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

<b>thus </b><a NAME="E1:111_1_1"/>
 <a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font> is <a href="amistd_2.html#V11">IC-good</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="111_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">I</font> be   <a href="ami_1.html#NM3">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D18">AMISTD_2:def 18</a><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:111_1_1_1_1"/>
( <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmring2.html#K4">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K5">AddTo</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K6">SubFrom</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K7">MultBy</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K9">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">a</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmring2.html#K10">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">a</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> ex <font color="Olive">r</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmring2.html#K8">:=</a> <font color="Olive">r</font> )
 </span><b>by </b><i><a class="ref" href="scmring2.html#T8">SCMRING2:8</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:111_1_1_1_1_1"/>
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span>
 ;<br/><div class="add"><a NAME="E2:111_1_1_1_1_1"/><b>then </b>
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring2.html#T30">SCMRING2:30</a></i>;<br/><b>hence </b><a NAME="E3:111_1_1_1_1_1"/>
<font color="Maroon">I</font> is <a href="amistd_2.html#V10">IC-good</a>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:111_1_1_1_1_2"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmring2.html#K4">:=</a> <font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">b</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:111_1_1_1_1_2"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">b</font>
 ;<br/><b>thus </b><a NAME="E4:111_1_1_1_1_2"/>
<font color="Maroon">I</font> is <a href="amistd_2.html#V10">IC-good</a>
 <b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_1_1_3"><b>suppose </b></a><a NAME="E1:111_1_1_1_1_3"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K5">AddTo</a> <font color="Olive">a</font>,<font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">b</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:111_1_1_1_1_3"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K5">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><b>thus </b><a NAME="E4:111_1_1_1_1_3"/>
<font color="Maroon">I</font> is <a href="amistd_2.html#V10">IC-good</a>
 <b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_1_1_4"><b>suppose </b></a><a NAME="E1:111_1_1_1_1_4"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K6">SubFrom</a> <font color="Olive">a</font>,<font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">b</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:111_1_1_1_1_4"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K6">SubFrom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><b>thus </b><a NAME="E4:111_1_1_1_1_4"/>
<font color="Maroon">I</font> is <a href="amistd_2.html#V10">IC-good</a>
 <b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_1_1_5"><b>suppose </b></a><a NAME="E1:111_1_1_1_1_5"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K7">MultBy</a> <font color="Olive">a</font>,<font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">b</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:111_1_1_1_1_5"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K7">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><b>thus </b><a NAME="E4:111_1_1_1_1_5"/>
<font color="Maroon">I</font> is <a href="amistd_2.html#V10">IC-good</a>
 <b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_1_1_6"><b>suppose </b></a><a NAME="E1:111_1_1_1_1_6"/>
 ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K9">goto</a> <font color="Olive">i1</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">i1</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span><b> such that </b><br/><a NAME="E3:111_1_1_1_1_6"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K9">goto</a> <font color="Maroon">i1</font>
 ;<br/><b>let </b><font color="Maroon">k</font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D17">AMISTD_2:def 17</a><br/><b>let </b><font color="Maroon">s1</font> be   <a href="ami_1.html#NM4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>, <font color="Maroon">s2</font> be   <a href="ami_1.html#NM4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>;<br/><b>assume </b><a NAME="E4:111_1_1_1_1_6"/>
<font color="Maroon">s2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s1</font> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span></span>)</span>
 ;<br/><i><font color="Green">E69</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
<font color="Maroon">i1</font>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring2.html#T17">SCMRING2:17</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">i1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, <a class="ref" href="scmring2.html#T17">SCMRING2:17</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmring2.html#K9">goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">i1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s2</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s2</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring3.html#T12" target="_self">Th12</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_1_1_7"><b>suppose </b></a><a NAME="E1:111_1_1_1_1_7"/>
 ex <font color="Olive">a</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmring2.html#K10">=0_goto</a> <font color="Olive">i1</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">i1</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span><b> such that </b><br/><a NAME="E3:111_1_1_1_1_7"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmring2.html#K10">=0_goto</a> <font color="Maroon">i1</font>
 ;<br/><b>let </b><font color="Maroon">k</font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D17">AMISTD_2:def 17</a><br/><b>let </b><font color="Maroon">s1</font> be   <a href="ami_1.html#NM4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>, <font color="Maroon">s2</font> be   <a href="ami_1.html#NM4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>;<br/><b>assume </b><a NAME="E4:111_1_1_1_1_7"/><i><font color="Green">E112</font></i>: 
<font color="Maroon">s2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s1</font> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span></span>)</span>
 ;<br/><a NAME="E5:111_1_1_1_1_7"/><i><font color="Green">E126</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E6:111_1_1_1_1_7"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/><a NAME="E7:111_1_1_1_1_7"/><b>then </b>
not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E8:111_1_1_1_1_7"/><b>then </b><i><font color="Green">E156</font></i>: 
<font color="Maroon">s1</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="111_1_1_1_1_7_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_1_1_7_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:111_1_1_1_1_7_1_1"/>
( <font color="Maroon">s1</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font> or <font color="Maroon">s1</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_1_1_7_1_1_1"><b>suppose </b></a><a NAME="E1:111_1_1_1_1_7_1_1_1"/><i><font color="Green">E157</font></i>: 
<font color="Maroon">s1</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font>
 ;<br/><div class="add"><i><font color="Green">E158</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
<font color="Maroon">i1</font>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring3.html#T18" target="_self">Th18</a>, <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="scmring2.html#K10">=0_goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">i1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T17" target="_self">Th17</a>, <a class="ref" href="scmring3.html#T18" target="_self">Th18</a>, <a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="scmring2.html#K10">=0_goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">i1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s2</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s2</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring3.html#T13" target="_self">Th13</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_1_1_7_1_1_2"><b>suppose </b></a><a NAME="E1:111_1_1_1_1_7_1_1_2"/><i><font color="Green">E159</font></i>: 
<font color="Maroon">s1</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font>
 ;<br/><div class="add"><a NAME="E2:111_1_1_1_1_7_1_1_2"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/><a NAME="E3:111_1_1_1_1_7_1_1_2"/><b>then </b><i><font color="Green">E160</font></i>: 
 <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><i><font color="Green">E161</font></i>:  <a href="ami_1.html#K6">IC</a> <font color="Maroon">s2</font> = 
<font color="Maroon">s2</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, <a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
 <a href="amistd_1.html#K5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font></span>)</span>
<b>by </b><i><a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>
;<br/><i><font color="Green">E162</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s2</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring3.html#T17" target="_self">Th17</a>, <a class="ref" href="scmring3.html#T18" target="_self">Th18</a>, <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>
<br/>.= 
 <a href="amistd_1.html#K9">NextLoc</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s2</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T11" target="_self">Th11</a></i>
<br/>.= 
 <a href="amistd_1.html#K5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T20" target="_self">Th20</a>, <a class="ref" href="amistd_1.html#D13">AMISTD_1:def 13</a></i>
<br/>.= 
 <a href="amistd_1.html#K5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font></span>)</span>

;<br/><i><font color="Green">E164</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring3.html#T18" target="_self">Th18</a>, <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>
<br/>.= 
 <a href="amistd_1.html#K9">NextLoc</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T11" target="_self">Th11</a></i>
<br/>.= 
 <a href="amistd_1.html#K5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>

;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> = 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T21" target="_self">Th21</a>, <a class="ref" href="scmring3.html#T22" target="_self">Th22</a>, <a class="ref" href="amistd_1.html#D13">AMISTD_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s2</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring3.html#T17" target="_self">Th17</a>, <a class="ref" href="scmring3.html#T18" target="_self">Th18</a>, <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="scmring2.html#K10">=0_goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">i1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T17" target="_self">Th17</a>, <a class="ref" href="scmring3.html#T18" target="_self">Th18</a>, <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="scmring2.html#K10">=0_goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">i1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s2</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s2</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring3.html#T13" target="_self">Th13</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E10:111_1_1_1_1_7"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s2</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_1_1_8"><b>suppose </b></a><a NAME="E1:111_1_1_1_1_8"/>
 ex <font color="Olive">a</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> ex <font color="Olive">r</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmring2.html#K8">:=</a> <font color="Olive">r</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">r</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:111_1_1_1_1_8"/><i><font color="Green">E165</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">r</font>
 ;<br/><b>thus </b><a NAME="E4:111_1_1_1_1_8"/>
<font color="Maroon">I</font> is <a href="amistd_2.html#V10">IC-good</a>
 <b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>

<b>let </b><font color="Maroon">I</font> be   <a href="ami_1.html#NM3">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D20">AMISTD_2:def 20</a><br/><b>let </b><font color="Maroon">s1</font> be   <a href="ami_1.html#NM4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>, <font color="Maroon">s2</font> be   <a href="ami_1.html#NM4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D19">AMISTD_2:def 19</a><br/>



<b>assume </b><a NAME="E2:111_1_1"/><i><font color="Green">E166</font></i>: 
<font color="Maroon">s1</font>,<font color="Maroon">s2</font> <a href="funct_7.html#R1">equal_outside</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 ;<br/>

<a NAME="E3:111_1_1"/><i><font color="Green">E167</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> the <a href="ami_1.html#U5">Object-Kind</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="card_3.html#T18">CARD_3:18</a></i>;<br/>
<a NAME="E4:111_1_1"/><b>then </b><i><font color="Green">E168</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="card_3.html#T18">CARD_3:18</a></i>;<br/>
<a NAME="E5:111_1_1"/><i><font color="Green">E169</font></i>: 
 <a href="relat_1.html#K1">dom</a> the <a href="ami_1.html#U5">Object-Kind</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E6:111_1_1"/><i><font color="Green">E170</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <font color="Maroon">s2</font>
 
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmfsa6a.html#T29">SCMFSA6A:29</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:111_1_1_2"/>
( <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmring2.html#K4">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K5">AddTo</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K6">SubFrom</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K7">MultBy</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K9">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">a</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmring2.html#K10">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">a</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> ex <font color="Olive">r</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmring2.html#K8">:=</a> <font color="Olive">r</font> )
 </span><b>by </b><i><a class="ref" href="scmring2.html#T8">SCMRING2:8</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_1"><b>suppose </b></a><a NAME="E1:111_1_1_2_1"/>
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span>
 ;<br/><div class="add"><a NAME="E2:111_1_1_2_1"/><b>then </b>
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring2.html#T30">SCMRING2:30</a></i>;<br/><b>hence </b><a NAME="E3:111_1_1_2_1"/>
 <a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font>, <a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font> <a href="funct_7.html#R1">equal_outside</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="amistd_2.html#D19">AMISTD_2:def 19</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_2"><b>suppose </b></a><a NAME="E1:111_1_1_2_2"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmring2.html#K4">:=</a> <font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">b</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:111_1_1_2_2"/><i><font color="Green">E171</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">b</font>
 ;<br/><a NAME="E4:111_1_1_2_2"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="111_1_1_2_2_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:111_1_1_2_2_1"/><i><font color="Green">E190</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 ;<br/>

<a NAME="E2:111_1_1_2_2_1"/><b>then </b><i><font color="Green">E191</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:111_1_1_2_2_1"/><i><font color="Green">E192</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmring3.html#T20" target="_self">Th20</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:111_1_1_2_2_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> or ( <font color="Maroon">x</font> is    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font> ) )
 </span><b>by </b><i><a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, <a class="ref" href="scmring3.html#T17" target="_self">Th17</a>, <a class="ref" href="scmring3.html#T21" target="_self">Th21</a>, <a class="ref" href="scmring3.html#T22" target="_self">Th22</a>, </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_2_1_1_1"><b>suppose </b></a><a NAME="E1:111_1_1_2_2_1_1_1"/><i><font color="Green">E193</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
 <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring2.html#T13">SCMRING2:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T18" target="_self">Th18</a>, <a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="ref" href="scmring2.html#T13">SCMRING2:13</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_2_1_1_2"><b>suppose </b></a><a NAME="E1:111_1_1_2_2_1_1_2"/><i><font color="Green">E194</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">s1</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring2.html#T13">SCMRING2:13</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="ref" href="scmring2.html#T13">SCMRING2:13</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_2_1_1_3"><b>suppose </b></a><b>that </b><a NAME="E1:111_1_1_2_2_1_1_3"/><i><font color="Green">E195</font></i>: 
<font color="Maroon">x</font> is    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>
 <b>and </b><br/><a NAME="E2:111_1_1_2_2_1_1_3"/><i><font color="Green">E196</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">s1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="txt" href="scmring3.html#E24"><i><font color="Green">Lemma86</font></i></a>, <a class="ref" href="scmring2.html#T13">SCMRING2:13</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="txt" href="scmring3.html#E24"><i><font color="Green">Lemma86</font></i></a>, <a class="ref" href="scmring2.html#T13">SCMRING2:13</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><b>hence </b><a NAME="E5:111_1_1_2_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, <a class="ref" href="scmfsa6a.html#T9">SCMFSA6A:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_7.html#D2">FUNCT_7:def 2</a><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_3"><b>suppose </b></a><a NAME="E1:111_1_1_2_3"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K5">AddTo</a> <font color="Olive">a</font>,<font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">b</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:111_1_1_2_3"/><i><font color="Green">E197</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K5">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><a NAME="E4:111_1_1_2_3"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="111_1_1_2_3_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:111_1_1_2_3_1"/><i><font color="Green">E198</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 ;<br/>

<a NAME="E2:111_1_1_2_3_1"/><b>then </b><i><font color="Green">E199</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:111_1_1_2_3_1"/><i><font color="Green">E200</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmring3.html#T20" target="_self">Th20</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:111_1_1_2_3_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> or ( <font color="Maroon">x</font> is    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font> ) )
 </span><b>by </b><i><a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, <a class="ref" href="scmring3.html#T17" target="_self">Th17</a>, <a class="ref" href="scmring3.html#T21" target="_self">Th21</a>, <a class="ref" href="scmring3.html#T22" target="_self">Th22</a>, </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_3_1_1_1"><b>suppose </b></a><a NAME="E1:111_1_1_2_3_1_1_1"/><i><font color="Green">E201</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
 <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring2.html#T14">SCMRING2:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T18" target="_self">Th18</a>, <a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="ref" href="scmring2.html#T14">SCMRING2:14</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_3_1_1_2"><b>suppose </b></a><a NAME="E1:111_1_1_2_3_1_1_2"/><i><font color="Green">E202</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring2.html#T14">SCMRING2:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="ref" href="scmring2.html#T14">SCMRING2:14</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_3_1_1_3"><b>suppose </b></a><b>that </b><a NAME="E1:111_1_1_2_3_1_1_3"/><i><font color="Green">E203</font></i>: 
<font color="Maroon">x</font> is    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>
 <b>and </b><br/><a NAME="E2:111_1_1_2_3_1_1_3"/><i><font color="Green">E204</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">s1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="txt" href="scmring3.html#E24"><i><font color="Green">Lemma86</font></i></a>, <a class="ref" href="scmring2.html#T14">SCMRING2:14</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="txt" href="scmring3.html#E24"><i><font color="Green">Lemma86</font></i></a>, <a class="ref" href="scmring2.html#T14">SCMRING2:14</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><b>hence </b><a NAME="E5:111_1_1_2_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, <a class="ref" href="scmfsa6a.html#T9">SCMFSA6A:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_7.html#D2">FUNCT_7:def 2</a><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_4"><b>suppose </b></a><a NAME="E1:111_1_1_2_4"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K6">SubFrom</a> <font color="Olive">a</font>,<font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">b</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:111_1_1_2_4"/><i><font color="Green">E205</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K6">SubFrom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><a NAME="E4:111_1_1_2_4"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="111_1_1_2_4_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:111_1_1_2_4_1"/><i><font color="Green">E206</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 ;<br/>

<a NAME="E2:111_1_1_2_4_1"/><b>then </b><i><font color="Green">E207</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:111_1_1_2_4_1"/><i><font color="Green">E208</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmring3.html#T20" target="_self">Th20</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_4_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:111_1_1_2_4_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> or ( <font color="Maroon">x</font> is    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font> ) )
 </span><b>by </b><i><a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, <a class="ref" href="scmring3.html#T17" target="_self">Th17</a>, <a class="ref" href="scmring3.html#T21" target="_self">Th21</a>, <a class="ref" href="scmring3.html#T22" target="_self">Th22</a>, </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_4_1_1_1"><b>suppose </b></a><a NAME="E1:111_1_1_2_4_1_1_1"/><i><font color="Green">E209</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
 <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring2.html#T15">SCMRING2:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T18" target="_self">Th18</a>, <a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="ref" href="scmring2.html#T15">SCMRING2:15</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_4_1_1_2"><b>suppose </b></a><a NAME="E1:111_1_1_2_4_1_1_2"/><i><font color="Green">E210</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring2.html#T15">SCMRING2:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="ref" href="scmring2.html#T15">SCMRING2:15</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_4_1_1_3"><b>suppose </b></a><b>that </b><a NAME="E1:111_1_1_2_4_1_1_3"/><i><font color="Green">E211</font></i>: 
<font color="Maroon">x</font> is    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>
 <b>and </b><br/><a NAME="E2:111_1_1_2_4_1_1_3"/><i><font color="Green">E212</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">s1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="txt" href="scmring3.html#E24"><i><font color="Green">Lemma86</font></i></a>, <a class="ref" href="scmring2.html#T15">SCMRING2:15</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="txt" href="scmring3.html#E24"><i><font color="Green">Lemma86</font></i></a>, <a class="ref" href="scmring2.html#T15">SCMRING2:15</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><b>hence </b><a NAME="E5:111_1_1_2_4"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, <a class="ref" href="scmfsa6a.html#T9">SCMFSA6A:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_7.html#D2">FUNCT_7:def 2</a><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_5"><b>suppose </b></a><a NAME="E1:111_1_1_2_5"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K7">MultBy</a> <font color="Olive">a</font>,<font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">b</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:111_1_1_2_5"/><i><font color="Green">E213</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K7">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><a NAME="E4:111_1_1_2_5"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="111_1_1_2_5_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:111_1_1_2_5_1"/><i><font color="Green">E214</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 ;<br/>

<a NAME="E2:111_1_1_2_5_1"/><b>then </b><i><font color="Green">E215</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:111_1_1_2_5_1"/><i><font color="Green">E216</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmring3.html#T20" target="_self">Th20</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_5_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:111_1_1_2_5_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> or ( <font color="Maroon">x</font> is    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font> ) )
 </span><b>by </b><i><a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, <a class="ref" href="scmring3.html#T17" target="_self">Th17</a>, <a class="ref" href="scmring3.html#T21" target="_self">Th21</a>, <a class="ref" href="scmring3.html#T22" target="_self">Th22</a>, </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_5_1_1_1"><b>suppose </b></a><a NAME="E1:111_1_1_2_5_1_1_1"/><i><font color="Green">E217</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
 <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring2.html#T16">SCMRING2:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T18" target="_self">Th18</a>, <a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="ref" href="scmring2.html#T16">SCMRING2:16</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_5_1_1_2"><b>suppose </b></a><a NAME="E1:111_1_1_2_5_1_1_2"/><i><font color="Green">E218</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">a</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring2.html#T16">SCMRING2:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">a</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">a</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="ref" href="scmring2.html#T16">SCMRING2:16</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_5_1_1_3"><b>suppose </b></a><b>that </b><a NAME="E1:111_1_1_2_5_1_1_3"/><i><font color="Green">E220</font></i>: 
<font color="Maroon">x</font> is    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>
 <b>and </b><br/><a NAME="E2:111_1_1_2_5_1_1_3"/><i><font color="Green">E221</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">s1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="txt" href="scmring3.html#E24"><i><font color="Green">Lemma86</font></i></a>, <a class="ref" href="scmring2.html#T16">SCMRING2:16</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="txt" href="scmring3.html#E24"><i><font color="Green">Lemma86</font></i></a>, <a class="ref" href="scmring2.html#T16">SCMRING2:16</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><b>hence </b><a NAME="E5:111_1_1_2_5"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, <a class="ref" href="scmfsa6a.html#T9">SCMFSA6A:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_7.html#D2">FUNCT_7:def 2</a><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_6"><b>suppose </b></a><a NAME="E1:111_1_1_2_6"/>
 ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K9">goto</a> <font color="Olive">i1</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">i1</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span><b> such that </b><br/><a NAME="E3:111_1_1_2_6"/><i><font color="Green">E222</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K9">goto</a> <font color="Maroon">i1</font>
 ;<br/><a NAME="E4:111_1_1_2_6"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="111_1_1_2_6_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:111_1_1_2_6_1"/><i><font color="Green">E223</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 ;<br/>

<a NAME="E2:111_1_1_2_6_1"/><b>then </b><i><font color="Green">E224</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:111_1_1_2_6_1"/><i><font color="Green">E225</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmring3.html#T20" target="_self">Th20</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_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="E1:111_1_1_2_6_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> or <font color="Maroon">x</font> is    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> )
 </span><b>by </b><i><a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, <a class="ref" href="scmring3.html#T17" target="_self">Th17</a>, <a class="ref" href="scmring3.html#T21" target="_self">Th21</a>, <a class="ref" href="scmring3.html#T22" target="_self">Th22</a>, </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_6_1_1_1"><b>suppose </b></a><a NAME="E1:111_1_1_2_6_1_1_1"/><i><font color="Green">E226</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">i1</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring2.html#T17">SCMRING2:17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="ref" href="scmring2.html#T17">SCMRING2:17</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_6_1_1_2"><b>suppose </b></a><a NAME="E1:111_1_1_2_6_1_1_2"/><i><font color="Green">E227</font></i>: 
<font color="Maroon">x</font> is    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">s1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring2.html#T17">SCMRING2:17</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="ref" href="scmring2.html#T17">SCMRING2:17</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><b>hence </b><a NAME="E5:111_1_1_2_6"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, <a class="ref" href="scmfsa6a.html#T9">SCMFSA6A:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_7.html#D2">FUNCT_7:def 2</a><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_7"><b>suppose </b></a><a NAME="E1:111_1_1_2_7"/>
 ex <font color="Olive">a</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmring2.html#K10">=0_goto</a> <font color="Olive">i1</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">i1</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span><b> such that </b><br/><a NAME="E3:111_1_1_2_7"/><i><font color="Green">E228</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmring2.html#K10">=0_goto</a> <font color="Maroon">i1</font>
 ;<br/><a NAME="E4:111_1_1_2_7"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="111_1_1_2_7_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:111_1_1_2_7_1"/><i><font color="Green">E229</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 ;<br/>

<a NAME="E2:111_1_1_2_7_1"/><b>then </b><i><font color="Green">E230</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:111_1_1_2_7_1"/><i><font color="Green">E231</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmring3.html#T20" target="_self">Th20</a></i>;<br/>
<a NAME="E4:111_1_1_2_7_1"/><i><font color="Green">E232</font></i>: 
<font color="Maroon">s1</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_7_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:111_1_1_2_7_1_1"/>
( ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> &amp; <font color="Maroon">s1</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> &amp; <font color="Maroon">s1</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font> ) or <font color="Maroon">x</font> is    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> )
 </span><b>by </b><i><a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, <a class="ref" href="scmring3.html#T17" target="_self">Th17</a>, <a class="ref" href="scmring3.html#T21" target="_self">Th21</a>, <a class="ref" href="scmring3.html#T22" target="_self">Th22</a>, </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_7_1_1_1"><b>suppose </b></a><b>that </b><a NAME="E1:111_1_1_2_7_1_1_1"/><i><font color="Green">E233</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 <b>and </b><br/><a NAME="E2:111_1_1_2_7_1_1_1"/><i><font color="Green">E234</font></i>: 
<font color="Maroon">s1</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font>
 ;<br/><div class="add"><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">i1</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="txt" href="scmring3.html#E24"><i><font color="Green">Lemma86</font></i></a>, , <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="txt" href="scmring3.html#E24"><i><font color="Green">Lemma86</font></i></a>, , <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_7_1_1_2"><b>suppose </b></a><b>that </b><a NAME="E1:111_1_1_2_7_1_1_2"/><i><font color="Green">E235</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 <b>and </b><br/><a NAME="E2:111_1_1_2_7_1_1_2"/><i><font color="Green">E236</font></i>: 
<font color="Maroon">s1</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font>
 ;<br/><div class="add"><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
 <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="txt" href="scmring3.html#E24"><i><font color="Green">Lemma86</font></i></a>, , <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T18" target="_self">Th18</a>, <a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="txt" href="scmring3.html#E24"><i><font color="Green">Lemma86</font></i></a>, , <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_7_1_1_3"><b>suppose </b></a><a NAME="E1:111_1_1_2_7_1_1_3"/><i><font color="Green">E237</font></i>: 
<font color="Maroon">x</font> is    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">s1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="txt" href="scmring3.html#E24"><i><font color="Green">Lemma86</font></i></a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="txt" href="scmring3.html#E24"><i><font color="Green">Lemma86</font></i></a>, <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><b>hence </b><a NAME="E5:111_1_1_2_7"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, <a class="ref" href="scmfsa6a.html#T9">SCMFSA6A:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_7.html#D2">FUNCT_7:def 2</a><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_8"><b>suppose </b></a><a NAME="E1:111_1_1_2_8"/>
 ex <font color="Olive">a</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> ex <font color="Olive">r</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmring2.html#K8">:=</a> <font color="Olive">r</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">r</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:111_1_1_2_8"/><i><font color="Green">E238</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">r</font>
 ;<br/><a NAME="E4:111_1_1_2_8"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="111_1_1_2_8_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:111_1_1_2_8_1"/><i><font color="Green">E239</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 ;<br/>

<a NAME="E2:111_1_1_2_8_1"/><b>then </b><i><font color="Green">E240</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:111_1_1_2_8_1"/><i><font color="Green">E241</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmring3.html#T20" target="_self">Th20</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_8_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:111_1_1_2_8_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> or ( <font color="Maroon">x</font> is    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font> ) )
 </span><b>by </b><i><a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, <a class="ref" href="scmring3.html#T17" target="_self">Th17</a>, <a class="ref" href="scmring3.html#T21" target="_self">Th21</a>, <a class="ref" href="scmring3.html#T22" target="_self">Th22</a>, </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_8_1_1_1"><b>suppose </b></a><a NAME="E1:111_1_1_2_8_1_1_1"/><i><font color="Green">E242</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
 <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring2.html#T19">SCMRING2:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T18" target="_self">Th18</a>, <a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="ref" href="scmring2.html#T19">SCMRING2:19</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_8_1_1_2"><b>suppose </b></a><a NAME="E1:111_1_1_2_8_1_1_2"/><i><font color="Green">E243</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">r</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring2.html#T19">SCMRING2:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="ref" href="scmring2.html#T19">SCMRING2:19</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_2_8_1_1_3"><b>suppose </b></a><b>that </b><a NAME="E1:111_1_1_2_8_1_1_3"/><i><font color="Green">E244</font></i>: 
<font color="Maroon">x</font> is    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>
 <b>and </b><br/><a NAME="E2:111_1_1_2_8_1_1_3"/><i><font color="Green">E245</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">s1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="txt" href="scmring3.html#E24"><i><font color="Green">Lemma86</font></i></a>, <a class="ref" href="scmring2.html#T19">SCMRING2:19</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmring3.html#T19" target="_self">Th19</a>, <a class="ref" href="scmring3.html#T23" target="_self">Th23</a>, <a class="txt" href="scmring3.html#E24"><i><font color="Green">Lemma86</font></i></a>, <a class="ref" href="scmring2.html#T19">SCMRING2:19</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><b>hence </b><a NAME="E5:111_1_1_2_8"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">s2</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, <a class="ref" href="scmfsa6a.html#T9">SCMFSA6A:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_7.html#D2">FUNCT_7:def 2</a><br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
