:37"><i><font color="Green">E34</font></i></a>, , <a class="ref" href="ami_3.html#T25">AMI_3:25</a></i>;<br/><a NAME="E20:37_2_6_1_1_2"/><b>then </b><i><font color="Green">E191</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i>, <a class="txt" href="ami_5.html#E4:37"><i><font color="Green">E45</font></i></a>, <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</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="ami_3.html#K1">SCM</a> </span>)</span> = 
 <a href="ami_3.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_3.html#T12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</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="ami_3.html#K1">SCM</a> </span>)</span>
<b>by </b><i>, , <a class="ref" href="ami_3.html#T12">AMI_3:12</a></i>
;<br/><a NAME="E22:37_2_6_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="txt" href="ami_5.html#E1:37"><i><font color="Green">E34</font></i></a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><b>hence </b><a NAME="E23:37_2_6_1_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></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">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i>, <a class="ref" href="relat_1.html#T185">RELAT_1:185</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="37_2_7"><b>suppose </b></a><a NAME="E1:37_2_7"/>
 <a href="ami_5.html#K1" target="_self">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 6
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">loc</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E3:37_2_7"/><i><font color="Green">E192</font></i>: 
<font color="Maroon">l</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8">goto</a> <font color="Maroon">loc</font>
 <b>by </b><i/>;<br/><a NAME="E4:37_2_7"/><i><font color="Green">E193</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_5.html#T19" target="_self">Th19</a>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E5:37_2_7"/><i><font color="Green">E194</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E6:37_2_7"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a>  holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_7_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:37_2_7_1"/><i><font color="Green">E195</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 ;<br/>

<b>then reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as    <a href="ami_3.html#M1">Data-Location</a>  <b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/>
<a NAME="E3:37_2_7_1"/><i><font color="Green">E196</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="ami_3.html#T13">AMI_3:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="ami_3.html#T13">AMI_3:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/>


</div><b>end;</b></div><a NAME="E7:37_2_7"/><b>then </b><i><font color="Green">E197</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i>, <a class="ref" href="ami_5.html#T22" target="_self">Th22</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</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="ami_3.html#K1">SCM</a> </span>)</span> = 
<font color="Maroon">loc</font>
<b>by </b><i>, <a class="ref" href="ami_3.html#T13">AMI_3:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</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="ami_3.html#K1">SCM</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="ami_3.html#T13">AMI_3:13</a></i>
;<br/><a NAME="E9:37_2_7"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="txt" href="ami_5.html#E1:37"><i><font color="Green">E34</font></i></a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><b>hence </b><a NAME="E10:37_2_7"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></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">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i>, <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_8"><b>suppose </b></a><a NAME="E1:37_2_8"/>
 <a href="ami_5.html#K1" target="_self">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 7
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">loc</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> , <font color="Maroon">da</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E3:37_2_8"/><i><font color="Green">E198</font></i>: 
<font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">loc</font>
 <b>by </b><i><a class="ref" href="ami_5.html#T15" target="_self">Th15</a></i>;<br/><a NAME="E4:37_2_8"/><i><font color="Green">E199</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_5.html#T19" target="_self">Th19</a>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E5:37_2_8"/><i><font color="Green">E200</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E6:37_2_8"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a>  holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_8_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:37_2_8_1"/><i><font color="Green">E201</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 ;<br/>

<b>then reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as    <a href="ami_3.html#M1">Data-Location</a>  <b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/>
<a NAME="E3:37_2_8_1"/><i><font color="Green">E202</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="ami_3.html#T14">AMI_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="ami_3.html#T14">AMI_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/>


</div><b>end;</b></div><a NAME="E7:37_2_8"/><b>then </b><i><font color="Green">E203</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i>, <a class="ref" href="ami_5.html#T22" target="_self">Th22</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E8:37_2_8"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</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="ami_3.html#K1">SCM</a> </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">l</font>,<font color="Maroon">s2</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="ami_3.html#K1">SCM</a> </span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_8_2"><b>proof </b></a><div class="add">

<a NAME="E1:37_2_8_2"/><i><font color="Green">E204</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/>
<b>then </b><i><font color="Green">E205</font></i>: <font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font>
<b>by </b><i>, <a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, <a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_8_2_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:37_2_8_2_2"/>
( <font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</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="37_2_8_2_2_1"><b>suppose </b></a><a NAME="E1:37_2_8_2_2_1"/><i><font color="Green">E206</font></i>: 
<font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</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="ami_3.html#K1">SCM</a> </span>)</span> = 
<font color="Maroon">loc</font>
<b>by </b><i>, <a class="ref" href="ami_3.html#T14">AMI_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</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="ami_3.html#K1">SCM</a> </span>)</span>
<b>by </b><i>, , <a class="txt" href="ami_5.html#E4:37"><i><font color="Green">E45</font></i></a>, <a class="ref" href="ami_3.html#T14">AMI_3:14</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_8_2_2_2"><b>suppose </b></a><a NAME="E1:37_2_8_2_2_2"/><i><font color="Green">E207</font></i>: 
<font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</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="ami_3.html#K1">SCM</a> </span>)</span> = 
 <a href="ami_3.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_3.html#T14">AMI_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</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="ami_3.html#K1">SCM</a> </span>)</span>
<b>by </b><i>, , , <a class="txt" href="ami_5.html#E4:37"><i><font color="Green">E45</font></i></a>, <a class="ref" href="ami_3.html#T14">AMI_3:14</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E9:37_2_8"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="txt" href="ami_5.html#E1:37"><i><font color="Green">E34</font></i></a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><b>hence </b><a NAME="E10:37_2_8"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></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">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i>, <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_9"><b>suppose </b></a><a NAME="E1:37_2_9"/>
 <a href="ami_5.html#K1" target="_self">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 8
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">loc</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> , <font color="Maroon">da</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E3:37_2_9"/><i><font color="Green">E208</font></i>: 
<font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="ami_3.html#K10">&gt;0_goto</a> <font color="Maroon">loc</font>
 <b>by </b><i/>;<br/><a NAME="E4:37_2_9"/><i><font color="Green">E209</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_5.html#T19" target="_self">Th19</a>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E5:37_2_9"/><i><font color="Green">E210</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E6:37_2_9"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a>  holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_9_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:37_2_9_1"/><i><font color="Green">E211</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 ;<br/>

<b>then reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as    <a href="ami_3.html#M1">Data-Location</a>  <b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/>
<a NAME="E3:37_2_9_1"/><i><font color="Green">E212</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="ami_3.html#T15">AMI_3:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="ami_3.html#T15">AMI_3:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/>


</div><b>end;</b></div><a NAME="E7:37_2_9"/><b>then </b><i><font color="Green">E213</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i>, <a class="ref" href="ami_5.html#T22" target="_self">Th22</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E8:37_2_9"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</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="ami_3.html#K1">SCM</a> </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">l</font>,<font color="Maroon">s2</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="ami_3.html#K1">SCM</a> </span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_9_2"><b>proof </b></a><div class="add">

<a NAME="E1:37_2_9_2"/><i><font color="Green">E214</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="ami_3.html#D2">AMI_3:def 2</a></i>;<br/>
<b>then </b><i><font color="Green">E215</font></i>: <font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font>
<b>by </b><i>, <a class="txt" href="ami_5.html#E3:37"><i><font color="Green">E35</font></i></a>, <a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_9_2_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:37_2_9_2_2"/>
( <font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or <font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</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="37_2_9_2_2_1"><b>suppose </b></a><a NAME="E1:37_2_9_2_2_1"/><i><font color="Green">E216</font></i>: 
<font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</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="ami_3.html#K1">SCM</a> </span>)</span> = 
<font color="Maroon">loc</font>
<b>by </b><i>, <a class="ref" href="ami_3.html#T15">AMI_3:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</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="ami_3.html#K1">SCM</a> </span>)</span>
<b>by </b><i>, , <a class="txt" href="ami_5.html#E4:37"><i><font color="Green">E45</font></i></a>, <a class="ref" href="ami_3.html#T15">AMI_3:15</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_9_2_2_2"><b>suppose </b></a><a NAME="E1:37_2_9_2_2_2"/><i><font color="Green">E217</font></i>: 
<font color="Maroon">s1</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">da</font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</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="ami_3.html#K1">SCM</a> </span>)</span> = 
 <a href="ami_3.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_3.html#T15">AMI_3:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</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="ami_3.html#K1">SCM</a> </span>)</span>
<b>by </b><i>, , , <a class="txt" href="ami_5.html#E4:37"><i><font color="Green">E45</font></i></a>, <a class="ref" href="ami_3.html#T15">AMI_3:15</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E9:37_2_9"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="txt" href="ami_5.html#E1:37"><i><font color="Green">E34</font></i></a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><b>hence </b><a NAME="E10:37_2_9"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></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">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i>, <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
