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

<b>let </b><font color="Maroon" title="c1">s1</font>, <font color="Maroon" title="c2">s2</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ;<br/>

<b>assume </b><a NAME="E1:31"/><i><font color="Green" title="E22">A1</font></i>: 
<font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 ;<br/>

<a NAME="E2:31"/>
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E3:31"/><b>then </b><i><font color="Green" title="E23">A2</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E4:31"/><i><font color="Green" title="E24">A3</font></i>: 
<a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 
<b>by </b><i><a class="ref" href="ami_5.html#T23" target="_self" title="AMI_5:th.23">Th23</a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E5:31"/><b>then </b>
<a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">s1</font>
 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<a NAME="E6:31"/><b>then </b><i><font color="Green" title="E25">A4</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E3:31"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/>
<a NAME="E7:31"/>
<a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">s2</font>
 
<b>by </b><i><a class="txt" href="ami_5.html#E4:31"><i><font color="Green" title="E24">A3</font></i></a>, <a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<a NAME="E8:31"/><b>then </b><i><font color="Green" title="E26">A5</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E3:31"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/>
<i><font color="Green" title="E27">A6</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c1">s1</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E6:31"><i><font color="Green" title="E25">A4</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s2</font>
<b>by </b><i><a class="txt" href="ami_5.html#E8:31"><i><font color="Green" title="E26">A5</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>
;<br/>
<b>let </b><font color="Maroon" title="c3">l</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ;<br/>

<a NAME="E10:31"/><i><font color="Green" title="E28">A7</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<a NAME="E11:31"/><i><font color="Green" title="E29">A8</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<a NAME="E12:31"/><i><font color="Green" title="E30">A9</font></i>: 
 <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E13:31"/><i><font color="Green" title="E31">A10</font></i>: 
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">l</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 8
 
<b>by </b><i><a class="ref" href="ami_5.html#T36" target="_self" title="AMI_5:th.36">Th36</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:31_2"/>
(  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 )
 </span><b>by </b><i><a class="txt" href="ami_5.html#E13:31"><i><font color="Green" title="E31">A10</font></i></a>, <a class="ref" href="nat_1.html#T33" title="NAT_1:th.33">NAT_1:33</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_2_1"><b>suppose </b></a><a NAME="E1:31_2_1"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><a NAME="E2:31_2_1"/><b>then </b><i><font color="Green" title="E32">A11</font></i>: 
<font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 <b>by </b><i><a class="ref" href="ami_5.html#T46" target="_self" title="AMI_5:th.46">Th46</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> = 
<font color="Maroon" title="c2">s2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E2:31_2_1"><i><font color="Green" title="E32">A11</font></i></a>, <a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_2_2"><b>suppose </b></a><a NAME="E1:31_2_2"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">da</font>, <font color="Maroon" title="c5">db</font> being    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> <b> such that </b><br/><a NAME="E3:31_2_2"/><i><font color="Green" title="E32">A12</font></i>: 
<font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">da</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c5">db</font>
 <b>by </b><i><a class="ref" href="ami_5.html#T47" target="_self" title="AMI_5:th.47">Th47</a></i>;<br/><a NAME="E4:31_2_2"/>
<font color="Maroon" title="c4">da</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green" title="E33">A13</font></i>:  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  = 
<a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T46" title="ZFMISC_1:th.46">ZFMISC_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39" title="XBOOLE_1:th.39">XBOOLE_1:39</a></i>
;<br/><a NAME="E6:31_2_2"/><i><font color="Green" title="E34">A14</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/><a NAME="E7:31_2_2"/><i><font color="Green" title="E35">A15</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/><a NAME="E8:31_2_2"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_2_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:31_2_2_2"/><i><font color="Green" title="E36">A16</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/>

<a NAME="E2:31_2_2_2"/><b>then </b><i><font color="Green" title="E37">A17</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:31_2_2_2"/><i><font color="Green" title="E38">A18</font></i>: 
not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_2_2"><i><font color="Green" title="E36">A16</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">a</font> = <font color="Maroon" title="c6">x</font> as    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  <b>by </b><i><a class="txt" href="ami_5.html#E2:31_2_2_2"><i><font color="Green" title="E37">A17</font></i></a>, <a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/>
<a NAME="E5:31_2_2_2"/><i><font color="Green" title="E39">A19</font></i>: 
<font color="Maroon" title="c7">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">da</font>
 
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_2_2"><i><font color="Green" title="E38">A18</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E6:31_2_2_2"/><i><font color="Green" title="E40">A20</font></i>: 
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E2:31_2_2_2"><i><font color="Green" title="E37">A17</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">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" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_2_2"><i><font color="Green" title="E36">A16</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_2"><i><font color="Green" title="E32">A12</font></i></a>, <a class="txt" href="ami_5.html#E5:31_2_2_2"><i><font color="Green" title="E39">A19</font></i></a>, <a class="ref" href="ami_3.html#T8" title="AMI_3:th.8">AMI_3:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E6:31_2_2_2"><i><font color="Green" title="E40">A20</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E6:31_2_2_2"><i><font color="Green" title="E40">A20</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_2"><i><font color="Green" title="E32">A12</font></i></a>, <a class="txt" href="ami_5.html#E5:31_2_2_2"><i><font color="Green" title="E39">A19</font></i></a>, <a class="ref" href="ami_3.html#T8" title="AMI_3:th.8">AMI_3:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_2_2"><i><font color="Green" title="E36">A16</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/>


</div><b>end;</b></div><a NAME="E9:31_2_2"/><b>then </b><i><font color="Green" title="E36">A21</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_5.html#E6:31_2_2"><i><font color="Green" title="E34">A14</font></i></a>, <a class="txt" href="ami_5.html#E7:31_2_2"><i><font color="Green" title="E35">A15</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/><a NAME="E10:31_2_2"/><i><font color="Green" title="E37">A22</font></i>: 
<font color="Maroon" title="c5">db</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font> = 
<font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">db</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_2"><i><font color="Green" title="E32">A12</font></i></a>, <a class="ref" href="ami_3.html#T8" title="AMI_3:th.8">AMI_3:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">db</font>
<b>by </b><i><a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="txt" href="ami_5.html#E10:31_2_2"><i><font color="Green" title="E37">A22</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">db</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="txt" href="ami_5.html#E10:31_2_2"><i><font color="Green" title="E37">A22</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_2"><i><font color="Green" title="E32">A12</font></i></a>, <a class="ref" href="ami_3.html#T8" title="AMI_3:th.8">AMI_3:8</a></i>
;<br/><a NAME="E12:31_2_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="grfunc_1.html#T90" title="GRFUNC_1:th.90">GRFUNC_1:90</a></i>;<br/><a NAME="E13:31_2_2"/><b>then </b><i><font color="Green" title="E38">A23</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="ami_5.html#E5:31_2_2"><i><font color="Green" title="E33">A13</font></i></a>, <a class="txt" href="ami_5.html#E9:31_2_2"><i><font color="Green" title="E36">A21</font></i></a>, <a class="ref" href="relat_1.html#T185" title="RELAT_1:th.185">RELAT_1:185</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> = 
 <a href="ami_3.html#K11" title="AMI_3:func.11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c1">s1</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_2"><i><font color="Green" title="E32">A12</font></i></a>, <a class="ref" href="ami_3.html#T8" title="AMI_3:th.8">AMI_3:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E9:31"><i><font color="Green" title="E27">A6</font></i></a>, <a class="txt" href="ami_5.html#E3:31_2_2"><i><font color="Green" title="E32">A12</font></i></a>, <a class="ref" href="ami_3.html#T8" title="AMI_3:th.8">AMI_3:8</a></i>
;<br/><a NAME="E15:31_2_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="grfunc_1.html#T90" title="GRFUNC_1:th.90">GRFUNC_1:90</a></i>;<br/><b>hence </b><a NAME="E16:31_2_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_5.html#E13:31_2_2"><i><font color="Green" title="E38">A23</font></i></a>, <a class="ref" href="relat_1.html#T185" title="RELAT_1:th.185">RELAT_1:185</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_2_3"><b>suppose </b></a><a NAME="E1:31_2_3"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">da</font>, <font color="Maroon" title="c5">db</font> being    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> <b> such that </b><br/><a NAME="E3:31_2_3"/><i><font color="Green" title="E32">A24</font></i>: 
<font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K4" title="AMI_3:func.4">AddTo</a> <font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font>
 <b>by </b><i><a class="ref" href="ami_5.html#T48" target="_self" title="AMI_5:th.48">Th48</a></i>;<br/><a NAME="E4:31_2_3"/>
<font color="Maroon" title="c4">da</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green" title="E33">A25</font></i>:  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  = 
<a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T46" title="ZFMISC_1:th.46">ZFMISC_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39" title="XBOOLE_1:th.39">XBOOLE_1:39</a></i>
;<br/><a NAME="E6:31_2_3"/><i><font color="Green" title="E34">A26</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/><a NAME="E7:31_2_3"/><i><font color="Green" title="E35">A27</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/><a NAME="E8:31_2_3"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_2_3_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:31_2_3_2"/><i><font color="Green" title="E36">A28</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/>

<a NAME="E2:31_2_3_2"/><b>then </b><i><font color="Green" title="E37">A29</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:31_2_3_2"/><i><font color="Green" title="E38">A30</font></i>: 
not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_3_2"><i><font color="Green" title="E36">A28</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">a</font> = <font color="Maroon" title="c6">x</font> as    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  <b>by </b><i><a class="txt" href="ami_5.html#E2:31_2_3_2"><i><font color="Green" title="E37">A29</font></i></a>, <a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/>
<a NAME="E5:31_2_3_2"/><i><font color="Green" title="E39">A31</font></i>: 
<font color="Maroon" title="c7">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">da</font>
 
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_3_2"><i><font color="Green" title="E38">A30</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E6:31_2_3_2"/><i><font color="Green" title="E40">A32</font></i>: 
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E2:31_2_3_2"><i><font color="Green" title="E37">A29</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">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" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_3_2"><i><font color="Green" title="E36">A28</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_3"><i><font color="Green" title="E32">A24</font></i></a>, <a class="txt" href="ami_5.html#E5:31_2_3_2"><i><font color="Green" title="E39">A31</font></i></a>, <a class="ref" href="ami_3.html#T9" title="AMI_3:th.9">AMI_3:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E6:31_2_3_2"><i><font color="Green" title="E40">A32</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E6:31_2_3_2"><i><font color="Green" title="E40">A32</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_3"><i><font color="Green" title="E32">A24</font></i></a>, <a class="txt" href="ami_5.html#E5:31_2_3_2"><i><font color="Green" title="E39">A31</font></i></a>, <a class="ref" href="ami_3.html#T9" title="AMI_3:th.9">AMI_3:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_3_2"><i><font color="Green" title="E36">A28</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/>


</div><b>end;</b></div><a NAME="E9:31_2_3"/><b>then </b><i><font color="Green" title="E36">A33</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_5.html#E6:31_2_3"><i><font color="Green" title="E34">A26</font></i></a>, <a class="txt" href="ami_5.html#E7:31_2_3"><i><font color="Green" title="E35">A27</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/><a NAME="E10:31_2_3"/><i><font color="Green" title="E37">A34</font></i>: 
<font color="Maroon" title="c5">db</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/><a NAME="E11:31_2_3"/><i><font color="Green" title="E38">A35</font></i>: 
<font color="Maroon" title="c4">da</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green" title="E39">A36</font></i>: <font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="txt" href="ami_5.html#E11:31_2_3"><i><font color="Green" title="E38">A35</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/><i><font color="Green" title="E40">A37</font></i>: <font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">db</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">db</font>
<b>by </b><i><a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="txt" href="ami_5.html#E10:31_2_3"><i><font color="Green" title="E37">A34</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">db</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="txt" href="ami_5.html#E10:31_2_3"><i><font color="Green" title="E37">A34</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">db</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_3"><i><font color="Green" title="E32">A24</font></i></a>, <a class="ref" href="ami_3.html#T9" title="AMI_3:th.9">AMI_3:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_3"><i><font color="Green" title="E32">A24</font></i></a>, <a class="txt" href="ami_5.html#E12:31_2_3"><i><font color="Green" title="E39">A36</font></i></a>, <a class="txt" href="ami_5.html#E13:31_2_3"><i><font color="Green" title="E40">A37</font></i></a>, <a class="ref" href="ami_3.html#T9" title="AMI_3:th.9">AMI_3:9</a></i>
;<br/><a NAME="E15:31_2_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="grfunc_1.html#T90" title="GRFUNC_1:th.90">GRFUNC_1:90</a></i>;<br/><a NAME="E16:31_2_3"/><b>then </b><i><font color="Green" title="E41">A38</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="ami_5.html#E5:31_2_3"><i><font color="Green" title="E33">A25</font></i></a>, <a class="txt" href="ami_5.html#E9:31_2_3"><i><font color="Green" title="E36">A33</font></i></a>, <a class="ref" href="relat_1.html#T185" title="RELAT_1:th.185">RELAT_1:185</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> = 
 <a href="ami_3.html#K11" title="AMI_3:func.11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c1">s1</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_3"><i><font color="Green" title="E32">A24</font></i></a>, <a class="ref" href="ami_3.html#T9" title="AMI_3:th.9">AMI_3:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E9:31"><i><font color="Green" title="E27">A6</font></i></a>, <a class="txt" href="ami_5.html#E3:31_2_3"><i><font color="Green" title="E32">A24</font></i></a>, <a class="ref" href="ami_3.html#T9" title="AMI_3:th.9">AMI_3:9</a></i>
;<br/><a NAME="E18:31_2_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="grfunc_1.html#T90" title="GRFUNC_1:th.90">GRFUNC_1:90</a></i>;<br/><b>hence </b><a NAME="E19:31_2_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_5.html#E16:31_2_3"><i><font color="Green" title="E41">A38</font></i></a>, <a class="ref" href="relat_1.html#T185" title="RELAT_1:th.185">RELAT_1:185</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_2_4"><b>suppose </b></a><a NAME="E1:31_2_4"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">da</font>, <font color="Maroon" title="c5">db</font> being    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> <b> such that </b><br/><a NAME="E3:31_2_4"/><i><font color="Green" title="E32">A39</font></i>: 
<font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K5" title="AMI_3:func.5">SubFrom</a> <font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font>
 <b>by </b><i><a class="ref" href="ami_5.html#T49" target="_self" title="AMI_5:th.49">Th49</a></i>;<br/><a NAME="E4:31_2_4"/>
<font color="Maroon" title="c4">da</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green" title="E33">A40</font></i>:  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  = 
<a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T46" title="ZFMISC_1:th.46">ZFMISC_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39" title="XBOOLE_1:th.39">XBOOLE_1:39</a></i>
;<br/><a NAME="E6:31_2_4"/><i><font color="Green" title="E34">A41</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/><a NAME="E7:31_2_4"/><i><font color="Green" title="E35">A42</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/><a NAME="E8:31_2_4"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_2_4_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:31_2_4_2"/><i><font color="Green" title="E36">A43</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/>

<a NAME="E2:31_2_4_2"/><b>then </b><i><font color="Green" title="E37">A44</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:31_2_4_2"/><i><font color="Green" title="E38">A45</font></i>: 
not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_4_2"><i><font color="Green" title="E36">A43</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">a</font> = <font color="Maroon" title="c6">x</font> as    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  <b>by </b><i><a class="txt" href="ami_5.html#E2:31_2_4_2"><i><font color="Green" title="E37">A44</font></i></a>, <a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/>
<a NAME="E5:31_2_4_2"/><i><font color="Green" title="E39">A46</font></i>: 
<font color="Maroon" title="c7">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">da</font>
 
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_4_2"><i><font color="Green" title="E38">A45</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E6:31_2_4_2"/><i><font color="Green" title="E40">A47</font></i>: 
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E2:31_2_4_2"><i><font color="Green" title="E37">A44</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">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" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_4_2"><i><font color="Green" title="E36">A43</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_4"><i><font color="Green" title="E32">A39</font></i></a>, <a class="txt" href="ami_5.html#E5:31_2_4_2"><i><font color="Green" title="E39">A46</font></i></a>, <a class="ref" href="ami_3.html#T10" title="AMI_3:th.10">AMI_3:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E6:31_2_4_2"><i><font color="Green" title="E40">A47</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E6:31_2_4_2"><i><font color="Green" title="E40">A47</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_4"><i><font color="Green" title="E32">A39</font></i></a>, <a class="txt" href="ami_5.html#E5:31_2_4_2"><i><font color="Green" title="E39">A46</font></i></a>, <a class="ref" href="ami_3.html#T10" title="AMI_3:th.10">AMI_3:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_4_2"><i><font color="Green" title="E36">A43</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/>


</div><b>end;</b></div><a NAME="E9:31_2_4"/><b>then </b><i><font color="Green" title="E36">A48</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_5.html#E6:31_2_4"><i><font color="Green" title="E34">A41</font></i></a>, <a class="txt" href="ami_5.html#E7:31_2_4"><i><font color="Green" title="E35">A42</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/><a NAME="E10:31_2_4"/><i><font color="Green" title="E37">A49</font></i>: 
<font color="Maroon" title="c5">db</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/><a NAME="E11:31_2_4"/><i><font color="Green" title="E38">A50</font></i>: 
<font color="Maroon" title="c4">da</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green" title="E39">A51</font></i>: <font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="txt" href="ami_5.html#E11:31_2_4"><i><font color="Green" title="E38">A50</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/><i><font color="Green" title="E40">A52</font></i>: <font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">db</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">db</font>
<b>by </b><i><a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="txt" href="ami_5.html#E10:31_2_4"><i><font color="Green" title="E37">A49</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">db</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="txt" href="ami_5.html#E10:31_2_4"><i><font color="Green" title="E37">A49</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">db</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_4"><i><font color="Green" title="E32">A39</font></i></a>, <a class="ref" href="ami_3.html#T10" title="AMI_3:th.10">AMI_3:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_4"><i><font color="Green" title="E32">A39</font></i></a>, <a class="txt" href="ami_5.html#E12:31_2_4"><i><font color="Green" title="E39">A51</font></i></a>, <a class="txt" href="ami_5.html#E13:31_2_4"><i><font color="Green" title="E40">A52</font></i></a>, <a class="ref" href="ami_3.html#T10" title="AMI_3:th.10">AMI_3:10</a></i>
;<br/><a NAME="E15:31_2_4"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="grfunc_1.html#T90" title="GRFUNC_1:th.90">GRFUNC_1:90</a></i>;<br/><a NAME="E16:31_2_4"/><b>then </b><i><font color="Green" title="E41">A53</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="ami_5.html#E5:31_2_4"><i><font color="Green" title="E33">A40</font></i></a>, <a class="txt" href="ami_5.html#E9:31_2_4"><i><font color="Green" title="E36">A48</font></i></a>, <a class="ref" href="relat_1.html#T185" title="RELAT_1:th.185">RELAT_1:185</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> = 
 <a href="ami_3.html#K11" title="AMI_3:func.11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c1">s1</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_4"><i><font color="Green" title="E32">A39</font></i></a>, <a class="ref" href="ami_3.html#T10" title="AMI_3:th.10">AMI_3:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E9:31"><i><font color="Green" title="E27">A6</font></i></a>, <a class="txt" href="ami_5.html#E3:31_2_4"><i><font color="Green" title="E32">A39</font></i></a>, <a class="ref" href="ami_3.html#T10" title="AMI_3:th.10">AMI_3:10</a></i>
;<br/><a NAME="E18:31_2_4"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="grfunc_1.html#T90" title="GRFUNC_1:th.90">GRFUNC_1:90</a></i>;<br/><b>hence </b><a NAME="E19:31_2_4"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_5.html#E16:31_2_4"><i><font color="Green" title="E41">A53</font></i></a>, <a class="ref" href="relat_1.html#T185" title="RELAT_1:th.185">RELAT_1:185</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_2_5"><b>suppose </b></a><a NAME="E1:31_2_5"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">da</font>, <font color="Maroon" title="c5">db</font> being    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> <b> such that </b><br/><a NAME="E3:31_2_5"/><i><font color="Green" title="E32">A54</font></i>: 
<font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K6" title="AMI_3:func.6">MultBy</a> <font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font>
 <b>by </b><i><a class="ref" href="ami_5.html#T50" target="_self" title="AMI_5:th.50">Th50</a></i>;<br/><a NAME="E4:31_2_5"/>
<font color="Maroon" title="c4">da</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green" title="E33">A55</font></i>:  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  = 
<a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T46" title="ZFMISC_1:th.46">ZFMISC_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39" title="XBOOLE_1:th.39">XBOOLE_1:39</a></i>
;<br/><a NAME="E6:31_2_5"/><i><font color="Green" title="E34">A56</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/><a NAME="E7:31_2_5"/><i><font color="Green" title="E35">A57</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/><a NAME="E8:31_2_5"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_2_5_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:31_2_5_2"/><i><font color="Green" title="E36">A58</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/>

<a NAME="E2:31_2_5_2"/><b>then </b><i><font color="Green" title="E37">A59</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:31_2_5_2"/><i><font color="Green" title="E38">A60</font></i>: 
not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_5_2"><i><font color="Green" title="E36">A58</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">a</font> = <font color="Maroon" title="c6">x</font> as    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  <b>by </b><i><a class="txt" href="ami_5.html#E2:31_2_5_2"><i><font color="Green" title="E37">A59</font></i></a>, <a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/>
<a NAME="E5:31_2_5_2"/><i><font color="Green" title="E39">A61</font></i>: 
<font color="Maroon" title="c7">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">da</font>
 
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_5_2"><i><font color="Green" title="E38">A60</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E6:31_2_5_2"/><i><font color="Green" title="E40">A62</font></i>: 
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E2:31_2_5_2"><i><font color="Green" title="E37">A59</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">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" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_5_2"><i><font color="Green" title="E36">A58</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_5"><i><font color="Green" title="E32">A54</font></i></a>, <a class="txt" href="ami_5.html#E5:31_2_5_2"><i><font color="Green" title="E39">A61</font></i></a>, <a class="ref" href="ami_3.html#T11" title="AMI_3:th.11">AMI_3:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E6:31_2_5_2"><i><font color="Green" title="E40">A62</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E6:31_2_5_2"><i><font color="Green" title="E40">A62</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_5"><i><font color="Green" title="E32">A54</font></i></a>, <a class="txt" href="ami_5.html#E5:31_2_5_2"><i><font color="Green" title="E39">A61</font></i></a>, <a class="ref" href="ami_3.html#T11" title="AMI_3:th.11">AMI_3:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_5_2"><i><font color="Green" title="E36">A58</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/>


</div><b>end;</b></div><a NAME="E9:31_2_5"/><b>then </b><i><font color="Green" title="E36">A63</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_5.html#E6:31_2_5"><i><font color="Green" title="E34">A56</font></i></a>, <a class="txt" href="ami_5.html#E7:31_2_5"><i><font color="Green" title="E35">A57</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/><a NAME="E10:31_2_5"/><i><font color="Green" title="E37">A64</font></i>: 
<font color="Maroon" title="c5">db</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/><a NAME="E11:31_2_5"/><i><font color="Green" title="E38">A65</font></i>: 
<font color="Maroon" title="c4">da</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green" title="E39">A66</font></i>: <font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="txt" href="ami_5.html#E11:31_2_5"><i><font color="Green" title="E38">A65</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/><i><font color="Green" title="E40">A67</font></i>: <font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">db</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">db</font>
<b>by </b><i><a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="txt" href="ami_5.html#E10:31_2_5"><i><font color="Green" title="E37">A64</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">db</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="txt" href="ami_5.html#E10:31_2_5"><i><font color="Green" title="E37">A64</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">db</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_5"><i><font color="Green" title="E32">A54</font></i></a>, <a class="ref" href="ami_3.html#T11" title="AMI_3:th.11">AMI_3:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_5"><i><font color="Green" title="E32">A54</font></i></a>, <a class="txt" href="ami_5.html#E12:31_2_5"><i><font color="Green" title="E39">A66</font></i></a>, <a class="txt" href="ami_5.html#E13:31_2_5"><i><font color="Green" title="E40">A67</font></i></a>, <a class="ref" href="ami_3.html#T11" title="AMI_3:th.11">AMI_3:11</a></i>
;<br/><a NAME="E15:31_2_5"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="grfunc_1.html#T90" title="GRFUNC_1:th.90">GRFUNC_1:90</a></i>;<br/><a NAME="E16:31_2_5"/><b>then </b><i><font color="Green" title="E41">A68</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="ami_5.html#E5:31_2_5"><i><font color="Green" title="E33">A55</font></i></a>, <a class="txt" href="ami_5.html#E9:31_2_5"><i><font color="Green" title="E36">A63</font></i></a>, <a class="ref" href="relat_1.html#T185" title="RELAT_1:th.185">RELAT_1:185</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> = 
 <a href="ami_3.html#K11" title="AMI_3:func.11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c1">s1</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_5"><i><font color="Green" title="E32">A54</font></i></a>, <a class="ref" href="ami_3.html#T11" title="AMI_3:th.11">AMI_3:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E9:31"><i><font color="Green" title="E27">A6</font></i></a>, <a class="txt" href="ami_5.html#E3:31_2_5"><i><font color="Green" title="E32">A54</font></i></a>, <a class="ref" href="ami_3.html#T11" title="AMI_3:th.11">AMI_3:11</a></i>
;<br/><a NAME="E18:31_2_5"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="grfunc_1.html#T90" title="GRFUNC_1:th.90">GRFUNC_1:90</a></i>;<br/><b>hence </b><a NAME="E19:31_2_5"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_5.html#E16:31_2_5"><i><font color="Green" title="E41">A68</font></i></a>, <a class="ref" href="relat_1.html#T185" title="RELAT_1:th.185">RELAT_1:185</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_2_6"><b>suppose </b></a><a NAME="E1:31_2_6"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">da</font>, <font color="Maroon" title="c5">db</font> being    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> <b> such that </b><br/><a NAME="E3:31_2_6"/><i><font color="Green" title="E32">A69</font></i>: 
<font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font>
 <b>by </b><i><a class="ref" href="ami_5.html#T51" target="_self" title="AMI_5:th.51">Th51</a></i>;<br/><b>thus </b><a NAME="E4:31_2_6"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_2_6_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_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="E1:31_2_6_1_1"/>
( <font color="Maroon" title="c4">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">db</font> or <font color="Maroon" title="c4">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">db</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_2_6_1_1_1"><b>suppose </b></a><a NAME="E1:31_2_6_1_1_1"/><i><font color="Green" title="E33">A70</font></i>: 
<font color="Maroon" title="c4">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">db</font>
 ;<br/><div class="add"><a NAME="E2:31_2_6_1_1_1"/>
<font color="Maroon" title="c4">da</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green" title="E34">A71</font></i>:  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  = 
<a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T46" title="ZFMISC_1:th.46">ZFMISC_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39" title="XBOOLE_1:th.39">XBOOLE_1:39</a></i>
;<br/><a NAME="E4:31_2_6_1_1_1"/><i><font color="Green" title="E35">A72</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/><a NAME="E5:31_2_6_1_1_1"/><i><font color="Green" title="E36">A73</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/><a NAME="E6:31_2_6_1_1_1"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_2_6_1_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:31_2_6_1_1_1_2"/><i><font color="Green" title="E37">A74</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/>

<a NAME="E2:31_2_6_1_1_1_2"/><b>then </b><i><font color="Green" title="E38">A75</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:31_2_6_1_1_1_2"/><i><font color="Green" title="E39">A76</font></i>: 
not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_6_1_1_1_2"><i><font color="Green" title="E37">A74</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">a</font> = <font color="Maroon" title="c6">x</font> as    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  <b>by </b><i><a class="txt" href="ami_5.html#E2:31_2_6_1_1_1_2"><i><font color="Green" title="E38">A75</font></i></a>, <a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/>
<a NAME="E5:31_2_6_1_1_1_2"/><i><font color="Green" title="E40">A77</font></i>: 
<font color="Maroon" title="c7">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">da</font>
 
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_6_1_1_1_2"><i><font color="Green" title="E39">A76</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E6:31_2_6_1_1_1_2"/><i><font color="Green" title="E41">A78</font></i>: 
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E2:31_2_6_1_1_1_2"><i><font color="Green" title="E38">A75</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">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" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_6_1_1_1_2"><i><font color="Green" title="E37">A74</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_6"><i><font color="Green" title="E32">A69</font></i></a>, <a class="txt" href="ami_5.html#E1:31_2_6_1_1_1"><i><font color="Green" title="E33">A70</font></i></a>, <a class="txt" href="ami_5.html#E5:31_2_6_1_1_1_2"><i><font color="Green" title="E40">A77</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E6:31_2_6_1_1_1_2"><i><font color="Green" title="E41">A78</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E6:31_2_6_1_1_1_2"><i><font color="Green" title="E41">A78</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_6"><i><font color="Green" title="E32">A69</font></i></a>, <a class="txt" href="ami_5.html#E1:31_2_6_1_1_1"><i><font color="Green" title="E33">A70</font></i></a>, <a class="txt" href="ami_5.html#E5:31_2_6_1_1_1_2"><i><font color="Green" title="E40">A77</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_6_1_1_1_2"><i><font color="Green" title="E37">A74</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/>


</div><b>end;</b></div><a NAME="E7:31_2_6_1_1_1"/><b>then </b><i><font color="Green" title="E37">A79</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_5.html#E4:31_2_6_1_1_1"><i><font color="Green" title="E35">A72</font></i></a>, <a class="txt" href="ami_5.html#E5:31_2_6_1_1_1"><i><font color="Green" title="E36">A73</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/><a NAME="E8:31_2_6_1_1_1"/><i><font color="Green" title="E38">A80</font></i>: 
<font color="Maroon" title="c4">da</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green" title="E39">A81</font></i>: <font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="txt" href="ami_5.html#E8:31_2_6_1_1_1"><i><font color="Green" title="E38">A80</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_6"><i><font color="Green" title="E32">A69</font></i></a>, <a class="txt" href="ami_5.html#E1:31_2_6_1_1_1"><i><font color="Green" title="E33">A70</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_6"><i><font color="Green" title="E32">A69</font></i></a>, <a class="txt" href="ami_5.html#E1:31_2_6_1_1_1"><i><font color="Green" title="E33">A70</font></i></a>, <a class="txt" href="ami_5.html#E9:31_2_6_1_1_1"><i><font color="Green" title="E39">A81</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
;<br/><a NAME="E11:31_2_6_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">da</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="grfunc_1.html#T90" title="GRFUNC_1:th.90">GRFUNC_1:90</a></i>;<br/><a NAME="E12:31_2_6_1_1_1"/><b>then </b><i><font color="Green" title="E40">A82</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_6_1_1_1"><i><font color="Green" title="E34">A71</font></i></a>, <a class="txt" href="ami_5.html#E7:31_2_6_1_1_1"><i><font color="Green" title="E37">A79</font></i></a>, <a class="ref" href="relat_1.html#T185" title="RELAT_1:th.185">RELAT_1:185</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> = 
 <a href="ami_3.html#K11" title="AMI_3:func.11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c1">s1</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_6"><i><font color="Green" title="E32">A69</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E9:31"><i><font color="Green" title="E27">A6</font></i></a>, <a class="txt" href="ami_5.html#E3:31_2_6"><i><font color="Green" title="E32">A69</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
;<br/><a NAME="E14:31_2_6_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="grfunc_1.html#T90" title="GRFUNC_1:th.90">GRFUNC_1:90</a></i>;<br/><b>hence </b><a NAME="E15:31_2_6_1_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_5.html#E12:31_2_6_1_1_1"><i><font color="Green" title="E40">A82</font></i></a>, <a class="ref" href="relat_1.html#T185" title="RELAT_1:th.185">RELAT_1:185</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_2_6_1_1_2"><b>suppose </b></a><a NAME="E1:31_2_6_1_1_2"/><i><font color="Green" title="E33">A83</font></i>: 
<font color="Maroon" title="c4">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">db</font>
 ;<br/><div class="add"><a NAME="E2:31_2_6_1_1_2"/><i><font color="Green" title="E34">A84</font></i>: 
<font color="Maroon" title="c4">da</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/><a NAME="E3:31_2_6_1_1_2"/>
<font color="Maroon" title="c5">db</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green" title="E35">A85</font></i>:  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  = 
<a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
<b>by </b><i><a class="txt" href="ami_5.html#E2:31_2_6_1_1_2"><i><font color="Green" title="E34">A84</font></i></a>, <a class="ref" href="zfmisc_1.html#T48" title="ZFMISC_1:th.48">ZFMISC_1:48</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39" title="XBOOLE_1:th.39">XBOOLE_1:39</a></i>
;<br/><a NAME="E5:31_2_6_1_1_2"/><i><font color="Green" title="E36">A86</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/><a NAME="E6:31_2_6_1_1_2"/><i><font color="Green" title="E37">A87</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/><a NAME="E7:31_2_6_1_1_2"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_2_6_1_1_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:31_2_6_1_1_2_2"/><i><font color="Green" title="E38">A88</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/>

<a NAME="E2:31_2_6_1_1_2_2"/><b>then </b><i><font color="Green" title="E39">A89</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:31_2_6_1_1_2_2"/><i><font color="Green" title="E40">A90</font></i>: 
not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_6_1_1_2_2"><i><font color="Green" title="E38">A88</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">a</font> = <font color="Maroon" title="c6">x</font> as    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  <b>by </b><i><a class="txt" href="ami_5.html#E2:31_2_6_1_1_2_2"><i><font color="Green" title="E39">A89</font></i></a>, <a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/>
<a NAME="E5:31_2_6_1_1_2_2"/><i><font color="Green" title="E41">A91</font></i>: 
( <font color="Maroon" title="c7">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">da</font> &amp; <font color="Maroon" title="c7">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">db</font> )
 
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_6_1_1_2_2"><i><font color="Green" title="E40">A90</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<a NAME="E6:31_2_6_1_1_2_2"/><i><font color="Green" title="E42">A92</font></i>: 
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E2:31_2_6_1_1_2_2"><i><font color="Green" title="E39">A89</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">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" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_6_1_1_2_2"><i><font color="Green" title="E38">A88</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_6"><i><font color="Green" title="E32">A69</font></i></a>, <a class="txt" href="ami_5.html#E5:31_2_6_1_1_2_2"><i><font color="Green" title="E41">A91</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E6:31_2_6_1_1_2_2"><i><font color="Green" title="E42">A92</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E6:31_2_6_1_1_2_2"><i><font color="Green" title="E42">A92</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_6"><i><font color="Green" title="E32">A69</font></i></a>, <a class="txt" href="ami_5.html#E5:31_2_6_1_1_2_2"><i><font color="Green" title="E41">A91</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_6_1_1_2_2"><i><font color="Green" title="E38">A88</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/>


</div><b>end;</b></div><a NAME="E8:31_2_6_1_1_2"/><b>then </b><i><font color="Green" title="E38">A93</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_5.html#E5:31_2_6_1_1_2"><i><font color="Green" title="E36">A86</font></i></a>, <a class="txt" href="ami_5.html#E6:31_2_6_1_1_2"><i><font color="Green" title="E37">A87</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/><a NAME="E9:31_2_6_1_1_2"/><i><font color="Green" title="E39">A94</font></i>: 
<font color="Maroon" title="c5">db</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/><a NAME="E10:31_2_6_1_1_2"/><i><font color="Green" title="E40">A95</font></i>: 
<font color="Maroon" title="c4">da</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/><b>then </b><i><font color="Green" title="E41">A96</font></i>: <font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="txt" href="ami_5.html#E10:31_2_6_1_1_2"><i><font color="Green" title="E40">A95</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/><i><font color="Green" title="E42">A97</font></i>: <font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">db</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">db</font>
<b>by </b><i><a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="txt" href="ami_5.html#E9:31_2_6_1_1_2"><i><font color="Green" title="E39">A94</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">db</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="txt" href="ami_5.html#E9:31_2_6_1_1_2"><i><font color="Green" title="E39">A94</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/><i><font color="Green" title="E43">A98</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">db</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_6"><i><font color="Green" title="E32">A69</font></i></a>, <a class="txt" href="ami_5.html#E1:31_2_6_1_1_2"><i><font color="Green" title="E33">A83</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_6"><i><font color="Green" title="E32">A69</font></i></a>, <a class="txt" href="ami_5.html#E1:31_2_6_1_1_2"><i><font color="Green" title="E33">A83</font></i></a>, <a class="txt" href="ami_5.html#E11:31_2_6_1_1_2"><i><font color="Green" title="E41">A96</font></i></a>, <a class="txt" href="ami_5.html#E12:31_2_6_1_1_2"><i><font color="Green" title="E42">A97</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">db</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">da</font></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">db</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_6"><i><font color="Green" title="E32">A69</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">db</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_6"><i><font color="Green" title="E32">A69</font></i></a>, <a class="txt" href="ami_5.html#E11:31_2_6_1_1_2"><i><font color="Green" title="E41">A96</font></i></a>, <a class="txt" href="ami_5.html#E12:31_2_6_1_1_2"><i><font color="Green" title="E42">A97</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
;<br/><a NAME="E15:31_2_6_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c4">da</font>,<font color="Maroon" title="c5">db</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="txt" href="ami_5.html#E13:31_2_6_1_1_2"><i><font color="Green" title="E43">A98</font></i></a>, <a class="ref" href="grfunc_1.html#T91" title="GRFUNC_1:th.91">GRFUNC_1:91</a></i>;<br/><a NAME="E16:31_2_6_1_1_2"/><b>then </b><i><font color="Green" title="E44">A99</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="ami_5.html#E4:31_2_6_1_1_2"><i><font color="Green" title="E35">A85</font></i></a>, <a class="txt" href="ami_5.html#E8:31_2_6_1_1_2"><i><font color="Green" title="E38">A93</font></i></a>, <a class="ref" href="relat_1.html#T185" title="RELAT_1:th.185">RELAT_1:185</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> = 
 <a href="ami_3.html#K11" title="AMI_3:func.11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c1">s1</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_6"><i><font color="Green" title="E32">A69</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E9:31"><i><font color="Green" title="E27">A6</font></i></a>, <a class="txt" href="ami_5.html#E3:31_2_6"><i><font color="Green" title="E32">A69</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
;<br/><a NAME="E18:31_2_6_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="grfunc_1.html#T90" title="GRFUNC_1:th.90">GRFUNC_1:90</a></i>;<br/><b>hence </b><a NAME="E19:31_2_6_1_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_5.html#E16:31_2_6_1_1_2"><i><font color="Green" title="E44">A99</font></i></a>, <a class="ref" href="relat_1.html#T185" title="RELAT_1:th.185">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="31_2_7"><b>suppose </b></a><a NAME="E1:31_2_7"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">loc</font> being    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> <b> such that </b><br/><a NAME="E3:31_2_7"/><i><font color="Green" title="E32">A100</font></i>: 
<font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <font color="Maroon" title="c4">loc</font>
 <b>by </b><i><a class="ref" href="ami_5.html#T52" target="_self" title="AMI_5:th.52">Th52</a></i>;<br/><a NAME="E4:31_2_7"/><i><font color="Green" title="E33">A101</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/><a NAME="E5:31_2_7"/><i><font color="Green" title="E34">A102</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/><a NAME="E6:31_2_7"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_2_7_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:31_2_7_1"/><i><font color="Green" title="E35">A103</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c6">a</font> = <font color="Maroon" title="c5">x</font> as    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  <b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/>
<a NAME="E3:31_2_7_1"/><i><font color="Green" title="E36">A104</font></i>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_7_1"><i><font color="Green" title="E35">A103</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">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" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_7_1"><i><font color="Green" title="E35">A103</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_7"><i><font color="Green" title="E32">A100</font></i></a>, <a class="ref" href="ami_3.html#T13" title="AMI_3:th.13">AMI_3:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_7_1"><i><font color="Green" title="E36">A104</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E3:31_2_7_1"><i><font color="Green" title="E36">A104</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_7"><i><font color="Green" title="E32">A100</font></i></a>, <a class="ref" href="ami_3.html#T13" title="AMI_3:th.13">AMI_3:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_7_1"><i><font color="Green" title="E35">A103</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/>


</div><b>end;</b></div><a NAME="E7:31_2_7"/><b>then </b><i><font color="Green" title="E35">A105</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="ami_5.html#E4:31_2_7"><i><font color="Green" title="E33">A101</font></i></a>, <a class="txt" href="ami_5.html#E5:31_2_7"><i><font color="Green" title="E34">A102</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> = 
<font color="Maroon" title="c4">loc</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_7"><i><font color="Green" title="E32">A100</font></i></a>, <a class="ref" href="ami_3.html#T13" title="AMI_3:th.13">AMI_3:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_7"><i><font color="Green" title="E32">A100</font></i></a>, <a class="ref" href="ami_3.html#T13" title="AMI_3:th.13">AMI_3:13</a></i>
;<br/><a NAME="E9:31_2_7"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="grfunc_1.html#T90" title="GRFUNC_1:th.90">GRFUNC_1:90</a></i>;<br/><b>hence </b><a NAME="E10:31_2_7"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_5.html#E7:31_2_7"><i><font color="Green" title="E35">A105</font></i></a>, <a class="ref" href="relat_1.html#T185" title="RELAT_1:th.185">RELAT_1:185</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_2_8"><b>suppose </b></a><a NAME="E1:31_2_8"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">loc</font> being    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> , <font color="Maroon" title="c5">da</font> being    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> <b> such that </b><br/><a NAME="E3:31_2_8"/><i><font color="Green" title="E32">A106</font></i>: 
<font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">da</font> <a href="ami_3.html#K9" title="AMI_3:func.9">=0_goto</a> <font color="Maroon" title="c4">loc</font>
 <b>by </b><i><a class="ref" href="ami_5.html#T53" target="_self" title="AMI_5:th.53">Th53</a></i>;<br/><a NAME="E4:31_2_8"/><i><font color="Green" title="E33">A107</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/><a NAME="E5:31_2_8"/><i><font color="Green" title="E34">A108</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/><a NAME="E6:31_2_8"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_2_8_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:31_2_8_1"/><i><font color="Green" title="E35">A109</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c7">a</font> = <font color="Maroon" title="c6">x</font> as    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  <b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/>
<a NAME="E3:31_2_8_1"/><i><font color="Green" title="E36">A110</font></i>: 
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_8_1"><i><font color="Green" title="E35">A109</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">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" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_8_1"><i><font color="Green" title="E35">A109</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_8"><i><font color="Green" title="E32">A106</font></i></a>, <a class="ref" href="ami_3.html#T14" title="AMI_3:th.14">AMI_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_8_1"><i><font color="Green" title="E36">A110</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E3:31_2_8_1"><i><font color="Green" title="E36">A110</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_8"><i><font color="Green" title="E32">A106</font></i></a>, <a class="ref" href="ami_3.html#T14" title="AMI_3:th.14">AMI_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_8_1"><i><font color="Green" title="E35">A109</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/>


</div><b>end;</b></div><a NAME="E7:31_2_8"/><b>then </b><i><font color="Green" title="E35">A111</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="ami_5.html#E4:31_2_8"><i><font color="Green" title="E33">A107</font></i></a>, <a class="txt" href="ami_5.html#E5:31_2_8"><i><font color="Green" title="E34">A108</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/><a NAME="E8:31_2_8"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_2_8_2"><b>proof </b></a><div class="add">

<a NAME="E1:31_2_8_2"/><i><font color="Green" title="E36">A112</font></i>: 
<font color="Maroon" title="c5">da</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/>
<b>then </b><i><font color="Green" title="E37">A113</font></i>: <font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="txt" href="ami_5.html#E1:31_2_8_2"><i><font color="Green" title="E36">A112</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_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="E1:31_2_8_2_2"/>
( <font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_2_8_2_2_1"><b>suppose </b></a><a NAME="E1:31_2_8_2_2_1"/><i><font color="Green" title="E38">A114</font></i>: 
<font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> = 
<font color="Maroon" title="c4">loc</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_8"><i><font color="Green" title="E32">A106</font></i></a>, <a class="ref" href="ami_3.html#T14" title="AMI_3:th.14">AMI_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_8"><i><font color="Green" title="E32">A106</font></i></a>, <a class="txt" href="ami_5.html#E2:31_2_8_2"><i><font color="Green" title="E37">A113</font></i></a>, <a class="txt" href="ami_5.html#E1:31_2_8_2_2_1"><i><font color="Green" title="E38">A114</font></i></a>, <a class="ref" href="ami_3.html#T14" title="AMI_3:th.14">AMI_3:14</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_2_8_2_2_2"><b>suppose </b></a><a NAME="E1:31_2_8_2_2_2"/><i><font color="Green" title="E38">A115</font></i>: 
<font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> = 
 <a href="ami_3.html#K11" title="AMI_3:func.11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c1">s1</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_8"><i><font color="Green" title="E32">A106</font></i></a>, <a class="ref" href="ami_3.html#T14" title="AMI_3:th.14">AMI_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E9:31"><i><font color="Green" title="E27">A6</font></i></a>, <a class="txt" href="ami_5.html#E3:31_2_8"><i><font color="Green" title="E32">A106</font></i></a>, <a class="txt" href="ami_5.html#E2:31_2_8_2"><i><font color="Green" title="E37">A113</font></i></a>, <a class="txt" href="ami_5.html#E1:31_2_8_2_2_2"><i><font color="Green" title="E38">A115</font></i></a>, <a class="ref" href="ami_3.html#T14" title="AMI_3:th.14">AMI_3:14</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E9:31_2_8"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="grfunc_1.html#T90" title="GRFUNC_1:th.90">GRFUNC_1:90</a></i>;<br/><b>hence </b><a NAME="E10:31_2_8"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_5.html#E7:31_2_8"><i><font color="Green" title="E35">A111</font></i></a>, <a class="ref" href="relat_1.html#T185" title="RELAT_1:th.185">RELAT_1:185</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_2_9"><b>suppose </b></a><a NAME="E1:31_2_9"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">loc</font> being    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> , <font color="Maroon" title="c5">da</font> being    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> <b> such that </b><br/><a NAME="E3:31_2_9"/><i><font color="Green" title="E32">A116</font></i>: 
<font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">da</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c4">loc</font>
 <b>by </b><i><a class="ref" href="ami_5.html#T54" target="_self" title="AMI_5:th.54">Th54</a></i>;<br/><a NAME="E4:31_2_9"/><i><font color="Green" title="E33">A117</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/><a NAME="E5:31_2_9"/><i><font color="Green" title="E34">A118</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/><a NAME="E6:31_2_9"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_2_9_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:31_2_9_1"/><i><font color="Green" title="E35">A119</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c7">a</font> = <font color="Maroon" title="c6">x</font> as    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  <b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/>
<a NAME="E3:31_2_9_1"/><i><font color="Green" title="E36">A120</font></i>: 
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_9_1"><i><font color="Green" title="E35">A119</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">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" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_9_1"><i><font color="Green" title="E35">A119</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_9"><i><font color="Green" title="E32">A116</font></i></a>, <a class="ref" href="ami_3.html#T15" title="AMI_3:th.15">AMI_3:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_9_1"><i><font color="Green" title="E36">A120</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E3:31_2_9_1"><i><font color="Green" title="E36">A120</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c7">a</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_9"><i><font color="Green" title="E32">A116</font></i></a>, <a class="ref" href="ami_3.html#T15" title="AMI_3:th.15">AMI_3:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31_2_9_1"><i><font color="Green" title="E35">A119</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/>


</div><b>end;</b></div><a NAME="E7:31_2_9"/><b>then </b><i><font color="Green" title="E35">A121</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="ami_5.html#E4:31_2_9"><i><font color="Green" title="E33">A117</font></i></a>, <a class="txt" href="ami_5.html#E5:31_2_9"><i><font color="Green" title="E34">A118</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/><a NAME="E8:31_2_9"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_2_9_2"><b>proof </b></a><div class="add">

<a NAME="E1:31_2_9_2"/><i><font color="Green" title="E36">A122</font></i>: 
<font color="Maroon" title="c5">da</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/>
<b>then </b><i><font color="Green" title="E37">A123</font></i>: <font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font>
<b>by </b><i><a class="txt" href="ami_5.html#E1:31"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="ami_5.html#E12:31"><i><font color="Green" title="E30">A9</font></i></a>, <a class="txt" href="ami_5.html#E1:31_2_9_2"><i><font color="Green" title="E36">A122</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_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="E1:31_2_9_2_2"/>
( <font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_2_9_2_2_1"><b>suppose </b></a><a NAME="E1:31_2_9_2_2_1"/><i><font color="Green" title="E38">A124</font></i>: 
<font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> = 
<font color="Maroon" title="c4">loc</font>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_9"><i><font color="Green" title="E32">A116</font></i></a>, <a class="ref" href="ami_3.html#T15" title="AMI_3:th.15">AMI_3:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_9"><i><font color="Green" title="E32">A116</font></i></a>, <a class="txt" href="ami_5.html#E2:31_2_9_2"><i><font color="Green" title="E37">A123</font></i></a>, <a class="txt" href="ami_5.html#E1:31_2_9_2_2_1"><i><font color="Green" title="E38">A124</font></i></a>, <a class="ref" href="ami_3.html#T15" title="AMI_3:th.15">AMI_3:15</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_2_9_2_2_2"><b>suppose </b></a><a NAME="E1:31_2_9_2_2_2"/><i><font color="Green" title="E38">A125</font></i>: 
<font color="Maroon" title="c1">s1</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">da</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> = 
 <a href="ami_3.html#K11" title="AMI_3:func.11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c1">s1</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E3:31_2_9"><i><font color="Green" title="E32">A116</font></i></a>, <a class="ref" href="ami_3.html#T15" title="AMI_3:th.15">AMI_3:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_5.html#E9:31"><i><font color="Green" title="E27">A6</font></i></a>, <a class="txt" href="ami_5.html#E3:31_2_9"><i><font color="Green" title="E32">A116</font></i></a>, <a class="txt" href="ami_5.html#E2:31_2_9_2"><i><font color="Green" title="E37">A123</font></i></a>, <a class="txt" href="ami_5.html#E1:31_2_9_2_2_2"><i><font color="Green" title="E38">A125</font></i></a>, <a class="ref" href="ami_3.html#T15" title="AMI_3:th.15">AMI_3:15</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E9:31_2_9"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_5.html#E10:31"><i><font color="Green" title="E28">A7</font></i></a>, <a class="txt" href="ami_5.html#E11:31"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="grfunc_1.html#T90" title="GRFUNC_1:th.90">GRFUNC_1:90</a></i>;<br/><b>hence </b><a NAME="E10:31_2_9"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c1">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_5.html#E7:31_2_9"><i><font color="Green" title="E35">A121</font></i></a>, <a class="ref" href="relat_1.html#T185" title="RELAT_1:th.185">RELAT_1:185</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
